FREE COMPOSITION Tsgwss^r Loogma? Mwrie Series Series Editor Gerald Warfield FREE COMPOSITION {Der freie Satz) Volume III of New Musical Theories and Fantasies Heinrich Schenker Semper idem sed non eodem modo Translated and edited by Ernst Oster nun LONGMAN New York and London Published in cooperation with the American Musicological Society FREE COMPOSITION (Der freie Satz) Longman Inc., New York Associated companies, branches, and representatives throughout the world. Copyright 1935 by Universal Edition A.G. © Revised edition copyright 1956 by Universal Edition A.G., Wien The English language edition has been authorized by Universal Edition A.G. Copyright © 1979 by Longman Inc. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of the publisher. Developmental Editor: Gordon T. R. Anderson Interior Design: Albert M. Cetta Cover Design: Dan Serrano Manufacturing and Production Supervisor: Louis Gaber Composition: Kingsport Press Printing: The Murray Printing Company Binding: The Book Press Library of Congress Cataloging in Publication Data Schenker, Heinrich, 1868-1935. Free composition (Der freie Satz) (Longman music series) "Published in cooperation with the American Musi-cological Society." "The text is based mainly on the second German edition (ed. Oswald Jonas, Vienna, 1956), but the first edition (Vienna, 1935) was also consulted." Includes bibliographical references. 1. Music—Theory. 2. Counterpoint. I. Oster, Ernst II. Jonas, Oswald. III. Title. IV. Title: Der freie Satz. MT40.S29213 781 79-14797 Manufactured in the United States of America 987654321 HEINRICH SCHENKER was born in Podhyce (Podgajcy), Galícia, on June 19, 1868. (His birthplace lies in what is today the western region of the Ukraine, near Lvov.) As a youth he demonstrated great talent as a pianist and received encouragement from Carl Mikuli, a student of Chopin. He emigrated to Vienna where, in the late 1880s, he studied at the Conservatory and also earned the Dr. Jur. degree at the University. Before the appearance in 1906 of his first major theoretical work, Harmonielehre, Schenker was active chiefly as a practical musician—as a pianist, a conductor, an editor, and a composer. He toured as accompanist to one of the greatest singers of the period, the Dutch baritone Johannes Messchaert. In connection with his activity as a conductor, he made continuo realizations and arrangements of music of earlier periods, including Bach cantatas, piano concerti by C.P.E. Bach, and organ con-certi by Handel. His compositions gained the approval of Brahms, who recommended them to his publisher, Simrock. Bu-soni also took an interest in Schenker's music and programmed several of his works on a concert series in Berlin beginning around 1905. During the 1890s Schenker wrote essays in musical criticism for various periodicals in Berlin, Leipzig, and Vienna. It was partly the desire to establish a more precise foundation for criticism, both of composition and of performance, that motivated Schenker to embark upon the path that led to the connected series of original theoretical works culminating with Free Composition. Dissatisfied with the prevalent approach to music theory with its abstract speculations (for example, the question of harmonic "dualism") and rigid formal schemata, Schenker set out to discover and formulate the principles of tonal art as they were manifested in the greatest products of that art. For Schenker, it was their intimate connection to the musical artwork that set his theories apart from all others then in vogue. Thus the cover of Harmonielehre attributes the work merely to "einem Künstler," without further specification of the artist's identity. vi FREE COMPOSITION From the writing of Harmonielehre until the end of his life, theorists and performers on an individual basis. Schenker died Schenker devoted himself primarily to his theoretical work, to in Vienna on January 22, 1935. editing masterworks, and to teaching musical interpretation to For my beloved wife Contents Series Editor's Acknowledgment x Preface to the English Edition xi Preface to the Second German Edition xv Introduction to the English Edition xvii Introduction xxi PARTI THE BACKGROUND Chapter 1 The Background 3 1 The Concept of Background in General 3 2 The Background in Music 4 3 The Fundamental Structure as the Content of the Background in Music 4 4 The Significance of the Fundamental Structure for Composition, Instruction, and Performance 6 Chapter 2 The Fundamental Structure 10 1 The Fundamental Structure in General (§§ 1-3) 10 2 The Fundamental Line in General (§§ 4-14) 11 3 The Bass Arpeggiation in General (§§ 15-19) 14 4 Specific Characteristics of the Fundamental Structure (§§ 20-26) 15 Chapter 3 The Forms of the Fundamental Structure 17 1 The Forms of the Fundamental Structure: General Remarks (§§ 27-30) 17 2 The Possible Forms of the Fundamental Structure in the Cases of §, 5, and 8 (§§ 31-44) 19 PARTII THE MIDDLEGROUND Chapter 1 The Middleground in General (§§ 45-52) 25 Chapter 2 Specific Characteristics of the Middleground: The First Level 29 1 The Combination of Fundamental Line with Bass Arpeggiation (§§ 53-86) 29 vu viii FREE a An Unprolonged Fundamental Line Combined with an Ascending Bass Arpeggiation I—V That Is Prolonged by Contrapuntal-melodic Means 29 b Working-out and Consequences of the Contrapuntal Structure in the Case of 3, 5 or 8 31 c The Combination of an Unprolonged Fundamental Line with Two Bass Arpeggiations 34 d Conclusions 34 e V—I at the First Level 36 2 Division of the Fundamental Line (§§ 87-101) 36 a Division by Interruption in the Case of 3 36 b Division by Interruption in the Case of 5 39 c Division by 8—5—1 in the Case of § 40 3 Mixture (§§ 102-103) 40 4 The Phrygian 2 in the Fundamental Line (§§ 104-105) 41 5 The Neighboring Note (§§ 106-112) 42 6 Linear Progressions (§§ 113-124) 43 a General 43 b Descending Linear Progressions of the First Order 44 c The Ascending Linear Progression 45 7 Arpeggiation (§§ 125-128) 46 8 Reaching-over (§§ 129-134) 47 9 Motion from the Inner Voice (§§ 135-139) 49 10 Unfolding (§§ 140-144) 50 11 Substitution (§§ 145-146) 51 12 Ascending Register Transfer (§§ 147-150) 51 13 Descending Register Transfer (§ 151) 52 14 Coupling (§§ 152-154) 52 15 The Combination of Different Types of Prolongations at the First Structural Level (§ 155) 52 PARTIU THE FOREGROUND Chapter 1 The Concepts of Strict Counterpoint 55 1 Perfect Consonances (§§ 156-164) 55 2 Imperfect Consonances (§§ 165-167) 60 3 The Passing Tone at the Foreground Level (§§ 168-174) 61 4 The Change of Harmony 5—6 (§ 175) 63 5 The Seventh (§§ 176-179) 6 The Syncopation (§§ 180-182) 63 65 Chapter 2 The Later Structural Levels 68 A The Later Structural Levels in General (§§ 183-185) 68 B The Prolongations of the Later Levels in Particular 68 1 Prolongations of the Bass Arpeggiation (§§ 186-191) 68 2 Structural Division (§ 192) 70 3 Mixture (§ 193) 70 4 The \>2 (§§ 194-195) 71 5 The Neighboring Note (§§ 196-202) 71 6 Linear Progressions (§§ 203-229) 73 a General 73 b Illusory Linear Progressions 74 c The Ascent and Descent of Linear Progressions 75 d The Individual Linear Progressions 75 e The Closure of Linear Progressions 77 f The Combination of Two or More Linear Progressions 78 7 Arpeggiation (§ 230) 82 8 Reaching-over (§§ 231-232) 83 9 Motion from the Inner Voice (§ 233) 83 10 Unfolding (§ 234) 83 11 Substitution (§ 235) 84 12 Exchange of Voices (§§ 236-237) 84 13 Ascending Register Transfer (§ 238) 85 14 Descending Register Transfer (§ 239) 85 15 Coupling (§§ 240-241) 85 Chapter 3 Specific Foreground Events 87 1 Transference of the Forms of the Fundamental Structure to Individual Harmonies (§§ 242-243) 87 2 Incomplete Transference of the Forms of the Fundamental Structure; Auxiliary Cadences (§§ 244-246) 88 3 Addition of a Root (§ 247) 90 4 Chromatic Tones (§ 248) 91 5 Avoidance of Chromatic Steps (§ 249) 91 6 Cross-relation (§ 250) 92 7 Diminution (§§ 251-266) 93 8 Cover Tones (§ 267) 9 Obligatory Register (§§ 268-270) 10 Articulation (§§ 271-275) 11 The Scale Degree (§§ 276-283) Chapter 4 Meter and Rhythm 1 Meter and Rhythm in General (§ 284) 2 Meter in Music (§§ 285-289) 3 Rhythm in Music (§§ 290-291) 4 Antimetric Rhythmic Situations (§§ 292-300) Chapter 5 Form A Form in General (§§ 301-306) B Form in Particular . 1 Undivided Form (§ 307) CONTENTS ix 107 107 108 111 118 118 118 122 122 128 128 130 130 2 The Song Forms (§§ 308-310) 131 3 Sonata Form (§§ 311-316) 133 4 Four-part Form (§ 317) 141 5 Rondo Form (§§ 318-321) 141 6 Fugue (§322) 143 7 Variations (§ 323) 144 Epilogue (§ 324) 145 Appendix 1 Contents of Figures (Works Arranged by Composer) 149 Appendix 2 List of References to Figures 154 Appendix 3 Works of Heinrich Schenker 156 Appendix 4 Omissions from the Original German Edition 158 Appendix 5 List of Terms 163 About the Translator 165 Series Editor's Acknowledgment Ernst Oster died before the initial stages of the publication of Free Composition had begun. As a result, many authorial responsibilities for the production of the book had to be assumed by friends and colleagues whom we would like to thank for their gracious and dedicated assistance. Gail Rehman, who checked the entire translation, was meticulous in proofreading, checking data, translating and preparing copy for the example volume, and offering invaluable suggestions about all phases of production. While Ernst Oster restored some deletions made by Oswald Jonas in the second German edition, he retained others and deleted some additional passages which he mentions in the Preface to the English Edition. However, for the sake of comprehensiveness it was decided to provide these passages in an appendix. John Rothgeb translated the deleted passages which appear in Appendix 4. He checked the entire translation, and several footnotes have been added which bear his initials. In addition, he provided the biographical sketch of Schenker and was a second proofreader for the entire text. Gratitude is due the American Musicological Society for financial support; its president, James Haar, and the chairman of the editorial committee, Martin Picker, gave enthusiastic encouragement to the publication. Gerald Warfield Preface to the English Edition Almost half a century has passed since the publication of this book shortly after Heinrich Schenker's death in 1935. The political events of the subsequent years naturally made it impossible for Schenker's ideas to become widely known in Europe;*1 to this day they find relatively little recognition there, even in German-speaking countries. In contrast to this, interest in Schenker has been growing at an ever-increasing pace in the , United States. More and more colleges and universities are offering courses devoted to Schenker's theories, his name appears almost regularly in the programs of musical conventions, and, especially during the past decade, the number of "Schenker-oriented" or more or less "Schenker-influenced" books has increased to a remarkable degree. In view of this situation, it is astonishing that of Schenker's major works only one has been available in English up to now: his Harmonielehre, originally published in 1906. (This book is actually volume one of a larger, three-volume work which *1. He was Jewish and his works were suppressed by the National-Socialist government. (Oster) Schenker entitled Neue musikalische Theorien und Phantasien. The second volume of this comprehensive work was Kontrapunkt, whose two parts appeared in 1910 and 1922, and the third is the present volume, Der freie Satz.) In Harmonielehre,** Schenker laid the foundation for the harmonic aspect of his theory. But the specific voice-leading aspect of the theory was a considerably later development that begins rather suddenly in 1919. The first publication to reflect this was his analysis of Beethoven's Sonata op. 101,*8 which contains the first rudimentary examples of "graphic" notation, that is, of specifically linear reductions. During the ensuing 15 years of Schenker's life, the development of the concept of voice-leading progressed with astonishing rapidity and brilliance; the present volume forms the culmination of this process, for it is here that the idea of voice-leading receives its most detailed and precise formulation. Since voice-leading is the chief *2. Harmony (University of Chicago Press and M.I.T. Press). See Appendix 3: "Works of Heinrich Schenker." (Oster) *3. See Appendix 3: "Works of Heinrich Schenker." (Oster) xi xii FREE subject of Der freie Satz, the reading of this volume requires at least a rudimentary understanding of Schenker's earlier ideas. The English-speaking reader has, as noted, the translation of Harmony. In addition, its editor, Oswald Jonas, has provided an excellent introduction and a profuse number of footnotes that relate the material of this book to Schenker's later works. But the unfortunate fact remains that, with the exception of a few isolated essays and analyses, none of these later works has been published in English or, for that matter, in any language other than German. The almost unavoidable result is that much that has been said and written about Schenker shows an incomplete understanding and, consequently, distortion of his original thoughts. It is to be hoped that the appearance of the present translation, by making Schenker's most important ideas accessible to a wider musical public, will at least partly remedy this situation. Translating this important contribution to music theory has presented some rather special problems. The first of these arises from the sheer breadth of Schenker's thought, which ranged over all the aspects of music and attempted to elucidate them in the most detailed and penetrating way. The intellectual demands which Schenker makes of us come directly from the scope and depth of this achievement. To help the reader meet these demands, I would like to offer some remarks about the difficulties of language and style in the work and about the translation itself. Schenker was concerned about making the book as concise as possible in order that it might not become unmanageably large. Therefore his comments on the musical examples and his definitions of terms are often quite brief—sometimes too brief to be understood. I could do little to remedy this other than to make occasional editorial insertions or a footnote. The way in which the book was written down makes for another difficulty. Schenker dictated the greater part of his later works to his wife, who transcribed them from shorthand into ordinary script. Though Schenker then made corrections, im- provements, and additions, the general effect often remains that of spoken language with its inevitable omissions and poorly chosen words. On the other hand, this very same spoken quality produces a poetic, sometimes almost rhapsodic, quality in the German original. To make sure that the thought was always understandable, it became necessary for me to paraphrase in a few places, and in two instances (see "Reaching-over," at § 134, and "Sonata Form," at § 316) substantial editorial commentary seemed the best way to make the material clear. The difficulties of style and language make the translator's task an arduous one, for he must follow the original as closely as possible lest the meaning be in the slightest degree modified. But faithfulness to Schenker's concise style results in an English that the reader will occasionally find awkward. In these instances I must ask the reader's indulgence and direct his attention to the thought rather than to its elegant expression. The most conspicuous problem which the book presents to the translator is its title: there is no English equivalent for Der freie Satz. The literal translation "Free Composition" might give the misleading impression that the book is a treatise on free-style compositions such as fantasies. In order to preclude such misunderstanding, I decided to retain the original German as a subtitle; it is necessary, however, to indicate what Schenker meant by "freier Satz." As Oswald Jonas points out in the preface to the second German edition (p. xvi of this book), Schenker originally meant to publish the first version of Der freie Satz as the third volume (part VII) of his Kontrapunkt. He intended to demonstrate that the voice-leading principles of strict counterpoint (der strenge Satz) also underlie the voice-leading events of actual "free" compositions, that is, of music written in freier Satz. (The emphasis is on Satz, meaning contrapuntal, or voice-leading, structure.) In freier Satz, the original "strict" laws of counterpoint are extended and prolonged, not just through freer treatment, but particularly through the composing-out process (Auskomponierung) and the inclusion of other aspects of music, notably harmony. So, too, the present, PREFACE TO THE ENGLISH EDITION xiii final version of Der freie Satz deals essentially with voice-leading: this remains the primary viewpoint even in chapters that concern themselves with other aspects of music such as diminution, rhythm, and, most remarkably, form. The least of the difficulties encountered was to decide on English equivalents for Schenker's terms. Thanks to the work of Allen Forte and Felix Salzer, most of these terms have already found generally accepted English equivalents. My bilingual list, which appears in Appendix 5, includes these equivalents and supplies yet a few new ones. It remains for me to say a few words about my editorial procedures. The text is based mainly on the second German edition (ed. Oswald Jonas, Vienna, 1956), but the first edition (Vienna, 1935) was also consulted. From the first edition I have reinstated a few short passages and, above all, the headings of the individual smaller sections. I have also corrected the many important misprints, such as wrong pitch-names and other musical symbols, and errors in references. Finally, I have corrected a few misengravings which I overlooked when helping to prepare the example volume in 1956. In his editorial preface Oswald Jonas mentions briefly that he omitted a number of passages that have no bearing on the musical content of the work. These passages were almost exclusively taken from Schenker's introduction and the first chapter, "The Background." (The introduction and first chapter in the original edition give the impression of being a collection of more or less unrelated remarks and aphorisms; it is impossible to determine whether this material was given its final, published form by Schenker himself or by an editor.) I felt it best to omit several additional passages of a very general, sometimes semiphilosophical nature here; these omissions are not expressly indicated. The few deletions in later parts of the book, made either by Jonas or by me, are mentioned in footnotes.*4 *4. All deletions have, in fact, been reinstated in Appendix 4. For an explanation, see "Series Editor's Acknowledgment," p. vii. Schenker's cross-references to other parts of the text and to figures are differentiated from those of the editors by the following system of brackets: (Schenker), [Jonas], . My own editorial insertions are also set off by < >'s. In closing, I would like to turn from matters of text and translation in order to share some of my experiences of this work with its future readers. A very practical suggestion to the uninitiated reader might be that he adopt a somewhat unusual procedure and not begin at the beginning. The opening part, "The Background," assumes a more than superficial knowledge of the whole of Schenker's system; without this knowledge this part would probably remain largely meaning-. less. The reader should instead begin with the section on diminution (§§ 251 ffi), a very good introduction to Schenker's way of thinking, and continue through the next three sections (up to § 275). Next, he should study part III, "The Foreground," in its entirety, skipping, however, the difficult section on linear progressions (§§ 203 to 229). At this point, he will be ready to tackle the opening part—"The Background." Of course, reread-ings and continued use of the example volume in reference to particular compositions will lead to an ever greater understanding of the work. As an aid to studying this book I would strongly advise the reader to have at hand Schenker's Five Graphic Music Analyses.*6 This publication shows, as no other work from Schenker's late period does, the complete picture of all the structural levels. (This was, unfortunately, not possible for Schenker in the present work, for reasons of space limitation.) Der freie Satz makes frequent reference to the Five Graphic Analyses and the five compositions it contains. In conclusion I would very much like to extend my thanks to several friends and associates for their helpful efforts: Allen Forte helped the work move forward in many ways; Charles Burkhart made several helpful suggestions; Carl Schachter *5. See Appendix 3: "Works of Heinrich Schenker." (Oster). xiv FREE COMPOSITION showed unflagging interest in the work and gave it his critical attention; Oswald Jonas made necessary diplomatic overtures on behalf of the work; Gail Rehman spent many hours in the huge undertaking of preparing the final typescript; finally I must thank the Robert Owen Lehman Foundation for a grant of funds which enabled me to undertake this translation. New York, 1977 Ernst Oster Preface to the Second German Edition My concepts present, for the first time, a genuine theory of tonal language. Free Composition This book, here published in a new form, first appeared in 1935, only a few months after the death of its author. It is deeply to be regretted that Heinrich Schenker was not granted to see this crowning achievement of his most productive life in print. We can take comfort only in the fact that his death spared him from what might well have been a dire fate in the storm of the years that followed. The controversy surrounding Schenk-er's work is not at an end, but the number of those who are convinced of the truth of his teaching steadily increases. The time of indifference—when one might merely have overlooked his work without saying yes or no to it—is over. If I speak of this book as the crowning achievement of Schenk-er's work, this phrase must also describe the book's conception and the attainment of its final form. For twenty years it occupied Schenker's mind and musical thought, from initial ideas to several attempts to write down the entire work in a more or less definitive form. Even the final manuscript is full of numerous changes, revisions, and significant improvements.*1 This slow process toward final formulation can also be seen in several *1. The editor had opportunity to examine the manuscript through the kindness of Mr. Anthony van Hoboken, who did so much to make the first edition possible. (Jonas) other of Schenker's major writings. For example, the germinal thoughts of his Harmonielehre, published in 1906, had already appeared in 1895 in the brochure "Der Geist der musikalischen Technik" ("The Spirit of Musical Technique"), and important ideas for his monograph Beethovens Neunte Sinfonie (1912) can be found in a 1901 newspaper article (Wiener Abendpost) entitled "Beethoven-Retouche" ("Retouching Beethoven"). A complete history of Der freie Satz cannot, of course, be presented here. This belongs to the biography of Schenker, which sooner or later must be written.*2 Sketches, thoughts quickly jotted down on thousands of little pieces of paper, as well as more or less integrated discussions, even in fair copy, are lying in the folders which were left after his death.*3 The earliest version of the book was begun in 1915. It gives us *2. A brief survey by this editor of the development of Schenker's theories can be found in the Introduction to the English edition of Harmony. (Jonas) *3. These folders, along with a great deal of other unpublished material, including a "Lehre des Vortrags" (an essay on "Performance"), are in the possession of Mr. Ernst Oster, to whom the editor is especially indebted for his careful revision of the example volume. (Jonas) xv xvi FREE evidence that Schenker first thought of the book as a continuation of his work on counterpoint: "free composition," section VII of the theory of counterpoint. Here he meant to show how the laws of strict counterpoint continued to operate in free composition. Even at this point, Schenker speaks of the "composing-out" of the scale degree and of "horizontalization." The concept of the "fundamental line" already appears, first as "melodic line," then as "line," graphically indicated by vertical arrows over the relevant notes of the example. In a later version there is a special section on "piano style" (Klaviersatz), and also a section devoted to thoroughbass. The various later stages in the development of his theories found their expression in a series of publications—Der Tonwille and Jahrbücher—which appeared in the nineteen-twenties. In them Schenker refers to his definitive, concluding work, even though it was yet to appear. Thus, one must regard Der freie Satz as the definitive form, indeed the codification of Schenker's concepts. The clarification and formulation of the theory pursued and possessed its creator like a demon. He felt that it was his mission to present this concept of the masterworks to the world, to reveal the laws of art which he saw fulfilled in the works of the great masters—and in them alone—according to his motto semper idem sed non eodem modo ("always the same, but not in the same way"). In 1921, on his departure for a vacation in the Tyrolean Alps, Schenker wrote to his beloved friend and helper, Moritz Violin, "Now, as I said, to the Tyrol, and then further climbing, climbing to the peaks of IP (Freier Satz)!" And later (July 1928), again to Violin, documenting the practical purpose of the work: "Der freie Satz, which I am busy putting into final form, will include, in addition to the text, a great many examples in a separate volume. These are intended expressly for the teacher, as instructional material." May the work now fulfill the wish of its author in this new edition! Because Schenker himself could not supervise the printing of his work and because publication was brought about as quickly as possible (perhaps out of false piety), the form of the first edition, unfortunately, left something to be desired. Aside from an unusually large number of misprints, both in the text and the example volume, the layout itself was highly questionable. Its failure to present an organized picture to the eye only served to make a difficult work even more difficult. Here, then, lay the editor's task: to present the text in a fashion that is, above all, clearer to the eye. In the course of this endeavor some stylistic changes proved necessary. An additional number of references and cross-references were also provided, which should aid the reader in comprehending the work. The references added by the editor are enclosed in brackets. The editor also felt himself justified in omitting certain passages which have no bearing on the musical content. Finally, the editor would like to express his gratitude both to the Austrian Ministry of Education and to the president of the Academy for Music and the Performing Arts, Professor Dr. Hans Sittner. Their active support made it possible for the editor to carry out his tasks in Vienna and for him to arouse and maintain an interest in Schenker's teachings during this time by giving a course at the Academy in the work of Heinrich Schenker. Vienna, 1955 Oswald Jonas Introduction to the English Edition It is entirely appropriate that the English translation of Heinrich Schenker's Der freie Satz be published in the United States, since it is here that Schenker's ideas have gained widest acceptance and have been broadly disseminated. The tradition of instruction in Schenker's theory in the United States began with Hans Weisse (1892-1940), who initiated courses at the Mannes School of Music in New York after his arrival from Vienna in 1931. In Vienna he had taught several young Americans, notably William J. Mitchell (1906-1971), who later became an eminent scholar and professor at Columbia University. The tradition continued with Felix Salzer (b. 1904) at the Mannes School, a student of Schenker and Weisse, with Oswald Jonas (1897-1978), a student of Schenker, at Roosevelt College in Chicago, and with Ernst Oster (1909-1977), a student of Jonas, who taught in his private studio in New York for a number of years before being appointed to the faculties of the New England Conservatory of Music and the Mannes College of Music. In a growing number of institutions of higher learning in the United States the tradition continues today. No one was better qualified to undertake the definitive translation of Der freie Satz than Ernst Oster. His entire life was devoted to Schenker, to understanding his writings in as much depth as possible, to applying the analytical procedures to a large number of compositions, and to teaching.*1 From 1938 Oster was the sole custodian of most of the Schenker Nachlass, a large collection of unpublished analytical and other material, including the manuscript of an earlier version of Der freie Satz, which had been given to him by Mrs. Schenker in Vienna in order to save it from destruction by the invading German forces. Access to these documents enabled Oster to understand Schenker's work methods and creative *1. Some of Oster's own excellent contributions include "The Dramatic Character of the Egmont Overture," Musicology, vol. 2, no. 3,1949; "Chopin's Fantasie-Impromptu; op. 66: A Tribute to Beethoven," Musicology, vol. 1, no. 4, 1947; "Register and the Large-Scale Connection" and "An Analysis of Mozart's Menuetto, K.355" republished in Yeston, Maury, ed., Readings in Schenker Analysis and Other Approaches, Yale University Press, New Haven, 1977. xvii xviii FREE processes in a special way not available to anyone else. Thus, it is not surprising that the English language translation of Der freie Satz is more lucid than the original German in a number of instances. Moreover, a number of mistakes that persisted through the second German edition were corrected, as well as errors in the volume of musical examples. The publication history of Der freie Satz is rather unusual. It was brought out posthumously (as indicated in Oswald Jo-nas's Preface to the Second German Edition), so that Schenker did not have the opportunity to correct proofs and to make changes in the manner ordinarily available to an author. Responsibility for the first edition was assumed by Schenker's students, Oswald Jonas and Moritz Violin. The volume was hastily prepared for publication, with the unfortunate consequences described by Jonas in his Preface. Again, the English translation will prove to be superior to both German editions in clarity as well as in format. The modern-day English language reader may be somewhat puzzled, or perhaps even offended, by the polemical and quasi-philosophical material in Schenker's introduction and elsewhere, most of which was deleted from the second edition, but restored to the English translation in an appendix. In part, this material is typical of many other German language authors of an older period; in part, it is characteristic of Schenker, and must be placed in proper perspective. Almost none of the material bears substantive relation to the musical concepts that he developed during his lifetime and, from that standpoint, can be disregarded; it is, however, part of the man and his work. The extreme German nationalism which is evident in other portions of Schenker's published writings is not very apparent in Der freie Satz. Schenker's political views would certainly have changed radically had he lived to witness the 1938 Anschluss of Austria and its aftermath. Schenker's polemics against the musical establishment must also be understood in the context of the time and with respect to the way in which his work was received. During Schenker's lifetime, instruction in music theory almost completely disregarded the traditional disciplines of species counterpoint (after Fux) and figured bass (for which Schenker cites C. P. E. Bach). "This false theory" to which he refers in his introduction is not specifically identified. However, he probably had in mind the German theorists of the early part of the 19th century, A.B. Marx (1795-1866) and Gottfried Weber (1779-1839) among them, and the most influential theorist in Vienna, Simon Sechter (1788-1867). And surely he would have included Hugo Riemann (1849-1919), whose Rameau-influenced theory of harmony dominated instruction in German music institutions at the time Schenker completed Der freie Satz (and beyond). Schenker felt, justifiably so, that the traditional disciplines of species counterpoint and figured bass had demonstrated their worth in that they had been studied seriously by composers who had produced a large repertory of culturally significant and highly valued musical works. Brahms was the last of these, and, typically, Schenker dedicated his 1912 study of Beethoven's Ninth Symphony to the memory of that composer, "the last master of German composition." Thus, Schenker's view of the musical situation from the time he reached manhood to his death in 1935 was very pessimistic. The other factor involved in Schenker's view of the musical situation was the reception accorded his writings. With the exception of the Ninth Symphony study mentioned above, his work was ignored by all but a few musicians—what Jonas has called "a conspiracy of silence." He was able to make a living as a pianist—and a very highly regarded one—in Vienna, accompanying well-known singers and participating in chamber music concerts. He also wrote newspaper critiques and, most important, gave lessons in piano, counterpoint, thorough-bass, and analysis in his private studio. However, he was excluded from the higher academic circles to which he should have had access. Hence, his bitterness against the musical establishment can be seen to have had a personal as well as a purely musical-intellectual basis. INTRODUCTION TO THE ENGLISH EDITION six A thorough understanding of Schenker's work requires many years of serious study, not only because of the extent and complexity of his writings, although that is, of course, an important factor, but also because of the time required to learn to construct analytical graphs. It is therefore important to bear in mind that although Der freie Satz is Schenker's final and summational work, it is not a textbook on analysis, but is organized as a presentation of this theory in accord with the major concept that governed his approach to the study of tonal music, the concept of structural levels.