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 (a stack of four 17-3-comma) 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: 53, 200, 253, 306, 665, 971, 1277, 4137, 5414, 6691, 7968

Monzism (53&612)

See also: Ragismic microtemperaments

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. Tempering out the monzisma slices the interval of fourth 4/3 in two.

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

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

POTE generator: ~310078125/268435456 = 249.0207

Vals: 53, 559, 612, 1277, 1889

Badness: 0.046569

See also