Nanisma: Difference between revisions
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'''Nanisma''' ( | '''Nanisma''' ({{monzo|legend=1| 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 | 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 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. | 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. | ||
=== | === Nanismic === | ||
[[Subgroup]]: 2.3.5.7 | |||
[[Comma list]]: {{monzo| 109 -67 0 -1 }} | |||
{{Mapping|legend=1| 1 0 0 109 | 0 -1 0 67 | 0 0 1 0 }} | |||
: sval mapping generators: ~2, ~3, ~5 | |||
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9578, ~5/4 = 386.3137 | |||
{{Optimal ET sequence|legend=1| 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<sup>-3</sup> | |||
=== Nanic === | |||
[[Subgroup]]: 2.3.7 | [[Subgroup]]: 2.3.7 | ||
[[Comma list]]: {{monzo| 109 -67 -1 }} | [[Comma list]]: {{monzo| 109 -67 -1 }} | ||
{{Mapping|legend=2| 1 0 109 | 0 -1 67 }} | |||
: sval mapping generators: ~2, ~3 | |||
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9578 | |||
{{Optimal ET sequence|legend=1| 53, 200, 253, 306, 665, 971, 1277, 6691, 7968, 9245, 10522, 11799, 13076, 40505, 53581, 66657, 79733 }} | |||
[[Badness]]: 0.0138 | |||
== See also == | == See also == | ||
Revision as of 07:49, 2 June 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.
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 = 1\1, ~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
Nanic
Subgroup: 2.3.7
Comma list: [109 -67 -1⟩
Subgroup-val mapping: [⟨1 0 109], ⟨0 -1 67]]
- sval mapping generators: ~2, ~3
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.9578
Optimal ET sequence: 53, 200, 253, 306, 665, 971, 1277, 6691, 7968, 9245, 10522, 11799, 13076, 40505, 53581, 66657, 79733
Badness: 0.0138