325/324: Difference between revisions
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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 | 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: | ||
Being a [[triangle-particular|triangle superparticular]], it factors neatly into ([[625/624]])([[676/675]]). Other factorizations are ([[385/384]])([[2080/2079]]) | * [[16/13]] and two [[10/9]]'s | ||
* [[13/8]] and [[81/50]] ([[8/5]] * [[81/80]]) | |||
* [[13/9]] and two [[6/5]]'s | |||
* [[1053/1024]] and two [[81/80]]'s | |||
* [[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]]) | |||
* ([[595/594]])([[715/714]]) In the 17-limit. | |||
== Temperaments == | == Temperaments == | ||
Revision as of 18:52, 1 February 2026
| 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 two 10/9's
- 13/8 and 81/50 (8/5 * 81/80)
- 13/9 and two 6/5's
- 1053/1024 and two 81/80's
- 25/24 and 27/26
- 100/99 and 144/143
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)
- (351/350)(4375/4374)
- (595/594)(715/714) In the 17-limit.
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.