Kalismic temperaments: Difference between revisions

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The initial gens were correct. VIxen (talk)
Tag: Undo
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Hnoss: +17-23-limit
Line 124: Line 124:


[[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 }}]
Mapping generators: ~99/70, ~3, ~144/77


{{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 weaker 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.
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 }}]
Mapping generators: ~99/70, ~3, ~154/65


{{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 }}]
Mapping generators: ~99/70, ~3, ~45/19


{{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 }}