Septimal Comma - Specific Commas

Specific Commas

The 64/63 septimal comma ( 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 Pythagorean minor seventh (the composition of two 4/3 perfect fourths) and the 7/4 harmonic seventh. Its size is 27.264 cents, slightly larger than the Pythagorean 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 a quarter tone. The septimal diesis appears as the difference between many septimal intervals and their 5-limit counterparts: the minor seventh (9/5) and the seventh harmonic (7/4), the 8/7 septimal whole tone and the 10/9 minor whole tone, the 7/6 septimal minor third and the 6/5 minor third, the 9/7 septimal major third and the 5/4 major third, and many more.

Other septimal commas include 49/48 (occasionally called the slendro diesis) ( 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 tritones, 7/5 and 10/7, or Erlich's decatonic comma, because it plays an important role in the ten-tone scales of Paul Erlich (the intervals are tempered so that 50/49 vanishes).

The septimal kleisma and the septimal semicomma are smaller septimal commas.