Semicomma

Interval information

Ratio	2109375/2097152
Factorization	2-21 × 33 × 57
Monzo	[-21 3 7⟩
Size in cents	10.061¢
Names	semicomma, orson comma, Fokker's comma
Color name	Ly7-3, Lasepyo comma
FJS name	[math]\displaystyle{ \text{dddd}{-3}^{5,5,5,5,5,5,5} }[/math]
Special properties	reduced, reduced harmonic
Tenney height (log2 nd)	42.0084
Weil height (log2 max(n, d))	42.0168
Wilson height (sopfr(nd))	86
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~2.08903 bits
Comma size	small
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The semicomma or Fokker's comma (ratio: 2109375/2097152, monzo: [-21 3 7⟩), is a small 5-limit comma of 10.061 cents which is the amount by which three classic augmented second intervals of 75/64 exceed 8/5. That means (75/64)³/(8/5), which can also be written ((9/8)(25/24))³/(8/5). In terms of commas, it factors into simpler commas as (15625/15552)(32805/32768), the kleisma and the schisma. It is also the difference between the 31-comma (3³¹/2⁴⁹) and seven syntonic commas (81/80).

Temperaments

Tempering out this comma in the 5-limit leads to the orson temperament.

See also

Intervals with the word "semicomma" in the name:

• Medium semicomma, aka sensipent comma
• Septimal semicomma, aka starling comma
• Semicomma majeur, aka kleisma