Nanisma

Interval information

Factorization	2109 × 3-67 × 7-1
Monzo	[109 -67 0 -1⟩
Size in cents	0.1890355¢
Name	nanisma
Color name	s10r7, quinbisaru 7th
FJS name	[math]\displaystyle{ \text{9d7}_{7} }[/math]
Special properties	reduced, reduced subharmonic
Tenney height (log2 nd)	218
Weil height (log2 max(n, d))	218
Wilson height (sopfr(nd))	426
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~1.19855 bits
Comma size	unnoticeable
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The nanisma (monzo: [109 -67 0 -1⟩) is an unnoticeable 7-limit (also 2.3.7-subgroup) comma measuring about 0.189 cents. It is the tiny interval between the pythagorean ratio [107 -67⟩ and the harmonic minor seventh 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. It can also be thought of as the difference between Mercator's comma and the garischisma.

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.

Nanic

See Very high accuracy temperaments #Nanic.

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 = 1200.0000, ~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

Etymology

This comma was named by Margo Schulter in 2002.

External links

• Tonalsoft Encyclopedia| Nanisma