*2 It begins with the background level (the fundamental structure), proceeds to the middleground level with its prolongations of the fundamental structure, and finally deals with the complexities of the foreground, or what Schenker characterizes as the later levels. Something like sixty percent of the book is devoted to the foreground, a fact at variance with the opinion one has sometimes heard to the effect that Schenker was concerned only with background and middle-ground. The traditional way of learning how to do Schenkerian analysis has been to study with someone who studied with Schenker or with a student of such a person. Only after much practical experience in constructing analytical graphs was reading of Schenker's work undertaken. For the reader of Der freie Satz who does not have a background of direct instruction in Schenkerian analysis, the advice given by Ernst Oster to begin with the later sections of the book—for example, with the section on diminution—is certainly excellent. To that should be added the exhortation to study the graphs in the example volume very carefully while reading the text. The graphic methods that Schenker developed concurrently with his powerful concepts of musical structure are unique in the history of music theory and analysis. And he invested them with singular importance. He tells us that ". . . the graphic representation is part of the actual composition, not merely *2. Only one of his writings, the first volume of Kontrapunkt (Cantus Firm/us und Zweistimmiger Satz), 1910, can be regarded as a textbook. an educational means." (p. xxiii) In this remarkable statement, which at first seems puzzling, Schenker dramatizes the significance of the graphs: They are not to be regarded merely as pedagogical devices but rather as accurate representations of the musical structures. It is valuable, if not absolutely necessary, to learn to read the graphs. This is because a particular example almost always contains information in graphic form that is not discussed in the text. With experience the serious reader will learn to read and understand the graphs. A survey of the graphic symbols may be of assistance, however, and the reader may wish to return to this part of the introduction as he begins to study the graphs. (Schenker, unfortunately, does not supply any explanations.) Before undertaking this survey of Schenker's graphic notation it is essential to warn the reader that Schenker's use of the various symbols is flexible. The normative usage is discussed below; a completely systematic interpretation, however, is not possible, and any effort to do so would certainly be subject to serious errors. It is also necessary to point out that there are two basic kinds of graphs presented in the volume of examples, in addition to the examples which reproduce the composer's notation with few or no symbols added. The first of these may be characterized as "rhythmic." In a graph of this kind Schenker retains the basic durational values of the music, but enlarges them now and then to eliminate decorating notes (diminutions) which do not affect the basic voice-leading. An instance is figure 54, 15. Comparing the second measure of Schenker's example with the Bach score one finds that Schenker has omitted a turn, an anticipation, a trill, and a lower neighbor-note figure, thus reducing a complicated rhythmic succession to quarter note followed by half note. The second type of graph is the "structural" graph, in which some of the traditional durational note values are used to represent structural relations among the musical components. It is the structural graph that is the subject of the following exposition. XX FREE In general, the larger note values, half and whole notes, belong to the deeper structural levels, that is, to middleground and background. Beams and stems are used to connect components of the fundamental line and components of linear progressions at the middleground level. They are also used to connect the main bass notes of a span of music. Slurs delineate structurally cohesive motions involving two or more components (and thus are similar to performance slurs in ordinary notation). The doubly curved slur is used in the bass to show a motion from tonic to dominant via a secondary harmony such as supertonic or subdominant. Large parentheses are sometimes used (as in figure 12) to delimit passages that are in some way preparatory to the initial structural statement. Usually, the half note with eighth-note flag indicates a bass note with special function, such as a third-divider. The large V marks a hiatus of some kind, such as a discontinuity in a linear progression or a break in an otherwise stepwise bass motion. The diagonal line serves a number of purposes, the most important of which are to show that a particular bass note and a particular soprano note belong together even though they do not coincide temporally, and to indicate an octave displacement of a note. To designate components of the fundamental line, carets above scale-degree numbers are used. If a succession of such numbers is enclosed in parentheses, it means that the succession replicates the fundamental line but is not equivalent to it. The short double thin barline above the upper staff is the symbol for interruption of the progression of the fundamental line. A long-range connection of some kind between unison-related or octave-related notes (for example, an octave coupling) is indicated by a dotted line, and dotted lines are rarely used for any other purpose. Right brackets above the staff point to parallel fifths or octaves. One frequently used graphic device requires special explanation: the beam connecting the down stem of the first note of a pair with the up stem of the other, or vice versa. One or both of the notes may have an additional stem (and flag). This is the symbol for an unfolding, one of the most important types of prolongations in free composition. In addition to these symbols, which belong to Schenker's special graphic system, he employs conventional symbols, such as figured bass, Roman numerals to specify scale degrees upon which harmonies are based (often at more than one level), numerals to show contrapuntal patterns, such as 10-10, and letters designating form. Labels are frequently given to show the type of prolongation in operation at a particular point, such as initial ascent, or to indicate contrapuntal function, such as neighbor or passing note. Finally, a symbol of which Schenker was very fond: the exclamation point. This graphic always marks an event that is unusual in some very striking respect, one to which Schenker wished to draw special attention. Schenker's work has been very influential, especially during the past twenty years in the United States, as indicated at the beginning of this introduction. The general concept of structural levels, which Schenker began to develop as early as the 1906 Harmonielehre, has attracted the serious attention not only of scholars in music but also of scholars in other fields. Of these, structural linguistics is perhaps most prominently represented, for it is clear that the modern notion of leveled structures in language corresponds in a remarkable way to Schenker's concept of musical organization. With the publication of the present volume, Schenker will be able to address the English-speaking portion of the musical world directly, thus permitting serious composers, performers, and scholars to judge for themselves the value of his work. It is hoped that the publication of the English translation of Der freie Satz will be followed by English translations of similarly high quality of Schenker's other important writings. Hamden, Ct., 1978 Allen Forte Introduction But those who are like the master go forth, And beauty and sense appear in all they see. Hugo von Hofmannsthal: "The Death of Titian" To every thing there is a season, and a time to every purpose under the heaven. Ecclesiastes 3:1 The hearing ear, and the seeing eye, The Lord hath made even both of them. Proverbs 20:12 For more than a century, a theory has been taught which claims to provide aefeesi? to the art of music, but in fact does quite the opposite. This false theory has obscured the musical discipline of previous centuries—that is, strict counterpoint and true thoroughbass. One might explain this break by looking to the impatience of the generation which lived during the third decade of the nineteenth century: dazzled by the tremendous outburst of genius which had come before them, they sought, as mediocrity usually does, to cut the shortest possible path to genius. This shortcut, a "practical" one, proved to be a failure, since it was essentially contrary to the historical background and artistic development of the great composers. It did not lead to the masters; indeed, it ultimately led away from them. In our day it seems that this betrayal is no longer acceptable. The flight from music which characterizes our time is in truth a flight from an erroneous method of instruction, one which renders impossible an effective approach to art. In opposition to this theory, I here present a new concept, one inherent in the works of the great masters; indeed, it is the very secret and source of their being: the concept of organic coherence. The following instructional plan provides a truly practical understanding of this concept. It is the only plan which corresponds exactly to the history ^nd development of the mas-terworks, and so is the only feasible sequence: instruction in strict counterpoint (according to Fux-Schenker), in thoroughbass (according to J. S. and C. P. E. Bach), and in free composition xxi xxii FREE (Schenker). Free composition, finally, combines all the others, placing them in the service of the law of organic coherence as it is revealed in the fundamental structure (fundamental line and bass arpeggiation) in the background, the voice-leading transformations in the middleground, and ultimately in the appearance of the foreground. C. P. E. Bach wrote his treatise on thoroughbass when he realized, to his grief, that the discipline of thoroughbass might disappear both in theory and in practice, because it was not really understood. His incomparably great work was motivated by a desire to do his utmost to save and clarify that discipline. Now the time has come for me—"To every thing there is a season," says the writer of Ecclesiastes—to proclaim the new concept of organic coherence and thereby to give the fullest possible expression to what the music of the masters was and must continue to be if we wish to keep it alive. After the publication of some of my earlier works (those which already reached toward a clearer presentation of the new concept, especially the volumes of Der Tonwille and the three yearbooks, Das Meisterwerk in der Musik), the objection was often raised, "But did the masters also know about all this?" This objection, intended to be a trap, only betrays a lack of education. Those who raised the question were unaware that the masters in fact knew nothing of that false theory which for more than a century has been taught and learned as the only practical one. Neither J.S. Bach, C.P.E. Bach, Haydn, Mozart, Beethoven, Schubert, nor Mendelssohn knew any such concepts of harmony, thoroughbass, or form. And Brahms would have none of it! The objection can be answered very simply: the great composers in their works have shown a mastery which evinces, both in preconception and in total recall, such a clear overall comprehension of the laws of art that they need say no more to us; of necessity, every artistic act—indeed any action at all— requires a preconception of inner relationships. Consequently, should the reader find that what I say about a composition is verified in the work itself, he must surely concede that the masters did have a keen awareness of such relationships. Those who advocate the present courses of instruction explain that their teaching is an expedient, that it is designed especially to lead the young and the moderately gifted to music. Even if this were true, we would still have to ask where, in what books, in which institutions can we find a way to the true art of music, and not merely an expedient? Where does the student or the serious music-lover learn what is essential to a true fugue, sonata, or symphony, what makes a true orchestration, what produces a truly great performance, true in the sense of the truth of the great masters? Expediency can give us no answer. This explanation is simply too weak. There is yet a further disgrace, for the so-called expedient could only have arisen through ignorance of the true nature of strict counterpoint and thoroughbass. But the advocates of these erroneous teachings withhold the most important excuse: these theories have enabled many generations of teachers and musicians to earn their livelihood. Art in its truth and beauty has been ignored, but the practicalities of life have been assured, which made it easier to ascribe practicality to the teaching, whether honestly or dishonestly. These persons now fear lest my new teaching undermine their existence; they allege that its inherent difficulties make it unsuitable for large-scale exploitation in the schools. No such danger would exist, however, if teachers would devote themselves solely to one task, to training their students to hear music as the masters conceived it. The schools cannot pretend to breed composers (much less geniuses), though certain vain and arrogant young people would like them to do precisely that. Such sowing and reaping must be left to God. Only by the patient development of a truly perceptive ear can one grow to understand the meaning of what the masters learned and experienced. If a student, under firm discipline, is brought to recognize and experience the laws of music, he will also grow to love them. He will perceive that the goal toward which he strives is so meaningful and noble that it will compensate for the fact that he himself may lack a genuine talent for composition. Thus my teaching, in contrast to more rapid methods, slows the tempo of the educational process. This not only leads the student to genuine knowledge, but also improves the morale of artistic activities in general. Surely it is time to put a stop to the teaching of music in condensed courses, as languages are taught for use in commerce. It is also time that educational authorities cease to employ textbooks which are designed only for the less capable student. In spite of all this, I would hope for a great increase in educational activity, for a multiplicity of geniuses by nature demands also a multiplicity of nongeniuses. Even though it is fundamentally only vanity which causes the average musician to compose, we must be grateful that, through vanity itself, people are brought to dedicate themselves to art. APHORISMS All that is organic, every relatedness belongs to God and remains His gift, even when man creates the work and perceives that it is organic. The whole of foreground, which men call chaos, God derives from His cosmos, the background. The eternal harmony of His eternal Being is grounded in this relationship. The astronomer knows that every system is part of a higher system; the highest system of all is God himself, God the creator. My concepts show that the art of music is much simpler than present-day teachings would have it appear. However, the fact that the simplicity does not lie on the surface makes it no less simple. Every surface, seen for itself alone, is of necessity confusing and always complex. Specifically, my concepts demonstrate the following: A firmly established linear progression can withstand even the most discordant friction of voices as they move contrapun-tally. xziii A firmly established tonality can guide even a large number of chromatic phenomena securely back into the basic triad. A performance, in serving background, middleground, and foreground, can employ the greatest variety of color. Even the richest and most varied resources of performance can be taught—and learned—with great exactness. On the other hand, commitment to background, middleground, and foreground excludes all arbitrary personal interpretation. The musical examples which accompany this volume are not merely practical aids; they have the same power and conviction as the visual aspect of the printed composition itself (the foreground). That is, the graphic representation is part of the actual composition, not merely an educational means. Therefore the presentation of the examples required extreme care.*1 There is no doubt that the great composers—in contrast to performers and listeners—experienced even their most extended works not as a sum total of measures or pages, but as entities which could be heard and perceived as a whole. Music is always an art—in its composition, in its performance, even in its history. Under no circumstances is it a science. Since the linear progression, as I have described it, is one of the main elements of voice-leading, music is accessible to all races and creeds alike. He who masters such progressions in a creative sense, or learns to master them, produces art which is genuine and great. In its linear progressions and other comparable tonal events, music mirrors the human soul in all its metamorphoses and moods—"alles Vergängliche ist nur ein Gleichnis" ("what is passing is only resemblance," Goethe). How different is today's idol, the machine! It simulates the organic, yet since its parts *1. Since the task of revealing the world of the background in music fell to me, I was not spared the difficulty of finding symbols for it. This required many years. Furthermore, the engravers did not always demonstrate the necessary degree of understanding. For these reasons the illustrations in Der Ton-mile and in the Jahrbücher do not always represent the definitive form. (Schenker) XXIV FREE are directed toward only a partial goal, a partial achievement, its totality is only an aggregate which has nothing in common with the human soul. Every organic being yearns for another organic being. And art, which is organic, drives toward the organic human soul. However, in these times when man himself destroys his organic nature, how is he to respond to organically developed art? It is certain that almost half of mankind is unmusical, even incapable of singing a folk tune—a sorry ratio, one which would be unthinkable in the case of language. How then can the ear be expected to hear polyphony, which is fundamental to the linear progression? The musical person, however, is certainly capable of recognizing linear progressions and of learning to use them. Therefore, let him apply himself to this task and refrain from the "experiments" so popular today and, alas, so costly. It follows that he must also be taught the theory of organic coherence; but this does not mean that the drafting of extensive analytical sketches (Urlinie-Tafeln) is necessary, since this would be tantamount to a demand for creative powers.*2 Philosophers and aestheticians will be able to establish a general theory of music as an art only after they have absorbed my concepts.*3 Ultimately it will be possible to set forth the highest principle which is common to all arts: the principle of inner tension and its corresponding outward fulfillment, a princi- *2. Passage (A), omitted here, is supplied in Appendix 4: "Omissions from the Original German Edition." (Rothgeb) *3. Nietzsche complains ("The Will to Power," 838): "What we lack in music is an aesthetic which would impose laws upon musicians and give them a conscience; and as a result of this we lack a real contest concerning 'principles.' For as musicians we laugh at Herbart's velleities just as heartily as we laugh at Schopenhauer's. As a matter of fact, great difficulties present themselves here. We no longer know on what basis to found our concepts of what is 'exemplary,' 'masterly,' 'perfect.' With the instincts of old loves and old admiration we grope about in a realm of values, and we almost believe, 'that is good which pleases us.' " (Schenker) pie which manifests itself differently in different material. Man lives his whole life in a state of tension. Rarely does he experience fulfillment; art alone bestows on him fulfillment, but only through selection and condensation. If a differentiation is to be made between "classic" and "romantic," only the degree of tension and fulfillment should be considered. A classical work will exceed a romantic one in the height and extent of its tension and in the profundity of its fulfillment, even if it may be a short work. Thus Schubert's Wanderers Nachtlied ("Der du von dem Himmel bist")** is classical in every way by virtue of the power and tension of its few scale-degrees which unify the entire text. The phenomenon of genius signifies a breath drawn from the unconscious, a breath which keeps the spirit ever young.*8 The cultivation of genius is neither romantic nor "living in the past." Rather it is the cultivation of a contemporaneity that bridges time; it is a strong belief in the absoluteness of art and its masters. If, after centuries have passed, only one person is once more capable of hearing music in the spirit of its coherence, then even in this one person music will again be resurrected in its absoluteness. "And the Spirit of God moved upon the face of the waters." But the Creative Will has not yet been extinguished. Its fire continues in the ideas which men of genius bring to fruition for the inspiration and elevation of mankind. In the hour when an idea is born, mankind is graced with delight. That rapturous first hour in which the idea came to bless the world shall be hailed as ever young! Fortunate indeed are those who shared their young days with the birth and youth of that idea. They may justly proclaim the praise of their youth to their descendants! Heinrich Schenker *4. Fig. 37a in the example volume. (Schenker) *5. Passage (B), omitted here, is supplied in Appendix 4. (Rothgeb) Parti The Background Sometimes a most curious demand is made: that one should present experiences and perceptions without recourse to any kind of theoretical framework, leaving the student to establish his conviction as he will. But this demand cannot be fulfilled even by those who make it. For we never benefit from merely looking at an object. Looking becomes considering, considering becomes reflecting, reflecting becomes connecting. Thus, one can say that with every intent glance at the world we theorize. To execute this, to plan it consciously, with self-knowledge, with freedom, and, to use a daring word—with irony—requires a considerable degree of skill, particularly if the abstraction which we fear is to be harmless and if the empirical result which we hope to achieve is to be alive and useful. Goethe, Farbenlehre Chapter 1 The Background Section 1: The Concept of Background in General The origin of every life, whether of nation, clan, or individual, becomes its destiny. Hegel defines destiny as "the manifestation of the inborn, original predisposition of each individual." The inner law of origin accompanies all development and is ultimately part of the present. Origin, development, and present I call background, middle-ground, and foreground; their union expresses the oneness of an individual, self-contained life. In the secret perception of the interaction of origin, development, and present, as well as in the cultivation of this awareness until it becomes definite knowledge, lies what we call tradition: the conscious handing down, passing on of all relatedness which flows together into the wholeness of life. To the person who is vitally aware of such relatedness, an idea is also part of real life, be that idea religion, art, science, law, the state. Therefore the principle of origin, development, and present as background, middleground, and foreground applies also to the life of the idea within us.*1 In order to comprehend what lives and moves behind the phenomena of life, behind ideas in general and art in particular, we ourselves require a definite background, a soul predisposed to accept the background. Such a soul, which constitutes a peculiar enhancement of nature in man—being almost more art than nature—is given only to genius. The masses, however, lack the soul of genius. They are not aware of background, they have no feeling for the future. Their lives are merely an eternally disordered foreground, a continuous present without connection, unwinding chaotically in empty, animal fashion. It is always the individual who creates and transmits connection and coherence.*2 Until now it was unknown that a background and middle- *1. Passage (C), omitted here, is supplied in Appendix 4: "Omissions from the Second German Edition." (Rothgeb) *2. Passage (D), omitted here, is supplied in Appendix 4. (Rothgeb) 4 FREE ground were also indispensable prerequisites to a musical work of art. My work is the first to introduce that concept. Section 2: The Background in Music The history of music reveals that music really began and flourished in ecclesiastical, royal, and aristocratic circles. This is confirmed by the fact that music developed polyphony, which must forever remain alien to the masses. For them music has always been and remains only an accompaniment to dance, march, or song: at best, a kind of utilitarian art, if one can accept the inherent contradiction. A feeling for such music fills head and heart, even those of the masses, but this feeling is not adequate to comprehend the true and lofty art of Bach, Handel, Haydn, Mozart, Beethoven. Indeed, it tends to lead away from those concepts and responses which are essential to music as an art. Although J.S. Bach in his Passions provides the aurally "visible," the greater portion of his art remains incomprehensible to the masses. Although Haydn offers them his oratorios, the absolute music of his chamber works and symphonies can never assume real importance in their lives. Mozart lets them view his operas, yet they will never comprehend the distance which separates his great operatic art from the operatic music of other composers. Beethoven jubilantly sings the praise of womanly fidelity in the visible Fidelio, and in the Ninth Symphony, together with Schiller, he sings the "Hymn to Joy"—nevertheless, the masses will never have access to the rest of his art. But who can make the masses realize that, contrary to their impression, the highest art of the genius takes part in human life as they themselves live it, and that this high art furthers life and health just as milk and bread do, and can lead to Eros in the way any sacrament does? It is useless, therefore, to look to the masses for the support of art—an effort which is being made everywhere today. Indeed, it is highly probable that this effort will prevent our time from developing into a background for the music of the future, into one as valid as was the period a thousand years ago when men believed in gods and heroes and patiently created polyphony. The fate of the art of music is especially bound to the law of its origin. Polyphony, once discovered, has become indispensable for music. So the art irrevocably belongs only to those who have ears capable of perceiving polyphony. This the historical background of music reveals. Section 3: The Fundamental Structure as the Content of the Background in Music The background in music is represented by a contrapuntal structure which I have designated the fundamental structure:*3 Fig. 1 Fundamental line is the name which I have given to the upper voice of the fundamental structure. It unfolds a chord horizontally while the counterpointing lower voice effects an arpeggiation of this chord through the upper fifth. Since it is a melodic succession of definite steps of a second, the fundamental line signifies motion, striving toward a goal, and ultimately the completion of this course. In this sense we perceive our own life-impulse in the motion of the fundamental line, a full analogy to our inner life. Similarly, the arpeggiation of the bass signifies movement toward a specific goal, the upper fifth, and the completion of the course with the return to the fundamental tone. The life of the fundamental line and the bass arpeggiation manifests itself not only in the first horizontal succession and in the first arpeggiation; it also expands through the mid- *3. Fig. 1 shows a third-progression in the upper voice. The fundamental line may also show a fifth-progression or an octave-progression (Figs. 10 and 11). (Oster) THE dleground, through what I have called the voice-leading and transformation levels, prolongations, elaborations, and similar means, into the foreground. Whatever the manner in which the foreground unfolds, the fundamental structure of the background and the transformation levels of the middleground guarantee its organic life. The fundamental structure represents the totality. It is the mark of unity and, since it is the only vantage point from which to view that unity, prevents all false and distorted conceptions. In it resides the comprehensive perception, the resolution of all diversity into ultimate wholeness. Even a bouquet of flowers requires an ordering of some kind, lines which lead the eye to comprehend the whole in a brief glance. The ear requires guiding lines all the more, since it is, in a sense, a younger organ than the eye. I call the content of the fundamental line, counterpointed by the bass arpeggiation, diatony (Diatonie) <§ 4>. This is the fundamental, determinate melodic succession, the primal design of melodic content. In contrast, tonality, in the foreground, represents the sum of all occurrences, from the smallest to the most comprehensive—including illusory keys and all the various musical forms. Within the poles of fundamental line and foreground, of diatony and tonality, the spatial depth of a musical work is expressed—its distant origin in the simplest element, its transformation through subsequent stages, and, finally, the diversity of its foreground.*4 The goal and the course to the goal are primary. Content comes afterward: without a goal there can be no content. In the art of music, as in life, motion toward the goal encounters obstacles, reverses, disappointments, and involves great distances, detours, expansions, interpolations, and, in short, retardations of all kinds. Therein lies the source of all artistic delaying, from which the creative mind can derive content that *4. Passage (E), omitted here, is supplied in Appendix 4. (Rothgeb) 5 is ever new. Thus we hear in the middleground and foreground an almost dramatic course of events. As the image of our life-motion, music can approach a state of objectivity, never, of course, to the extent that it need abandon its own specific nature as an art. Thus, it may almost evoke pictures or seem to be endowed with speech; it may pursue its course by means of associations, references, and connectives; it may use repetitions of the same tonal succession to express different meanings; it may simulate expectation, preparation, surprise, disappointment, patience, impatience, and humor. Because these comparisons are of a biological nature, and are generated organically, music is never comparable to mathematics or to architecture, but only to language, a kind of tonal language.*8 The fact that the fundamental line itself traverses a third, a fifth, or an octave in linear fashion is of great significance to horizontal motion in general. Since the smallest compass of the fundamental line is the third, neither a tone which is simply stationary in the foreground nor a tone which, by virtue of octave coupling or register transfer is understood to be stationary, is relevant to diminution or to the so-called melody. A person stretches forth his hand and indicates a direction with his finger. Immediately another person understands this sign. The same gesture-language exists in music: every linear progression is comparable to a pointing of the finger—its direction and goal are clearly indicated to the ear. In the linear progressions the composer lives his own life as well as that of the linear progressions. And, conversely, their life must be his, if they are to signify life to us. i -rJi''- .'