Gamelismic clan: Difference between revisions
→Gorgo: redirect lemma bold |
+guiron, moved from schismatic family since it's a strong ext for slendric and the map for 7 is much simpler |
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To the gamelisma itself we need to add the comma which appears next on the modified [[Normal lists #Normal interval list|normal comma list]], which is often a 5-limit comma. The second comma on the list for mothra is 81/80, for rodan 245/243, for guiron 32805/32768, for gorgo 36/35, and for gidorah 256/245. These all use 8/7 as a generator, though in the case of gidorah that's the same as 6/5. Miracle adds 33075/32768 and uses the secor, half an 8/7, as generator. Lemba adds 525/512 to the list, and has a half-octave period. Valentine adds 6144/6125 with a generator of 21/20 and superkleismic adds 875/864 with a generator of 6/5. Unidec adds 4375/4374, and has a generator of 10/9 with a half-octave period. Hemithirds adds 65625/65536 with a generator half of a major third. Finally, tritikleismic adds 15625/15536 and has a generator of 6/5 with a 1/3 octave period. | To the gamelisma itself we need to add the comma which appears next on the modified [[Normal lists #Normal interval list|normal comma list]], which is often a 5-limit comma. The second comma on the list for mothra is 81/80, for rodan 245/243, for guiron 32805/32768, for gorgo 36/35, and for gidorah 256/245. These all use 8/7 as a generator, though in the case of gidorah that's the same as 6/5. Miracle adds 33075/32768 and uses the secor, half an 8/7, as generator. Lemba adds 525/512 to the list, and has a half-octave period. Valentine adds 6144/6125 with a generator of 21/20 and superkleismic adds 875/864 with a generator of 6/5. Unidec adds 4375/4374, and has a generator of 10/9 with a half-octave period. Hemithirds adds 65625/65536 with a generator half of a major third. Finally, tritikleismic adds 15625/15536 and has a generator of 6/5 with a 1/3 octave period. | ||
Discussed elsewhere are [[Archytas clan #Blacksmith|blacksmith]], [[Meantone family #Mothra|mothra]], [[Diaschismic family #Echidnic|echidnic]], [[Magic family #Trismegistus|trismegistus]], [[Hemimean clan #Hemithirds|hemithirds | Discussed elsewhere are [[Archytas clan #Blacksmith|blacksmith]], [[Meantone family #Mothra|mothra]], [[Diaschismic family #Echidnic|echidnic]], [[Magic family #Trismegistus|trismegistus]], [[Hemimean clan #Hemithirds|hemithirds]], [[Semicomma family #Triwell|triwell]] and [[Sensipent family #Heinz|heinz]]. The rest are considered below. | ||
== Subgroup extensions == | == Subgroup extensions == | ||
| Line 444: | Line 444: | ||
Badness: 0.0323 | Badness: 0.0323 | ||
= Guiron = | |||
{{see also| Schismatic family }} | |||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 1029/1024, 10976/10935 | |||
[[Mapping]]: [{{val| 1 1 7 3 }}, {{val| 0 3 -24 -1 }}] | |||
Mapping generators: ~2, ~8/7 | |||
[[POTE generator]]: ~8/7 = 233.930 | |||
{{Multival|legend=1| 3 -24 -1 -45 -10 65 }} | |||
[[Minimax tuning]]: | |||
* 7- and [[9-odd-limit]] | |||
: [{{monzo| 1 0 0 0 }}, {{monzo| 15/8 0 -1/8 0 }}, {{monzo| 0 0 1 0 }}, {{monzo| 65/24 0 1/24 0 }}] | |||
: [[Eigenmonzo]]s: 2, 5/4 | |||
{{Val list|legend=1| 36, 41, 77, 118, 277d }} | |||
[[Badness]]: 0.0475 | |||
== 11-limit == | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 385/384, 441/440, 10976/10935 | |||
Mapping: [{{val| 1 1 7 3 -2 }}, {{val| 0 3 -24 -1 28 }}] | |||
Mapping generators: ~2, ~8/7 | |||
POTE generator: ~8/7 = 233.931 | |||
Minimax tuning: | |||
* 11-odd-limit | |||
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 15/8 0 -1/8 0 0 }}, {{monzo| 0 0 1 0 0 }}, {{monzo| 65/24 0 1/24 0 0 }}, {{monzo| 37/6 0 -7/6 0 0 }}] | |||
: Eigenmonzos: 2, 5/4 | |||
{{Val list|legend=1| 36e, 41, 77, 118, 159, 277d }} | |||
Badness: 0.0266 | |||
== 13-limit == | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 196/195, 352/351, 385/384, 729/728 | |||
Mapping generators: ~2, ~8/7 | |||
Mapping: [{{val| 1 1 7 3 -2 0 }}, {{val| 0 3 -24 -1 28 19 }}] | |||
POTE generator: ~8/7 = 233.890 | |||
{{Val list|legend=1| 36e, 41, 77, 118 }} | |||
Badness: 0.0284 | |||
= Valentine = | = Valentine = | ||