Lesser tendoneutralisma

Interval information

Ratio	70368744177664/69894255367443
Factorization	246 × 3-1 × 13-12
Monzo	[46 -1 0 0 0 -12⟩
Size in cents	11.71306¢
Name	lesser tendoneutralisma
FJS name	[math]\displaystyle{ \text{6d}{-2}_{13,13,13,13,13,13,13,13,13,13,13,13} }[/math]
Special properties	reduced, reduced subharmonic
Tenney norm (log2 nd)	91.9902
Weil norm (log2 max(n, d))	92
Wilson norm (sopfr(nd))	251
Comma size	small
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The lesser tendoneutralisma is a small comma of the 2.3.13 subgroup which is the amount by which a stack of twelve 16/13's minus three octaves exceeds 3/2; that is, it is equal to (16/13)¹² / (3/2) / (2/1)³ and so equivalently also to 16/13)¹¹ / (39/4). Because the ~11 ¢ of error is distributed over twelve 16/13's in the pure-3's tuning, it is a very accurate way of connecting a chain of 13's to prime 3. A slightly less accurate but still good way of doing this is using the greater tendoneutralisma.

Temperaments

Lesser Tendoneutralic

Tempering the lesser tendoneutralisma in 2.3.13 leads to the highly notable 10 & 77 temperament, where 10edo is the trivial tuning approximately equal to the pure-13's tuning and 77edo can be used to approximate the pure-3's tuning, although 67edo is an interesting choice for combining this temperament with meantone and perhaps more notably 87edo is a very good choice for combining this temperament with parapyth and 13-limit harmony generally (although it doesn't appear in the optimal ET sequence).

Subgroup: 2.3.13

Comma list: [46 -1 (0 0 0) -12⟩

Mapping: [⟨1 10 3], ⟨0 -12 1]]

Optimal tuning (CTE): ~13/8 = 841.503 ¢

Optimal ET sequence: 10, 47, 57, 67, 77, 164, 241, 405, 646f

Badness (Dirichlet): 3.930

See also

• Greater tendoneutralisma
• Tridecapyth comma