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]] | '''Nanisma''' ([[monzo]]: {{monzo| 109 -67 0 -1 }}) is a no-five [[7-limit]] [[unnoticeable comma]] measuring about 0.189 [[cent]]s in size. It is the tiny interval between the pythagorean ratio {{monzo| 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 {{monzo|108 -68}} (a stack of four [[17 | 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]]s) and the septimal minor third of ratio [[7/6]], and also the difference between {{monzo| -109 69 }} and the wide septimal major third of ratio [[9/7]]. | ||
== Temperament == | == Temperament == | ||
The nanisma is tempered out in such notable | The nanisma is tempered out in such notable edos as {{EDOs| 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) === | === No-five nanismic (1277&2860) === | ||
[[Subgroup]]: 2.3.7 | |||
[[Comma list]]: {{monzo| 109 -67 -1 }} | |||
[[Sval]] [[mapping]]: [{{val| 1 2 -25 }}, {{val| 0 -1 67 }}] | |||
[[Optimal tuning]] ([[POTE]]): ~3/2 = 701.9578 | |||
{{Val list|legend=1| 53, 200, 253, 306, 665, 971, 1277, 4137, 5414, 6691, 7968 }} | |||
{{ | |||
== See also == | == See also == | ||
* [[Unnoticeable comma]] | * [[Unnoticeable comma]] | ||
Revision as of 09:07, 15 January 2023
| Interval information |
reduced subharmonic
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.
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)
Subgroup: 2.3.7
Comma list: [109 -67 -1⟩
Sval mapping: [⟨1 2 -25], ⟨0 -1 67]]
Optimal tuning (POTE): ~3/2 = 701.9578