Harmonisma

Interval information

Ratio	10648/10647
Factorization	23 × 3-2 × 7-1 × 113 × 13-2
Monzo	[3 -2 0 -1 3 -2⟩
Size in cents	0.1625954¢
Name	harmonisma
FJS name	[math]\displaystyle{ \text{m}{-2}^{11,11,11}_{7,13,13} }[/math]
Special properties	superparticular, reduced
Tenney norm (log2 nd)	26.7565
Weil norm (log2 max(n, d))	26.7566
Wilson norm (sopfr(nd))	78
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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

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.