Semicomma

The semicomma,[1] also Fokker's comma (after 31-TET pioneer Adriaan Fokker), is type of small musical interval, or comma, in microtonal music equivalent to 2109375:2097152,[1] or 3³×5⁷ : 2²¹. This is a ratio of approximately 1:1.0058283805847168, or about 10.06 cents[2] (Play ). It is derived from the difference in pitch between three 75:64 just augmented seconds (Play just augmented second ) and one 8:5 just minor sixth (Play minor sixth ) begun on the same root ((3 × 274.58) − (1 × 813.69) = 823.74 − 813.69 = 10.05 cents).[3] It can also be viewed as the amount by which three tritaves exceed seven minor sixths.

Semicomma on C Play .

See also

• Septimal kleisma
• Septimal semicomma

Sources

1. Haluska, Jan (2003). The Mathematical Theory of Tone Systems, p.xxix. ISBN 80-88683-28-9.
2. "List of Intervals", Huygens-Fokker.org.
3. "Semicomma", on Xenharmonic Wiki.