Gamelismic clan: Difference between revisions

Undo the formatting; +link to trismegistus
Tag: Undo
-hemithirds (moved to hemimean clan for sharing generator)
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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]], [[Schismatic family #Guiron|guiron]], [[Semicomma family #Triwell|triwell]] and [[Sensipent family #Heinz|heinz]]. The rest are considered below.
Discussed elsewhere are [[Archytas clan #Blacksmith|blacksmith]], [[Meantone family #Mothra|mothra]], [[Diaschismic family #Echidnic|echidnic]], [[Magic family #Trismegistus|trismegistus]], [[Hemimean clan #Hemithirds|hemithirds]], [[Schismatic family #Guiron|guiron]], [[Semicomma family #Triwell|triwell]] and [[Sensipent family #Heinz|heinz]]. The rest are considered below.


== Subgroup extensions ==
== Subgroup extensions ==
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Scales: [[unidec26]]
Scales: [[unidec26]]
= Hemithirds =
{{main| Hemithirds }}
{{see also| Luna family #Hemithirds }}
Subgroup: 2.3.5.7
[[Comma list]]: 1029/1024, 3136/3125
[[Mapping]]: [{{val| 1 4 2 2 }}, {{val| 0 -15 2 5 }}]
{{Multival|legend=1| 15 -2 -5 -38 -50 -6 }}
[[POTE generator]]: ~28/25 = 193.244
[[Minimax tuning]]:
* [[7-odd-limit]]
: [{{monzo| 1 0 0 0 }}, {{monzo| 5/2 3/4 0 -3/4 }}, {{monzo| 11/5 -1/10 0 1/10 }}, {{monzo| 5/2 -1/4 0 1/4 }}]
: [[Eigenmonzo]]s: 2, 7/6
* [[9-odd-limit]]
: [{{monzo| 1 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 }}, {{monzo| 82/35 -4/35 0 2/35 }}, {{monzo| 20/7 -2/7 0 1/7 }}]
: [[Eigenmonzo]]s: 2, 7/6
{{Val list|legend=1| 31, 87, 118 }}
Badness: 0.0443
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 385/384, 441/440, 3136/3125
Mapping: [{{val| 1 4 2 2 7 }}, {{val| 0 -15 2 5 -22 }}]
POTE generator: ~28/25 = 193.227
Minimax tuning:
* 11-odd-limit
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 11/9 0 0 -5/9 5/9 }}, {{monzo| 64/27 0 0 2/27 -2/27 }}, {{monzo| 79/27 0 0 5/27 -5/27 }}, {{monzo| 79/27 0 0 -22/27 22/27 }}]
: Eigenmonzos: 2, 11/7
{{Val list|legend=1| 31, 87, 118 }}
Badness: 0.0190
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 352/351, 385/384, 625/624
Mapping: [{{val| 1 4 2 2 7 0 }}, {{val| 0 -15 2 5 -22 23 }}]
POTE generator: ~28/25 = 193.166
{{Val list|legend=1| 31, 56, 87, 118, 205d }}
Badness: 0.0217


= Hemiseven =
= Hemiseven =