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
Open this interval in xen-calc

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.

Name

Given the other intervals called "semicomma", it is likely that "semicomma" refers to the comma's size as about half the size of the syntonic comma. The name "Fokker's comma" comes from Adriaan Fokker.

See also

Intervals with the word "semicomma" in the name:

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