Keemic family: Difference between revisions
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{{Technical data page}} | {{Technical data page}} | ||
The '''keemic family''' is a family of [[rank-3 temperament]]s which [[temper out]] the [[keema]] | The '''keemic family''' is a family of [[rank-3 temperament]]s which [[tempering out|temper out]] the [[keema]] ({{monzo|legend=1| -5 -3 3 1 }}, [[ratio]]: 875/864). | ||
== Supermagic == | == Supermagic == | ||
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{{Mapping|legend=1| 1 0 0 5 | 0 1 0 3 | 0 0 1 -3 }} | {{Mapping|legend=1| 1 0 0 5 | 0 1 0 3 | 0 0 1 -3 }} | ||
: mapping generators: ~2, ~3, ~5 | : mapping generators: ~2, ~3, ~5 | ||
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: Angle (6/5, 3/2) = 77.834 | : Angle (6/5, 3/2) = 77.834 | ||
[[Optimal tuning]] ([[POTE]]): ~2 = | [[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 701.8733{{c}}, ~5/4 = 380.4684{{c}} | ||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
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{{Optimal ET sequence|legend=1| 7, 12d, 15, 19, 41, 142cd, 183cd, 224ccd }} | {{Optimal ET sequence|legend=1| 7, 12d, 15, 19, 41, 142cd, 183cd, 224ccd }} | ||
[[Badness]]: 0.212 × 10<sup>-3</sup> | [[Badness]] (Smith): 0.212 × 10<sup>-3</sup> | ||
[[Projection pair]]: 7 864/125 | [[Projection pair]]: 7 864/125 | ||
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{{Mapping|legend=1| 1 0 0 5 2 | 0 1 0 3 -2 | 0 0 1 -3 2 }} | {{Mapping|legend=1| 1 0 0 5 2 | 0 1 0 3 -2 | 0 0 1 -3 2 }} | ||
[[Optimal tuning]] ([[POTE]]): ~2 = | [[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 704.1985{{c}}, ~5/4 = 381.5394{{c}} | ||
{{Optimal ET sequence|legend=1| 7, 15, 19, 22, 37, 41, 104 }} | {{Optimal ET sequence|legend=1| 7, 15, 19, 22, 37, 41, 104 }} | ||
[[Badness]]: 0.641 × 10<sup>-3</sup> | [[Badness]] (Smith): 0.641 × 10<sup>-3</sup> | ||
Scales: [[supermagic15]] | Scales: [[supermagic15]] | ||
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{{Mapping|legend=1| 1 0 2 -1 0 | 0 5 1 12 0 | 0 0 0 0 1 }} | {{Mapping|legend=1| 1 0 2 -1 0 | 0 5 1 12 0 | 0 0 0 0 1 }} | ||
: mapping generators: ~2, ~5, ~11 | : mapping generators: ~2, ~5, ~11 | ||
[[Optimal tuning]] ([[POTE]]): ~2 = | [[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~5/4 = 380.3520{{c}}, ~11/8 = 547.5758{{c}} | ||
{{Optimal ET sequence|legend=1| 19, 22, 38d, 41, 60e, 101cd, 164c, 224ccde * }} | {{Optimal ET sequence|legend=1| 19, 22, 38d, 41, 60e, 101cd, 164c, 224ccde * }} | ||
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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]] (Smith): 0.888 × 10<sup>-3</sup> | ||
=== 13-limit === | === 13-limit === | ||
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Mapping: {{mapping| 1 0 2 -1 0 -2 | 0 5 1 12 0 18 | 0 0 0 0 1 0 }} | Mapping: {{mapping| 1 0 2 -1 0 -2 | 0 5 1 12 0 18 | 0 0 0 0 1 0 }} | ||
Optimal tuning (POTE): ~2 = | Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~5/4 = 380.0401{{c}}, ~11/8 = 546.6672{{c}} | ||
{{Optimal ET sequence|legend=1| 19, 22f, 38df, 41, 60e, 79d, 101cd }} | {{Optimal ET sequence|legend=1| 19, 22f, 38df, 41, 60e, 79d, 101cd }} | ||
Badness: 1.14 × 10<sup>-3</sup> | Badness (Smith): 1.14 × 10<sup>-3</sup> | ||
[[Category:Temperament families]] | [[Category:Temperament families]] | ||
Revision as of 12:51, 10 October 2025
- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
The keemic family is a family of rank-3 temperaments which temper out the keema (monzo: [-5 -3 3 1⟩, ratio: 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
Mapping 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
Optimal tuning (POTE): ~2 = 1200.0000 ¢, ~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⟩]
- unchanged-interval (eigenmonzo) basis: 2.3.7/5
Optimal ET sequence: 7, 12d, 15, 19, 41, 142cd, 183cd, 224ccd
Badness (Smith): 0.212 × 10-3
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]]
Optimal tuning (POTE): ~2 = 1200.0000 ¢, ~3/2 = 704.1985 ¢, ~5/4 = 381.5394 ¢
Optimal ET sequence: 7, 15, 19, 22, 37, 41, 104
Badness (Smith): 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]]
- mapping generators: ~2, ~5, ~11
Optimal tuning (POTE): ~2 = 1200.0000 ¢, ~5/4 = 380.3520 ¢, ~11/8 = 547.5758 ¢
Optimal ET sequence: 19, 22, 38d, 41, 60e, 101cd, 164c, 224ccde *
Badness (Smith): 0.888 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 196/195, 245/243
Mapping: [⟨1 0 2 -1 0 -2], ⟨0 5 1 12 0 18], ⟨0 0 0 0 1 0]]
Optimal tuning (POTE): ~2 = 1200.0000 ¢, ~5/4 = 380.0401 ¢, ~11/8 = 546.6672 ¢
Optimal ET sequence: 19, 22f, 38df, 41, 60e, 79d, 101cd
Badness (Smith): 1.14 × 10-3