94-comma

Interval information

Factorization	2149 × 3-94
Monzo	[149 -94⟩
Size in cents	16.22992¢
Names	94-comma, garistearn comma
Color name	94wM, fosebiwama
FJS name	[math]\displaystyle{ \text{13d10} }[/math]
Special properties	reduced, reduced subharmonic
Tenney norm (log2 nd)	297.986
Weil norm (log2 max(n, d))	298
Wilson norm (sopfr(nd))	580
Comma size	small
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The 94-comma, or garistearn comma (monzo: [65 -41⟩), is a 3-limit interval of 16.23 cents. It is the amount by which a stack of 94 perfect fifths (3/2) falls short of 149 octaves, in other words 2⁵⁵/(3/2)⁹⁴. It can also be described as the difference between 16 limmas and a doubly augmented octave (two apotomes + octave), or the difference between the 41-comma and Mercator's comma.

Temperaments

Tempering out this comma leads to the octave being split into 94 equal parts, with the fifth being equal to 55\94, and the Pythagorean comma being split in halves, each half corresponding to a 53- or 41-comma; of course, this also means the octave is split in half. For equal divisions N up to 3478edo, the comma is tempered out if and only if 94 divides N. Notable examples are 94edo and 282edo.

See also

• Small comma
• Schismic–countercommatic equivalence continuum
• Schismic–Mercator equivalence continuum