■ ■' The principles of voice-leading, organically anchored, remain the same in background, middleground, and foreground, even *5. See Figs. 62,2; 119,7; 119,10; 121,1-3; 148,3, and Schenker's comments on these examples. (Oster) 6 FREE when they undergo transformations. In them the motto of my work is embodied, semper idem sed non eodem modo ("always the same, but not in the same way"). Nothing new is to be expected, yet this need not surprise us when we see that even in technology, which today stands in the forefront of all thought and activity, nothing truly new appears: we witness only further transformations.*6 The power of will and imagination which lives through the transformations of a masterwork reaches us in our spirit as a power of imagination—whether we have specific knowledge of the fundamental structure and the transformations or not. The life of the transformations conveys its own nature to us. We receive not only profound pleasure from a masterwork, but we also derive benefits in the form of a strengthening of our lives, an uplifting, and a vital exercise of the spirit—and thus achieve a heightening of our moral worth in general. Section 4: The Significance of the Fundamental Structure for Composition, Instruction, and Performance *7 Musical coherence can be achieved only through the fundamental structure in the background and its transformations in the middleground and foreground. It should have been evident long ago that the same principle applies both to a musical organism and to the human body: it grows outward from within. Therefore it would be fruitless as well as incorrect to attempt to draw conclusions about the organism from its epidermis. The hands, legs, and ears of the human body do not begin to grow after birth; they are present at the time of birth. Similarly, in a composition,, a limb which was not somehow born with the middle and background cannot grow to be a diminution. Hugo von Hofmannsthal has found ingenious words for this: "One must conceal the depths. Where? On the surface." And: *6. Passage (F), omitted here, is supplied in Appendix 4. (Rothgeb) *7. Passage (G), omitted here, is supplied in Appendix 4. (Rothgeb) ITION "No part of the surface of a figure can be formed except from the innermost core outward." Thus, in the foreground, coherence lies behind the tones, as, in speech, the coherence of thought lies behind the words. Consequently, one can understand that the layman is unable to hear such coherence in music; but this unfortunate situation obtains also at higher levels, among musicians of talent. Even they have not yet learned to hear true coherent relationships. Since most people today lack coherence themselves, they are quite unable to bear the tension of musical coherence. As a motion through several levels, as a connection between two mentally and spatially separated points, every relationship represents a path which is as real as any we "traverse" with our feet. Therefore, a relationship actually is to be "traversed" in thought—but this must involve actual time. Even the remarkable improvisatory long-range vision of our great composers, which I once referred to as "aural flight," presupposes, indeed, includes time.*8 And what has become of the concept of time at the present? Technology enables distant parts of the world to be connected at a rate of speed which is approaching the point of frenzy. This has also conditioned our attitude to art. Today one flies over the work of art in the same manner as one flies over villages, cities, palaces, castles, fields, woods, rivers, and lakes. This contradicts not only the historical bases of the work of art but also—more significantly—its coherence, its inner relationships, which demand to be "traversed." *9 The ability in which all creativity begins—the ability to compose extempore, to improvise fantasies and preludes—lies only in a feeling for the background, middleground, and foreground. Formerly such an ability was regarded as the hallmark of one truly gifted in composition, that which distinguished him from the amateur or the ungifted. Subsequently the rise of the masses made it necessary for the composer to give consideration *8. Der Tonwille 5, p. 55. (Schenker) *9. Passage (H), omitted here, is supplied in Appendix 4. (Rothgeb) THE to the incapabilities of an ever-growing number of musicians. So it would be of greatest importance today to study thoroughly the fantasies, preludes, cadenzas, and similar embellishment which the great composers have left to us. All music instruction, be it public or private, should assign high priority to such stády. Anyone who has seen sketches by the great composers must have encountered voice-leading progressions which are far more than brief ideas or mere suggestions. These voice-leading progressions really present structural goals and the paths to them in a manner which could only stem from the far-flung inspiration of a genius. Such a vision, which is based upon the relationship of background, middleground, and foreground, can create a purely musical coherence even, as it were, in flight.*10 Therefore, a thoroughgoing study of the extant sketches of the masters is most necessary. These sketches reveal musical coherence in the process of evolution. What a deplorably low value is generally placed on music is reflected in the fact that sketches by the masters, although long a commercially viable commodity, have been little understood by musicians. The exigencies which the composer encounters as he creates are foreign to these persons; therefore the written records of the composers' successful struggle with such exigencies must necessarily also have a foreign look about them. Under these circumstances Nottebohm's Beethoveniana, which Brahms so strongly recommended for publication, had to wait almost a half-century for the printing of its second edition. It is the musicians themselves who abandon their art! How different is the case of the first drafts, fragments, or sketches of great poets and painters—they have always met with a more general and lively appreciation! Since the musicians up to the present have been unable to perceive the musical coherence in the masterworks, they have been even less able to read the autographs of the great compos- *10. In my work, particularly in the annotated editions (Erläuterungsausgabe) of op. 101, 109, 110, and 111, I have often referred to this quality in Beethoven's sketches. (Schenker) 7 ers. These last present the additional difficulty of problems of notation which are highly individual, ever new, and never schematic, but which always correspond to the musical content. Autograph-study, a completely new and special field of knowledge, thus goes hand in hand with the theory of musical coherence. The extent to which I have surpassed my few predecessors in this subject—editors, analysts, and the like—is indicated by those works of mine which secure for me the honor of being the true founder of the discipline of autograph-study.*11 Organic coherence also underlies the art of orchestration and the treatment of the instruments in chamber music. In the masterworks, orchestral colors are not mixed according to whim and applied at random; they are subject to the laws of *11. In my edition of the Beethoven piano sonatas, the following texts are based upon the autographs: op. 27 no. 2, op. 28, 57, 78, 81a (first movement), 90 (after the manuscript copy by Archduke Rudolph), 101, 109, 110, and 111 (cf. also the Erläuterungsausgabe). In addition, I revised the "Philharmonia" edition of Schubert's Symphony in B Minor according to its autograph. The analytic presentations of Beethoven's Fifth Symphony (Universal Edition), Mozart's Symphony in G Minor (Jahrb. II), Chopin's Etudes op. 10 nos. 5 and 6 (Jahrb. I), and Schubert's Menuetto in B Minor (Kunstwart, March 1929) are based upon autographs. In the Five Graphic Analyses, the autographs of J.S. Bach's Prelude in C (WTC I), Haydn's Sonata in Eb (Hob. 49), and Chopin's Etude op. 10 no. 12 were of the utmost value. The presentation of the Eroica in Jahrbuch III relies upon a copy of the manuscript revised by Beethoven. As a result of a suggestion I made in the preface to my Erläuterungsausgabe, which was later orally reinforced in private instruction, Mr. Anthony van Hobo-ken, a Dutch music enthusiast equipped with the finest musical intelligence, established an archive for Photogramme von Meisterwerken and presented it to the Nationalbibliothek in Vienna in 1927. This collection has already increased in size to more than 30,000 prints. However, this invaluable treasure is appreciated least of all by the musicians. They gaze at the prints as they would at locks of hair, watches, writing desks and the like, which are shown at exhibits that honor the memory of the great dead. I have often stressed that information of the greatest significance regarding the principles of art, the creation of musical coherence, the individual style of notation, etc., is to be derived from autographs as well as from sketches. (Schenker) 8 FREE the whole (cf. Jahrb. Ill, Scherzo of the Eroica Symphony). [§ 269] The performance of a musical work of art can be based only upon a perception of that work's organic coherence. Interpretation cannot be acquired through gymnastics or dancing; one can transcend "motive," "theme," "phrase," and "bar line" and achieve true musical punctuation only by comprehending the background, middleground, and foreground. As punctuation in speech transcends syllables and words, so true punctuation in music strives toward more distant goals. This, of course, does not mean that the tones of the fundamental line need be overemphasized, as are the entrances in a poor performance of a fugue. The player who is aware of the coherence of a work will find interpretative means which allow the coherence to be heard. He who performs in this way will take care not to destroy the linear progressions; such destruction would paralyze our participation. Nor will he overestimate the value of the bar line, which indicates neither linear progression nor direction. Consequently, the concept of background, middleground, and foreground is of decisive and practical importance for performance *12 [§§ 252-54, 265, 299].*13 All previous theory has succeeded in blighting the art of music; it has instilled its own chaos into what is yet an unshakeable organism. It is not the province of theory to provide anything that is totally new or truly its own—yet theory seeks for one, new solution after the other, with the emphasis usually upon the "new" and not upon "solution." Since conventional theory is not able to measure all musical *12. Passage (I), omitted here, is supplied in Appendix 4. (Rothgeb) *13. Many of Schenker's publications contain beautiful and deeply considered suggestions for performers. See especially the Erläuterungsausgabe of the late Beethoven sonatas; also Beethoven's op. 57 in Der Tonwille 7, Brahms's Handel Variations in Der Tonmlle 8, Mozart's (7-Minor Symphony in Jahrbuch II. (Oster) motion in relation to the filling-in of the space of a third, fifth, or octave, it postulates the overtone series and, further, a series of subharmonics as the origin of the major-minor system.*14 But the subdominant, which most definitely forms part of the diatonic system, cannot have its origin in the overtone series. Theory has never departed from this contradictory teaching. Even up to the present day, theory has not always been able to read foreground intervals correctly; one can only recognize them by examining their relation to background and middle-ground. All too frequently theory has failed to recognize many events in the foreground, simply because it has not understood their origin in the more elemental. Since thoroughbass figures can be understood only in terms of such relations, theory also fails when treating thoroughbass. To theory, the figures represent empty, frozen concepts; consequently, musicians of today cannot intelligently realize a continuo part. But the most baleful error of conventional theory is its recourse to "keys" when, in its lack of acquaintance with foreground and middleground, it finds no other means of explanation. Often its helplessness is so great that it abandons even this most comfortable means of avoiding difficulties. Nothing is as indicative of the state of theory and analysis as this absurd abundance of "keys." The concept of the "key" as a higher unity in the foreground is completely foreign to theory: it is even capable of designating a single unprolonged chord as a key. To be sure, the great composers spoke of keys in the incorrect sense in their letters and notes. However, when we consider the singularly profound and masterly character of their works, we can certainly disregard their theoretical nomenclature. But we, incapable of such mastery, dare not permit ourselves the luxury of erroneous theories. It is no wonder, then, that the masterwork remains inaccessi- *14. Bruckner used to teach (following Sechter) that even the sixth tone of the diatonic scale was dissonant and therefore had to be resolved downward. (Schenker) THE ble to theory, and that its analyses resemble unsuccessful decipherings of papyrus rolls. From such theory, who could expect to learn how to improvise, or to develop all the capabilities which lead to the secrets of truly organic and artistic activity? *15 Music is not only an object of theoretical consideration. It is subject, just as we ourselves are subject. Even the octave, fifth, and third of the harmonic series are a product of the organic activity of the tone as subject, just as the urges of the human being are organic. Accordingly, the quest for a new form of music is a quest for a homunculus. But nature will endure, indeed, will conquer, in music also; she has revealed herself in the works of the masters and, in this form, she will prevail. My concepts present, for the first time, a genuine theory of tonal language. Instruction at least in the linear progressions, the primary means of coherence, is indispensable. Because these progressions are anchored in polyphony, we must first learn to think contrapuntally. Even though counterpoint has long existed in the West, it is not yet at home in the mind of Western man. His ear is more apt to disregard counterpoint, to follow the upper voice which is the bearer of the melodic element, just as children rely on the right hand at their first piano lesson. At best, one hears a bass which is inactive; but when the bass goes beyond mere support and undertakes contrapuntal motion, the ear immediately turns back toward the upper voice. *15. Passage (J), omitted here, is supplied in Appendix 4. (Rothgeb) 9 My theory shows that music is a self-contained unity in every respect,j^atjgives it its particular life among the arts. I would not presume to say how inspiration comes upon the genius, to declare with any certainty which part of the middleground or foreground first presents itself to his imagination: the ultimate secrets will always remain inaccessible to us [§§ 29, 85]. The greatest disaster for music is the so-called composition school. At best, one might allow music schools to serve as centers where the construction and performance of the instruments would be taught. Without any right, the schools attempt to justify their existence by providing instruction in composition: they even dispense legally binding documents testifying to the results of their instruction. Is not learning to hear the first task, during which time the student might well dispense with composition? Admittedly, to hear correctly and to compose correctly are equally difficult; but no music school can be released from the obligation of teaching to hear correctly. We cannot indulge the student in his favorite objection that he will never be able to reach such a high goal. Do not people devote themselves to many ends, even though they are conscious that they can never attain complete mastery? Are not the masses in the public schools instructed in matters which have no place in everyday life? Therefore, why should they not learn that strange mysteries also lie behind tones? [§ 316] Goethe's words are true: "That which the masses believe is easy to believe"; and, "What the intelligent person knows is difficult to know." It is also true that the fundamental structure amounts to a sort of secret, hidden and unsuspected, a secret which, incidentally, provides music with a kind of natural preservation from destruction by the masses. But, despite all difficulties, the schools ought definitely to give some suggestion of this secret! Chapter 2 The Fundamental Structure Section 1: The Fundamental Structure in General § 1. Arpeggiation as an outgrowth of the harmonic series In nature sound is a vertical phenomenon: Fig. 2 In this form, however, it cannot be transferred to the human larynx; nor is such a transfer desirable, for the mere duplication of nature cannot be the object of human endeavor. Therefore art manifests the principle of the harmonic series in a special way, one which still lets the chord of nature shine through. The overtone series, this vertical sound of nature, this chord in which all the tones sound at once, is transformed into a succession, a horizontal arpeggiation, which has the added advantage of lying within the range of the human voice. Thus the harmonic series is condensed, abbreviated for the purposes of art {Harm. §13). 10 This basic transformation of the chord of nature into an arpeggiation must not be confused with the voice-leading transformations of the fundamental structure which occur in the middle-ground. § 2. The fundamental structure as transmitter of the primary arpeggiation In the service of art, the arpeggiation throws off the restrictions of nature and claims the right to assert itself in either an upward or a downward direction. The following two forms represent the briefest and most direct ways for the harmonic series to be realized by human vocal organs: Fig. 3 The upper voice . As in the natural development of the arpeggiation, the ascending direction is the original one; indeed, in the fundamental structure it serves as a constant reminder of the presence of the chord of nature [§§ 10, 12]. § 3. The fundamental structure as a unity The combination of fundamental line and bass arpeggiation constitutes a unity. This unity alone makes it possible for voice-leading transformations to take place in the middleground and enables the forms of the fundamental structure to be transferred to individual harmonies (§§ 242 if.). Neither the fundamental line nor the bass arpeggiation can stand alone. Only when acting together, when unified in a contrapuntal structure, do they produce art.*1 Section 2: The Fundamental Line in General § 4. The path toward diatonic organization After centuries of striving, when creative ears had finally learned to mold several voices successfully into a contrapuntal complex, it became possible to fill in the spaces in the arpeggiation in the upper voice of the fundamental structure with passing tones in a manner which did justice to both nature and art. In the process musicians also gradually learned to conform to nature by adjusting the horizontal and vertical aspects simultaneously: they adopted the octave, fifth, and third, which dominate the fundamental arpeggiation of the chord of nature. In addition they learned how to treat the passing tone as consonant *1. Those new to the concept of musical background tend to turn their attention exclusively to the fundamental line, because it is the upper voice. They all too hastily accept any tone series as the fundamental line, without determining whether it rests securely upon the counterpoint of the lower voice. Thus they often meet with disappointment (§§ 210, 257). (Schenker) STRUCTURE 11 or dissonant according to what the practice of strict counterpoint them as fifth or third of a particular bass tone, it is only because we recognize in them the same relationships which establish the octave, fifth, and third of the harmonic series. But these notes are no longer actual overtones: they are only images of the overtones. Still less should the passing tones in the spaces of the arpeggi- THE ation be taken for overtones; they are not contained in the harmonic series at all. It is therefore not permissible to ascribe the same significance to passing tones as to the main bass tone; by definition, a passing tone is dependent upon the consonant tones which surround it.*3 § 10. The fundamental line begins with 8, 5, or 3 and moves to 1 via the descending leading tone 2 *4 To man is given the experience of ending, the cessation of all tensions and efforts. In this sense, we feel by nature that the fundamental line must lead downward until it reaches 1, and that the bass must fall back to the fundamental. With T all tensions in a musical work cease. Thus a fundamental line can never end, for example, with 3—2.*5 *3. It is therefore a contradiction to maintain, for example, that all scale tones between C and c have real independence or, to use a current but certainly musically unsuitable expression, "equal rights." No matter how one would divide this tone series, any division compels recognition of diatony in the sense of a relationship of all tones of the series to the fundamental, C. In compositional practice, the error of this point of view results in a constant violation of the tonality in the foreground. One feels justified in setting down any key whatsoever, claiming for it independence, without any relation to the fundamental key. The effect may well be imagined .... (Schenker) *4. In German theoretical writings the second step of the scale is sometimes referred to as der abwärtssteigende Leitton, literally "the descending leading tone." Schenker's reference in § 17 to "both leading tones" designates the second and seventh scale degrees. (Rothgeb) *5. The question often arises why the fundamental line always descends to i but never ascends, for example, from 5 to 8. Since Schenker nowhere explained this phenomenon, the following may serve as an answer.—As Schenker said in § 9, the 8, 5, and 3 are only images of overtones. But, like true overtones, they too seem to be generated by a fundamental tone, which in the fundamental structure is the I. And the "tensions" come to rest only when the 8, 5, or 3 have "gone home"—when they have returned to where they came from, that is, to the fundamental which created them. Accordingly, they have to move in the direction of the fundamental, and this means downward. But the fundamental line does not have to descend to the I in the bass register in order to STRUCTURE 13 A sequence of tones cannot live in the foreground unless the total tension of the fundamental linear progression provides it with breath; na }ife c^abe^breathed into it from the foreground. How preposterous therefore to try to fashion an organic, living work by assembling various tone series without background! §11. The ascending leading tone is not contained in the fundamental line Since the fundamental line can descend to 1 only through 2, the ascending leading tone is excluded; in all cases it appears as an inner-voice tone <§ 118). § 12. 8, 5, 3 anticipated chordally Since the fundamental line rests on the counterpoint of the 8 5 3 bass, its first pitch-level, or or , is anticipated, all at once, in chordal fashion [§ 122]. *6 The acknowledgment of the principle of nature is reiterated in the opening interval, a vertical event. From that point on, the fundamental line descends according to the principles of art and of diatony. In the middleground and foreground, however, the first actual interval of the fundamental structure can be altered by means of a prolongation (§§ 120 ff., 125 ff., 129 ff.). For this reason caution is advised when regarding a foreground-beginning: are we hearing the actual opening interval of the fundamental-line progression or merely a prolongational interval which precedes it? come to rest. For exactly as the 5 or the 3 are only images of the third or fifth overtones, so the final í is an image of the fundamental bass tone and represents the return to it. (Oster) *6. That is, instead of reaching this pitch-level by means of arpeggiation (§2). (Oster) 14 FREE § 13. The horizontal fulfillment of the fundamental line as tone-space By the concept tone-space I understand the space of the horizontal fulfillment of the fundamental line. Thus, only the fundamental-line progression of the third 3—2—1 represents the tone-space 3—1; only the fundamental line of a fifth or an octave represents the tone-space of a fifth or an octave. A vertical third (tenth), fifth, or octave as the first interval of the composition cannot represent a tone-space; misunderstandings easily arise in connection with these beginning intervals.*7 Therefore, I repeat: tone-space is only to be understood horizontally . § 19. The sacred triangle May the musician always carry in his heart the image of the bass arpeggiation (Fig. 7)! Let this triangle be sacred to him! Creating, interpreting—may he bear it always in ear and eye! By extension, every triad, whether it belongs to middleground or foreground, strives for its own triangle (§§ 242 if.). Section 4: Specific Characteristics of the Fundamental Structure § 20. Significance of high and low register with respect to fundamental line and bass Even in the fundamental structure, the fundamental line presents its arpeggiation filled in with seconds, whereas the bass presents its arpeggiation bare. This is because of the general difference between high and low register [§ 53]. The difference between fundamental line and bass arpeggiation makes itself felt in all levels, including the foreground. Because of its low register, the bass diminution always remains STRUCTURE 15 more restrained than that of the upper voice [§§ 64, 185, 210, 257]. § 21. The fundamental structure is arrhythmic Rhythm can no more exist in the fundamental structure than it can in a strict-counterpoint cantus firmus exercise. Only when, through voice-leading transformations, linear progressions arise in the upper and lower voices of the middle-ground, does a rhythmic ordering issue from the necessity of counterpointing the voices against each other. All rhythm in music comes from counterpoint and only from counterpoint (§§ 284 ff.) [§ 67]. In the middleground every individual level has its own specific rhythm, according to the extent of its contrapuntal content. Thus rhythm, too, progresses through various transformational stages until it reaches the foreground, just as do meter and form, which also represent end-results of a progressive contrapuntal differentiation (§ 290) . § 33. The first glimpse of form in the foreground This type of fundamental structure can maintain itself undivided in the foreground and therefore result in an undivided form (§ 307). 2 However, the linear progression of a fifth, suggested by v, presents, after an exploratory probe into the foreground, the possibility of a modulation (in the foreground sense) to the key of the dominant, which then would provide special support for the interruption form 3—21| 3—2—i (§§ 87, 309 ff.). § 34. The form of the fundamental structure in the case of 5 The form of the fundamental structure in the case of 5 is as follows: Fig. 10 § 35. The 4 as a dissonant passing tone in the fundamental line 5—Í Fig. 10,1 shows that the 4 is dissonant as it passes over the root. As a dissonant interval the 4 permits no composing-out, for an interval which is itself passing cannot at the same time serve as a primary tone of a linear progression. Such a primary tone must necessarily be consonant. Therefore in a dissonant state the 4 remains without the emphasis which a consonant 20 FREE interval receives: no linear progressions can be derived from it (§§ 169, 170) [§ 69]. § 36. The apparent subdivision 5—3—1; the unsupported stretch Fig. 10,2: If after the dissonant 4 the 3 asserts itself as a consonance—as a tenth or third above the root—the semblance of a subdivision 5—3—1 immediately arises [§§ 77, 95]. In this context the first part of the fundamental line 5—4— 3 has more the effect of a transiently filled space of a third; it is not quite like a linear progression of a third that is worked out with the help of a counterpointing bass progression. This creates a certain void, or unsupported stretch, at the very outset of the fundamental line of a fifth, and occasionally gives rise to the question whether the form of the fundamental structure is not actually 3^2—1 as it is shown in Fig. 9 [§ 116]. § 37. The apparent subdivision 5—2—1 2 Fig. 10,3: Lastly, through an emphasis upon 2 results, which makes an especially strong contrast with the previous unsupported stretch. Thereby another subdivision seems to appear in the linear progression of a fifth: as though with 2 the linear progression of a fourth, 5—2, had come into being [§ 76]. § 38. Affirmation of the indivisibility and unity of the fundamental line of a fifth despite any appearance of subdivision However, the forward compulsion toward 1 still exists at the end of the fundamental-line segments 5—3 or 5—2. This necessity reaffirms the indivisibility of the progression of the fifth in the fundamental structure, no matter how much the appearance of a subdivision might seem to deny it (§ 6). § 39. Tasks posed by the form of the fundamental structure in the case of 5 It follows from the foregoing paragraphs that the tasks of the middleground and foreground are to eliminate the unsupported stretch at the passing 4 by making that 4 consonant and composing it out, and ultimately to establish and fulfill the structural subdivision 5—3—I or 5—2—1 [§ 170]. § 40. A glimpse of form in the foreground In the possibility of the structural subdivision 5—2 lies the root of the interruption-form 5—21| 5—i in the middleground (§§ 95 ff.) and also in the foreground [§ 192]. § 41. The form of the fundamental structure in the case of 8 This form is shown in: Fig. 11 § 42. The appearance of several subdivisions Fig. 11,1: Since 5 and 3 are consonant with the root of the triad, an effect of several subdivisions arises. Fig. 11,2 and 3 show that the unsupported stretch is apparent to a much greater degree than in the case of 5—1. For this reason doubt often might arise as to whether we are instead confronted with a linear progression of a third or a fifth. Fig. 11,4 and 5: Even when the root of V is placed under 7 or 5, the phenomenon of the unsupported stretch has not been eliminated. THE FORMS OF THE FUNDAMENTAL STRUCTURE 21 § 43. The task posed by the fundamental structure in the case of 8 Above all, the unsupported stretch must be eliminated in order to establish that the fundamental line 8—1 actually exists. This can be achieved through the subdivision 8—5—I with two arpeg-giations in the bass (Figs. 19b; 27, a and b). § 44. The 7 is diatonic The 7 in a linear progression 8—1 must be strictly diatonic if a genuine fundamental line is involved [§ 102] and not merely an octave line in a coda, where a lowered seventh may appear (Fig. 73,4). Partii The Middleground Chapter 1 The Middleground in General § 45. Assignment of names A name or term always implies a simultaneous verbal and logical connection, an essential unity. Therefore the assignment of names to concepts is of utmost importance in intellectual discourse. For the sake of continuity with my earlier theoretical and analytical works, I am retaining in this volume the words of Latin derivation prolongation and diminution as designations for the voice-leading levels in the middleground. However, as in the past, I shall also utilize German term,s for these concepts, as, for example, Stimmfiihrungsschichten (voice-leading levels), Stimmführungsverwandlungen (voice-leading transformations), or shorter, Verwandlung (transformation), Mehrung (increase of content), Ausmcklung (unwinding), Auflösung (dissolution), Umwandlung (reshaping), Umbildung (recasting), and similar ones. § 46. Voice-leading transformations also spring from a vital natural power The fundamental structure shows us how the chord of nature comes to life through a vital natural power. But the primal power of this established motion must grow and live its own full life: that which is born to life strives to fulfill itself with the power of nature. For this reason, it is not artistically accurate to consider the voice-leading transformations merely superficial variations (§ 30). § 47. Freedom of the prolongations A particular form of the fundamental structure by no means requires particular prolongations; if it did, all forms of the fundamental structure would have to lead to the same prolonga-tional forms. Indeed, the choice of prolongations remains essentially free, provided that the indivisibility and connection of all relationships are assured [§ 183]. The rapport between the particular form of the fundamental structure and the later levels—ultimately also the foreground— determines the choice of prolongations more specifically. It is 25 26 FREE this rapport which forms the actual picture of the background, middleground, and foreground (§ 29). Fig. 12 Thus, the neighboring-note harmony at the beginning may have arisen in the composer's imagination together with the first tone of the fundamental line. Fig. 13 Similarly, the setting of the first arpeggiation might have originated together with the first tone of this fundamental line ** [§§ 125-27]. In any event, it is the fundamental structure which guides the composer. § 48. The number of structural levels It is impossible to generalize regarding the number of structural levels, although in each individual instance the number can be specified exactly, as I have shown in many examples in my work. In.any event, the first two levels already contain the branching-out into the particulars of a work of art. Moreover, there are some prolongations which would occur only at the first level, others which take place only at the second. The prolongations at the later levels evolve from those at the first two levels [§§ 183-85]. § 49. The danger of confusing structural levels Merely to discuss prolongations orally or to suggest them is a rather fruitless undertaking. One must write them out, take hold of them with the fingers, in order to bring them most accurately to one's consciousness. Only when a very exact pic- *1. Chopin's op. 31, usually referred to as the Scherzo in B\> Minor because of its initial harmony, must be regarded as being in the key of D\> major <§ 303>. (Schenker) ture is laid out on paper do questions arise which demand clarification, especially those concerned with the smallest details of the voice-leading. The composer who lacks the gift of true ingenuity knows from experience how he stumbles in the foreground—stumbles, indeed, over the foreground itself, over the difficulties of creating diminutions. Let him go forth and learn their laws! The illustrations which I have called Urlinie-Tafeln (literal translation: graphs of the fundamental line) diagram the penultimate prolongational level, after which follows the foreground.