[druhá odmocnina z] 2 [se nerovná] a : b jako problém tonality.

CELHOFFER, Martin. [druhá odmocnina z] 2 [se nerovná] a : b jako problém tonality. ([the root of] 2 [is not equal to] a : b as a tonality issue.). Musicologica Brunensia. Stanislav Tesař at 70. Brno: Masarykova univerzita, 2010, roč. 45, 1-2, p. 69-76. ISSN 1212-0391.

Basic information

• Original name: [druhá odmocnina z] 2 [se nerovná] a : b jako problém tonality.
• Name (in English): [the root of] 2 [is not equal to] a : b as a tonality issue.
• Authors: CELHOFFER, Martin (703 Slovakia, guarantor, belonging to the institution).
• Edition: Musicologica Brunensia. Stanislav Tesař at 70. Brno, Masarykova univerzita, 2010, 1212-0391.

Other information

• Original language: Czech
• Type of outcome: Article in a journal
• Field of Study: Art, architecture, cultural heritage
• Country of publisher: Czech Republic
• Confidentiality degree: is not subject to a state or trade secret
• RIV identification code: RIV/00216224:14210/10:00047271
• Organization unit: Faculty of Arts
• Keywords in English: pythagorean comma; Boethius; Ptolemy; syntonic diatonic tetrachord; limma; apotome
• Tags: RIV-OK
• Tags: International impact, Reviewed

Abstract

Studie se zabývá problémem nedělitelnosti proporce oktávy a jeho důsledky na organizaci tónového systému. Proporce oktávy 2:1 není možné rozdělit na stejné části – dva tritony, tři ditony nebo šest celých tónů, protože druhá odmocnina z proporce 2 : 1 je iracionální číslo. Tato skutečnost měla zásadní význam pro problematiku nerovnoměrnosti ladění.

Abstract (in English)

This study deals with natural consequences of the indivisibility of the octave 2:1 on tonal structures. The proportion of the octave 2:1 cannot be divided into equal parts – two tritones, three ditones or six whole tones because the root of 2:1 is irrational number. This fact has a cardinal importance for the problem of unequal temperament. The syntonic diatonic tetrachord, as known from Ptolemaios, became a pattern for most of unequal tunings (Zarlino, Rameau). The inequality causes irregular distributions of “pure” intervals and “perfect” chords within the modus and is the reason for hierarchy of particular tonal steps.