Nanisma: Difference between revisions
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'''Nanisma''' is a no-five [[7-limit]] [[unnoticeable comma]]. It is the tiny interval between the pythagorean ratio {{monzo|107 -67}} and the harmonic minor-7th of ratio [[7/4]]; {{monzo|109 -67 0 -1}} in [[monzo]] and 0.18903555 [[cent]]s in size. | '''Nanisma''' is a no-five [[7-limit]] [[unnoticeable comma]]. It is the tiny interval between the pythagorean ratio {{monzo|107 -67}} and the harmonic minor-7th of ratio [[7/4]]; {{monzo|109 -67 0 -1}} in [[monzo]] and 0.18903555 [[cent]]s in size. | ||
The nanisma is considered as a 3=7 xenharmonic-bridge. It also describes the difference between {{monzo|108 -68}} and the septimal minor-3rd of ratio [[7/6]], and also the difference between {{monzo|-109 69}} and the wide septimal major-3rd of ratio [[9/7]]. | The nanisma is considered as a 3=7 xenharmonic-bridge. It also describes the difference between {{monzo|108 -68}} (a stack of four [[17-comma|17-3-comma]]) and the septimal minor-3rd of ratio [[7/6]], and also the difference between {{monzo|-109 69}} and the wide septimal major-3rd of ratio [[9/7]]. | ||
== Temperament == | == Temperament == | ||
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=== 7-limit Monzism (53&612) === | === 7-limit Monzism (53&612) === | ||
The ''monzism'' temperament (53&612, named by [[User:Xenllium|Xenllium]]) is a rank-two temperament which tempers out the [[monzisma]], {{monzo|54 -37 2}}, as well as the ragisma, [[4375/4374]]. | The ''monzism'' temperament (53&612, named by [[User:Xenllium|Xenllium]]) is a rank-two temperament which tempers out the [[monzisma]], {{monzo|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, {{monzo|-55 30 2 1}} | Comma list: 4375/4374, {{monzo|-55 30 2 1}} | ||
Revision as of 05:05, 11 April 2021
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: 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. 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: 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