*2 Those who feel no desire to expend effort in exploring the background and middleground should confine themselves to the Urlinie-Tafeln. Readers who have acclaimed my presentation of the foreground (e.g., in my monograph on Beethoven's Ninth Symphony) because it has revealed to them new relationships, will surely approve of the Urlinie-Tafeln for the same reason. And yet, I recommend that everyone take the trouble to feel his way from the foreground to the middleground and background; he need only employ the familiar method of reducing more extensive diminutions, as taught in textbooks and schools. So he will arrive at shorter and shorter versions, and finally the shortest, the fundamental structure! § 50. Rejection of the conventional terms "melody," "motive," "idea," and the like Great composers trust their long-range vision. For this reason they do not base their compositions upon some "melody," "motive," or "idea." Rather, the content is rooted in the voice-leading transformations and linear progressions whose unity allows *2. Schenker refers here to illustrations in previous publications, Der Ton-wille, the three volumes Jahrbücher (Das Meisterwerk in der Musik), and finally the Five Graphic Analyses (Fünf Urlinie-Tafeln). Compare the presentation of three voice-leading levels in Fig. 22b. Due to limitation of space, however, the fundamental structure and the first level are not specifically shown in this example. (Oster) THE no segmentation or names of segments <§§ 308,311,313>. Every linear progression, provided it does not quickly pass by in sixteenths or thirty-seconds, presupposes a certain extended vision, and has nothing to do with "melody" or "idea." While fashioning linear progressions, the great composer feels secure and does not fea£ .momentary obviousness or incompleteness, nor does he act precipitously from helplessness in the midst of a linear progression. Without shame, he often places the simplest kind of composing-out at the very beginning of a work, one which the least gifted composition student would reject as too uninteresting. Of course, the great composer already hears the continuation, and with it a series of composings-out. These form a totality and present a melody of far higher order and greater inevitability than a "melody" or "idea" could provide. What is to be designated as "melody" or "idea" in those pieces whose entire course is identical with the fundamental structure (§ 26)? One cannot speak of "melody" and "idea" in the work of the masters; it makes even less sense to speak of "passage," "sequence," "padding," or "cement" as if they were terms that one could possibly apply to art. Drawing a comparison to language, what is there in a logically constructed sentence that one could call "cement"? How does one distinguish an "idea" from "cement"? It is certainly not out of place here to distinguish "fundamental structure" composers from "idea" composers. The latter must always be concerned with the effect of the moment; they ramble constantly instead of deriving higher entities from the background and middleground. They frequently defend their inability by saying that that is precisely how they wanted to write and thus give one to understand that they could compose just as well as the masters if they so desired. If only they would once attempt to create a truly organic work! Under extreme duress, however, they take refuge in emotion, where they believe themselves to be unassailable; I should consider them unworthy of an attack. It is impossible to present in specific and perceptible forms IN GENERAL 27 all the events which occur through the miraculous rapport of fundamental structure with foreground—especially in forms which would satisfy the superficial interest of the curious. A wonder remains a wonder and can be experienced only by those blessed with special perception. Its secrets are inaccessible to every sort of metaphysics; they are neither teachable nor learn-able. Up to the present we have not even learned to comprehend those events which lie on the surface. The simplest linear progressions in the foreground are still inaccessible even to very sensitive ears. § 51. The status of music history Music history, as I have repeatedly indicated, should pursue the questions of where, when, and how musical material found the path from incoherence to coherence: when did the first creative ear develop a sense for linear progressions as the essential unities, complete with their constraint to move forward in the horizontal dimension? When did composers begin to demonstrate the sustaining power of these linear progressions by constructing more and more extended prolongations? When one considers the art of such prolongations, it becomes immaterial whether (as the historians suppose) J.S. Bach composed monothematically or Beethoven composed polythematically. Despite the eternal sameness of the linear progressions, there is still room in the art of music for countless gifted composers! But the historian should avoid placing the master and the man of moderate ability on the same level: such a grouping has led to a false concept of culture. The master composer enters the scene in isolated instances—the man of moderate ability is always there. Never can there be a connection between them! When genius has been absent, mere talent has always plodded onward. But even the simultaneous presence of genius and talent has never meant true culture for the average man.*3 *3. Passage (L), omitted here, is supplied in Appendix 4. (Rothgeb) 28 FREE § 52. The present situation On the one hand, the battle against diminution is raging. Since musicians can no longer cope with diminution, they simply abolish it. Composers attempt to return to the technique of those first contrapuntal creations which exhibit the first traces of diminution. They imagine a rebirth of the primitive, a bond with the old masters. Such composers never realize that only the diminutions in the masterworks of the epoch of genius represent the truly creative in music, music's actual nature and significance [§§ 251-66]. Moreover, in today's desperate struggle to expand content, diminution certainly does not have the worth of even those first efforts; then the power of diminution was still youthful and yearned to create linear progressions. Diminu- tion today is the product of withering imitation alone, pursued without talent. For the same reason, we find constant misunderstandings in today's editions of the masterworks and in the performance of their diminutions. On the other hand one hears the cry for melody—most frequently meaning a tasty aural bonbon. It is amusing to watch those persons who woo melody also striving to attain a wide span. They somehow sense that music needs a certain length in which to expand and soar. But melody and length always will remain at odds, and so they devise theories to justify themselves in producing length artificially and force themselves to expand material whose nature is extreme brevity. There is hardly a compositional technique more fraught with danger than that of the "wide span of melody." Chapter 2 Specific Characteristics of the Middleground: The First Level Section 1: The Combination of Fundamental Line with Bass Arpeggiation (a) An Unprolonged Fundamental Line Combined with an Ascending Bass Arpeggiation I—V That Is Prolonged by Contrapuntal-melodic Means § 53. The contrapuntal-melodic prolongation in the ascending arpeggiation By the word melodic I do not mean "melody" in its customary sense (§ 50), but a filling-in of the space from I to V in the bass. This space-filling motion serves to counterpoint the fundamental line, which is as yet unprolonged (§ 20). Because the fundamental line remains unprolonged, one scarcely notices the space-filling motion with which the bass goes beyond the I—V—I of the fundamental structure. Yet, since it is a prolongation of the bass, we must regard the new contrapuntal structure as part of the first level. § 54. Ways in which the bass reaches the V The following illustration shows the possible space-fillings: Fig. 14 In order to make this illustration understandable it is necessary to apply the concept of harmonic scale-degree here, though its systematic presentation can only come later (§§ 276 ff.) [§ 79]. § 55. Arpeggiation through the third Fig. 14, Ex. 1: The paths in a) and b) represent an arpeggiation of the fifth through the third. This gives rise to the concept of a third-divider. The meaning of this third-divider changes according to whether it remains within the first harmonic degree, as at a), or whether it achieves the value of an independent root, especially when the third is raised (III*), as at b). However, 29 30 FREE in both instances the essential unity of the fifth-arpeggiation prevails over the third-divider.*1 § 56. The complete filling-in of the arpeggiation by means of seconds Exx. 2a and 2b show the birth of seconds, which are the true bearers of the contrapuntal-melodic element. The arpeggiation is completely filled in as though it were an upper voice which is filled in by passing tones. In this way a certain state of indecision is generated between the fundamental harmonic arpeggiation and the melodic filling-in. However, this state of indecision eventually finds its resolution in the descending fifth V—I, which underscores the harmonic division of the triad more than does the melodic filling-in of the ascending arpeggiation. Exx. 2a and 2b present the filling-in of the paths shown in Ex. 1. The filling-in can also take on other meanings, depending on the position of the tones of the fundamental line, as shown in Exx. 2c and 2d. When, as in Ex. 2c, the fourth bass tone F is emphasized by a tone of the fundamental line, we then have, within the I—V motion, a linear progression of a fourth, C—F, with the effect of I—IV. I indicate this relationship by means of interlocking slurs, thus: I—-IY^V. The V is the goal, the IV represents the subsidiary contrapuntal-melodic step of a second {Jahrb. II, pp. 21 if.) [§§ 164, 186]. If, as at Ex. 2d, the second bass tone is made prominent by a tone of the fundamental line, there arises the relationship I—Hp>£y, in which case I—II represents the contrapuntal-melodic step of a second. § 57. The omission of the initial second In Ex. 3, the illustrations of the omission of the initial second show at a) and b) an arpeggiation in thirds, corresponding to *1. The special type of third-divider shown in Fig. 131 appears in conjunction with an interruption. (Oster) that shown in Exx. 1 and 2, a) and b). The illustrations at c) and d) show the effect of I—IV—V or I—II6—V, as in 2c) and d). In the latter two instances the third implies only a passing-motion, even though the second tone of the filling-in is missing, and even when, as at d), there is a ^j it is the stress upon the following second, given by a tone of the fundamental line, which reveals the true intention, the contrapuntal setting I—IV—V or I—II6—V (Fig. 15,3c). Those who still hear in terms of Rameau's concept of harmony obviously cannot bring themselves to disregard the third in favor of the fourth. This assuredly makes the foreground inaccessible to them. . § 62. The contrapuntal settings of Fig. 14 in relation to form at the foreground level I have already mentioned that the unprolonged version of the bass of the fundamental structure suffices to achieve a form at the foreground level (Figs. 9-11). This is also the case with the contrapuntally prolonged versions shown in Fig. 14. The transference of the bass patterns shown in Fig. 14 to individual scale-degrees at various structural levels, even in the foreground, heightens their significance and creates additional content (§§ 242 ff.). § 63. Further interpolations and their abbreviation Since the unity of the bass arpeggiation is so strong, further interpolations can occur in the filling-in motion. These take the form of descending fifths which move down to each principal tone of the melodic filling-in. The bass, in its own fashion, abbreviates these descending fifths, by drawing them together for easy contrapuntal handling, in such a way that melodically desirable seconds arise. Thus the resulting bass line appears only as a melodic enlivening of the ascending fifth descending fourth) (§ 283 and Fig. 135,1 and 2). § 64. The difference between a contrapuntally prolonged bass and the bass of a cantusfirmus exercise Even the constant tendency of the bass to imitate the melodic characteristic of the fundamental line with seconds does not alter the fact that it must constantly and exclusively be concerned with the arpeggiation through the fifth. This is in sharp contrast to the bass of a cantusfirmus exercise. The approach to the dominant is also different in the contrapuntally prolonged bass from the analogous movement in the bass of a cantus firmus exercise. In the former it takes place through the step of a second, IV—V, whereas in the latter such a second is not required, nor is it always possible to execute it [§ 56]. Therefore, the step of a second from IV to V in foreground cadences stems from the contrapuntal aspect of music! At this point we can finally answer the question of the origin of this remarkable second. Although the spirit of the fifth (the harmonic aspect) can realize the scale-degrees, including the IV, only by means of the fifth (or the fourth as its inversion), this in no way denies the contrapuntal origin of the step of a second from IV to V. [§ 164; Figs. 37a and 44,2.] § 65. A prolongation of the descending arpeggiation V—I cannot occur at the first level 2__J At the first structural level, v T provides no opportunity for a prolongation in contrapuntal-melodic terms (Figs. 15-18; §§ 74, 86, 189). (b) Working-out and Consequences of the Contrapuntal Structure in the Case of 3, 5, or 8 § 66. The laws of strict counterpoint remain valid in the newly achieved structure If an unprolonged fundamental line, beginning either with 3, 5, or 8, is to be coordinated with the contrapuntal basses shown in Fig. 14 to form a structure, it must be done according to the rules of strict counterpoint. Thus, the consonance remains 32 FREE the fundamental principle of voice-leading; the dissonance appears only as a passing tone or as a syncopation. The intervals which are gained in the new structure indicate the tasks of the next structural level <§ 170>. § 67. Two lines in contrary motion in the outer voices; the necessity of balancing them rhythmically The descending fundamental line and the melodically rising bass constitute the first example of two linear progressions in contrary motion; this motion, regulated according to strict counterpoint, indicates the path for what follows c), decides between the IV<5>-6 and the II [§ 280]. In the foreground the 5—6 exchange mentioned above can prove to be a rhythmic shift (§ 294). Ex. 3: The structures shown in a) through c) have already been explained at 2a)-c) above. With regard to the skip preceding the passing tone at c) see § 57. Ex. 4: This is similar to 1, 2, and 3. Exx. 5 and 6: The explanation given for 2c) and d) also applies here. § 74. Two descending fifths combined with the descending second 2—1 In Fig. 15,6 it is highly significant that the step of a second, 2—I, progresses together with the two descending fifths: i2i~vd(§60)- *2. The necessity for the seventh to descend. (Oster) MIDDLEGROUND: THE FIRST LEVEL 33 In terms of voice-leading, the situation presents only the avoidance of parallel octaves by means of an interpolated fifth, 8—5—8 (§ 163). However, since the 2 is already present in the first octave, the two descending fifths accompany only one descending second of the fundamental line. Thus it is possible to strengthen the descent of the fundamental line by two descending fifths in the bass; at later levels this procedure can be transferred to an upper voice that prolongs a harmony on any scale-degree [§ 242 and Fig. 109a]. The fact that the first descending fifth (D—G) is expressed as an ascending fourth is allied with the striving of the bass to conform to the principles of counterpoint. § 75. Structural consequences in the case of 5—1 The structural consequences in the case of 5—i are shown in Fig. 16 What was said in §§ 72-74 applies here also. § 76. Structural consequences in the case of 8 In the case of 8, one must recognize significant differences between the fundamental-line segments 3—2, 5—2, 8—2, all counterpointed by I—V: Fig. 17 a) Here, because of the step of the second, a harmonic division 3__§ of the fundamental-line segment T v does not yet occur. This second moves downward. 5__2 b) In T v a fourth is expressed. Harmonically it is equivalent to a fifth and also moves downward [§ 7]. 34 FREE c) Here, by contrast, instead of the descending motion T__v, one would hear a rising second (=c2—d2); but an ascending step would be contrary to the progression of a fundamental line. This resultant effect of a rising second creates an ambiguity in all the settings of 8; none of them permits a thor- g__2 oughgoing harmonic division of T „to occur (§§ 41-44,100). There are too many possible versions to present them all in one illustration. I have given only a few here: Fig. 18 (c) The Combination of an Unprolonged Fundamental Line with Two Bass Arpeggiations § 77. General considerations In Fig. 10,2 and Fig. 11,2 and 3 lies the key to further prolongation of the bass: here the bass is provided with two arpeggiations instead of one. Though it was stationary during 5—3, 8—5, and 8—3, the bass now forms its own cadence: Fig. 19 Although the two cadences tend to emphasize an apparent structural division 5—3—1, 8—5—1, or 8—3—1, the fundamental line remains in an unprolonged state. This is in strong contrast to the prolongation of the fundamental line by means of an interruption (§§ 87-101). If one can use a special bass arpeggiation with the first segment of the fundamental structure (in the case of 5 and 8), then one can also apply the same principle when the bass arpeg- giation serves linear progressions that prolong individual harmonies (§§ 242 ff.). § 78. Examples of the above The graphic presentation of the examples in Fig. 20 shows the fundamental line's progressions and the two bass arpeggiations in accordance with Fig. 19a and b. The beams serve this special purpose. Ex. 1: In the composition the bass is only implied, but I have indicated it here. Ex. 2: Here we have a case similar to Ex. 1. The beginning of the Fugue is preceded by a Fantasy, which in toto expresses the I, so that the fugue subject can enter on III in the middle of the first bass arpeggiation. Ex. 4: This example is related to Fig. 19b, first example. Compare this also with J. S. Bach's Little Prelude no. 6 in D Minor (BWV 940) in Jahrbuch I, pp. 101 ff. The second example in Fig. 19b may be compared with the Little Prelude no. 12 in A Minor (BWV 942) in Jahrbuch I, pp. 117 ff. (d) Conclusions § 79. The contrapuntal aspect of the harmonic degrees Of course, the descending fifths in the bass present the fifth as verified by nature. But upon considering the results of §§ 56, 57, 59, 60, 63, 73, and 74, we find that such fifths are also a necessary outgrowth of voice-leading. Thus they combine in themselves a harmonic and a contrapuntal principle. This becomes even more apparent in the case of fifths interpolated in the service of expanding diminutions. These foreground SPECIFIC CHARACTERISTICS OF THE MIDDLEGROUND: THE FIRST LEVEL 35 fifths, secured through both fifth-relationship and counterpoint, have the effect of harmonic degrees in the foreground. Therefore, the harmonic degrees are inextricably bound up with counterpoint (§§ 276 if.). § 80. The structures of Figs. 15,16, and 18 in relation to form in the foreground Though the voice-leading in Figs. 15, 16, and 18 may appear insignificant, it nevertheless has the capacity to develop foreground forms, not only of small but also of larger pieces (§§ 301 ff.). § 81. Open and close positions at the first level At the first level 3 represents open position, as in strict counterpoint, whereas the 5 and 8 represent the close position . § 82. Voice-leading constraint in prolonged structure For the moment, let us disregard what the fundamental line mjeans for diatony, for form and synthesis as a whole; what the bass means for the unity of the fundamental chord; and last, what their combination means for tonality and for the synthesis of the whole. These considerations aside, the prolonged structure at the first level displays the same inner necessity of the voice-leading which ensures onward motion as in any cantusfirmus structure <§73, seventh-constraint}.*3 § 83. Significance of the voice-leading constraint with regard to "tone-readiness" *3. The title Der Tonwille expresses a similar thought: the tones have a "will" of their own, to which even the composer must submit. (Oster) The voice-leading constraint creates a certain "readiness" which imparts to music the same flow as language displays in its constant readiness for thought and word. In language, flow derives from the fact that the speaker knows in advance what he wants to say and therefore formulates it: if he were to delay thought until he spoke, only stammering would result. In music, however, there are even talented men, creators and interpreters, who are still far from a similar "tone-readiness." True musical fluency comparable to that in speech is to be found only in works of genius. All such readiness springs only from the voice-leading of the fundamental structure and its subsequent prolongations. Tone-readiness is something quite different from what is commonly called "inventiveness"—the ability, for example, to invent isolated "motives." Tone-readiness presupposes the whole, whereas so-called inventiveness concerns itself only with separate elements, and with these only haphazardly. One sometimes speaks of "halting" inventiveness, or one which somehow falters. For a composer who possesses tone-readiness this cannot exist [§ 301]. Just as a pianist or a string or wind player prepares all motions of the arm, hand, finger, bow, and breath, and does not wait to form them until he has begun playing, so the composer ought to establish his linear progressions in advance. § 84. Voice-leading constraint controls all individual harmonies As a consequence of voice-leading constraint, all those individual harmonies that arise from the progression,of»th§, various voices are forced to move forward. All transient; harmonies which appear in the course of a work have their source in the necessities of voice-leading [§§ 178, 180]. § 85. To create art by means of intellect alone is impossible 36 FREE One might feel tempted to entrust musical creativity entirely to the intellect and expect favorable results. But every attempt in this direction must founder, for even prolongations bring with them occurrences intangible, inaccessible to the intellect. The true profundities of creativity are not attainable by intellect alone [§ 29]. (e) V—I at the First Level § 86. At the first level there is no contrapuntal prolongation within the bass progression V—I 2 With v the rhythmic adjustment between the fundamental line and the contrapuntal-melodic settings of the bass comes to an end (Fig. 14). Because of the step of a second in the 2__i fundamental line, the situation v T provides no occasion for any further rhythmic conflict. Only at later levels can possible prolongations of the 2 also provide opportunity for a special contrapuntal-melodic development of the bass. Yet, these new structures must lack the significance of the forms of the fundamental structure shown in Figs. 15, 16, and 18, because they 2__i have their origin in the descending fifth v T, which has no contrapuntal power in its unprolonged state [§ 65] <§ 189>. Section 2: Division of the Fundamental Line (a) Division by Interruption in the Case of 3 § 87. Concept of interruption As a linear progression of a third, the fundamental line 3—1 represents the smallest range of composing-out, the ultimate unity which cannot be further split. Therefore, the funda- mental line 3—Í admits of only one form of division, the interruption 3—2||3—2—1. The initial succession 3—2 gives the impression that it is the first attempt at the complete fundamental line. Fig. 21 § 88. The return to 3 is not a cadence From the concept of interruption it follows that the return 3 to T does not represent a cadence. If this return were really a 2 1 full close, v would have to move down to T with the effect of 2 a descending leading tone.*4 Hence v appears as the limit of an initial forward motion of the fundamental line. The return 2 to 3 affects us so strongly precisely because v signifies, in the case of 3—1, the last possible point of interruption . The interruption has such a strong effect that no connective linear progressions or similar features can obscure it: Fig. 22 a) Here we find an interruption . The direct transfer of the octave is often replaced by an ascending linear progression: Fig. 26 This linear progression can begin either with the next-to-last tone, as in a), or with the last tone, as in b), of the descending fourth.*10 *9. This means that the 5, the primary tone, could actually appear above the 2—and not only conceptually as in the case of 3. (Jonas) *10. Both cases occur predominantly in the minor mode, particularly Fig. 26a. In Fig. 26b there is usually a transformation of the V"3 into a V*3 (§§ 89, 249, and 314). Compare 26a with Fig. 154,3 and 7. Compare 26b with Fig. 152,6. (Jonas) 40 FREE § 99. 5—215—I as a source of form in the foreground Interruption first of all points to the two-part form, The initial linear progression already encompasses four tones of the total line. This distance provides the opportunity to prolong, step by step, each tone of the line (especially the 3 and 2 even more so the v). One can even create the effect of modulation and a new key in the foreground or reinforce the entire fourth-progression by repeating it. All these emphases and delays only intensify the desire to reach the final 1. Generally such prolongations lead to three-part form, as shown in Fig. 26a and b. Thus we see that three-part form develops out of two-part form, which in turn is brought about by interruption— all again tracing back to the undivided fundamental structure (§§34ff.). Again, one must marvel at the inexorable control of the fundamental structure and the logic of the resulting development. The apparent halt after 5—4—3 in Fig. 26a does not denote an interruption of the linear progression of a fourth in the strict sense of the concept; the unity of the line extends to 2. For example, in the first movement of Mozart's G-Minor Symphony (Jahrb. II) we have: 5 4 3 d2 c2 th1 i---------------------------------- Exp.---------------------Dev.--------Recap. The linear progression of a fourth forces itself through the exposition and development, even in the larger forms, no matter how much this motion may be concealed by a return to 5 [§ 313, explanation of Fig. 154,3; also Fig. 154,4]. (c) Divison by 8—5—1 in the Case of § § 100. Linear division in the case of 8 The linear progression of an octave 8—1 makes an interrup- 2 tion at v impossible. The reason for this has been given in §76. 