Harmonisma
| Interval information |
10648/10647, the harmonisma, is a no-5's 13-limit unnoticeable comma of about 0.1626 cents. It is equal to (16/13 × 11/9)/(14/11 × 13/11). In terms of other commas, it is (352/351)/(364/363), (3025/3024)/(4225/4224), or (9801/9800)/(123201/123200).
Temperaments
Tempering out this comma in the full 13-limit gives the rank-5 harmonismic temperament. Equal temperaments where this comma is tempered with very high accuracy will have an interval corresponding to a "sharp fifth" of (ideally) 706.7 to 706.9 cents, corresponding to the range of fifths from 13/11 × 14/11 (→182/121) on the lower end and 11/9 × 16/13 (→176/117) on the higher end, and this interval is not mapped to 3/2. However, such temperaments are generally very precise, so 224edo, 270edo and 311edo offer slightly more manageable tunings. For less accurate temperaments still, 10648/10647 is notable as a comma of parapyth.
Etymology
The harmonisma was named by Margo Schulter in 2002 in honor of the harmoniai of Kathleen Schlesinger.