Kalismic temperaments: Difference between revisions
Tag: Undo |
→Hnoss: +17-23-limit |
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[[Mapping]]: [{{val| 2 0 1 2 6 -3 }}, {{val| 0 1 4 0 2 1 }}, {{val| 0 0 -5 2 -3 4 }}] | [[Mapping]]: [{{val| 2 0 1 2 6 -3 }}, {{val| 0 1 4 0 2 1 }}, {{val| 0 0 -5 2 -3 4 }}] | ||
{{Val list|legend=1| 10c, 22f, 32cf, 54cff, 72, 166, 198, 270, 634, 904, 1174, 1880ef }} | {{Val list|legend=1| 10c, 22f, 32cf, 54cff, 72, 166, 198, 270, 634, 904, 1174, 1880ef }} | ||
[[Badness]]: 0.867 × 10<sup>-3</sup> | [[Badness]]: 0.867 × 10<sup>-3</sup> | ||
=== 17-limit === | |||
Subgroup: 2.3.5.7.11.13.17 | |||
[[Comma list]]: 715/714, 1089/1088, 1225/1224, 2025/2023 | |||
[[Mapping]]: [{{val| 2 0 1 2 6 -3 0 }}, {{val| 0 1 4 0 2 1 6 }}, {{val| 0 0 -5 2 -3 4 -6 }}] | |||
{{Val list|legend=1| 22f, 54cffgg, 72, 166g, 198g, 270, 364, 436, 634g, 706f }} | |||
[[Badness]]: 0.862 × 10<sup>-3</sup> | |||
=== 19-limit === | |||
Subgroup: 2.3.5.7.11.13.17.19 | |||
[[Comma list]]: 715/714, 1225/1224, 1540/1539, 2080/2079, 4200/4199 | |||
[[Mapping]]: [{{val| 2 0 1 2 6 -3 0 13 }}, {{val| 0 1 4 0 2 1 6 2 }}, {{val| 0 0 -5 2 -3 4 -6 -6 }}] | |||
{{Val list|legend=1| 72, 94, 166g, 198g, 270, 436, 634g, 706f }} | |||
[[Badness]]: 0.901 × 10<sup>-3</sup> | |||
=== 23-limit === | |||
Subgroup: 2.3.5.7.11.13.17.19.23 | |||
[[Comma list]]: 715/714, 1225/1224, 1540/1539, 2080/2079, 2530/2527, 2737/2736 | |||
[[Mapping]]: [{{val| 2 0 1 2 6 -3 0 13 19 }}, {{val| 0 1 4 0 2 1 6 2 -2 }}, {{val| 0 0 -5 2 -3 4 -6 -6 -2 }}] | |||
{{Val list|legend=1| 72, 94, 166g, 270, 342f, 436, 706fi }} | |||
[[Badness]]: 1.14 × 10<sup>-3</sup> | |||
=== Gersemi === | === Gersemi === | ||
The extension to 13-limit with [[4225/4224]] is | The extension to 13-limit with [[4225/4224]] is weak but facilitates the use of 18/7 as the equave. Fokker blocks of 128 notes are available for the latter, corresponding to 94edo. 18/7 is split into 4 parts that become ~19/15 in 19-limit. Also, (18/7)<sup>3</sup> ~ 17/1 via the [[5832/5831|chlorisma]]. However, the tones 9/8 and (19/15)/(9/8) = 152/135 have distinct mappings. | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 154: | Line 188: | ||
[[Mapping]]: [{{val| 2 0 1 2 6 9 0 }}, {{val| 0 1 9 -2 5 -6 12 }}, {{val| 0 0 -10 4 -6 7 -12 }}] | [[Mapping]]: [{{val| 2 0 1 2 6 9 0 }}, {{val| 0 1 9 -2 5 -6 12 }}, {{val| 0 0 -10 4 -6 7 -12 }}] | ||
{{Val list|legend=1| 44, 50, 94, 144g, 176g, 220g, 270, 364, 414, 634g, 684 }} | {{Val list|legend=1| 44, 50, 94, 144g, 176g, 220g, 270, 364, 414, 634g, 684 }} | ||
| Line 182: | Line 214: | ||
[[Mapping]]: [{{val| 2 0 1 2 6 9 0 1 7 }}, {{val| 0 1 9 -2 5 -6 12 11 3 }}, {{val| 0 0 -10 4 -6 7 -12 -11 -3 }}] | [[Mapping]]: [{{val| 2 0 1 2 6 9 0 1 7 }}, {{val| 0 1 9 -2 5 -6 12 11 3 }}, {{val| 0 0 -10 4 -6 7 -12 -11 -3 }}] | ||
{{Val list|legend=1| 44, 50, 94, 144gh, 176g, 220g, 226, 270, 320i, 364i, 414hi }} | {{Val list|legend=1| 44, 50, 94, 144gh, 176g, 220g, 226, 270, 320i, 364i, 414hi }} | ||