2 As a substitute for the interruption at v, the division T, in the form shown in the first example of Fig. 19b, is used. § 101. The linear division 8—51| 5—1 as a source of form in the foreground This division gives rise to a two- or three-part form: Fig. 27 In both of these divisions, prolongations in the 7—6—5 succession bring about even stronger effects of modulation and key in the foreground. Section 3: Mixture § 102. Mixture at the third of the fundamental line is mixture of the first order In the fundamental structure (Figs. 9-11), the fundamental line remains strictly diatonic. At the first level, however, it can contain a mixture of the major and the minor third. In this SPECIFIC CHARACTERISTICS OF THE MIDDLEGROUND: THE FIRST LEVEL 41 regard, it makes no difference whether the fundamental line begins with 3, 5, or 8: Fig. 28 Mixture at the sixth of course cannot occur in the case of 3 and 5. It is not feasible even in the case of 8—1: the fourth 8—5 is artificial (§ 7), and, specifically, the interval succession 6—5 *" makes the decisive cadential figure I—V—I impossible: Fig. 29 However, in the foreground, particularly in a coda, one is free to use mixture at the sixth of an octave-progression. A possible chromatic alteration of the fifth in the inner voice, as in Fig. 15,1, 2, 3b, has no bearing upon mixture of the third in the fundamental line. Fig. 30 The examples in Fig. 30 refer to Fig. 28a. Compare also Brahms's "Auf dem Kirchhofe," Chopin's Prelude in D\> Major, and his Waltz in CÍ Minor. In connection with Fig. 28b, note Beethoven's Seventh Symphony, Allegretto; Haydn's Symphony no. 103 in Eb (Drum Roll), Andante; and his Andante and Variations in F Minor for piano. *11. In the first edition, the interval succession is displayed as follows: 6—5 6—5. The second German edition reads (paradoxically) the interval succession "é— 5." The meaning of the sentence as a whole is somewhat obscure: the cadential progression I—V—I is no more readily available for a diatonic 6—5 succession than it is for one involving mixture at the sixth (b6—5). And there are several reasons against assuming that Schenker has in mind a I—V—I progression relating to V in the sense of a tonicization. (Rothgeb) § 103. Relation of mixture of the first order to form The mixed third does not represent a linear progression or a neighboring note. It provides no occasion for a cadence, but can only give form the opportunity to set off two or three sections against one another. Certainly, this also means a delay, a tension, but, in a strict organic sense, mixture is less form-indicating, less form-generating than division or interruption [§ 312]. Section 4: The Phrygian 2 in the Fundamental Line § 104. The b2 at the first level In the fundamental structure a Phrygian 2 can no more exist than can a mixture. At the first level, however, because of the constant rapport with the middleground and foreground, the voice-leading frequently creates the necessity of admitting the b2, just as mixture may be admitted [§ 194]. § 105. The setting of the b2 and the so-called Neapolitan sixth In accord with Fig. 9, the harmonic-contrapuntal setting of the b2 would read as in a) of Fig. 31 In this way, either an augmented fourth or a diminished fifth would result in the bass line. Also, because of the cross-relation, the root of the bll would make it difficult to adjust the b2 by restoring diatonic 2. In order to avoid all these difficulties, a sixth (the bass tone which is also the root of IV) is placed below the b2—as in Fig. 31b). This sixth has been misunderstood and introduced into theory as the "Neapolitan sixth." It is, however, an event that originates only in voice-leading and has nothing 42 FREE to do with a Neapolitan school {Harm. § 50) [§ 280, below commentary on Fig. 132,4]. Section 5: The Neighboring Note § 106. Only the upper neighboring note is possible at the first level If it occurred in the fundamental line, the lower neighboring note would give the impression of an interruption [§ 91]. The upper neighboring note, however, is free from the danger of such misunderstanding. Hence it alone can appear at the first level, as a neighboring note of the first order. At the same time, it provides a glimpse into the next higher tone-space without working it out completely [§ 112]. Thus the essential space a Nbn a a n a j-. in the case of 3—4—3—2—1 remains 3—1. In the case of 5, since the interruption-form 5—41| 5—1 is impossible, only the upper neighboring-note 6 can occur. This does not alter the essential space 5—1. In the case of 8 the upper neighboring note can never occur, because it would overstep the bounds of the octave space. As substitution for 8—9—8, a neighboring note may appear at a later level as an embellishment to the 5. A final observation: the neighboring note of 3 is dissonant to the I, whereas the neighboring note of 5 is consonant. This affects not only the harmonic-contrapuntal setting of the neighboring note, but also, indirectly, the form [§§ 111, 175, 247]. § 107. The position of the neighboring note of the first order The neighboring note of the fundamental line thus belongs to the primary tones 3 or 5. Hence, the following forms are r Ä ^ „ Nbn Ä ~ ÄÄ 'Nbn ^ °* impossible: 3—2—3—2—1 or 5—4—5—4—3—2—1. Thus, in doubtful cases only the neighboring note of the first order can decide whether 3 or 5 is the primary tone. The neighboring- A won a note figure 3—4—3 is not, however, to be confused with a neighboring-note harmony which precedes the 3, such as that shown in Fig. 12 or Fig. 63,3. Since, in the case of 8—i, a neighboring note can appear only with the 5, one occasionally might misconstrue the 5 as the primary tone (§ 106). § 108. The setting of the neighboring note The neighboring-note concept, as understood in the second or third species of strict counterpoint, requires the return of the main tone with a consonant interval. Thus, the neighboring-note figure is based upon a consonance at the beginning as well as at the end. This is shown in Exx. 1 and 2 of Fig. 32 The same requirement of strict counterpoint is also met in the Exx. 3 to 7, where we have: Nbn Nbn Nbn_^____^ I—IV—I, I—VI—I (3 and 4); I—IV8—V7—I (5); IV and finally a neighboring note arising from I—V5-7—I (7). § 109. The neighboring note as retardation The melodic expansion of the fundamental line by means of the neighboring note (and the consequent illusion of a new tone in the fundamental line) has the effect of a delaying [§§ 30, 70, 90]. § 110. How the neighboring-note formation differs from an interruption SPECIFIC CHARACTERISTICS OF THE MIDDLEGROUND: THE FIRST LEVEL 43 In contrast to the interruption, the neighboring-note formation remains at the same pitch level and thus reinforces the primary tone. The neighboring note cannot be supported by the V in the same manner as can the 2 in the interruption shown in Figs. 2 21 and 24. Therefore, it lacks the weight of the v and stresses rather the effect of delay, particularly in cases where it is supported only by the IV or VI (Fig. 32,3 and 4). Where it has its own cadential bass (Fig. 32,5 and 6), the neighboring note is more organically established. In interruption, the main part of the line has already run its course with 3—2 or 5—2. But in the case of the neighboring note, no matter how it is structurally supported, greater importance is attached to the descending line which follows the return of the main tone. Since structural division and the neighboring note represent two different concepts, independent of one another, they can be combined. Thus, in the case of 8—i the employment of the neighboring note to 5 represents such a combination of division and neighboring note (§ 155). § 111. The neighboring note as a source of form The neighboring note, however humble it may appear to be in content and nature, carries within itself a fundamental musical idea, a great voice-leading occurrence. The neighboring note of the fundamental line is in most cases form generative; its inherent delaying quality brings organic unity to that which in the foreground is a two- or three-part form. The plagal setting in Fig. 32,3 and 4 is self-contained. Therefore, it is not permissible to read the neighboring-note harmony (IV or VI) together with the final V as a cadence. Nevertheless, , the neighboring note in such a setting can be expanded at the foreground level to become the middle part of a three-part form. The two cadences in the bass in Fig. 32,5 and 6, the first of which organically establishes the neighboring note, suggest a two-part form, which can eventually lead to a three-part form at the foreground level. An interruption such as that in Fig. 32,7 indicates a two-part form, as does the apparent neighboring note brought about by the register transfer of the seventh. This does not exclude the possibility that a more significant working-out of the seventh could bring about a three-part form (§ 92 and Fig. 23a). § 112. Preliminary discussion of the neighboring note at subsequent levels At later levels a neighboring note can occur with any tone. The further it departs from the basic version found in strict counterpoint, the less form generative it is. It then serves only purposes of embellishment or expansion. Section 6: Linear Progressions (a) General §113. A linear progression at the first level always relates to a tone of the fundamental line A linear progression at the first level I call a linear progression of the first order. An ascending or descending linear progression of the first order must, by definition, be related to a tone of the fundamental line. This can be any fundamental-line tone. In the case of a descending line, the fundamental-line tone will be the primary tone, the point of departure; in an ascending line, it will be the goal tone. '^cendin. SU4. the \ FREE COMPOSITION „f tb« »»st Order § 115, * přece The des, lo - of the desí ions r progres- \ ^escendi11^^ desce* ^^ ndinglinepref^^^asystem- , 1- „of th^^lofthe % *me 01 ^»i „ Q innervoice to a« m ^ „ríerS'Wes apro- nfr0nUheA As a , \< ' a d/S^^tóomaW»f^amental Ne ■£ *?. <*e 4 VU ^^f moon, the ***an *°" ^ «iSľ ínear £ í V?" fr J^°- -ogressioltof ^osestinner ^(l0x flnallľ VertlV %irďPr°^^^o-woL« to *eSeeond inner n ^ tľ f<^yi0nf of %> - oftheŕ^f^ ľ> ^'thpef fth NVVerVa °oiZ^ •*■ voM^beunder-£ the c?" !UnNlbVT UPP /*m^>t> , b^nterpointWHe f f ^^sr-.ature-fe^>elves not ^ a J* al«o in fiiV\Vd of n»^^, ™m LV s y1 °r 5-1 and ^.íľ'Äll-lÄS^SÄ í« UwtK fv, .Vi ^ 'HorC^^-ationot1 ^ch descend Thľarta.ss must be clearly defined, exactly as in the case of a fundamental structure. The possibilities of the linear progression must be fully utilized and thus fully realized [§36], That which is both will and necessity in the fundamental line is also will and necessity in the derived linear progressions; in other words, the derived linear progression wants itself to be a true linear progression. A negative example, that of a tonal succession which has no will to be a linear progression, is to be seen in Fig. 23b of § 92 (also §§ 205-7). Every linear progression shows the eternal shape of life— birth to death. The linear progression begins, lives its own existence in the passing tones, ceases when it has reached its goal— all as organic as life itself. S117. The setting of linear progressions descending from 3 or 5 The support provided by I—V—I or by the prolonged bass forms shown in Fig. 14 imparts to the linear progressions which descend from 3 or 5 the effect of a fundamental structure or of a form of the fundamental structure as shown in Figs. 15 and 16 (§§ 242 ff.): Fig. 33 Therefore, at the first level such linear progressions are chiefly encountered in connection with an interruption (Figs. 22b; 23) or with a neighboring note (Fig. 32,3-7) . Quite apart from its expansion of content, the linear progression which departs from the first tone of the fundamental line exerts a special charm: the deceptive effect of a fundamental line, which 44 FREE (b) Descending Linear Progressions of the First Order § 114. In the systematic presentation of linear progressions the descending line takes precedence over the ascending line Because of the relationship of the descending linear progression to the all-encompassing descending fundamental line, it is appropriate to give the descending line preference in a systematic presentation <§ 10>. § 115. The descending line of the first order signifies a progression from the upper to an inner voice As a result of the continuing presence of the primary tone : Fig. 37 § 121. The principle of the primary tone remains effective for the ascending line The principle of the primary tone also applies to the ascending linear progression <§ 93>. Thus, the ascending line contains both the primary tone and the goal tone, the latter having priority here because it is simultaneously the first tone of the fundamental line. § 122. The ascending line is a motion from the inner to the upper voice Because of the principle of the primary tone, the ascending line is basically only a motion from the inner voice to the upper 46 FREE voice <§ 115>. Therefore the first tone of the fundamental line comes into being through a melodic development, not in abbreviated chordal fashion (§ 12). § 123. Structure of the initial ascent The goal tones 3 and 5 prevent the effect of a complete close, such as is created by the descending line shown in Fig. 33. To be sure, the diatonic fourth-progression 5—8 displays the leading tone, and so an effective close could be made even though the line ascends. But a complete initial ascent to 8 (1—8) would result in too heavy a burden for the fundamental line 8—1. There is no example of this in the literature of music. For 5— 8, see Fig. 20,4. However, at a later level, a leading-tone effect may be achieved by means of a prolongational employment of chromatics, if such tones are aided by their respective dominants (§§ 244 ff.): Fig. 38 Especially in an initial ascent to 5, the #4 is frequently employed. The 5 receives thereby an extra emphasis, particularly when in the foreground the chromatic event takes the form of a modulation to the key of the dominant (Fig. 38,b-d) [§ 167]. § 124. The initial ascent as retardation The initial ascent represents a delaying at the very outset of the piece. This can serve various purposes: Fig. 39 Ex. 1: The initial ascent virtually depicts the breathing ("atme kühl im Licht des Mondes, träume süss im stillen Mute"— "breathing coolness in the moonlight, dreaming sweetly here in silence"). Ex. 2: Often it makes an onward movement of the bass possible, so that the first tone of the fundamental line appears over a degree other than I, effectively heightening the inner tension [§ 127]. *12 [Ex. 3: Cf. §277, last paragraph, and also Fig. 119,3 and Fig. 120,6a.] Section 7: Arpeggiation § 125. An arpeggiation of the first order ascends to the first tone of the fundamental line The only arpeggiation at the first level is that which ascends to the first tone of the fundamental line: Fig. 40 § 126. The space of the arpeggiation The distance encompassed by the arpeggiation depends on whether 3 or 5 is the goal. Of course, an arpeggiation of a third may lead up to 3. However, such a broken third is often employed in the service of an unfolding (§ 140); this easily leads to misunderstanding . Fig. 40, Exx. 1 and 2: The arpeggiation of a tenth represents that of a third. Exx. 3-6: The arpeggiation of a sixth up to 3 is properly understood as the upper part of an arpeggiation of a tenth. Root *12. The small vertical brackets which appear above the section of the lower example pertaining to bars 30-38 are intended merely to draw attention to the vertical intervals with which they are aligned: they point out the succession of three fifths, which is eliminated by the interpolated sixths (cf. § 164). In general, vertical brackets are used in the examples to point out vertical intervals, while horizontal brackets point out motivic parallelisms. (Rothgeb) SPECIFIC CHARACTERISTICS OF THE MIDDLEGROUND: THE FIRST LEVEL 47 and third appear to be skipped over; the arpeggiation begins with the fifth (Fig. 7a). Ex. 7: Octave arpeggiations beginning with the third are less frequently found (Fig. 13). Exx. 8 and 9: The arpeggiation to 5 can move through a fifth or an octave. § 127. The setting of arpeggiations of the first order During an arpeggiation the bass can do one of three things: 1. It can remain on I (Fig. 40,4 and 5). 2. It can move according to one of the prolonged forms shown in Fig. 14, as follows: in Fig. 40,2 as in Fig. 14,3c; in Fig. 40,1 as in Fig. 14,3d; in Fig. 40,3 as in Fig. 14,5. (In the last example an arpeggiation leads downward by thirds from I to II.) 3. It can display an irregular prolongation; compare the neighboring-note harmony in Fig. 13 [§ 303]. § 128. The relationship of the first arpeggiation to possible later ones The arpeggiation of the first order can evoke parallelisms: In Fig. 40,10 the second arpeggiation /2—6b2 forms a parallelism to the initial eh2—c3. In Fig. 40,9 the first ascending arpeggiation a1—e2 subsequently receives a droll reply in several descending arpeggiations, until, near the end, the ascending direction reasserts itself in the arpeggiations of the sixth and octave. In Fig. 40,4 and 5, by contrast, the line descending from 2 does not represent a parallelism to the first arpeggiation rising to 3. Section 8: Reaching-over *13 § 129. The nature of reaching-over When a group of at least two descending tones is used to place an inner voice into a higher register, I call the phenomenon a reaching-over (Uebergreifen). This can occur either in direct superposition or consecutively: Fig. 41 The purpose of reaching-over is either to confirm the original pitch-level or to gain another. The very statement of these purposes implies the necessity of rapport with both background and foreground. § 130. The succession of reaching-over The two-tone succession in the reaching-over must descend. An ascending succession would be contrary to the purpose of the reaching-over. A reaching-over has obligation only to its goal. Thus, the individual entries are permitted complete freedom with respect to interval; from the final tone of one entry to the first tone of the next this interval can be a third, fourth, fifth, or whatever. In order to clarify the visual representation of such irregular intervals, I have marked the individual entries with small slurs below the notes. § 131. The setting of the reaching-over Fig. 41a and Ex. 1: Here the direct superposition restricts the passage harmonically, since both the tones space which the reaching-over occupies does not affect the concept. The intervals are determined by the particularities of the work involved: the rapport with background and middleground is decisive^Thus. the space of a reaching-over can even read: 1—3—5—8—5 (Bach, Two-part Invention in Eb Major). § 133. The reaching-over differs from related prolongations: linear progressions, arpeggiations, register transfer The freedom in the choice of intervals between the individual entries distinguishes reaching-over from other related prolongations: from a linear progression, where all the passing tones must be present, and from an arpeggiation, which rests on chord tones alone. Register transfer, in contrast to reaching-over, cannot make use of a motive 3. See also Figs. 65,6; 89,2; 101,1. B. The general scheme of this form is shown in Fig. 41d. The superimposed inner-voice tone introduces a tone of the upper voice from above and so resembles an upper neighboring note. In this form, the lower tone is the main tone and is introduced by the upper tone. Examples: Fig. 47,2: measures 14-18. Fig. 53,5: a1, e2—d2. Fig. 102,3: eb\ g2—f2 (see Jahrb. Ill, p. 39 and illustrations). Fig. 123,5: c*2, e2—d%2. Fig. 153,3: measures 22 ff. In Fig. 23b, the tones d2, g2—/2 represent the basic idea of the reaching-over as it frequently appears in a sonata movement. See Fig. 47,2, measures 61 ff.; also Beethoven, Eroica, first movement, 6b2—ab2 in measures 144-52 (Jahrb. III). C. Both forms described above at Aj and B may appear in succession, as in Fig. 41, bl (contracted: Fig. 41, al) or at the beginnings of Fig. 41c and 41e. See Fig. 101,2; further Fig. 101,5 and the similar situation in Fig. 109, e6. (Oster)> Section 9: Motion from the Inner Voice § 135. The nature of motion from the inner voice Motion from the inner voice (Untergreifen) means a reaching-down to an inner voice at a lower register, in order to work back from there to the original register. This procedure is used to introduce a certain slowing down into the motion of the upper voice, and to postpone arrival at the goal if for some reason it would be reached too soon. As a result of this technique there appears on the surface a new voice which seems to spring forth from an unknown source. However, rapport with the fundamental structure makes it clear that this upper voice is only seemingly new. It is as though the original register were suspended until it is regained by the motion from the inner voice. § 136. Motion from the inner voice at the first level At the first structural level this motion from the inner voice cannot relate to the first tone of the fundamental line. It can only lead to a subsequent tone in the fundamental line or to a neighboring note. The specific means employed is in accord with the particular goal. Fig. 42 § 137. How a motion from an inner voice differs from an initial ascent An initial ascent applies only to the first tone of the fundamental line. As stated above, this relationship is denied to a motion from the inner voice at the first structural level.*14 § 138. The motion from the inner voice combined with other prolongations Most frequently, a motion from an inner voice at the first structural level appears in conjunction with other prolongations, for example with a neighboring note, as in Fig. 42 [§ 155]. *14. This may appear to be only a terminological convention, but in fact it is something more. Following the definition given in § 135, the concept of motion from the inner voice includes the notion of reaching-down from an already established higher register in order to rise back to the original one. Clearly, no such reaching-down could occur at the first level without the prior establishment of the first tone of the fundamental line. (Rothgeb) 50 FREE § 139. A glimpse into later levels At later structural levels the motion from an inner voice strives toward goals of various sorts. Section 10: Unfolding § 140. The nature of unfolding An unfolding occurs in the following situations: Fig. 43 1. when the vertical condition of a single chord is transformed into a horizontal condition in such a manner that a tone of the upper voice is connected to a tone of the inner voice and then moves back to the upper voice, or the reverse (a); 2. when in a succession of several chords a similar connection from the upper to the inner voice takes place (b to f). By means of unfolding the upper voice is expanded; the basic meaning is revealed by the background [§ 234]. § 141. Commentary on Fig. 43 In Fig. 43 b-f the beams indicate the upper and lower voices of the original vertical successions. Fig. 43b, 4 and 5: The two voices which are spread out in the upper or inner parts are not to be taken for a fourth-progression, since their origin lies only in the step of a second in the upper voice (§ 205). Observe also how the unfolding figure is counterpointed by itself and thus creates a two-part setting. Fig. 43f,2: Similarly here, the unfolding presents a third-progression in the upper voice, despite the apparent fifth-progression. Fig. 43b, 3 and 43e: Compare Fig. 40,3 and Fig. 7b. See also the examples accompanying Fig. 43 as well as Fig. 103 [§ 234]. § 142. Unfolding at the first level Unfolding at the first level applies only to the primary tone (Fig. 43, first example); to a series of fundamental-line tones, such as 3—2 (Fig. 40,3 and Fig. 43, second example); or to a neighboring note (Fig. 7b). The use of unfolding has become almost a formula in particular endings: Fig. 44 § 143. How unfolding differs from other types of prolongation Arpeggiation (§§ 125 ff.) must move in only one direction, either ascending or descending. Coupling (§ 152) is restricted to the octave, whereas in an unfolding other intervals can be expressed. A procedure identical with unfolding may have another significance; only the rapport with the fundamental structure can determine the true meaning, as here: Fig. 45 where the diminution above the actual upper voice is an instance of "boundary-play" (§ 260). Compare Fig. 45 and Fig. 82,2; also with Fig. 37a, measures 7-8. § 144. Unfolding at later levels Unfolding serves various purposes at the later levels. In the bass it plays a significant role, particularly in connection with SPECIFIC CHARACTERISTICS OF THE 5—6 successions and the avoidance of parallel fifths (§ 234) [Fig. 103,5a and b]. Section 11: Substitution § 145. The nature of substitution Even at the first level, a tone which is not part of the fundamental line can substitute for a fundamental-line tone. Such a substitution is generally combined with an interruption, an unfolding, or an ascending register transfer. However, it is easily recognizable as a substitution because the counter-pointing bass arpeggiation clearly indicates the actual tone of the fundamental line, even though it is hidden. § 146. Examples of substitution at the first level For the most part substitution at the first level is to be found in short pieces. Most frequently the substitution applies to the 2 [§ 235]: *15 Fig. 46 Substitution for 1 is occasionally found in a work comprised of short pieces, for example in a set of waltzes, where it makes the connection of the parts smoother. See Schubert: Valses Nobles no. 4, where, at the end, the third, bs, substitutes for 1, Section 12: Ascending Register Transfer § 147. The nature of ascending register transfer Ascending register transfer means a raising to a higher octave. The octave interval is the basis of this concept. *15. This allows the upper voice to bring in the ascending leading tone. (Jonas) MIDDLEGROUND: THE FIRST LEVEL 51 § 148. Ascending register transfer at the first level At the first level ascending register transfer is applicable to fundamental-line tones or their neighboring notes, and to a single tone or succession of tones of an inner voice. § 149. Means of effecting an ascending register transfer An ascending register transfer may proceed— 1. in direct fashion, by means of a simple raising to a higher octave, or; 2. in indirect fashion, by means of a connection to the higher octave through another prolongation at the first level, such as arpeggiation or reaching-over. § 150. Examples Examples of ascending register transfer are shown in Fig. 47 A direct register transfer is shown in 1, an indirect register transfer in 2 and 3. In Exx. 1 and 2 the fifth-progressions which descend from 2 arrive at the octave-doubling of V, which originally belonged to the inner voice but is now brought into the higher register also. Through 8—1)7 it then returns to the second 3 in the original register (Fig. 23). [Compare Fig. 47,1 with § 313 and with Fig. 88, c] Examples of direct register transfer of fundamental-line tones, combined with a substitution for 2, are shown in Fig. 46,1 and 2. The substitution itself is brought about by the ascending register transfer of a tone of the inner voice. Compare also Fig. 83,3, where, at the end, an impossible vocal register is avoided by means of the register transfer /If1—ft,2. Finally, the frequent adjustment of b2 by means of t)2 (as it 52 FREE appears in Chopin's Etude op. 10 no. 12, mm. 72-75) must be understood as a register transfer of the \\5 of the V, originally in the inner voice . Section 13: Descending Register Transfer § 151. The nature of descending register transfer In concept and its working-out, the descending register transfer is the reverse of the ascending register transfer: Fig. 48 It can serve tones of the fundamental line, as in Ex. 1, but it also can be used in the bass, for example, for the purpose of coupling, as in Ex. 2. Ex. 1: In this case there is a play between ascending and descending register transfers: first, the descending transfer from c3 to c2, then the ascending transfer to g2 by means of c3—6b2—ab2 , and finally the descending transfer to/1 via c2.*16 If we were to consider the register from c2 to f1 as the obligatory register, we would have to regard the g2 (the 2) as transferred upward. The coda, however, confirms c3 as the obligatory 5 [§§ 239, 268]. Ex. 2: In accord with Fig. 14,3 the third (e) should lie higher, that is, in the ascending direction toward the fifth. However, it is transferred downward in order to prepare the way for the coupling c1—c. In the second part of Ex. 2, the situation is similar [§ 152]. Section 14: Coupling § 152. Concept of coupling *16. The dotted lines connecting the c"s in Fig. 48,1 indicate octave couplings. (Oster) Coupling is the connection of two registers which lie an octave apart. § 153. Coupling at the first level Coupling at the first level may serve tones of the fundamental line; it also plays an important role in the bass [Fig. 48,2]. § 154. Interplay of registers In view of the existence of an obligatory register (the primary octave in the fundamental structure), which usually is dependent on the position of the primary tone, it is possible to employ a coupling even at the first level (§ 268): Fig. 49 In relation to the primary octave the coupled octave has only a reinforcing effect (Fig. 37, b; Fig. 41, Ex. 3). Section 15: The Combination of Different Types of Prolongations at the First Structural Level § 155. The combination of different prolongations at the first structural level Two or more prolongations can be combined even at the first level, yet each, independent of the others, brings its own nature and purpose to fulfillment: mixture and interruption; mixture and neighboring note; interruption and ascending register transfer; descending register transfer and substitution; reaching-over and ascending register transfer; interruption and linear progression. Part III The Foreground Chapter 1 The Concepts of Strict Counterpoint Section 1: Perfect Consonances § 156. General observations According to the presentation in parts I and II, the foreground has an organic relationship to the background and middle-ground; therefore strict counterpoint is implicitly present in the foreground. Everything which has been said regarding the intrinsic properties of the intervals and the motion of the voices in my Kontrapunkt, volumes I and II, retains its validity in free composition. Consequently, the tonal events of free composition and their possible modifications will be presented, wherever feasible, in the same order as in strict counterpoint. § 157. The octave In free composition, the octave remains only a change of register (Kpt. I, II/l, §§ 4, 8, 9). In the course of foreground prolongations it acts as the significant bearer of transpositions and thus tends to confirm its essential nature as a change of register. Such transpositions do not exist in strict counterpoint. In free composition the octave also makes the voice analogies soprano-tenor, alto-bass clearer than in strict counterpoint. § 158. The fifth The fifth remains the boundary interval in free composition (Kpt. I, 1/2, § 12; II/l, §§ 4, 8 ff.). The prerequisite for this is that the fifth actually must relate to the lower tone as unequivocally as it does in strict counterpoint. However, free composition, in contrast to strict counterpoint, contains deceptive, inauthentic intervals which displace and obscure the actual intervals which originate in the middle-ground <§ 261>. § 159. The fourth 55 56 FREE The fourth has been shown to be a dissonance in strict counterpoint. For it has an ambiguous nature and so is subordinate to the perfect boundary interval, the fifth (Kpt. I, II/l, § 3). How free composition can provide this ambiguity with an unambiguous meaning is explained in the same section of my Kontrapunkt. Here are further instances: Beethoven, Third Symphony, Scherzo, measures 15-17, where despite the thoroughbass fig- ures the fourth is illusory, and similarly, in the Finale, measures 227 ff. (both passages are explained in Jahrb. Ill, pp. 65 and 81-82). Fig. 50 Ex. 1: In a case like this Bach nevertheless avoids the fourth. Exx. 2 and 3: Here the fourths appear in passing. § 160. Forbidden parallel octaves and fifths in strict counterpoint Strict counterpoint maintains the unequivocal prohibition of parallel octaves and fifths. The reasons for this are given in Kontrapunkt 1(1/2, § 12; II/l, §§ 7-14; II/2, § 11). Here I want to mention only that strict counterpoint forbids parallel fifths principally because the fifth controls the harmony. Counterpoint has no means of counteracting this controlling quality, since its intervals are still unequivocal [§ 16]. By contrast, thoroughbass permits open fifths even in the outer voices: see C.P.E. Bach, < Versuch über die wahre Art, das Clavier zu spielen), "Generalbass," chapter 2, section 1, §§ 21-23 . It is refined and improved through an apparent 7 suspension id2 in m. 2>, which is resolved in the bass, in conjunction with an afterbeat effect, resolutions in the bass are marked with slurs.) Ex. 2: This shows octaves on the offbeats following the 7— 6 suspensions. They are nearly obliterated by the suspension series. Interpolations, such as 8—10—8—10—8 (Mozart, Sonata in A Minor, 1st mvt, mm. 88 ff.), 8—6—8—6—8 (Mozart, Rondo in A Minor, mm. 118-20), or 8—5—8—5—8 (Bach, Brandenburg Concerto No. 5, 2nd mvt., mm. 24 ff.), are encountered very frequently. They are easily recognized in the foreground (cf. Fig. 40,9 and 10; Fig. 41, Ex. 2) [§ 74]. Ex. 3: The tones forming the octaves (mm. 124-39) also have the effect of offbeats. In contrast to Exx. 1 and 2, the octaves *3. Paragraphs 1 and 2a of § 162 apply to Examples 1, 2, and 5 of Fig. 53; Examples 3 and 4 can best be understood in terms of paragraphs 1 and 2b; and Example 6 is unique in that the octaves are justified by the formal division which separates them. (Rothgeb) show themselves in the background only; it is the events of the middleground which justify these octaves. There is a wealth of hidden relationships—parallelisms—in this mazurka (see the brackets). [§ 310, b 4] Ex. 4: Here, likewise, the interpolation cannot be perceived as an interpolation without insight into the middleground and background. This insight makes the extended 8—10-^8 in measures 14-26 understandable. The 8—10—8 progression also shows that the last quarter note in the bass of measure 25 is unquestionably an Ab, despite the absence of the flat in Chopin's autograph (see the footnote in the Urtext-Ausgabe, Breitkopf und Härtel).*4 Ex. 5: Bach avoids the parallel octaves with a reaching-over (a1—(e2)—eř2>; afterbeats soften the octaves in measures 4 and 5. E* F8 Ex. 6: v and VT are without direct relationship; V closes like a dividing dominant, and a new attempt at a cadence begins with VI. Hence, there are neither parallel octaves nor a deceptive cadence. Because of other relationships, the octave successions in the coda of Beethoven's Third Symphony (1st mvt., mm. 551 ff.) are also not parallels in a true sense (see Jahrb. Ill, p. 53). § 164. The avoidance of parallel fifths in particular Examples of the elimination of parallel fifths follow, also arranged in the order of § 162,1, 2a and b: Fig. 54 Ex. 1: The means here is a simple arpeggiation of a third. j in the manner of an auxiliary cadence (§ 244). The means of breaking up *4. However, in the first autograph (which Schenker apparently did not know) a natural sign stands before the A in the last quarter of the right-hand part, even though it would not be necessary there. (Jonas) THE CONCEPTS OF the fifths in Exx. 3-7 are easily recognized in the foreground as syncopations. Ex. 5: Compare Five Graphic Analyses. Ex. 6: Compare Fig. 53,3, where measures 124-32 show the tone-space of a sixth which encloses the parallel fifths. The consecutive sevenths which accompany the fifths make it necessary to assume an underlying progression 5, 4—5, 4—5. These implied syncopations justify the fifths. Compare further Kontrapunkt I, Ex. 184; Brahms's Oktaven, Quinten u. A., p. 8 (p. 10 in the printed edition) under "Klaviersatz"; Schumann in his review of Chopin's op. 30.*5 Ex. 7: Compare Fig. 117,1. Interpolation must also be included among the means of elimination which are easily recognized in the foreground. The most frequent interpolation is the so-called 5—6 exchange. However, this means of avoiding 5—5 successions must not be confused with the simple change of harmony 5—6 (§ 175). Ex. 8: A 5—6 exchange can be employed, as here, in the outer 8 8 parts (cf. Fig. 39,2) or in situations such as . 