Keemic family: Difference between revisions
Tags: Mobile edit Mobile web edit |
Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
||
| Line 23: | Line 23: | ||
: Eigenmonzos: 2, 4/3, 7/5 | : Eigenmonzos: 2, 4/3, 7/5 | ||
{{ | {{Optimal ET sequence|legend=1| 7, 15, 19, 41 }} | ||
[[Projection pair]]: 7 864/125 | [[Projection pair]]: 7 864/125 | ||
| Line 38: | Line 38: | ||
[[POTE generator]]s: ~3/2 = 704.1985, ~5/4 = 381.5394 | [[POTE generator]]s: ~3/2 = 704.1985, ~5/4 = 381.5394 | ||
{{ | {{Optimal ET sequence|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> | ||
| Line 53: | Line 53: | ||
[[POTE generator]]s: ~5/4 = 380.3520, ~11/8 = 547.5758 | [[POTE generator]]s: ~5/4 = 380.3520, ~11/8 = 547.5758 | ||
{{ | {{Optimal ET sequence|legend=1| 19, 22, 41, 82e, 101cd, 224ccde, 265ccde * }} | ||
<nowiki>*</nowiki> [[optimal patent val]]: [[104edo|104]] | <nowiki>*</nowiki> [[optimal patent val]]: [[104edo|104]] | ||
| Line 68: | Line 68: | ||
[[POTE generator]]s: ~5/4 = 380.0401, ~11/8 = 546.6672 | [[POTE generator]]s: ~5/4 = 380.0401, ~11/8 = 546.6672 | ||
Optimal | {{Optimal ET sequence|legend=1| 19, 22f, 41, 60e, 101cd }} | ||
[[Category:Temperament families]] | [[Category:Temperament families]] | ||
Revision as of 17:43, 7 May 2023
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
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
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
Optimal ET sequence: 7, 15, 19, 41
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
Optimal ET sequence: 7, 15, 19, 22, 37, 41, 104, 145c, 201ce, 264bce, 305bcce
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
Optimal ET sequence: 19, 22, 41, 82e, 101cd, 224ccde, 265ccde *
Badness: 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]]
POTE generators: ~5/4 = 380.0401, ~11/8 = 546.6672