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The '''marveltwin comma''', '''325/324''', is a [[13-limit]] (also 2.3.5.13 [[subgroup]]) [[comma]] measuring about 5.3 | The '''marveltwin comma''', '''325/324''', is a [[small comma|small]] [[13-limit]] (also 2.3.5.13 [[subgroup]]) [[superparticular ratio|superparticular]] [[comma]] measuring about 5.3 [[cent]]s. Its significance is in that it marks the difference between [[16/13]] and a stack of two [[10/9]]'s, and [[13/9]] and a stack of two [[6/5]]'s. It can also be expressed as the difference between [[1053/1024]] and a stack of two [[81/80]]'s. | ||
Being a [[triangle-particular|triangle superparticular]], it factors neatly into ([[625/624]])([[676/675]]). Other factorizations are ([[385/384]])([[2080/2079]]) | In terms of other superparticular ratios, it is the difference between: | ||
* [[25/24]] and [[27/26]] | |||
* [[100/99]] and [[144/143]] | |||
Being a [[triangle-particular|triangle superparticular]], it factors neatly into ([[625/624]])⋅([[676/675]]). Other factorizations are: | |||
* ([[385/384]])⋅([[2080/2079]]) | |||
* ([[364/363]])⋅([[3025/3024]]) | |||
* ([[352/351]])⋅([[4225/4224]]) | |||
* ([[351/350]])⋅([[4375/4374]]) | |||
In the 17-limit it additionally factors into ([[595/594]])⋅([[715/714]]). | |||
== Temperaments == | == Temperaments == | ||
Tempering out this comma leads to the rank-5 [[Marveltwin|marveltwin temperament]], which identifies [[16/13]] by two [[10/9]]'s stacked and enables [[marveltwin chords]]. The most significant further temperament is to temper out 625/624 and/or 676/675, equating 26/25 with 25/24~27/26. This in the 2.3.5.13 [[subgroup]] is the rank-2 [[cata]] temperament. | [[Tempering out]] this comma leads to the rank-5 [[Marveltwin|marveltwin temperament]], which identifies [[16/13]] by two [[10/9]]'s stacked and enables [[marveltwin chords]]. The most significant further temperament is to temper out 625/624 and/or 676/675, equating 26/25 with 25/24~27/26. This in the 2.3.5.13 [[subgroup]] is the rank-2 [[cata]] temperament. | ||
== See also == | == See also == | ||
Latest revision as of 10:11, 2 February 2026
| Interval information |
Thoyoyo comma
reduced
S10/S12
The marveltwin comma, 325/324, is a small 13-limit (also 2.3.5.13 subgroup) superparticular comma measuring about 5.3 cents. Its significance is in that it marks the difference between 16/13 and a stack of two 10/9's, and 13/9 and a stack of two 6/5's. It can also be expressed as the difference between 1053/1024 and a stack of two 81/80's.
In terms of other superparticular ratios, it is the difference between:
Being a triangle superparticular, it factors neatly into (625/624)⋅(676/675). Other factorizations are:
In the 17-limit it additionally factors into (595/594)⋅(715/714).
Temperaments
Tempering out this comma leads to the rank-5 marveltwin temperament, which identifies 16/13 by two 10/9's stacked and enables marveltwin chords. The most significant further temperament is to temper out 625/624 and/or 676/675, equating 26/25 with 25/24~27/26. This in the 2.3.5.13 subgroup is the rank-2 cata temperament.