User:FloraC/Temperament name proposal: Difference between revisions
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* Lux (41 & 46 & 270) named in cooperation with Godtone | * Lux (41 & 46 & 270) named in cooperation with Godtone | ||
* Luminal (183 & 311) | * Luminal (183 & 311) | ||
* Superlimmal (80 & 311) | |||
= | == 22 & 46 & 72 == | ||
An 11-limit rank-3 temperament. Announced in FB group. <s>To be called "quasiquarter"</s> I don't like this name. | An 11-limit rank-3 temperament. Announced in FB group. <s>To be called "quasiquarter"</s> I don't like this name. | ||
It tempers out 1500625/1492992 = {{monzo| -11 -6 4 4 }} in the 7-limit, and the keenanisma, [[385/384]], the kalisma, [[9801/9800]], as well as the [[Alpharabian comma]], 131769/131072 = {{monzo| -17 2 0 0 4 }}, in the 11-limit. | It tempers out 1500625/1492992 = {{monzo| -11 -6 4 4 }} in the 7-limit, and the keenanisma, [[385/384]], the kalisma, [[9801/9800]], as well as the [[Alpharabian comma]], 131769/131072 = {{monzo| -17 2 0 0 4 }}, in the 11-limit. It features splitting the whole tone into four equal parts, each representing 36/35~33/32. Therefore, it is most valuable for those who would like to make extensive use of quartertones. It can be viewed as one which is joined by the three quartertone-sized edos: [[22edo]], [[24edo]], and [[26edo]]. It shares the [[optimal patent val]], [[284edo]] with [[Keenanismic family|keenanismic]]. | ||
=== 7-limit === | |||
Subgroup: 2.3.5.7 | |||
== 7-limit == | |||
[[Comma list]]: 1500625/1492992 | [[Comma list]]: 1500625/1492992 | ||
[[Mapping]]: [ | [[Mapping]]: [{{val| 2 1 0 7 }}, {{val| 0 2 0 3 }}, {{val| 0 0 1 -1 }}] | ||
Mapping generators: ~1225/864, ~35/24, ~5 | Mapping generators: ~1225/864, ~35/24, ~5 | ||
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[[Badness]]: 0.7042 × 10<sup>-3</sup> | [[Badness]]: 0.7042 × 10<sup>-3</sup> | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | |||
Comma list: 385/384, 9801/9800 | [[Comma list]]: 385/384, 9801/9800 | ||
Mapping: [ | [[Mapping]]: [{{val| 2 1 0 7 8 }}, {{val| 0 2 0 3 -1 }}, {{val| 0 0 1 -1 0 }}] | ||
Mapping generators: ~99/70, ~16/11, ~5 | Mapping generators: ~99/70, ~16/11, ~5 | ||
POTE | [[POTE generator]]s: ~33/32 = 50.7404 or ~11/8 = 549.2596, ~5/4 = 385.0315 | ||
{{Val list|legend=1| 22, 46, 68, 72, 118, 190, 212, 284, 330e }} | |||
Badness: 0.5292 × 10<sup>-3</sup> | [[Badness]]: 0.5292 × 10<sup>-3</sup> | ||
= 87 & 94 & 111 = | == 87 & 94 & 111 == | ||
An unnamed 13-limit rank-3 temperament. | An unnamed 13-limit rank-3 temperament. | ||
Subgroup: 2.3.5.7.11 | |||
[[Comma list]]: 352/351, 847/845, 14641/14580 | [[Comma list]]: 352/351, 847/845, 14641/14580 | ||
[[Mapping]]: [ | [[Mapping]]: [{{val| 1 0 2 12 1 6 }}, {{val| 0 1 2 -4 2 -1 }}, {{val| 0 0 4 4 1 1 }}] | ||
{{Val list|legend=1| 7, 17c, 24d, 87, 111, 181, 198 }} | {{Val list|legend=1| 7, 17c, 24d, 87, 111, 181, 198 }} | ||
