A **septimal comma** is a small musical interval in just intonation that contains the number seven in its prime 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 (27.26 cents).^{[1]}^{[2]}

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 major second. Composers who made extensive use of these intervals include Harry Partch and Ben Johnston. Johnston uses a "7" as an accidental to indicate a note is lowered 49 cents, or an upside down seven ("ㄥ" or "

The 64/63 septimal comma, also known as *Archytas' Comma*,^{[1]} 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.^{[4]} 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*.^{[1]} 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),^{[3]} 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*^{[1]}), 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*,^{[1]} 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.

Ratio | Size in cents | Ben Johnston's notation |
Names |
---|---|---|---|

64/63 | 27.26 | C |
Septimal comma, Archytas' comma |

50/49 | 34.98 | B |
Septimal sixth-tone, tritonic diesis, Erlich's decatonic comma |

49/48 | 35.7 | D |
Slendro diesis |

36/35 | 48.77 | C |
Septimal quarter tone |