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{{Infobox Interval | {{Infobox Interval | ||
| Name = marveltwin comma | | Name = marveltwin comma | ||
| Color name = 3oyy1, Thoyoyo comma | | Color name = 3oyy1, thoyoyo 1sn,<br>Thoyoyo comma | ||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
The '''marveltwin comma''', '''325/324''', is a [[13-limit]] (also 2.3.5.13 subgroup) [[comma]] measuring about 5.3{{cent}}. Its significance is in that it | The '''marveltwin comma''', '''325/324''', is a [[13-limit]] (also 2.3.5.13 [[subgroup]]) [[comma]] measuring about 5.3{{cent}}. Its significance is in that it marks the difference between [[16/13]] and a stack of two [[10/9]]'s, or between [[13/9]] and a stack of two [[6/5]]'s. It can also be expressed as ([[25/24]])/([[27/26]]) and ([[100/99]])/([[144/143]]), among other expressions. | ||
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]]), and ([[351/350]])([[4375/4374]]). In the 17-limit it additionally factors into ([[595/594]])([[715/714]]). | |||
Tempering | == 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. | |||
== See also == | == See also == | ||
* [[Marveltwin]] | * [[Marveltwin]] | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
[[Category:Marveltwin]] | [[Category:Marveltwin]] | ||
[[Category:Commas with unknown etymology]] | |||
Latest revision as of 00:00, 16 November 2024
| Interval information |
Thoyoyo comma
reduced
S10 / S12
The marveltwin comma, 325/324, is a 13-limit (also 2.3.5.13 subgroup) comma measuring about 5.3 ¢. Its significance is in that it marks the difference between 16/13 and a stack of two 10/9's, or between 13/9 and a stack of two 6/5's. It can also be expressed as (25/24)/(27/26) and (100/99)/(144/143), among other expressions.
Being a 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), and (351/350)(4375/4374). 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.