94-comma: Difference between revisions
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{{Infobox Interval|Monzo=149 -94|Name=94-comma, garistearn comma|Color name=94wM, fosebiwama|Comma=yes}}The '''94-comma''', or '''garistearn comma''' ([[monzo]]: {{monzo|65 -41}}), is a [[3-limit]] interval of 16.23 [[Cent|cents]]. It is the amount by which a stack of 94 [[3/2|perfect fifths (3/2)]] falls short of 149 [[Octave|octaves]], in other words 2<sup>55</sup>/(3/2)<sup>94</sup>. It can also be described as the difference between 16 [[Limma|limmas]] and a doubly augmented octave (two [[Apotome|apotomes]] + octave), or the difference between the [[41-comma]] and [[Mercator's comma]]. | {{Infobox Interval|Monzo=149 -94|Name=94-comma, garistearn comma|Color name=94wM, fosebiwama|Comma=yes}}The '''94-comma''', or '''garistearn comma''' ([[monzo]]: {{monzo|65 -41}}), is a [[3-limit]] interval of 16.23 [[Cent|cents]]. It is the amount by which a stack of 94 [[3/2|perfect fifths (3/2)]] falls short of 149 [[Octave|octaves]], in other words 2<sup>55</sup>/(3/2)<sup>94</sup>. It can also be described as the difference between 16 [[Limma|limmas]] and a doubly augmented octave (two [[Apotome|apotomes]] + octave), or the difference between the [[41-comma]] and [[Mercator's comma]]. | ||
Additionally, in the [[2.3.7 subgroup]], it is also the quotient between 6 [[Septischisma|septischismas]] and 1 [[stearnsma]]. | |||
== Temperaments == | == Temperaments == | ||
Latest revision as of 21:00, 2 October 2026
| Interval information |
garistearn comma
reduced subharmonic
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.
Additionally, in the 2.3.7 subgroup, it is also the quotient between 6 septischismas and 1 stearnsma.
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.