10 10 5—6' 5—6; 5—6, 5—6 10 10 Ex. 9: A similar situation exists here: _ „ _ „ 5—6, 5—6. Ex. 10: Occasionally a third is added below the root of the _ chord, which somewhat conceals the 5—6 exchange. Ex. 11a: The 5—6 exchange plays a special and important role when the harmonic degrees proceed by seconds: *5. ". . . the sudden close with the fifths, over which the German schoolmasters will wring their hands. . . . Naturally, a chromatic succession of fifths of this kind, if it be extended for some twenty measures, should be regarded not as admirable, but as deplorable. At the same time, one must not take such things out of context, but rather hear them in relation to what has gone before, as a part of the whole." Only with the last words does Schumann come close to the solution. (Schenker) COUNTERPOINT 59 T_____TT__v; this is particularly so in the cadence TV__,„,__v, no matter whether the remains a (Figs. 37a; 44,2) or the root of the II actually appears [§ 280]. Other interpolations are possible: 5—8, 5—8 (Fig. 30b); *6 5—7—5 (Fig. 62,2); or the interpolation of a passing tone that has been made consonant (§ 170). Ex. lib: This shows the reverse, a removal of parallels by means of omission. Of course, all of these devices can also be more or less hidden in the middleground. Particularly the 5—6 exchange is often so obscured in the foreground that it can only be understood from the middleground. Entirely of middleground nature are the solutions to parallel fifths which arise out of incidental encounters in the foreground: a principal note with an accented or unaccented passing tone or with a neighboring note; a passing tone with an anticipation, with an accented passing tone, or with a neighboring note; a neighboring note with another neighboring note, with the concluding turn of a trill, or with a suspension; the resolution of a suspension with a passing tone, with another suspension, and so forth. The Brahms study mentioned above shows numerous examples. Ex. 12: The first acceleration in the form of two quarter notes in measure 2 brings about two further quarters which restore the rhythmic balance. Ex. 13: The diminution which extends from the first measure *6. The voice-leading shown in Fig. 30b seems to present a 5—10—5—10 succession rather than the 5—8—5—8 indicated beneath the example. The latter indication apparently derives from the fact that eb1 in measure 1 basically moves to db1 in measure 2; this is clarified in the composition by the vertical thirds /Vrfb1 in measure 2. The impression of an ascending step eb1—f1 indicated by the slur in the example results from the descending line in the top voice from c2 to /'. Thus the progression eb1—f1 is, in a sense, produced by reaching-over (§§ 129-34). (Rothgeb) 60 FREE (second and third quarters) to the second (first quarter) represents b2. Therefore, the middleground shows only b2—b2 D—E and not the parallel fifths of the foreground (6-5) c$3—b2 FP-E_(cf. Fig. 40,1; Fig. 56,2e). (5-5) Ex. 14: The reinforcement eb1—f1 counteracts the parallel fifths . ,,,. The resulting sixth chords tend to absorb the paral-a1—ob1 lei succession. Such a reinforcement belongs to keyboard style. Ex. 15: Often it is the task of the foreground to circumvent a succession of fifths which threatens in the middleground (cf. Ex. 15b with Fig. 51). Section 2: Imperfect Consonances § 165. General considerations In the outer voices of the foreground, the advantage provided by imperfect consonances is obvious, just as in strict counterpoint. The refined employment of these intervals is one of the characteristics of a good outer-voice structure (Kpt. I, II/l, § 19; Kpt. II, III/l, § 20; IV/1, § 2). Sixths, in particular, may have their origins in other intervals (e.g., in parallel fifths at an earlier level); this phenomenon in no way prevents the use of sixths in an extended succession. Indeed, these successions are necessary to the composing-out process, which encourages more sixths-in-succession than the series of three which strict counterpoint permits . § 166. Open position in connection with the sixth The necessity for composing-out leads to the use of the open position of the sixth chord, that is, with the tenth between bass and upper voice. This applies not to an extended succession of sixth chords but rather to a single sixth chord which is to be prolonged: Fig. 55 The fifth between the upper and inner voices (a) represents a 5 area of its own and provides a welcome tone-space for a com- posing-out . § 167. Succession of two major thirds In free composition, too, the adverse effect of a succession of two major thirds is to be avoided (Kpt. I, II/l, § 18). However, even in strict counterpoint, two major thirds are permissible if the continuation of the voice-leading shows that the augmented fourth is not the sum of these intervals (Kpt. I, Ex. 196). This applies even more to free composition. Compare Beethoven, Fifth Symphony, Finale, measures 122-130-132: J y [especially in the case of I—II*—V; § 123 and Fig. 38].*7 *7. With a certain justification, our forefathers established the prohibition of mi contra fa and maintained that two hexachords were incompatible (solmiza-tion); thus, when there occurred a mi-fa within the G hexachord (B—C) they would not admit a mi-fa from the C hexachord (E-F) at the same time. They possessed as yet no real sense of key and no genuine tonal system, since, above all, they lacked the octave which contains the space of a fourth 5—8. This fourth-space would have necessitated a new hexachord. We, however, have the octave, containing two semitones which formerly would have belonged to hostile hexachords. From the standpoint of the octave, there are no grounds for opposing the two groups of semitones against one another. Therefore, I pointed out in Kontrapunkt II that mi contra fa was an empty fabrication, like the fallacies of the ecclesiastical modes and numberless intervals. Every prohibition based upon such reasons should be cast aside. Only the disagreeable total interval of an augmented fourth such as in Kontrapunkt I, Ex. 195, need cause the rejection of two successive major thirds. (Schenker) THE CONCEPTS OF Section 3: The Passing Tone at the Foreground Level § 168. General remarks Strict counterpoint requires a stationary tone for the verification of a consonant or dissonant passing tone, whether in the upper or the lower voice. This requirement can be dropped in free composition, where there is the possibility of transforming an originally stationary tone into a succession of moving tones . Thus, we must add the nature of background and middleground to the reasons already given for greater freedom in free composition.*8 Considerations of background and middle-ground are the final determinants; they also provide the greatest liberty. § 169. Impossibility of composing out a dissonant passing tone The dissonant passing tone, including the passing seventh, is itself a means of composing-out. Therefore, as long as it retains its dissonant quality, it cannot at the same time give rise to a further composing-out; only the transformation of the dissonance into a consonance can make composing-out possible. Such an opportunity was lacking in strict counterpoint [§ 35; Fig. 62,9]. § 170. The transformation of a dissonant passing tone into a consonance; the consonant passing tone The fundamental structure exhibits the first transformation of a dissonant fundamental-line tone into a consonance: above 2 all, 2 is changed into a consonance v by the counterpointing *8. Kpt I, II/2, §6; Kpt. II, III/2, §§2, 3; III/3, §1; VI/1, §2 under (2), §3; VI/2, §3; also "Erläuterungen" in Tw. 8/9, 10 and in Jahrb. I, II. (Schenker) COUNTERPOINT 61 bass arpeggiation of the tonic triad. When the fundamental line begins with 5 and 8, the originally dissonant passing tones 4 and 7 also await the transformation into consonances which will make composing-out possible (Figs. 5, 10, 11). This principle continues through all levels of the middle-ground, creating more and more new levels which present new possibilities of prolongations for dissonant passing tones either in the outer or in the inner voices. Finally the foreground, with its greatest freedom, shows voice-leading events which are not understandable as.passing motions unless one refers to relationships in the middleground and background <§ 66>. The voice-leading transformations are based upon the principle of the primary tone (§ 93). Its power completely controls the linear progressions; it alone permits understanding of the original, dissonant condition. Examples: Fig. 20,2, measure 2: The inner voices , originally dissonant passing tones in relation to the F of the preceding measure í _), are made consonant in the foreground through the y5\ Clo). This change into a triad is more favorable to the composing-out. Q____L. IT____L. ŕ*____C Fig. 20,4, measures 16-36: In , the passing seventh <7 appears in measure 21 first as a consonance (10). Compare, in addition, Fig. 35,1 and 2. Passing sevenths in the case of IV^-V (Fig. 22b, m. 2) and Il2=i_V (Fig. 49,2; Fig. 53,3, m. 21) are usually transformed into consonances. The passing tones in ť-^ (Fig. 11,1) often undergo a transformation. A beautiful example of this is to be found in Bach's Little Prelude No. 12 in A Minor (BWV 942) (Jahrb. I, p. 117). 62 FREE Fig. 42,2: The neighboring note eb2 (marked n.n.) is shown in the middleground as the seventh over V. In the foreground, however, it appears as part of a IV in a cadence. Further examples: Fig. 56 Ex. 1, a-c: These show descending passing tones made consonant. In Ex. la, the c2—6b1—g1 differs from the five-note melisma known as the nota cambiata (Kpt. I, II/3, § 7, especially Exx. 357-60). Ex. 2, a-f: These show ascending passing tones which are made consonant. In relation to d) and e) see §§ 244 ff., Fig. 40,1 and Fig. 54,13. Ex. 2, g and h: In g) the passing is avoided; in h) the passing motion is combined with a chromatic alteration (Tw. 3, p. 5).*9 § 171. Major seconds The corroborative power of linear progressions which stems from the middleground and background extends to the foreground, where it imparts conviction even to a series of major seconds in the upper or lower voice (cf. Kpt. I, 11/1, § 18, Exx. 200, 201): Fig. 57 § 172. Leaps that form part of a passing motion The concept of a leaping passing tone instead of proceeding to a1 provides not only a are completely subordinate to the main third-progression db—cb—Bb®. § 173. Tendency of passing motions to give rise to parallel formations Even the combined species reveal the tendency of passing tones to strengthen and intensify their effect by moving together, thus forming an almost independent contrapuntal setting of !? or 6. chords (Kpt. II, VI/1, §§ 1-2,7; VI/2, § 10). In o 4 the foreground, this tendency is furthered and reinforced by *10. See also Kontrapunkt II, Ex. 283,1, measures 4, 6, 8 (quoted in Felix Salzer and Carl Schachter, Counterpoint in Composition, Ex. 9-60, b. (Oster) *11. Since a in the bass would have been due at the beginning of measure 13, one might hear the last sixteenth of measure 12 as an anticipation rather than a leaping passing tone. (Oster) THE CONCEPTS OF the parallelistic bent of diminutions, whether in relation to the succession of intervals or to the composing-out process. Here belong the frequent 6 6,10 10 sequences which arise as a result of exchange of voices [Fig. 105], as well as others which will be discussed in § 236. Compare Fig. 43b, 4, 5; Fig. 43c, 4, 5. § 174. The accented passing tone Since the cantusfirmus exercise of strict counterpoint knows neither genuine meter nor genuine rhythm, it provides no opportunity for an accented passing tone, that is, a passing tone on the strong beat in a genuinely metrical situation. However, one might perhaps conceive of a passing dissonance on the third quarter in third species as the origin of the accented passing tone (Kpt. I, II/3, § 1, Ex. 332). The accented passing tone is thus a foreground concept. The necessity of bridging skips, whenever or in whatever voice they occur, easily produces accented passing tones. The strong beat need not be the downbeat but may, by implication, be a first or third eighth also, or even a sixteenth note: Fig. 59 Ex. 4: A fifth-progression and a fourth-progression appear in contrary motion (§§ 227 ff.); at a) the db2 is shown as an unaccented passing tone, at b) as an accented passing tone. At the foreground level db2 is placed in measure 5, which is metrically strong. This imparts to it a tension—basically only the tension of a passing tone!—which carries through to c2 in measure 11. Section 4: The Change of Harmony 5—6 § 175. The change of harmony 5—6 Like 6—5, the 5—6 succession in the second and third species is not adequate to eliminate parallel fifths. Rather, both successions signify the only natural change of harmony . § 178. Closure of the passing seventh Since it originates in the octave, the seventh must move onward in the descending direction [§ 73]. COUNTERPOINT 65 § 179. Strict counterpoint remains in control despite deviations From §§ 176-78 it follows that in free composition the necessity of composing-out seldom permits a seventh to remain stationary above the root. Section 6: The Syncopation § 180. General observations In Kontrapunkt I (II/4, § 12) I referred to the significance of the syncopation in free composition in the following words: "In their instinctive search for technical means which would expand the length of a tonal structure {Harm. § 88, note), musically creative minds were occupied with voice-leading practices which, apart from their own laws, did not yet manifest any higher necessity. Still, they found in the constraint of preparing and resolving a dissonance a most welcome means of simulating a type of musical causality and inner necessity, a means which operated at least from consonance to consonance [§ 73]. Of course, the germ of such a need to move onward lay also in the simplest passing tone—when studying the nature and history of music as an art, one must always keep in mind the problem of the creation of length—but it is clear that the constraint of the dissonant syncopation is incomparably stronger and more cogent." *14 Fig. 63 Ex. 1: Because of the chord progression in the foreground, a suspension over IV must be assumed, even though the bass tone is not stated until two measures later. Ex. 2: The principle of the "root property" . See Jahrbuch I, pp. 37-38, Fig. 19; also Jahrbuch I, p. 79 (Bach, Violin Partita III). Ex. 2: Here we see that the tying-over of a ninth may have great consequence also in free composition. Chopin originally wrote a ninth eb1 (at c, m. 7), and this ninth still appears in many editions. Yet, it can only have been Chopin himself who finally replaced the eb1 by the octave d1— and with good reason: since it is not tied over (compare to sketch d), the intended ninth eb1 has rather the effect of a sixth below c2 (see the diagonal lines at d).*16 In addi- *15. In connection with this section see text and examples in Kpt. I, II/4, §§ 5, 7, 8, 10, 15 and in Kpt. II, III/4, §§ 2, 4-6; VI/3, §§ 2-8. (Schenker) *16. The first German edition (Breitkopf) and the first French edition (Schlesinger) were published almost simultaneously. Schlesinger has eb1, Breitkopf, d1; and this d1 could very well be due to an engraver's error. Musicological reasoning alone is probably unable to decide with certainty in favor of either eb1 or d1, and one has to make one's decision on purely musical grounds. (Oster) tion, the example shows a tying-over of the passing tone g1 (at b) against which the bass executes an unfolding. Ex. 3: The "scattered" position <§ 177, Ex. 13>, with its vertically interlocking sevenths Eb—db, bb—ab1, and db2—c3, makes it possible to exploit the rich sound-potentialities of the piano. Failure to recognize such a "scattered" position leads to the false theory of eleventh and thirteenth chords. An example of the composing-out of^_ is found in Fig. 54,3. 5 Here the coda-like descent c%2—cp (=8—1) brings with it the diatonic tqT. Yet the^_ at gt1 provides the opportunity to make o use of the leading tone b%. This establishes the bass progression as a line which, in the service of 8—5, departs from C% and returns by way of F%—E—D% to C% (cf. Fig. 11,5). The circum- stance that the lowest tones of ^_ configurations are thirds of 5 the actual root permits the employment of chromatics in the sense of leading tones [cf. § 247]. This advantage does not exist m the case of . § 182. Preparation and resolution Examples of preparation and resolution of suspensions are given in Fig. 65 Ex. 1: In measure 86 the seventh is, in essence, tied over and prepared, not merely passing. The actual appearance of the II in measure 90 between VI and V reveals that a similar preparation of the seventh is implied in measure 86. Exx. 2-4: Formerly it was taught that no other tone should lead to the tone of resolution in similar motion. The errone- THE CONCEPTS OF ousness of this idea . Ex. 7: The resolution is omitted (see a) and thereby a rhythmic imbalance (as at b) of the two-tone groups d\>2—c2 and gb2—/2 is avoided. Ex. 8: The fifth is missing at the close, and the piece ends without a complete resolution of the suspension. Specific rhythmic events in the foreground which take place within the meter admit of a very free play with tyings-over of a merely rhythmic nature, be they in the service of leading tones, passing tones, or ascending and descending arpeggia-tions. These, however, are not genuine suspensions (Kpt. I, Exx. 397, 420-22, 426, 427). Chapter 2 The Later Structural Levels A. THE LATER STRUCTURAL LEVELS IN GENERAL § 184. Reappearance of first-level prolongations § 183. Content of the later levels The content of the second and the subsequent levels is determined by the content of the first level, but at the same time it is influenced by goals in the foreground, mysteriously sensed and pursued. The second level, even more clearly than the first, reveals how a work branches out into its own special characteristics. Yet I reiterate that the way in which the composer arrives at his initial inspiration—whether he derives it from an earlier or from a later level, perhaps even from the foreground—is one of the unfathomable secrets of creativity. This in no way affects the logical sequence of the levels, but rather gives evidence of a veritable clairvoyance which envisions a more distant level before the nearer one is clear in the consciousness. Only genius can command such far-reaching forward and backward perception (§ 47) [§ 29]. Such prolongations as are met at the first level can appear also at the later levels and undergo a further development. But new types of prolongation may appear as well—for example, exchange of voices, and combinations of all kinds of prolongations. § 185. Prolongation of the bass All manner of prolongations found in the upper voice may occur also in the lower voice—always, however, in keeping with its particular contrapuntal purposes (§ 20) [§§ 53, 64, 210, 257]. B. THE PROLONGATIONS OF THE LATER LEVELS IN PARTICULAR Section 1: Prolongations of the Bass Arpeggiation § 186. Inversions within the bass line I—V 68 THE LATER Some of the steps of the prolonged versions of I—V shown in Fig. 14 admit of inversion at the later levels: Fig. 66 Ex. 1: Only in the later levels, which gradually work out the obligatory register, can it be decided whether or not the descending sixth at a) and b) serves a register transfer ascending or descending. Ex. 2: The descending fifth at a) is conceptually equivalent to the fourth in Fig. 14,5 (I—IV). The succession IV—V counterbalances the fifth with a melodic second—a purely contrapuntal means which arises when an ascending fifth-progression is filled in by passing tones (Fig. 14,2c). Therefore, when a descending fifth is filled in by passing tones—even including a chromatically altered tone, as at b)—one must recall that this descending fifth has its origin in the contra-puntally ascending fifth-progression. For this reason, in the so-called cadence I—IV—V—I in free composition, the V has preeminence because of its prior development as arpeggiation tone of the harmony, whereas the placement of IV before V stresses the step of a second, and hence, primarily the contrapuntal element <§§ 56, 64>! Ex. 3: This illustration is related to Fig. 14,6. § 187. Inversion of the ascending fifth I—V to a descending fourth The whole ascending fifth in the bass can also be transformed into a descending fourth. Several possibilities for the structural consequences of such a fourth-progression in the bass in the case of 3 or 5 are shown in Fig. 67 § 188. The combination of various inversions LEVELS 69 The combination of various kinds of inversion is shown in Fig. 68 Especially when the contrapuntal bass formula is transferred to individual harmonies in the foreground, one must be careful to note whether the arpeggiation I—V is expressed in ascending or descending form; only thus can a combination be recognized (§§ 242 ff.). § 189. The arpeggiation of the descending fifth V—I proceeds through the third only Prolongations of V—I become possible only at the later levels. The arpeggiation of this descending fifth V—I can proceed through the third only: Fig. 69 Exx. 1-4: These are the possible forms. They represent a reversal of the prolongational forms of the ascending arpeggiation I—V, as shown in Fig. 14,1-4. Such arpeggiations through the third are to be found in all prolonged descending fifths at the later levels, in the middle sections of three-part song forms (Fig. 22b) as well as in the development sections of sonata movements, such as that of Beethoven's Violoncello Sonata op. 69, first movement, measures 94 127 152 E — er3 — A V--------------1. Exx. 5-6: Arpeggiations such as these, which reverse Fig. 14,5- 6, would be impossible. Ex. 7: In contrast, an arpeggiation through the third can occur in the simplest descending fifth. Of course, a descending arpeggiation is not the only means of prolonging V in the case of V—I. Sometimes this can also 70 FREE be effected by a neighboring note with interpolations, as, for example, Fig. 62,3, and 11; Fig. 76,9; Fig. 154,5; Fig. 158. In relation to this section, see §§ 65 and 86; also § 230, Fig. 100,3. § 190. Inversion of the descending fifth V—I to an ascending fourth The descending fifth V—I can be inverted to an ascending fourth. This remains indivisible, because the fourth, in contrast to the fifth which is based in the overtone series, must be brought into being artificially by voice-leading [§ 212]. Fig. 70 § 191. The so-called deceptive cadence The so-called deceptive cadence is shown in Fig. 71 Ex. 1: With the succession V—VI, the bass in a) sets out in the direction of the ascending fourth-progression (Fig. 70b)—but it can be led back by means of interpolated fifths into the direction of the descending fifth V—I, as in Fig. 71b. Ex. 2: Another means for the overcoming of V—VI is repetition in the form of an auxiliary cadence (§§ 244 if.). Section 2: Structural Division § 192. Structural division at the later levels Linear progressions which depart from 3, 2, or 5, as shown in Figs. 33 and 34, also admit of interruption at the later levels, by virtue of the principle described in § 117, thus: t f t i íg---------------2 Ij 3 2 í 1st Level: |3-------£1 2nd Level: 3 2 j| 3 2 1 Compare Fig. 42,2; Fig. 73,3; also Chopin, Étude op. 10 no. 8,' in Five Graphic Analyses. In other words, any and every third-progression or fifth-progression can undergo an interruption in the strict sense, 3 21| 3 2 1 or 5—21| 5—1, as though it were the fundamental line. This is the key to the application of the outer-voice forms with their prolongations, including interruption, to each individual harmony in the foreground (§§ 242 if.). Such strict forms of interruption must not be confused with forms such as those in Fig. 72 These must be considered diminutions in concept (§§ 251 ff.). . Ex. 10: A neighboring-note figure is particularly attractive when it appears in the same durational values as the main tones. In Bach's chorale settings, such figurations in the bass give rise to strange thoroughbass notation which can be understood only when the equality of the note values is disregarded (Fig. 125,1). The same holds true for similar figurations in instrumental music (Fig. 142,1 and 2). In rondo form the neighboring note plays an important role in the connection of the individual sections (§§ 318 if.). § 198. The neighboring-note motion 3—4—3 The neighboring-note motion 3—4—3 can be combined with 5—6—5 and 8—9—8 simultaneously, provided the fifth is not in the soprano—such a position would of course produce consecutive fifths. Fig. 77 § 199. The syncopated form of the neighboring-note motion 3—4—4—3 From earliest times, composers tended to introduce a neighboring-note motion on the third when they wanted to retard the flow at a given point: Fig. 78 With correct instinct they avoided the form shown at a), preferring instead the syncopated form 3—4—4—3 as at b), which already, as at c), hints at a third voice (Palestrina, Missa Papae Marcelli, Gloria, mm. 9-10). THE LATER § 200. Combining the neighboring-note figure 3—4—4—3 with other voices The figure 3—4—4—3 can also be combined with 5—6—5, 8—9—8, 8—7—8, 8—^—8 or with b7—6—5, bl—6—tj7—8, 7— 6—6—5, or with a neighboring-note motion of the bass: Fig. 79 § 201. Free use of the neighboring-note motion 3—4—4—3 Extensions and delays of this kind can appear in connection with I, IV, and V, as well as with other degrees and individual harmonies: Fig. 80 § 202. Linking of several 3—4—4—3 figures In the practice of the great masters, particularly in preludes and fugues, such neighboring-note motions are often linked together, generally in such a manner that the accidentals for the third at the beginning and end of the neighboring-note motion change, thus affording opportunity to interlock groups such as #3^-4^4—tfix^f^i^bß. Examples: Handel, Suite in Ä'Major (Prelude, mm. 16-18), Fugue no. 6 in C Minor (m. 7); Haydn, Sonata in Eb, Hob. XVL52, first movement (Tw. 3). Section 6: Linear Progressions (a) General § 203. Linear progressions at the later levels In the succession of voice-leading transformations we move farther and farther away from what was the new upper voice LEVELS 73 <§§ 115,116) and so gain new levels. Consequently, the purpose of the linear progressions undergoes a change, as the new goals dictate. Whatever the goal may be, the qualities inherent in the fundamental line and in the linear progressions at the first level remain the same at the later levels: a linear progression is, above all else, the principal means of creating content in passing motions, that is, of creating melodic content. The descending linear progression always signifies a motion from the upper to the inner voice; the ascending linear progression denotes a motion from the inner to the upper voice. § 204. Unity of the linear progressions In all linear progressions, whether descending or ascending, the principle of the primary tone holds (§ 93): the mental retention of the primary tone achieves coherence. Each previous level vouches for the succeeding one, thus guaranteeing the indivisibility and unity of the linear progressions at the later levels: unity prevails in the foreground as well as in the background. Whether a linear progression occurs in the upper, lower, or inner voice, its unity signifies a horizontal totality, before which the vertical retreats in importance. Fig. 81 Ex. 1: Only by mentally retaining the primary tone db1 can one understand a succession such as that of the tenor at c) as a third-progression in the inner voice. Ex. 2: This example shows a very expanded third-progression. Four small third-progressions, measures 1-5, 5-9,9-15, and 15-18 carry g2 down to ft1 and e1 (see a and b). The goal and effect of the overall third-progression could not have been achieved if the bass had not supplied its own organic prolongations. One of these is the arpeggiation E—C—A (as I—IV) in measures 1-5-15: C appears in measure 5 exactly with e2, which represents the conclusion of the first 74 FREE third-progression as well as the beginning of the second. Note also the octave-progression c—& in measures 5-15, which holds together the second and third third-progressions. The rhythm of the above groupings is an organic element which also deserves attention. In measures 5-8 we have two 2-measure units, then an acceleration to four whole notes in measures 9-12, and finally to four halves in measures 13-14. The accelerated third-progressions c2—a1 in measures 9 and 11 prepare the third-progression in halves in measures 13-15, where the second tone b1 is prolonged by its own special third-progression b1—a1—git1. The four halves in measures 13-14 also prepare the fourth-successions in measures 15-16, which are finally surpassed by the fifth-progression b1—e1 in measures 17-19. (b) Illusory Linear Progressions § 205. The essential characteristic of a genuine linear progression At the later levels, too, a genuine relationship must exist between the first and last tones of a linear progression, a relationship determined by the earlier levels. This interval relationship must be at least the size of a third, for not only the fundamental line, but every linear progression must contain a passing motion. The same applies to a fifth-progression, to a fourth-progression when it is equivalent to a fifth-progression, and to an octave-progression. § 206. The composing-out of a second simulates a linear progression Where a relationship of this kind is lacking, the succession is not a genuine linear progression [§ 141]. Therefore, a succession of passing tones, even if it is subdivided, does not constitute a linear progression if its ultimate result is only the interval of a second above or below. A prolongational connection of this kind represents only an indirect ascending or descending register transfer (§§ 147 if. and 151 if.). In connections of this kind there is indeed a goal, but there is no harmonic relationship between the point of departure and the final tone. A ninth therefore stands for a second, ascending as well as descending. The same is true of a seventh, except that a descending seventh stands for an ascending second, an ascending seventh for a descending second: Fig. 82 Exx. 1 and 2: The ninths stand for descending seconds [in relation to Ex. 2, see Fig. 134,8]. Ex. 3: At b) the ninth d1—eb2 (mm. 35-42) is equivalent to an ascending chromatic passing tone [§ 238]. Ex. 4: The example shows a seventh which means a step of a second. Ex. 5: In contrast, it would be incorrect to read the bass motion shown at b) in measures 9-10 as an ascending ninth d— e1, since the unfolding shown at a) determines its meaning. At c) the end of the fifth-progression c1—/in the bass coincides with the beginning of the fifth-progression a2—d2 in the soprano (m. 3). Therefore it would be incorrect to read the bass motion here as c1—d(=c—c#—d) in measures 1-4. § 207. The composing-out of a third, fourth, fifth, or octave occasionally simulates a linear progression Whether or not the filling-out of a harmonic space constitutes a true linear progression thus depends upon the relationships revealed by the structural levels. Fig. 83 Ex. 1: This is only seemingly a third-progression. THE LATER Ex. 2: Since g2 represents a neighboring note at an earlier level, we cannot read the succession 6b2—f2 in measures 9-12 as an interrupted fourth-progression (cf. Fig. 76,5 and §§ 212,217). For this reason the successions which introduce g2 and f2 are not genuine third-progressions. Ex. 3: In the same manner the successions preceding E and Ft in the bass do not constitute genuine linear progressions, despite the outward appearance of fourth- and fifth-progressions. Nor, incidentally, is the strict concept of an unfolding applicable to the soprano. The necessary ascending register transfer, f%2—(c#2)—b1 instead of /t1—(cj1)—b, must be assumed [see § 238]. The bass is determined by the motion T______tt_-V——T tw^ reference t° N.B., see § 261, commentary to Fig. 125,3]. (c) The Ascent and Descent of Linear Progressions § 208. Descending linear progressions From descending linear progressions of higher order, further descending linear progressions are logically derived: Fig. 84 The division 3—21| 3—2—1, including the linear progressions indicated by stems pointing downward, belongs to the first level (§§ 117 and 118, Figs. 33,34). In contrast, the linear progressions which descend from g2 and the first stemmed p belong to the second level, as does the division of the fifth-progression (§ 213). See in addition: Fig. 42,2; Fig. 30a; Fig. 73,3; Fig. 76,3. § 209. Ascending linear progressions After having established rapport with the foreground, the initial ascent to the first tone in the fundamental line can subsequently become a diminutional entity, which comes to full flower in the form of ascending linear progressions. These do not lead LEVELS 75 to tones of the fundamental line and hence belong to the later levels: Fig. 85 [Compare § 279, commentary to Fig. 130,3.] § 210. Linear progressions in the bass Linear progressions can also appear in the bass when the spaces of its arpeggiation are filled in with interpolations and passing tones (§ 257). Here, too, one must distinguish between ascending and descending linear progressions; both forms have, as always, their respective primary tones and goal tones. In the bass, however, a descending linear progression can never simulate a fundamental-line progression, since the bass and the fundamental line are separate entities: Fig. 86 I cannot recommend strongly enough the study of the bass motions in the works of J. S. Bach. One should begin with the Generalbass-Büchlein and attempt to ascertain the linear progressions implied in these seemingly simple basses. One should then study the basses of other masters in a similar manner, at first leaving out the question of fundamental line while seeking to ascertain the logic of the bass. In the final analysis, of course, the true situation can be determined only by a study of the contrapuntal relationship of the bass with the soprano [§ 3, footnote]. (d) The Individual Linear Progressions § 211. Third-progressions Third-progressions at the later levels are composed-out chiefly by means of the interruption 3—21| 3—2—1 and the neighboring note (see Figs. 42,2; 22b; 30; 73). 76 FREE § 212. Fourth-progressions Fourth-progressions at the later levels can have various meanings: Fig. 87 Ex. 1: The examples demonstrate that the identity of the fourth-progression can only be ascertained with finality by considering both counterpoint and harmonic degree. In both examples the changes of harmony make it impossible to mistake fourth-progressions for fifth-progressions.