Kalismic temperaments: Difference between revisions
+rishi +gersemi |
+hnoss (gersemi is weaker in 13-limit, so different names were needed) |
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* ''[[Semicanou]]'', {9801/9800, 14641/14580} → [[Canou family #Semicanou|Canou family]] | * ''[[Semicanou]]'', {9801/9800, 14641/14580} → [[Canou family #Semicanou|Canou family]] | ||
Considered below are odin, loki, van gogh, rishi, and gersemi, but we can begin by looking at the rank-4 temperament. | Considered below are odin, loki, van gogh, rishi, hnoss, and gersemi, but we can begin by looking at the rank-4 temperament. | ||
== Kalismic == | == Kalismic == | ||
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[[Badness]]: 0.505 × 10<sup>-3</sup> | [[Badness]]: 0.505 × 10<sup>-3</sup> | ||
== | == Hnoss == | ||
To the wizma [-6 -8 2 5⟩ = 420175/419904, the kalisma is a natural complement, as their product is the [[tinge]]. | To the wizma [-6 -8 2 5⟩ = 420175/419904, the kalisma is a natural complement, as their product is the [[tinge]]. | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | |||
[[Comma list]]: 1716/1715, 2080/2079, 17303/17280 | |||
[[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 }} | |||
[[Badness]]: 0.867 × 10<sup>-3</sup> | |||
=== Gersemi === | |||
18/7 is a possible equave. Fokker blocks of 128 notes are available for it, 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. | |||
==== 13-limit ==== | |||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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[[Badness]]: 1.06 × 10<sup>-3</sup> | [[Badness]]: 1.06 × 10<sup>-3</sup> | ||
=== 17-limit === | ==== 17-limit ==== | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
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[[Badness]]: 1.46 × 10<sup>-3</sup> | [[Badness]]: 1.46 × 10<sup>-3</sup> | ||
=== 19-limit === | ==== 19-limit ==== | ||
Subgroup: 2.3.5.7.11.13.19 | Subgroup: 2.3.5.7.11.13.19 | ||
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[[Badness]]: 1.11 × 10<sup>-3</sup> | [[Badness]]: 1.11 × 10<sup>-3</sup> | ||
=== 23-limit === | ==== 23-limit ==== | ||
Subgroup: 2.3.5.7.11.13.19.23 | Subgroup: 2.3.5.7.11.13.19.23 | ||