- Septimal comma
A septimal comma is a small musical interval in
just intonation that contains the number seven in itsprime factorization . There is more than one such interval, so the term "septimal comma" is ambiguous, but it most commonly refers to the interval 64/63.cite web | url = http://www.xs4all.nl/~huygensf/doc/intervals.html | title = List of intervals | accessdate = 2006-07-29 | author = Manuel Op de Coul | work = Stichting Huygens-Fokker] [cite journal | last = Perrett | first = Wilfrid | year = 1932 | month = April | title = The Heritage of Greece in Music | journal = Proceedings of the Musical Association | volume = 58 | pages = 85–103 | url = http://www.jstor.org.proxy.lib.fsu.edu/view/09588442/ap030059/03a00070/0 | format = GIF | accessdate = 2006-07-29 | doi = 10.1093/jrma/58.1.85]Use of septimal commas introduces new intervals that extend tuning beyond common-practice, extending music to the 7-limit, including the 7/6
septimal minor third , the 7/5 septimal tritone and the 8/7 septimal whole tone. Composers who made extensive use of these intervals inclueHarry Partch and Ben Johnston.pecific commas
The 64/63 septimal comma (Audio|Septimal comma on C.mid|play), also known as "
Archytas ' Comma", is the interval equal to the difference between a major and septimal whole tone (with 9/8 and 8/7 ratios, respectively). Alternatively, it can be viewed as the difference between the 16/9 Pythagoreanminor seventh (the composition of two 4/3 perfect fourths) and the 7/4harmonic seventh . Its size is 27.3 cents, slightly larger than thePythagorean comma .The composition of the septimal comma and the
syntonic comma is 36/35, known as the "septimal diesis". Its size is 48.8 cents, making it practically aquarter tone . The septimal diesis appears as the difference between many septimal intervals and their 5-limit counterparts: the 8/7 septimalwhole tone and the 10/9 minor whole tone, the 7/6septimal minor third and the 6/5minor third , the 9/7septimal major third and the 5/4major third , and many more.Other septimal commas include 49/48 (occasionally called the "slendro diesis") (Audio|Septimal diesis on C.mid|play), which commonly appears as the difference between a ratio with 7 in the denominator and another with 7 in the numerator, like 8/7 and 7/6; and 50/49, called the "tritonic diesis", because it is the difference between the two septimal
tritone s, 7/5 and 10/7, or "Erlich's decatonic comma", because it plays an important role in the ten-tone scales ofPaul Erlich (the intervals are tempered so that 50/49 vanishes).The
septimal kleisma and theseptimal semicomma are smaller septimal commas.ummary
References
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