Keemic family: Difference between revisions
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m fix heading structure |
m Make 11-limit supermagic the same header level as supernatural |
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== Supermagic == | == Supermagic == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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Scales: [[supermagic15]] | Scales: [[supermagic15]] | ||
=== | == Undecimal supermagic == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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Scales: [[supermagic15]] | Scales: [[supermagic15]] | ||
== Supernatural | == Supernatural == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||
[[Category:Temperament family]] | [[Category:Temperament family]] | ||
[[Category:Keemic]] | [[Category:Keemic family| ]] <!-- main article --> | ||
[[Category:Supermagic]] | [[Category:Supermagic]] | ||
[[Category:Rank 3]] | [[Category:Rank 3]] | ||
Revision as of 14:39, 22 August 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
Undecimal supermagic
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