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[[Badness]]: 0.0540 × 10<sup>-3</sup> | [[Badness]]: 0.0540 × 10<sup>-3</sup> | ||
= 41 & 46 & 53 & 58 = | == 41 & 46 & 53 & 58 == | ||
An unnamed 13-limit rank-4 temperament. | An unnamed 13-limit rank-4 temperament. | ||
Subgroup: 2.3.5.7.11.13 | |||
[[Comma list]]: 352/351, 847/845 | [[Comma list]]: 352/351, 847/845 | ||
[[Mapping]]: [ | [[Mapping]]: [{{val| 1 0 0 10 0 5 }}, {{val| 0 1 0 -6 0 -3 }}, {{val| 0 0 1 1 0 0 }}, {{val| 0 0 0 0 1 1 }}] | ||
{{Multival|legend=1|rank=4| 0 1 1 1 1 0 6 6 -3 -3 10 10 -5 -5 0 }} | {{Multival|legend=1|rank=4| 0 1 1 1 1 0 6 6 -3 -3 10 10 -5 -5 0 }} | ||
POTE | [[POTE generator]]s: ~3/2 = 702.9075, ~5/4 = 387.0723, ~11/8 = 551.4538 | ||
{{Val list|legend=1| 12f, 17c, 29, 41, 46, 53, 58, 87, 111, 140, 198 }} | {{Val list|legend=1| 12f, 17c, 29, 41, 46, 53, 58, 87, 111, 140, 198 }} | ||
[[Badness]]: 2.550 × 10<sup>-6</sup> | [[Badness]]: 2.550 × 10<sup>-6</sup> | ||
Revision as of 06:03, 12 June 2021
Ideas welcome!
- Canou (94 & 99 & 118) and various extensions
- Semicanousmic (14641/14580)
- Lux (41 & 46 & 270) named in cooperation with Godtone
- Luminal (183 & 311)
- Superlimmal (80 & 311)
22 & 46 & 72
An 11-limit rank-3 temperament. Announced in FB group. To be called "quasiquarter" I don't like this name.
It tempers out 1500625/1492992 = [-11 -6 4 4⟩ in the 7-limit, and the keenanisma, 385/384, the kalisma, 9801/9800, as well as the Alpharabian comma, 131769/131072 = [-17 2 0 0 4⟩, in the 11-limit. It features splitting the whole tone into four equal parts, each representing 36/35~33/32. Therefore, it is most valuable for those who would like to make extensive use of quartertones. It can be viewed as one which is joined by the three quartertone-sized edos: 22edo, 24edo, and 26edo. It shares the optimal patent val, 284edo with keenanismic.
7-limit
Subgroup: 2.3.5.7
Comma list: 1500625/1492992
Mapping: [⟨2 1 0 7], ⟨0 2 0 3], ⟨0 0 1 -1]]
Mapping generators: ~1225/864, ~35/24, ~5
Wedgie: ⟨⟨⟨ 4 -4 -6 11 ]]]
POTE generators: ~36/35 = 50.9529 or ~48/35 = 549.0471, ~5/4 = 385.3326
Badness: 0.7042 × 10-3
11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 9801/9800
Mapping: [⟨2 1 0 7 8], ⟨0 2 0 3 -1], ⟨0 0 1 -1 0]]
Mapping generators: ~99/70, ~16/11, ~5
POTE generators: ~33/32 = 50.7404 or ~11/8 = 549.2596, ~5/4 = 385.0315
Badness: 0.5292 × 10-3
87 & 94 & 111
An unnamed 13-limit rank-3 temperament.
Subgroup: 2.3.5.7.11
Comma list: 352/351, 847/845, 14641/14580
Mapping: [⟨1 0 2 12 1 6], ⟨0 1 2 -4 2 -1], ⟨0 0 4 4 1 1]]
Badness: 0.0540 × 10-3
41 & 46 & 53 & 58
An unnamed 13-limit rank-4 temperament.
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 847/845
Mapping: [⟨1 0 0 10 0 5], ⟨0 1 0 -6 0 -3], ⟨0 0 1 1 0 0], ⟨0 0 0 0 1 1]]
Wedgie: ⟨⟨⟨⟨ 0 1 1 1 1 0 6 6 -3 -3 10 10 -5 -5 0 ]]]]
POTE generators: ~3/2 = 702.9075, ~5/4 = 387.0723, ~11/8 = 551.4538
Badness: 2.550 × 10-6