*1 Ex. 2: The fourth-progressions 8—5 and 5—8 above a I or V require special attention. The same holds for other harmonic degrees which for various reasons assume the character of a I or a V. Ex. 3: When the fourth-progression occurs in the bass, the counterweight of the harmonic degrees is less perceptible, less powerful. The unity of the fourth-progression is determined more by its melodic succession than by the clear statement of harmonic degrees. It is as if the progression took place in an upper or inner voice which moved above implied harmonic degrees far below . a) Thus, this fourth-formula, which was often used in older music to connect movements of a suite or concerto grosso, is ambiguous; only from the emphases of the particular composition can it be determined whether I—V or I—II*—V is intended. b) Despite the „ over Bb, which represents the I in g minor, the fourth-progression in the bass imparts to Bb the significance of the root of III which moves to VI; for only Bb *1. Schenker refers here to the augmented fourths in the top voices. (Oster) as III can be the initial tone of the fourth-progression which is undeniably present here.*2 c) In the Eroica this fourth-progression unifies measures 28-93 of the Scherzo. The arpeggiation Bb—f—d—Bb belongs exclusively to Bb. The tension of the long fourth-progression is resolved only with the terminal tone Eb. d) The descending fourth-progression leads to the minor V more convincingly than the ascending fifth-progression would, because of the presence of the chromatic G%. Ex. 4: For the fourth to be heard as an indivisible entity, no emphasis must be placed on the third tone of the progression that would cause it to be understood as the goal of a true third-progression; it must, rather, be understood as a passing tone (Fig. 14,3c and d; Fig. 40,1, mm. 1-7; Fig. 114,2b). Ex. 5: The fourth-progression does, however, admit of subdivision. In this example it would be incorrect to read the first tone of the second third-progression as a neighboring note, since the counterpoint emphasizes the parallelism of the subordinate linear progressions. This parallelism subdivides the fourth-progression, but does not represent an interruption in the strict sense (§ 192, Fig. 72,1; Fig. 157). § 213. Fifth-progressions In addition to interruption (§ 192), fifth-progressions may exhibit freer divisions: Fig. 88 Ex. 1: This schematic interruption is illustrated by the musical example at a) (mm. 41-61), which also includes a particularly effective mixture. *2. In his personal copy of the Chaconne, Schenker wrote the III at the second beat of measure 6. This may serve as a clue to the understanding of Schenker's reading. (Oster) THE LATER Ex. 2: Compare Figs. 41,3; 72,3. Ex. 3: Compare Fig. 30b. Ex. 4: This scheme fits musical example b).*3 At c) there is no subdivision, but rather an expansion which occurs through the interpolation of yet another fifth-progression descending from the primary tone (Figs. 104,3; 40,4) [§ 93]. The example at d) shows a masterly interlocking of two fifth-progressions. In the bass too, the fifth-progressions may contain all manner of free division. As in the fourth-progression, the ascending fifth-progression in the bass may reveal a conflict between the melodically unified character of the progression and the harmonic degrees . § 214. Sixth-progressions Examples of sixth-progressions at the later structural levels are given in Fig. 89 Ex. 1: The division of the sixth-progression is counterpointed by a seventh-progression in the lower voice. Ex. 2: The sixth-progression rf2—f1 is subdivided by means of two fifth-progressions. Ex. 3: The sixth-progression really consists of a fourth-progression which continues into a lower inner voice. Ex. 4: In contrast to Ex. 3, the sixth-progression here is to be understood as the inversion of a third. § 215. Seventh-progressions *3. Compare Schenker's reading of the bass in Jahrbuch II, p. 17, which is, in my opinion, better than the one given here, although it is slightly self-contradictory. In this earlier reading, Schenker closely relates Ab to F (in the manner of Bb—G in Fig. Ilia) and reads 5—7—5 above Ab—F—G. (Oster) LEVELS 77 Fig. 62,1-4 shows examples of seventh-progressions. These differ from the composing-out of a seventh which stands in place of a second (as in Fig. 82,4) in that they emphasize their harmonic intervals, at least the third. § 216. Octave-progressions Wherever an octave-progression is used, its unity is commonly affirmed by a complete cadence. Fig. 90 Basically, the upper voice remains stationary on g%1. Compare Fig. 54,3; Fig. 73,4; Fig. 95, e4 [as well as §260, next-to-last paragraph]. § 217. The freest form of interruption In addition to the interruption forms 3—21| 3—1, 5—21| 5— 1, 8—51| 5—1 and the freer divisions, as in Fig. 72,1 and 2, and in Figs. 88-90, there is a type of interruption which is probably the freest. Its distinguishing feature is that the setting again takes up its initial position: Fig. 91 (e) The Closure of Linear Progressions § 218. General Linear progressions in an upper, inner, or lower voice are at an end as soon as they have reached, in ascent or descent, the goal determined by the context. Specifically, descending fifth-progressions come to an end only when they reach the fundamental tone (and not in the middle of the progression, at the third, even if a change of harmony 78 FREE occurs there). This is a natural outgrowth of the fact that all fifth-progressions are modelled after the fundamental line, which, regardless of its division, closes only with i [§ 245]: Fig. 92 Ex. 1: The recognition of the first fifth-progression, that is, that it concludes only with f1 in measure 2, is particularly important for the understanding of the middle section of this fugue [mm. 22 and 30]. § 219. Anticipation of the closing harmony The unity of a linear progression in the lower voice makes it possible for the upper voice (by means of an arpeggiation or other diminution) to anticipate the chord which belongs only to the final tone of the linear progression. Fig. 93 The root F remains in effect through the passing tones E and D. However, these passing tones provide the opportunity for the composing-out of the C triad, and the individual intervals conform to the principles of strict counterpoint—a very unusual and bold voice-leading. § 220. Further application of the principle of closure The principle of closure also applies to the motion of a second, even though the step of a second is not a linear progression; only when the last tone is actually reached is the motion completed: Fig. 94 (f) The Combination of Two or More Linear Progressions § 221. The concept of a leading linear progression When two or more linear progressions are combined, it is essential to determine—from background, middleground, and foreground—which of them is the leading progression. In relation to this leading progression the others must be considered only as counterpoints, whether they proceed in parallel, oblique, or contrary motion, in outer or inner voices. Once one has decided whether the leading linear progression is in the lower or in the upper voice, one must understand the counterpointing progressions as upper or lower thirds, tenths, or sixths. § 222. Rejection of the concept of double counterpoint at the tenth and twelfth From the concept of a leading linear progression counter-pointed by upper or lower thirds or sixths, it follows that the concept of so-called double counterpoint at the tenth or twelfth can have no validity. Double counterpoint therefore takes its place in the ranks of such fallacious concepts as the ecclesiastical modes, sequences, and the usual explanation of consecutive fifths and octaves (§ 229, Fig. 99,1). § 223. The inner voice In weighing the relative significance of the linear progressions in the upper and lower voices it is important to determine whether the motion of the inner voice agrees with the primary harmony throughout or whether it is opposed to it at the beginning or the end. THE LATER § 224. Linear progressions in parallel thirds (tenths) In a progression in parallel thirds (tenths) one must take into consideration whether it remains within the same harmony or moves to another, as well as the dimensions and extent of the progression. Fig. 95 a) Third-progressions are shown in Exx. 1-8: ascending or descending, involving one or two harmonies.*4 Exx. 2 and 4 show the lower voice moving in lower tenths. Exx. 7 and 8 show a substitution for the first and last tenths, c respectively. Exx. 5, 6, and 7 demonstrate the ever-present danger of parallel fifths in three-part settings. b) Fourth-progressions are shown here. Exx. 1-3 show lower and upper tenths involving one or more harmonies. The examples under 4 contain liberties of various kinds: in the first a change from 10—10 to 6—6 supplies the third of the C% harmony instead of the nonharmonic sixth a1 which would result were the tenth-motion to be continued as at Ex. bl. Conversely, the Mozart example shows the motion continuing to the fourth tenth, where in order to regain cit2 the octave d2 would have been required ; but also, in individual instances, the particular requirements of a prolongation may determine the contrapuntal setting. § 228. Examples The following examples show the contrapuntal organization of linear progressions which contain equal or unequal numbers of tones: Fig. 98 Ex. 1: A comparison of a) and b), which both express a single harmony, points up the difference between the commonplace setting at a), so one-sided and summarily harmonic, and the truly contrapuntal way of writing at b) which seems to produce independent chords and even endows the middle one with its own figures.*6 Insignificant as the example may appear, it suffices to indicate the decline of our musical sense. Ex. 2: A fourth-progression in the lower voice is at variance *6. The setting at b) comes from C.P.E. Bach; the one at a) was supplied by Schenker. (Oster) LEVELS 81 with a third-progression in the upper voice. The third-progression interpolates the chromatic passing tone ab2, thereby achieving balance with the four-note pattern. Ex. 3: At a) and b) a fourth-progression is balanced with a fifth-progression. In c) the lower voice traverses a fifth, the inner voice a fourth. The top voice moves parallel to the inner voice in upper thirds.*7 Ex. 4: At a) there occur within the two octave-progressions first a fifth- against a fourth-progression, then the reverse: a fourth- against a fifth-progression. At b) the diagonal lines indicate the actual intervals. Ex. 5: The fifth-progression of the inner voice eb—tio, with its line of upper thirds, is counterpointed against the octave-progression of the lower voice. Compare Fig. 56, lc, where the sixth-progression of the inner voice moves against the third-progression in the lower voice. See also Fig. 89,1, where the sixth-progression ôjf1—g%2 in the upper voice and the seventh-progression ft1—gt, in the lower voice adjust to one another. § 229. Linear progressions in mixed motion Combinations of linear progressions in various motions are given in Fig. 99 Ex. 1: We see here the combination of a fifth-progression in the bass with a fourth-progression in the tenor which moves in contrary motion. The fourth-progression is accompanied by the alto in upper thirds, while the bass is accompanied in upper tenths by the soprano. It is only the fifth-progression in the bass which leads here, including the upper tenths *7. Ex. c) is not a direct quotation from C. P. E. Bach, but is rather Schenker's interpretation of the voice-leading shown in one of Bach's examples. (Rothgeb) 82 FREE belonging to it. The fifth-progression also leads in b) and c). In the light of this evaluation, the specific teachings of double counterpoint become somewhat less significant (§ 222). Ex. 2: The octave-progression f2—f1 in measures 1-4 is followed by a series of reachings-over, aiming at the neighboring note gb2 in measure 8. This reaching-over is counter-pointed by an octave-progression in the bass, producing partial linear progressions which move in parallel sixths and tenths. Ex. 3: The outer voices show the combination of a fifth- with a sixth-progression in parallel motion; the sixth-progression in the bass, however, represents a rising third-arpeggiation. While this arpeggiation of the c-minor chord is continuing toward completion, a sixth-progression in contrary motion begins in the upper voice over the bass Eb. At the third tone of the sixth-progression, eb2, the bass arpeggiation arrives at the octave c, the root of I. From this point the bass moves down to a V by means of a fourth-progression. The sixth-progression also reaches its end at the V, and over this V the octave gl moves to the passing seventh (8—7) which leads to the Allegro.*8 Section 7: Arpeggiation § 230. Arpeggiation at the later levels The following examples show different types of arpeggiations: ascending or descending in an upper, inner, or lower voice, resulting in a triad or four-note chord. Fig. 100 *8. For a more detailed discussion of the "dissonances" in this Introduction, see Oswald Jonas's commentary in Schenker's Harmony, p. 346. (Oster) Ex. 1: The first arpeggiation, which leads to the first tone of the fundamental line, belongs to the first level. In contrast, the second arpeggiation, leading to the 2, belongs to a later level, primarily because it has the effect of a parallelism (Fig. 40,10; Fig. 93). Indeed, for the most part, arpeggiations appear in parallelistic fashion—connecting one or more inner voices with the upper voice. They may be integrated and concealed in a diminution, or they may be produced by a reaching-over (cf. Fig. 47,2; also Haydn, Sonata in Eb Major, Hob. 49, in Five Graphic Analyses). Especially in the works of the older masters, the polyphonic style frequently obscures the arpeggiations (cf. J.S. Bach, Sonata III for Solo Violin, Largo, in Jahrb. I, p. 61). Ex. 2: The ascending arpeggiations and such intervals . Ex. 3: We see here how each descending arpeggiation of a fifth is equivalent to the formula V—I, no matter what specific harmonic degrees or prolongation each individual situation may express. All of these arpeggiations add up to triads (Fig. 69). Ex. 4: Here are descending arpeggiations which develop into four-note harmonies. Ex. 5: This presents a descending register transfer by means of an arpeggiation through the fifth below, which basically can be regarded as a neighboring note of the third (Figs. 79, 80). Ex. 6: Here we have a descending register transfer by means of three major thirds . In addition, compare Figs. 30b; 37a; 40,3; 40,6; 68a; 76,6; 81,2; 96,4; 103,1; 104,1. THE LATER Section 8: Reaching-over*9 § 231. Reaching-over at the later levels Despite the descending direction of the entries, reachings-over at the later levels serve (a) to maintain the original pitch, (b) to produce an ascending motion in order to gain an upper neighboring note, (c) to prevent a descending arpeggiation from moving beyond its goal. We must remember that, at the later levels too, a reaching-over can occur either in direct superposition or in succession (§§ 129-33 and Fig. 41). § 232. Examples Examples of reachings-over at the later levels, all in succession, are given in Fig. 101 Ex. 1: The pitch level g1 is maintained by means of a reaching-over. Ex. 2: The reaching-over produces the effect of a neighboring note, since the interval between the final tone of the first and the initial tone of the second entry is a third, e1—g1. Ex. 3: In this example, we see a fourth arising between the final tone of one entry and the initial tone of the next: the reaching-over results in a series of seconds leading upward to the neighboring note . In measures 1-2, the suspended e1 of the opening entry continues into djf1, a fifth below the initial tone of the next entry. Ex. 4: The reaching-over occurs in the form of three-tone successions.*10 *9. See editorial comments after § 134. (Oster) *10. The left arrows in Ex. 4 would seem to serve the same purpose as those in Ex. 5 and may, simply through an engraver's error, point to the suspension rather than its resolution. (Oster) LEVELS 83 Ex. 5: The reaching-over aims at the arpeggiation of the triad a—ct1—e1. Thus, there would normally be fourths between the individual entries . Mozart combines a reaching-over-in-succession . Ex. 7: Compare Fig. 62,2. Compare also Figs. 39,2; 54,15; 64,3; 96,4. Section 10: Unfolding § 234. Examples Examples of unfoldings at the later levels, with references to the schematically presented forms in Fig. 43, are given in 84 FREE Fig. 103 Ex. 1: Compare Fig. 43, bl and also Fig. 76,2. Ex. 2: As stated in § 141, the usual setting of the form'of unfolding in Fig. 43, b4 consists of an exchange of voices, giving rise to the sequence 10—10, 6—6 (§ 236). When the setting is freer, as here at a), this type of unfolding may be somewhat ambiguous; at b) (which is similar to Fig. 43, d3 and 4> it is less ambiguous Major, measures 29-31, in Jahrbuch I, p. 32. Section 13: Ascending Register Transfer § 238. Examples A desire to exploit the brilliance of an instrument, the establishment of a relationship between registers, the general necessity of creating new content, the accentuation of formal divisions—all these lead to an ascending register transfer at the later levels. Fig. 106 Ex. 1: The coda is stressed by the ascending register transfer. Ex. 2: The basic form of an unfolding assumes quite another appearance through the transfer of the inner voice to the higher octave. The higher position can obscure the meaning of the unfolding and cover even the obligatory register. Ex. 3: The register transfer at a) serves to produce an expansion and a singular and highly declamatory diminution. At b) the highest register of the etude is employed because of the close of the composition. See also Fig. 82,3b: d1—e\>2— e3, as well as Fig. 83,3, measure 3, where the nature of the human voice sets a limit to further descent—hence the ascending register transfer ft1—ft2. *13. E and D are placed into the inner voice, which is not- shown in the example. (Oster) LEVELS 85 Section 14: Descending Register Transfer § 239. Examples Examples of descending register transfer at the later levels are given in Fig. 107 The neighboring note c3 descends to b1, the 2. This descent comprises two fifths, the first of which is realized in a very complicated fashion through an octave-arpeggiation downward followed by a seventh-arpeggiation upward (Fig. 100,2a and 6a). What a remarkable compulsion toward diminution, and how organic the effect of the constant rapport with the voice-leading shown in Fig. 76,3! Observe in Fig. 76,2 the descending register transfer b2— c2—b1. Also note the varied interplay of ascending and descending register transfers in the coda of Haydn's Variations in F Minor. These even surpass the play of registers in the theme (§151, Fig. 48,1). Section 15: Coupling § 240. Coupling at the later levels Although the purpose of a coupling is only the connection of two registers, it nevertheless requires a composing-out of the connective passage. The significance of a coupling lies in the role which it plays as a generator of content. A fleeting connection between octaves, an interplay of registers such as that in J.S. Bach's "Aria Variata," is foreign to the coupling. § 241. Examples Examples of couplings are given in 86 FREE COMPOSITION Fig. 108 Ex. 2: A most magical coupling! Fundamentally, the 1Bb in measure 98 is intended to support the last six measures of the Adagio and to ring through them. However, since the close requires an echoing of the two-line and three-line octaves, the left hand must temporarily abandon the 1Bb reg- ister to follow the right hand. Yet the final eighth note in the left hand manages to give the impression that the 1Bb has been ringing throughout! In addition, the final measure appears to be filled to the brim—a relationship to the first measure always borne in mind by the masters. Thus, the coupling here serves the obligatory register (§ 268). Chapter 3 Specific Foreground Events Section 1: Transference of the Forms of the Fundamental Structure to Individual Harmonies § 242. General The tendency to propagate the forms of the fundamental structure (as shown in Figs. 9-11 and 14-19) goes through all voice-leading levels. Hence, such transferred forms appear in greatest abundance in the foreground. Every transferred form has the effect of a self-contained structure within which the upper and lower voices delimit a single space. Self-contained units of this kind are often difficult to decipher; dividing dominants and other interpolations can often be confusing before one has learned to understand them in relation to the mid-dleground and background (§§ 28, 117, 188, 192, 194). § 243. Specific examples The multiplicity of transference of forms of the fundamental structure is shown in Fig. 109 a) Exx. 1 and 2 show transferences which have the effect of the linear progression 3 2 1 or the interruption 3 21| 3 2 1 (Fig. 42,2). The situation is similar when the tones of the fundamental line 7 6 5 are set in the same way as J y j (Figs. 20,4; 76,4). b) The example shows the fifth-progression 5 4 3 2 1 (Figs. 35,2, mm. 5-8; 89,2). It is also possible to transfer the interruption form 5—21| 5—1 and the freer division forms 5—31| 5—I and 5—3||4—1 (Figs. 42,1; 87,5; 88,4 and b; 103,1). c) Octave-progressions in coda sections merit special attention, even when the fundamental line reads 3—1 or 5—1 (Figs. 54,3; 73,4) [§304]. d) However, transferring the prolonged bass of the fundamental structure alone will guarantee unity, even where the soprano shows no linear progression and instead takes the form of: 87 88 FREE an initial ascent (Figs. 37a; 39,1; 46,2; 104,1). In Fig. 39,2 the bass holds together both the initial ascent and the first third-progression which descends from the 3; an arpeggiation, no matter how expressed (Figs. 40,6; 41,3); an unfolding (Fig. 43a and b); or a diminution which, as in Fig. 109, dl, represents a stationary tone (cf. Fig. 99,2, mm. 1-4). A similar diminution is to be seen in Fig. 109, d2, where the coloratura passage forms a self-contained unit (cf. Fig. 90). It lies between the initial ascent and the descent of the fundamental line, clearly indicating an expansion of a2. This clarification should satisfy those who might object to the coloratura passage at this point in the aria. Its purpose here is not to relate to form, nor does it represent a main element of the aria—it is merely an interpolation, an expansion, e) Since the one-voice configurations of the foreground represent several voices, it is not difficult to perceive the bass progressions hidden in the settings: e2: The example would seem to express a stationary tone in the upper voice (cf. dl and d2). With regard to the passing Ft on the second quarter in measure 5, see Fig. 104,2. e3y: Compare Fig. 33a. e4: See the commentary upon Fig. 109a. e5: Particularly in fugue subjects it is most important to understand the implied bass formula. It determines the countersubject and) pervades the entire fugue. Compare the presentation of the C-Minor Fugue from the Well-Tempered Clavier, book I, in Jahrbuch II; also Fig. 20,1 and 2; Fig. 92,1. e6: Even the so-called elaborated cadenza (at a fermata) has a structure of its own (see C. P. E. Bach's < Versuch,} "Vom Vortrage," §§ 30-31) , the fact that it really belongs to its root always creates an organic connection; its ultimate explanation lies in the original vertical situation. This is what makes the above-mentioned "closing-off" of the voice-leading possible, and it further makes clear the auxiliary nature of the embellishment. It is in this sense that I speak of auxiliary cadence. Figs. 54,2 and 56,2e may be cited in this connection. Be- c#3— aV—e#3 cause in the latter example we have really A — Gt—C$, 10 —5 —10 the cř#3 passes through the third-progression with the effect of an accented passing tone (Figs. 40,1 and 54,13). Fig. 110,b3: [See also §309.] EVENTS 89 Fig. 110c: In the first example the abbreviated bass formula, an auxiliary cadence, supports a fifth-progression; in the second it supports a third-progression. Despite the root Bb in measure 4 of the first example, it would be incorrect to assume III at this point; III appears only at the end as the product of the auxiliary cadence (Fig. 82,5c, mm. 3-4, 7-8). Fig. HOd: In the first example the auxiliary cadence introduces a new chord in the service of more extended relationships. The second example shows an auxiliary cadence as the basis for the so-called second theme of a sonata movement, while the third shows such a cadence supporting even an entire piece (Fig. 39,2, mm. 13-21; Fig. 73,3, mm. 7-8). Fig. llOe: In the first example auxiliary cadences, worked out in fourth-progressions, lay out the path to the fifths above I and V, namely, A and E; that D and A are only tones of the arpeggiation I—V is determined by the middleground (Fig. 103,5b). In the second example the first theme of the movement enters over an auxiliary cadence.*1 The third example is particularly instructive: the main tones of a large arpeggiation, the goal of which is c3 as 3, are established by means of auxiliary cadences [§§ 303; 309]. In the fourth example, the Introduction shows first a descending third-progression as a unity above an essentially stationary bass tone. In the Allegro, however, the bass proceeds with II—V—I; thus the Introduction is, so to speak, connected, as if it were a prophecy, with the main section by the auxiliary cadence. § 246. The descending third, VII—V *1. Anton Bruckner was not capable of starting a musical thought, much less a whole first movement, with the aid of an auxiliary cadence. Thus the impression of a rigid succession of thought in his work: the ideas usually come in blocks, each one with a new tonic at the beginning. (Schenker) 90 FREE The descending third VII—V differs in essence from the descending third that divides a descending fifth: Fig. Ill a) In the major mode the diatonic chord which is presumably built upon the VII can be altered chromatically. b) In the minor mode the chromatic change is inherent. The second example shows a skip of a fifth upward from the III, giving the appearance of a connection from III to fqVII, whereas in actuality the tjVII belongs to V13 in the sense of an auxiliary cadence.*2 c) A descending third of this kind can even produce the effect of a ninth, while it avoids the vertical form 9—8 (Fig. 64,1). d) It is occasionally possible for IV—I to replace V—I, if IV 3 is. omitted and the passing tones are placed over the root of the IV. An illusory VII is thus created. One can only understand the true situation when one considers the omission. Section 3: Addition of a Root § 247. Examples Voice-leading may also arrive at roots by actually adding tones that are implicit in the context, that is, by placing them underneath the lowest voice.*3 Fig. 112 Ex. 1: When a chromatic tone has the effect of a leading tone, the third below, the root, is often added. The chromatic *2. See also Figs. 53,3 (mm. 95-97); 62,8; 113,1b; 114,la,5c and d. (Jonas) *3. In this process, then, an original , , or even a position that results So 4 from voice-leading is transformed into a root position. (Oster) passing tone is thus somewhat concealed, and in addition the stronger effect of a descending fifth is achieved shows a chord which has the effect of jflV1'7 in G major, and must have the V as its continuation. In prolonging such a fIV one can avoid a possible augmented second, ct—6b, by using the major second c#—b\ in its place. If in addition the diatonic c\ is used (as is the case here), it forms the interval of a diminished octave in relation to the raised root C#.*5 Such a diminished octave can be used in a composing-out process or in the realization of a figured bass, but in no way does it constitute an harmonic concept (Fig. 80,1; Harm. §§ 53 if.). [In relation to Fig. 113,2 and 3, see also § 279, Fig. 131.] Section 5: Avoidance of Chromatic Steps § 249. Examples The prohibition of chromatic steps in strict counterpoint no longer holds in free composition. However, since in free composition direct chromatic successions are generally avoided (thus affording the possibility of more abundant prolongations), the prohibition is in a certain sense reestablished. Various means for the avoidance of direct chromatic steps are shown in *5. Compare also Exx. 1-4 in the same section of C. P. E. Bach's work, which show fIV1*7 chords. I have completely paraphrased the first three sentences of this section. The original reads: "In the composing-out of a chord which has the effect of fIVb7, the augmented second is avoided by the use of the diatonic major second (8)— %1—#6—5 in its place. Thus a diminished octave arises if the diatonic seventh is placed above the raised root (IV." Schenker must surely have meant these figures and the diatonic seventh in relation to D, the V of G. (Oster) 92 FREE Fig. 114 Ex. 1: The examples confirm the freedom to use chromatic steps in all voices. Ex. 2: The direct chromatic succession is avoided by the interpolation of a neighboring note. This note can be supported— by a consonant passing tone or other means—or remain unsupported. Thus, in Ex. 2b the bass which supports the neighboring note must be considered only a passing tone. Ex. 2d gives evidence of a very special aural awareness (Figs. 7b; 71,2; 100,4a). All these examples illustrate that the issue is only the avoidance of direct chromatic steps; no further significance is attached to the chords. Ex. 3: The chromatic step can also be avoided by means of two neighboring notes (cf. Fig. 89,1). Chromatic steps are frequently separated by means of linear progressions (Ex. 4-6): Ex. 4: The descending skip of a third makes it possible to achieve the required chromatic alteration diatonically in the following ascent (Fig. 102,5; compare also Beethoven, op. 57, 1st mvt., mm. 217-20, ab-a\; also Chopin's Etude op. 10 no. 12, mm. 23-27, in Five Graphic Analyses, where the upper voice leaps down a sixth and the chromatic tone eti3 is reached only at the completion of the ascending sixth-progression). Ex. 5: As Exx. a and b show, two descending third-progressions make it possible to avoid the chromatic step represented by their boundary tones (§ 260). Exx. c-f show two simultaneous third-progressions with the effect of VII-*-V (§ 246): while the lower of the two voices traverses the path to the root of the chord which contains the chromatic tone, the upper proceeds to the chromatic tone itself. This is one of the most frequently employed means for avoiding direct chromatic successions. Yet such a case must not be regarded as a cross-relation (§ 250). In Ex. e, a third voice is expressly introduced in order to achieve the diatonic ad- justment of the 6b1. Ex. f shows an inversion of these progressions: the upper voice leads to the root, the bass descends to the chromatic tone—this removes the chromatic succession 7*-* (cf. Figs. 39,2; 40,4; 82,2) [§ 247 and Fig. 107]. Ex. 6: By means of an ascending and descending progression in the bass the chromatic step is avoided. The resulting 5 harmony over Ab is not, however, to be considered a . Ex. 7: Occasionally an enharmonic tone can introduce a chromatic change. The insertion of an enharmonic situation provides opportunity for a small but beautiful prolongation: here one finds an allusion to what is to come. [Exx. 8-10: Here, too, the effect of a direct chromatic succession is prevented by the insertion of enharmonic situations.] Section 6: Cross-relation § 250. Examples In contrast to strict counterpoint (see Kpt. I, II/2, § 28 and Kpt. II, III/l, § 25), free composition permits a succession of chromatic tones which have no actual relationship, using them merely as mixtures or for various other purposes. Fig. 115 Ex. 1: a) Extremely profound voice-leading! The relationships in the middleground make clear that eb1 (the original lies an octave lower) is only an embellishing chromatic passing tone leading to d1. Therefore, the lesser value of this chromatic tone also lessens the tonicizing value of the chromatic tone F% in the bass; the bass tone Ft is there only on account of the eb1. Once eb1 moves to d1 the Ft has no further purpose and F\\ is again desired, especially since only this tone can prepare SPECIFIC the 7 in the next measure. That F% does not move back to F\ is, however, quite understandable. It is instead preferable, according to C. P. E. Bach, to retain the /in the inner voice—here in the left hand—so that one has, as he says, "the interval (den Griff) in the hand." No actual relationship exists between F% in the bass and f\ in the middle voice; hence these tones cannot be regarded as a true succession. They do not therefore represent a cross-relation. Each of the two tones has its own origin; they do not belong to each other. The sixteenth-note figure of the right hand (m. 23) seems to occupy the space of a third in the foreground, whereas the actual harmonic situation presents only a second: the space of a second would not have permitted a composing-out in terms of the previous motive. b) In this example there are also no cross-relations. In measures 2-4, c%2 and C\, ft1 and f\\2 are without relationship to each other; the auxiliary cadences here (A—D, C—F) each start anew, that is, they have no connection to what has gone before (Fig. 110). In measure 5 there is a mixture. c) The upper voice composes out a diminished fifth based upon IV—V. The consonant passing tone (at a in the bass) obviates any close relationship of g1 in the inner voice and g in the bass to gp in the upper voice. Ex.2: Occasionally the desire for a register transfer causes a chromatic succession to be distributed between two voices. Such a succession of chromatic tones cannot be considered a cross-relation (cf. Jahrb. HI, p. 32). Ex. 3: a) The fact that g% and g§ follow each other in rapid succession has to do with the necessity of avoiding the augmented second g—a$. b) Here the auxiliary cadence counters the effect of a cross-relation. d) The 6 of the 5—6 exchange here calls forth the chro- EVENTS 93 matic tone elf in the lower voice. However, it would have been impossible to present this chromatic tone on the fourth eighth-note of the upper voice, since, as can be seen at N.B., eb2 and f2 are each to be retained for two full measures. In addition, an e\\2 already present on the fourth eighth-note of measure 2 would affect the eb? in measure 3 adversely. All of these considerations combine to make the eb2 and the e\\l in measure 2 unrelated. Therefore, one cannot speak of cross-relation in this instance either. Section 7: Diminution *6 § 251. Historical background; particulars concerning the concept of diminution We have already mentioned diminution, in the true sense of the term, in many places in the present work, but we have not had occasion to discuss the concept historically.