Nanisma

Interval information

Factorization	2109 × 3-67 × 7-1
Monzo	[109 -67 0 -1⟩
Size in cents	0.1890355¢
Name	nanisma
FJS name	[math]\displaystyle{ \text{9d7}_{7} }[/math]
Special properties	reduced, reduced subharmonic
Tenney norm (log2 nd)	218
Weil norm (log2 max(n, d))	218
Wilson norm (sopfr(nd))	426
Comma size	unnoticeable
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Nanisma (monzo: [109 -67 0 -1⟩) is a no-five 7-limit unnoticeable comma measuring about 0.189 cents in size. It is the tiny interval between the pythagorean ratio [107 -67⟩ and the harmonic minor-7th of ratio 7/4.

The nanisma is considered as a 3=7 xenharmonic bridge. It also describes the difference between [108 -68⟩ (a stack of four 17-commas) and the septimal minor third of ratio 7/6, and also the difference between [-109 69⟩ and the wide septimal major third of ratio 9/7.

Temperaments

The nanisma is tempered out in such notable edos as 306, 612, 1277, 1583, 2860, 4137, 4802, 5414, 6079, 6691, 11493, 12105, and 12770, leading to the nanismic temperament, in which sixty-seven fifths make up a septimal whole tone 8/7 with octave reduction.

Nanismic

Subgroup: 2.3.5.7

Comma list: [109 -67 0 -1⟩

Mapping: [⟨1 0 0 109], ⟨0 1 0 -67], ⟨0 0 1 0]]

sval mapping generators: ~2, ~3, ~5

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.9578, ~5/4 = 386.3137

Optimal ET sequence: 53, 147d, 200, 253, 306c, 359, 412, 506d, 559, 612, 1277, 1889, 3525, 4137, 4190, 4802, 5414, 6079, 6691, 18184, 24875, 92809, 117684, 142559

Badness: 6.09 × 10^-3

Nanic

Subgroup: 2.3.7

Comma list: [109 -67 -1⟩

Subgroup-val mapping: [⟨1 0 109], ⟨0 1 -67]]

sval mapping generators: ~2, ~3

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.9578

Optimal ET sequence: 53, 200, 253, 306, 665, 971, 1277, 6691, 7968, 9245, 10522, 11799, 13076, 40505, 53581, 66657, 79733

Badness: 0.0138

Etymology

This comma was named by Margo Schulter in 2002.

See also

• Unnoticeable comma

External links

• Tonalsoft Encyclopedia| Nanisma