351/350: Difference between revisions

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In terms of commas, it is [[4375/4374]] small of [[325/324]], and it factors into ([[676/675]])([[729/728]]), ([[540/539]])([[1001/1000]]), ([[441/440]])([[1716/1715]]), or ([[364/363]])([[9801/9800]]).  
In terms of commas, it is [[4375/4374]] small of [[325/324]], and 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 minthma, are extremely close in size and make up a consecutive pair of 13-limit superparticular commas. Their difference is [[chalmersia|123201/123200]], the chalmersma, 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.  


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]].  
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]].


== See also ==
== See also ==

Revision as of 06:21, 17 January 2024

Interval information
Ratio 351/350
Factorization 2-1 × 33 × 5-2 × 7-1 × 13
Monzo [-1 3 -2 -1 0 1
Size in cents 4.93933¢
Name ratwolfsma
Color name 3orgg1, thorugugu 1sn,
Thorugugu comma
FJS name [math]\displaystyle{ \text{d1}^{13}_{5,5,7} }[/math]
Special properties superparticular,
reduced
Tenney height (log2 nd) 16.9065
Weil height (log2 max(n, d)) 16.9107
Wilson height (sopfr(nd)) 41
Comma size small
S-expression S26 × S27
Open this interval in xen-calc

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 is 4375/4374 small of 325/324, and 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.

See also