Semicomma

Semicomma on C Playⓘ.

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.

  1. ^ a b 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.