Nanisma

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Nanisma is a no-five 7-limit unnoticeable comma. It is the tiny interval between the pythagorean ratio [107 -67 and the harmonic minor-7th of ratio 7/4; [109 -67 0 -1 in monzo and 0.18903555 cents in size.

The nanisma is considered as a 3=7 xenharmonic-bridge. It also describes the difference between [108 -68 and the septimal minor-3rd of ratio 7/6, and also the difference between [-109 69 and the wide septimal major-3rd of ratio 9/7.

Temperament

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.

No-five nanismic (1277&2860)

Comma list: [109 -67 0 -1

Mapping: [<1 2 -25|, <0 -1 67|]

POTE generator: ~3/2 = 701.9578

Vals: Template:Val list

7-limit Monzism (53&612)

The monzism temperament (53&612, named by Xenllium) is a rank-two temperament which tempers out the monzisma, [54 -37 2, as well as the ragisma, 4375/4374.

Comma list: 4375/4374, [-55 30 2 1

Mapping: [<1 2 10 -25|, <0 -2 -37 134|]

POTE generator: ~310078125/268435456 = 249.0207

Vals: Template:Val list

Badness: 0.046569

11-limit Monzism (53&612)

Comma list: 4375/4374, 41503/41472, 184549376/184528125

Mapping: [<1 2 10 -25 46|, <0 -2 -37 134 -205|]

POTE generator: ~231/200 = 249.0193

Vals: Template:Val list

Badness: 0.057083

See also