352/351: Difference between revisions

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The '''minthma''', '''352/351''', is a [[13-limit]] (also 2.3.11.13 subgroup) [[comma]] measuring about 4.9 cents. The tempering of this comma can be described in a number of ways. First, it identifies the tridecimal minor third of [[13/11]] by the Pythagorean minor third of [[32/27]], hence, the tridecimal comma of [[1053/1024]] by the undecimal comma of [[33/32]]. Second, it identifies various tridecimal intervals by adjacent undecimal intervals such as [[16/13]] by [[27/22]], and [[39/32]] by [[11/9]].  
The '''minthma''', '''352/351''', is a [[13-limit]] (also 2.3.11.13 subgroup) [[comma]] measuring about 4.9 cents. This comma can be described in a number of ways. First, it is the difference between the tridecimal minor third of [[13/11]] and the Pythagorean minor third of [[32/27]], hence, between the tridecimal quartertone of [[1053/1024]] and the undecimal quartertone of [[33/32]]. Second, it is the difference between various tridecimal intervals and their adjacent undecimal intervals such as between [[16/13]] and [[27/22]], and between [[39/32]] and [[11/9]].
 
352/351 and [[351/350]], the ratwolfsma, are extremely close in size and make up a consecutive pair of 13-limit superparticular commas. Their difference is [[123201/123200]], the chalmersma, the smallest 13-limit superparticular comma; their sum is [[176/175]], the valinorsma, an 11-limit superparticular comma.  


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

Revision as of 10:26, 26 September 2020

Interval information
Ratio 352/351
Factorization 25 × 3-3 × 11 × 13-1
Monzo [5 -3 0 0 1 -1
Size in cents 4.925278¢
Name minthma
FJS name [math]\displaystyle{ \text{P1}^{11}_{13} }[/math]
Special properties superparticular,
reduced
Tenney norm (log2 nd) 16.9148
Weil norm (log2 max(n, d)) 16.9189
Wilson norm (sopfr(nd)) 43
Open this interval in xen-calc

The minthma, 352/351, is a 13-limit (also 2.3.11.13 subgroup) comma measuring about 4.9 cents. This comma can be described in a number of ways. First, it is the difference between the tridecimal minor third of 13/11 and the Pythagorean minor third of 32/27, hence, between the tridecimal quartertone of 1053/1024 and the undecimal quartertone of 33/32. Second, it is the difference between various tridecimal intervals and their adjacent undecimal intervals such as between 16/13 and 27/22, and between 39/32 and 11/9.

352/351 and 351/350, the ratwolfsma, are extremely close in size and make up a consecutive pair of 13-limit superparticular commas. Their difference is 123201/123200, the chalmersma, the smallest 13-limit superparticular comma; their sum is 176/175, the valinorsma, an 11-limit superparticular comma.

See also