*7 This special chapter on diminution will supply such a discussion and should establish a secure foundation for the teaching and practice of diminution. Though music was destined to reach its culmination in the likeness of itself, without having recourse to outside associations, it was at first dominated by the needs of the word, the march, the dance. The word alone was the generator of tone successions. This condition prevailed during the prehistoric era when music had no rationale; it continued even for a considerable time into the historical ages of counterpoint, of monody, and of the newly found vocal forms which, without modification, were transferred to instruments. The chief representatives and *6. The term diminution as used by Schenker means embellishment in a general, broad sense. It has nothing to do with diminution meaning "repetition in smaller note values" (i.e., the opposite of augmentation). See the third paragraph of this section and what follows it. (Oster) *7. See part I, chapter 1, section 4; also §§ 26, 30, 46, 49-52, 83, 85, 116. (Schenker) 94 FREE creators of this music were the Italians, who with natural Latin logic viewed music through the lens of words, and so found it to be a carrier of outward reality. Music yearned for greater length, further extension in time, greater expansion of content from within, as do all physical or spiritual beings that obey nature's law of growth. But the slower pace of the text hindered this. For a long time words and music were bounded by the same limits, even during the period when counterpoint achieved diatonicism and specific linear progressions and so established the basic prerequisites for music as an art. But then the Italians began to embellish a series of tones, and even individual tones. So they were able to meet the inner needs of music, at least as far as was then possible, and also to yield to their natural desire for beautiful singing. This process of embellishment they called diminution. No matter where and how embellishment was used, however, the word continued to generate music. Thus, the embellishments related only to the words, not to one another, with the result that the embellishments lacked logic, proportion, and all else which would have made them part of a true musical organism. These embellishments often sprang less from musical impulse than from the caprices of vanity, especially since no two singers sang the same piece in the same way. Nor could the instrumental music of that time advance far from its vocal beginnings. The innate capabilities of the instruments, as well as the natural law of growth, called for an expansion of the musical material. And indeed the instrumental diminution tried to discover itself, as it were, in the fugue, the toccata, the ricercare, the cantata, the overture. But only diminution generated by the word was in the blood of the Italians and so they unconsciously gave it precedence.*8 As a result *8. Robert Haas, Aufführungspraxis der Musik (Wildpark-Potsdam, 1931) deals extensively with the early Italian diminutional practice as well as with later German diminution. The work contains a great number of musical examples. (Schenker) See also Ernest T. Ferand, Improvisation in Nine Centuries of Western Music (Köln, 1961). (Oster) they never made German instrumental diminution their own, despite the fact that this alone brought about a true art of music, self-generating, and developing from its own laws. Ultimately, however, the entire word-tone diminution of the Italian opera seria, and all of its later offshoots, collapsed. For the diminution did not mirror the text, and, more important, its lack of any organic inner relationship belied the truth of music— a fact which was not recognized at first. The art of absolute diminution in Germany has amply demonstrated the opposite. But the Italian musician could not follow the German example, and so he has had no choice—even to the present day—but to cling to the word-generated diminution of opera or, at »best, to create program music, which deals, after all, with word, picture, and idea. Incidentally, even the Italian program music had finally to yield to the German; the Italian musicians lacked training in absolute diminution, which is the indispensable basis even for program music. In only a single instance—that of Domenico Scarlatti—the Italian spirit revealed a superb capability for absolute diminution. Yet even he, a friend of Handel and a composer greatly revered by the last master of German tonal art, Johannes Brahms—even he had neither successors in his native country nor any real recognition of his unique worth. We must, however, give this Italian genius his rightful place with those Germans who mastered the art of absolute diminution. The musical characteristics of the chorale—the achievement of Luther and the object of faithful Protestant cultivation— kept the German musician from slipping into a practice of ornamentation that was musically unfounded. In addition, the German climate was hardly conducive to the exercise of sheer vocal beauty. So the form and diminution of German organ music at first remained under the influence of the chorale. Gradually, insofar as the organ permitted, this music came to acquire the freedom of absolute diminution, at least in those cases in which the music did not serve the word. The Germans also tended to turn away from the word, overexplicit as it is; they did not SPECIFIC usually allow it to generate the music. This tendency expressed itself in a stronger predilection for instrumental music. Left thus to itself, diminution had somehow to discover its own nature. So it did, thanks to those composers of incomparable genius who gave it consummate organic unity.*9 A choral setting by Hans Leo Hassler provides clarification: Fig. 116 One can easily recognize that this example is a setting of a text. The prosody of the original madrigal poem is faithfully reflected, as one can see from the passages set off by breath-commas. These passages correspond to the individual lines of verse, including their respective upbeat syllables. The rhythmic ordering 2 x 3 in measures 1, 3, 9, and 11 is in accord with the notational conventions of the time. Since a detailed contra-puntally worked-out subdivision was lacking in the music, the notation itself implied, indeed required, a certain freedom in performance; the apparent ordering 3 x 2 in measures 2, 4, 8, and 10 derives from the inclusion of the upbeat.*10 Nevertheless the tonal structure is remarkably independent of the word. As we know, Hassler's moving melody was later to he used as a chorale; the spirit of J.S. Bach was soon to novér over this melody, in the several settings of it which this master made. So the melody served both secular and liturgical texts. The chorale became, so to speak, a musical article of the Protestant faith. In the strictest sense of absolute music, Hassler's setting approaches perfection. In the foreground the upper voice pre- *9. Passage (M), omitted here, is supplied in Appendix 4. (Rothgeb) *10. Fig. 116 contains an engraver's error which it was impossible to correct. Measure 4 of the composition has a repeat sign after the fi-major harmony. In the prima volta, which is omitted in the example, this chord appears as whole notes, but as half notes in the seconda volta. Thus the prima volta, together with the repetition of the upbeat to measure 1, comprises three half-notes. This is the reason why Schenker included measure 4 among those measures which show a 3 x 2 ordering. See §298 for further discussion of this metrical scheme. (Oster) ND EVENTS 95 sents a definite composing-out of the Z>major harmony in the form of an octave transfer, ft1—ft2,*11 followed by a closure, 3—2—1. The conduct of the bass line is just as definite as it composes out the arpeggiation I—V—I. Thus, an unmistakable fundamental structure is present which supports the foreground. Other settings of Hassler's upper voice, such as those by J.S. Bach (in the edition of Erk-Smend nos. 122, 126, 127; in Breitkopf und Härtel—and Riemenschneider—nos. 21, 89, 345) offer only a superficial tribute to the lingering Phrygian system which musicians still believed in. In these settings, the Phrygian system was suggested, indeed almost required, by the final note. However, the latter is correctly understood as the third of the tonic chord in the major mode (as in Erk-Smend nos. 74, 123, 124; Breitkopf nos. 74, 98, 80). It is precisely the definiteness with which the major mode is achieved in the total span that allows Hassler to use an incomplete full close, in which the hidden i is understood. Despite the sparseness of tonal material in Hassler's setting, several bold events in the composing-out do arrest the attention. Bold though they are, they are all musically cogent. Measure 1: The a1 normally required by the arpeggiation f p— a1—d2—ft2 is missing here. Yet it is understood from the opening chord, and thus can be absent in the motion to d2. The diminution of the b1, which replaces a1, results from the composing-out of the third in ascending and descending directions: V^cí^d2—c%2— b\ Measure 4: The setting of the passing tone ft1 over the bass G (Gs~7) at the first structural level is ingenious. The passing tone is made consonant by the bass tone B. Measure 5: As the upper voice is composed out within the A-major harmony the bass follows it in parallel tenths. Measures 6-8: The composing-out of the descending sixth d2— ft1- *11. Regarding the eventual transfer of ft2 to ft1, see below. (Jonas) 96 FREE Measures 9-10: In the composing-out of the descending fifth e2—a1, c%2 replaces the a1 in measure 10, thus avoiding the ill-sounding total interval of a seventh, e2—ft1. In measure 10, in order to maintain the obligatory register, a descending register transfer finally occurs in which f%2 is replaced as 3 by /I1, which was already prepared by the ft1 in measure 8. The fact that the contrapuntal practice of that time restricted 5 6 itself to and chords throughout does not affect the above explanation (Harm., note following § 88). Even in this early music, the fundamental structure has so much strength that we have no difficulty in recognizing the passing tones in the middleground. Those passing tones which the earlier level shows as dissonances remain passing tones, even though the foreground shows them as consonances. Despite its origin in a text, this music, as art, is completely pure. It is clear and organically unified, as absolute music always is, in contrast to music generated by the word. During the composing-out, it can even forgo repetitions which ordinarily establish so-called motives. Of course, the brevity of the composition as well as the vocal element might also tend to oppose motivic patterns (§ 50). Now to the most important consideration: it is obvious that a composition such as that given in Fig. 116 does not admit of embellishment in the Italian style. Moreover, when the chorale text was introduced, embellishment was out of the question because of the words. Extensive embellishment in such a case could only lead to a "chorale prelude." Yet the strong bond to canonic repetition, whose origin ultimately lay in the word, stood in opposition to such a form of free diminution—genuine diminution which is completely self-generated. Therefore, other paths to genuine diminution had to be sought: just those which the great masters found. The setting by Hugo Riemann appended at N.B. below Fig. 116 illustrates the latter-day disastrous growth of chords in the exclusively vertical sense. These "chords" paralyze the contrapuntal flow of the bass as well as that of the inner voices— it matters not whether this flow occurs by means of a compositional technique such as that of Hassler or by means of the procedures of J. S. Bach, which are more elaborate melodically. § 252. Figurations and small notation Indeed, all foreground is diminution. But even within the foreground, figurations frequently appear which are based on previous statements in the foreground. The occurrence of both statement and variant (figuration) at the foreground level—that is, the presence of two structural levels within the foreground— creates the illusion that the variant belongs only to the foreground statement, but in fact, through this statement it also relates to the background and middleground. Nevertheless, in the masterworks it is often quite difficult to decipher such figurations, as the following examples illustrate: Fig. 117 Ex. 1: Statement and variant are presented under a) and b). The derivation of both from the middleground is evident from the other illustrations. The first line shows a third-progression which departs from the 3. In the second, the 6—5 suspension is added. The third line shows the diminution in eighth notes, and so the upbeat also becomes an eighth note. At a) the diminution appears in sixteenths, prepared by the subdivision of the /-upbeat into JT^, with b1 appearing as a neighboring note. In the next line this b1 appears at the beginning of the measure, so that the auxiliary harmony produces the effect of V7. The composing-out continues within this harmony in the form of J J J, two-voiced, with fifths on the afterbeats. Finally, SPECIFIC in the figuration at b), the two last thirty-second notes of the upbeat, c#2 and bP, prepare the chromatically filled-in span from b1 to eP. Only by experiencing these relationships can a performance of the figuration shown at b) really succeed. When statement and variant return, as for example in antecedent and consequent settings or in the parts of a song form, the figurations become ever more richly elaborated. In this way they evince a process of growth like that of an organism, which also adds to the unity of the whole he indicates, by distinguishing between large and small notation, the correct performance even of the bass.*17 *14. Compare my Beitrag zur Ornamentik, pp. 24 ff., 71. (Schenker) *15. Compare C. P. E. Bach, Klavierstücke mit veränderten Reprisen, edited by Oswald Jonas, who has also provided a separate commentary (in German and English) on the significance of the diminutions in these compositions (Universal Edition 13311). (Schenker, Oster) *16. The small notation is now reproduced in Hallische Händel-Ausgabe (Klavierwerke 1) and in Lea Pocket Scores (Works for Clavier, p. 123). (Oster) *17. In the manuscript of the first version of this etude, Chopin placed stems upon the quarter notes in the first ten measures before beginning to differentiate only by means of large and small noteheads. (Jonas) § 253. The achievement of organic relationship in genuine diminution (1) Through the whole It would be impossible to make a complete listing of all the forms of organic relationship which occur in true diminution. Therefore, I shall present here only the most essential. First, all diminution must be secured firmly to the total work by means which are precisely demonstrable and organically verified by the inner necessities of the voice-leading. The total work lives and moves in each diminution, even those of the lowest order. Not the smallest part exists without the whole. The establishment of an inner relationship to the whole is the principal problem not only in the creation of diminution out of background and middleground, but also even in its re-creation, where constant reference to middleground and background must be made. The atmosphere of diminution is the whole. True song is given to diminution. It is born with the movement in seconds of the fundamental line, and develops further life through the seconds of the lines which evolve from it. So it sings its way through all these seconds, the conveyors of the melodic, into the foreground and within it further and further. All the manifold experience of the lines—which are none other than our experiences—are transformed into song. Wherefore then words to generate music, to point up its meaning, when music itself organically lives, sings, and speaks? Its inner song elevates absolute diminution above word-generated diminution, which is eternally chained to "love," "hate," and "jealousy." Performance, too, must sing from the whole, whether the piece moves slowly or quickly. Everything in the genuine mas-terwork is song-like, not only those passages which are obviously "cantabile." C.P.E. Bach, in whose path Haydn followed, deserves praise as the originator of this deeply songful, absolute diminution. And he was tireless in his zeal for a singing manner of performance. Indeed every line of his immortal masterwork, Versuch über die wahre Art, das Klavier zu spielen, expresses SPECIFIC song! Alas, I fear that the day of this noble inner song is past, both in composition and performance. § 254. (2) Through repetition An enormously long time was required before music incorporated the principle of repetition. As long as the word interpreted music and determined its dimensions, music was absolved from the obligation to interpret and develop itself. Thus it was in the epoch when music had no rationale. Even in the first melis-mas, those first embellishments of individual syllables in which the human voice reveled with delight, repetition was lacking. Consequently these embellishments remained illogical for centuries, until counterpoint, by clarifying both vertical and rhythmic aspects, succeeded also in defining the horizontal dimension: a tonal succession could achieve a specific inner relatedness, limited and meaningful, since it was based upon specific intervals and also specifically determined in the manifold time-values of the individual notes <§§ 4, 21, 67>. Only a unity of this kind could have led, indeed it had to lead, to repetition. Repetition presented itself as a symbol of organic life in the world of tones, as though statement and variant were connected by bonds of blood. The ever stronger inner desire of music to follow its own corfrse, to strive toward expansion of content, found its counterpart in the pleasure the ear derived from repetition— a joy in recognition itself. And thus for centuries music proceeded through the school of the canon, the fugue, and related imitative forms. Repetition lay always on the surface; it was immediately and constantly perceptible to eye and ear as inversions, augmentations, contractions. These early discoveries made by Western man have remained effectual throughout subsequent time. Even now we find that kind of music most accessible in which there is repetition that is immediately recognizable. The ease with which we recognize a tonal series adds to the pleasure we derive from that recognition—what is simpler than to recognize a repetition of the brief succession of tones customarily designated a "motive"? EVENTS 99 However, the facility with which the tonal materials were enlarged and enjoyed ultimately decreased the interest in earlier imitative forms, especially since they became stereotyped and shop-worn in the hands of composers of little talent. New types of repetition then revealed themselves to composers of genius. Although these new types seem to lie just as clearly before eye and ear as the repetitions that occurred within the imitative forms, they remained less accessible because they did not oifer creator and listener the same ease of perception. They were fully as effective as the simpler repetitions; they, too, sprang only from the blood relationship of statement and variant, almost beyond the composer's volition—but they remained concealed. Yet it was precisely these concealed repetitions which freed music from the narrowness of strict imitation and pointed the way to the widest spans and most distant goals; thus even very extended tonal structures could be based upon repetition! In these concealed repetitions lie the seed and flowering of German creative genius. Therefore, the technique of "motive" repetition in the German music-drama, in program music, and in the sonata forms of the lesser talents signifies retrogression to the earlier stage, and thus a decline. Of course, the early type of immediately recognizable repetition coexisted with the new type of repetition. Each is, in its place, beneficial and advantageous. The new type of repetition is recognizable, above all, by its derivation of tonal successions from the simplest element (§ 30). The magnificent heritage of the German chorale brought forth many boldly conceived compositions. These compositions show how such a simple derivation can suffice for the creation of a great work of art—even without recourse to repetition in the foreground. The repetitions indicated in Fig. 118,1 and 2, which belong to the middleground, are not to be regarded as motive repetitions in the usual sense. They are, however, repetitions and they thus bring about relationship. And certainly the foreground here in no way suggests "motives." Exx. 1-21 in Fig. 119 confirm the fact that concealed repeti- 100 FREE tions are not merely imagined by the ear, nor are they only the result of fantasy. They could, in fact, even be grasped visually, if in music the eye were able to see without being guided by the ear. Repetitions of this kind have nothing to do with "motive" repetitions; they are so simple and so minute that they often do not fall within the concept of a motive. Fig. 119 Exx. 1, 2, 4-6, 8-10, 15: Repetitions by augmentation. Exx. 3 and 11: Repetitions by contraction. The following examples cannot be termed either augmentation or contraction: Ex. 7: Here gb2 and g2 are engaged in a struggle with one another—only two single tones, certainly not a motive repetition in the usual sense. And yet the synthesis of the entire first movement circles around this conflict. Ex. 13: The statement, a), shows an augmentation of a simple arpeggiation. Therefore, b) cannot be called an augmentation; it is rather an elaborate repetition of a). major. Cf. Fig. 102,6 and §303.) Ex. 14: Here we have the repetition of a mere neighboring-note figure which maintains its pitch position while the harmonic degrees (V—I, IV—I) change; yet precisely this feature contributes greatly to the cohesiveness of the whole. Exx. 16-18: These repetitions approach the very limits of what may be considered repetition; they are like the smallest cells of a diminution. Ex. 19: In such diminutions of the upper voice, the repetition would ordinarily begin with the upbeat. In both these examples, however, the downbeat must be included in the repetition, creating a somewhat peculiar effect. Both analysis and performance must show full recognition of this feature. (Compare the different situation in Fig. 147,4.) Ex. 20: The repetition here plays a decisive role in creating the form—the f1—eb1 in b) opposes itself to the f1—e\\l in a) and leads to the III of /minor, to the so-called second theme .*18 Ex. 21: (These repetitions take place in the middleground. Therefore,) only awareness of the middleground makes it possible to recognize them. Such repetitions, and similar ones, have a far-reaching effect in synthesis. They contrast strongly with the repetitions usually taught today, which tend only to restrict the scope of synthesis. It is surely time that we learn to recognize such repetitions as the prime carriers of synthesis in order to be able to express them in performance also. In view of the fact that the masters based their syntheses mainly upon such relationships, there can be no doubt of the importance of projecting them—it remains only to find the specific means of achieving such projection. Once the musician has made the perception of such relationships an integral part of his musical thought, he will know how to restore them to the synthesis. Ex. 15c, for instance, makes an entirely different effect when it is performed as a repetition and when it is performed as a completely new event, which the new diminution in measures 8ff. easily tempts one to do [§ 303]. And how different the "well-known" Overture to A Midsummer Night's Dream would sound if the conductor brought the repetition shown in Ex. 9a-e to life! One cannot repeat too often that the way to a true understanding of this type of repetition leads through the middleground and background. § 255. (3) Through preparation Diminution at the foreground level is often open to misunderstanding, for it frequently makes use of concealed repetitions *18. In Der Tonwille 7, p. 7 Schenker mentions that the chromatic step eti1— eb1 in measure 23 may have suggested /b3—eb3 in measures 26-27, and further on (mm. 30-31, 47-50, etc.). I believe that this is the case. (Oster) SPECIFIC in the middleground rather than obvious repetitions in the foreground. When such foreground diminutions occur, they require additional relationships in order to obviate misunderstanding. Fig. 120 These examples show how such relationships can also be established by preparing a diminution. Preparation makes the subsequent diminution organic. It is frequently so delicate that it hardly need penetrate into the artistic consciousness; one can almost assume a sort of self-generation. Here, strangely enough, the concealed process supports the organic element more strongly than literal repetition could. Ex. 1: Beethoven avoids proceeding directly from the g1 in measure 4, the final tone of the descending line, to g1 in measure 8. Instead, in measures 5-8, he inserts the ascending semitone ft1—g1 and thereby achieves a preparation for the chromatically ascending seconds which follow. In so doing, he also uses the third-arpeggiations in the bassoons to prepare the third-arpeggiation in measure 8, which later serves to eliminate consecutive fifths (Fig. 62,2). Exx. 2-4: Here the change of direction of the diminution which follows is prepared in simplest fashion. This preparation is invaluable in the service of unity. Ex. 5: With the change of octave in measures 1-2 the move into still higher registers is prepared. This move helps to bring about the unification of the measure group (cf. Fig. 62,4). Ex. 6: In this example, the peak tones (*) of the diminution relate to one another in a different sense. Under no circumstances may we read them as a genuine linear progression, for example, as a sixth-progression at a) (mm. 1-12, b1— g2> or as a fourth-progression at b) . However, this profound art has not yet been really heard or appreciated, nor has it ever been equaled, much less surpassed, by any other master of the tonal art. Altogether, J.S. Bach remains the master teacher of a genuinely contrapuntal bass; even with the most extensive unfolding of diminutions he never exceeds the limits set for the bass. Therefore, a nonlegató performance of his basses is usually appropriate. § 258. Descending diminution The various concealing devices of foreground diminution have a particular musical attractiveness. We delight in them, and diminution has its greatest triumph in the fact that it can make us forget the bare outlines of a work. (So we also delight in the human form, whose shape is made more attractive in flesh and color.) Particularly the high and low registers, which contribute to the expressive and ecstatic quality of instruments— and so are indispensable—often disguise the actual path of the diminution. In the case of descending foreground diminutions, the significance of the goal tone can be determined only if one considers the relationship to the middleground and background. Thus, a goal tone can be part of the fundamental line (Figs. 89,4; 91,4); it can be a neighboring note (Figs. 82,5c; 83,2); it can be a tone in an initial ascent (Fig. 120,6b), in a motion from an inner voice (Fig. 102,7) or in an arpeggiation (Fig. 110b, 3). Compare the examples in Jahrbuch ///(Beethoven, £VMajor Symphony). It is in the nature of such diminutions to be, as it were, closed off from the voice-leading which precedes their beginnings (§§ 244 ff.). Further examples follow: Fig. 122 Ex. 1: The tones g1 and a1 of the initial ascent are reached simultaneously by descending diminutions in the upper voice and ascending fourth-skips in the inner voice. These tones therefore result from the contrary motion of two voices (octave to unison), which has great charm. This attractive feature also requires special treatment in performance. Ex. 2: This example illustrates very clearly that the beginning of a descending diminution can be independent of the vertical element. This diminution begins at d3 and descends to the goal-tone ab2 on the fifth eighth. At the same time, the left hand has the ^~4—3 suspension eb1—d1. Despite this suspension, Chopin was able to write the d3, since it relates exclusively to the forthcoming ab2; it does not relate at all to the suspended eb1. The articulation, although it would seem to indicate otherwise, does not alter the situation.*19 Ex. 3: This example also illustrates independence of a descending diminution from the actual chord. There is no doubt *19. In his personal copy of the nocturne, Schenker described the diminution as an "interpolation" and placed it in parentheses, thus putting into relief the main melodic progression 6b1—c2—d2—eb2. With regard to the first slur 6b1— d:\ Schenker makes a suggestion for performance: "ôb1 to be sustained (hält an) to create the impression of a quarter note." (Oster) SPECIFIC that the chord in the second measure is to be understood 6 as a 4. Ordinarily, the sixteenth (*) would have read d2, not e2, especially since with d2 the initial octave-skip c2— c3 would find an answer. Nevertheless, C.P.E. Bach writes e2 as if it were part of an independent chord, e2—g2—d3, without, however, intending to allude to the E in the harmony which follows in measure 3. This subtlety brings to mind (see Ex. N.B.) the delicate way in which C.P.E. Bach, in another piece, avoids an augmented fourth in the diminution (cf. Kpt. I, Ex. 50). § 259. Ascending diminutions Examples of ascending diminutions are presented in Fig. 123 Ex. 1: a) The upper tones of the thirds are not to be regarded as goal tones with a consequent harmonic significance. They are only superposed as simple consonances. On the other hand, the lower primary tones form an ascending line. Thus there is no parallel-octave succession at the bar line [§ 162]. b) Similarly, gt2 must not be taken for a faulty doubling of the leading tone. c) Only the initial tones are determinant; hence, the four-tone groups are not true linear progressions of a fourth. Ex. 2: In the second measure, the fourth eighthnote is a goal tone; the fifth eighth, in contrast, is a primary tone of the ascending diminution. This reading of the intervals is based upon the first measure, of which the second measure is the inversion. EVENTS 103 Ex. 3: The primary tones of the diminutions serve the tones of the initial ascent. The peak tones of the diminutions id2 and e2 in mm. 3 and 5> are not to be considered goal tones, nor do they have a harmonic effect (Fig. 119,3 and Fig. 120,6). Ex. 4: In connection with an unfolding, a diminution often shows a superposition of the inner voice (Fig. 106,2). Ex. 5: This diminution, by ascending, produces an octave transfer of two tones from the inner voice, b1 and a#\ and, through this octave transfer, arrives at e2 at the reaching-over on the fourth quarter; this makes it possible to retain the position of e2, the 8. It is interesting to note that c%2 progresses to b2 through skips of thirds, without, however, implying a seventh chord. § 260. Balancing of directions; boundary-play No matter whether a diminution ascends or descends, the composer may seek to regain the position occupied earlier or to reach tones lower or higher. The first motion is followed by others; the tone which begins the total motion and the tone which ends it become its boundary tones [§ 143], The first tone sets out toward the goal, the last one brings us to it. Fig. 124 Ex. 1: a) The boundary tones of the motion, which takes place over the I, represent a stationary tone (Fig. 109e,2 and 5). b) Here again the motion <8—b7—iS^Xh^-S) has a stationary tone at its boundaries. At N.B. other possibilities are shown, which, however, have the disadvantage that they involve skips. With respect to this, compare Mozart, Symphony in G Minor, Andante, measures 44-47 {Jahrb. II, p. 140): 104 FREE b7—b6—5—\\