Keemic family: Difference between revisions
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= Supermagic = | = Supermagic = | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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: 6/5 length = 0.8879, 3/2 length = 1.3391 | : 6/5 length = 0.8879, 3/2 length = 1.3391 | ||
: Angle (6/5, 3/2) = 77.834 | : Angle (6/5, 3/2) = 77.834 | ||
[[POTE generator]]s: ~3/2 = 701.8733, ~5/4 = 380.4684 | |||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
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[[Projection pair]]: 7 864/125 | [[Projection pair]]: 7 864/125 | ||
Scales: [[supermagic15]] | |||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | |||
[[Comma list]]: 100/99, 385/384 | |||
[[Mapping]]: [{{val| 1 0 0 5 2 }}, {{val| 0 1 0 3 -2 }}, {{val| 0 0 1 -3 2 }}] | |||
[[POTE generator]]s: ~3/2 = 704.1985, ~5/4 = 381.5394 | |||
{{Val list|legend=1| 7, 15, 19, 22, 37, 41, 104, 145c, 201ce, 264bce, 305bcce }} | {{Val list|legend=1| 7, 15, 19, 22, 37, 41, 104, 145c, 201ce, 264bce, 305bcce }} | ||
Badness: 0.641 × 10<sup>-3</sup> | [[Badness]]: 0.641 × 10<sup>-3</sup> | ||
Scales: [[supermagic15]] | |||
= Supernatural = | = Supernatural = | ||
Subgroup: 2.3.5.7.11 | |||
[[Comma list]]: 225/224, 245/243 | |||
[[Mapping]]: [{{val| 1 0 2 -1 0 }}, {{val| 0 5 1 12 0 }}, {{val| 0 0 0 0 1 }}] | |||
[[POTE generator]]s: ~5/4 = 380.3520, ~11/8 = 547.5758 | |||
{{Val list|legend=1| 19, 22, 41, 82e, 101cd, 224ccde, 265ccde * }} | {{Val list|legend=1| 19, 22, 41, 82e, 101cd, 224ccde, 265ccde * }} | ||
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<nowiki>*</nowiki> [[optimal patent val]]: [[104edo|104]] | <nowiki>*</nowiki> [[optimal patent val]]: [[104edo|104]] | ||
Badness: 0.888 × 10<sup>-3</sup | [[Badness]]: 0.888 × 10<sup>-3</sup> | ||
[[Category:Theory]] | [[Category:Theory]] | ||
Revision as of 10:19, 28 March 2021
The keemic family of rank-3 temperaments are planar temperaments tempering out the keema, 875/864.
Supermagic
Subgroup: 2.3.5.7
Comma list: 875/864
Mapping: [⟨1 0 0 5], ⟨0 1 0 3], ⟨0 0 1 -3]]
Mapping generators: ~2, ~3, ~5
Map to lattice: [⟨0 0 -1 3], ⟨0 1 1 0]]
Lattice basis:
- 6/5 length = 0.8879, 3/2 length = 1.3391
- Angle (6/5, 3/2) = 77.834
POTE generators: ~3/2 = 701.8733, ~5/4 = 380.4684
- 7- and 9-odd-limit
- [[1 0 0 0⟩, [0 1 0 0⟩, [5/4 3/4 1/4 -1/4⟩, [5/4 3/4 -3/4 3/4⟩]
- Eigenmonzos: 2, 4/3, 7/5
Projection pair: 7 864/125
Scales: supermagic15
11-limit
Subgroup: 2.3.5.7.11
Comma list: 100/99, 385/384
Mapping: [⟨1 0 0 5 2], ⟨0 1 0 3 -2], ⟨0 0 1 -3 2]]
POTE generators: ~3/2 = 704.1985, ~5/4 = 381.5394
Badness: 0.641 × 10-3
Scales: supermagic15
Supernatural
Subgroup: 2.3.5.7.11
Comma list: 225/224, 245/243
Mapping: [⟨1 0 2 -1 0], ⟨0 5 1 12 0], ⟨0 0 0 0 1]]
POTE generators: ~5/4 = 380.3520, ~11/8 = 547.5758
Badness: 0.888 × 10-3