351/350: Difference between revisions
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The '''ratwolfsma''', '''351/350''', is a [[13-limit]] no-eleven [[comma]] measuring about 4.9 cents. It is the difference between [[28/27]] and [[26/25]], between [[81/70]] and [[15/13]], and between [[35/27]] and [[13/10]]. | The '''ratwolfsma''', '''351/350''', is a [[13-limit]] no-eleven [[comma]] measuring about 4.9 cents. It is the difference between [[28/27]] and [[26/25]], between [[81/70]] and [[15/13]], and between [[35/27]] and [[13/10]]. | ||
In terms of commas, it | In terms of commas, it often arises as the following differences: ([[78/77]])/([[100/99]]), ([[81/80]])([[105/104]]), ([[126/125]])([[196/195]]), ([[225/224]])/([[625/624]]), and ([[325/324]])([[4375/4374]]). It factors into ([[676/675]])([[729/728]]), ([[540/539]])([[1001/1000]]), ([[441/440]])([[1716/1715]]), or ([[364/363]])([[9801/9800]]). | ||
351/350 and [[352/351]], the major minthma, are extremely close in size and make up a consecutive pair of 13-limit superparticular commas. Their difference is [[chalmersia|123201/123200]], the chalmersia, the smallest 13-limit superparticular comma; their sum is [[176/175]], the valinorsma, an 11-limit superparticular comma. | 351/350 and [[352/351]], the major minthma, are extremely close in size and make up a consecutive pair of 13-limit superparticular commas. Their difference is [[chalmersia|123201/123200]], the chalmersia, the smallest 13-limit superparticular comma; their sum is [[176/175]], the valinorsma, an 11-limit superparticular comma. | ||
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[[Category:Ratwolf]] | [[Category:Ratwolf]] | ||
[[Category:Commas with unknown etymology]] | |||
Latest revision as of 00:01, 16 November 2024
| Interval information |
Thorugugu comma
reduced
The ratwolfsma, 351/350, is a 13-limit no-eleven comma measuring about 4.9 cents. It is the difference between 28/27 and 26/25, between 81/70 and 15/13, and between 35/27 and 13/10.
In terms of commas, it often arises as the following differences: (78/77)/(100/99), (81/80)(105/104), (126/125)(196/195), (225/224)/(625/624), and (325/324)(4375/4374). It factors into (676/675)(729/728), (540/539)(1001/1000), (441/440)(1716/1715), or (364/363)(9801/9800).
351/350 and 352/351, the major minthma, are extremely close in size and make up a consecutive pair of 13-limit superparticular commas. Their difference is 123201/123200, the chalmersia, the smallest 13-limit superparticular comma; their sum is 176/175, the valinorsma, an 11-limit superparticular comma.
Tempering it out leads to the rank-five ratwolfsmic temperament, or in the 2.3.5.7.13 subgroup ratwolf temperament, and enables the ratwolfsmic chords.