Semicomma

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).

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 norm (log2 nd)	42.0084
Weil norm (log2 max(n, d))	42.0168
Wilson norm (sopfr(nd))	86
Comma size	small
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English Wikipedia has an article on:

Semicomma

Temperaments

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

Etymology

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 "semicomma" was given by Adriaan Fokker, while the name "Fokker's comma" refers to him directly and was likely proposed later.

See also

• 126/125 (aka starling comma or septimal semicomma)
• 15625/15552 (aka kleisma or semicomma majeur)
• Sensipent comma (78732/78125, aka medium semicomma)

External links

• Semicomma on Tonalsoft Encyclopedia