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The diaschisma (or diacisma) is a small
Columbian cyclopedia, Volume 9
', np. Garretson, Cox & Company. pre-ISBN. Medieval theorists Boethius and Tinctoris described the diaschisma as one-half of the Pythagorean minor second, or 256/243, which would make the other half either 25/24 (70.67 cents) or about 45 cents. The diaschisma may be approximated by 89/88, 19.56 cents.
Tempering out the diaschisma, in the modern meaning of the term, leads to a diaschismic temperament. The diaschisma is tempered out in the usual system of
The diaschisma (or diacisma) is a small musical interval
In music theory, an interval is a difference in pitch between two sounds.
An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and vertical or ha ...
defined as the difference between three octave
In music, an octave ( la, octavus: eighth) or perfect octave (sometimes called the diapason) is the interval between one musical pitch and another with double its frequency. The octave relationship is a natural phenomenon that has been refer ...
s and four perfect fifth
In music theory, a perfect fifth is the Interval (music), musical interval corresponding to a pair of pitch (music), pitches with a frequency ratio of 3:2, or very nearly so.
In classical music from Western culture, a fifth is the interval fro ...
s plus two major thirds (in just intonation
In music, just intonation or pure intonation is the tuning of musical intervals
Interval may refer to:
Mathematics and physics
* Interval (mathematics), a range of numbers
** Partially ordered set#Intervals, its generalization from numbers to ...
). It can be represented by the ratio 2048:2025 and is about 19.5 cents. The use of the name diaschisma for this interval is due to Helmholtz
Hermann Ludwig Ferdinand von Helmholtz (31 August 1821 – 8 September 1894) was a German physicist and physician who made significant contributions in several scientific fields, particularly hydrodynamic stability. The Helmholtz Association, ...
; earlier Rameau had called that interval a "diminished comma" or comma minor.
A diaschisma is the difference between a schisma and a syntonic comma, as well as the difference between the greater chromatic semitone (135:128 = 92.18 cents) and the just minor second (16:15 = 111.73 cents). (1897). Columbian cyclopedia, Volume 9
', np. Garretson, Cox & Company. pre-ISBN. Medieval theorists Boethius and Tinctoris described the diaschisma as one-half of the Pythagorean minor second, or 256/243, which would make the other half either 25/24 (70.67 cents) or about 45 cents. The diaschisma may be approximated by 89/88, 19.56 cents.
Tempering out the diaschisma, in the modern meaning of the term, leads to a diaschismic temperament. The diaschisma is tempered out in the usual system of 12 equal temperament
Twelve-tone equal temperament (12-TET) is the musical system that divides the octave into 12 parts, all of which are equally tempered (equally spaced) on a logarithmic scale, with a ratio equal to the 12th root of 2 ( ≈ 1.05946). That result ...
; in fact, 12 equal temperament can be characterized as the 5-limit
Five-limit tuning, 5-limit tuning, or 5-prime-limit tuning (not to be confused with 5-odd-limit tuning), is any system for tuning a musical instrument that obtains the frequency of each note by multiplying the frequency of a given reference note ...
temperament that tempers out both the syntonic comma of 81/80 and the diaschisma. However, it is possible to improve the tuning a good deal over that of 12-et and still temper out the diaschisma; the equal temperaments with 22, 34 and 46 notes all temper it out.
See also
* Comma (music)References
{{Intervals, state=expanded 5-limit tuning and intervals Commas (music)