Gamelismic clan: Difference between revisions
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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]], [[Diaschismic family|echidnic]], [[ | 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. | ||
== Subgroup extensions == | == Subgroup extensions == | ||
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== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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=== Miraculous === | === Miraculous === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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=== Benediction === | === Benediction === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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==== 17-limit ==== | ==== 17-limit ==== | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
| Line 121: | Line 125: | ||
=== Manna === | === Manna === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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=== Semimiracle === | === Semimiracle === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 147: | Line 153: | ||
==== 17-limit ==== | ==== 17-limit ==== | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
| Line 160: | Line 167: | ||
=== Hemisecordite === | === Hemisecordite === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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==== 17-limit ==== | ==== 17-limit ==== | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
| Line 186: | Line 195: | ||
=== Phicordial === | === Phicordial === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 199: | Line 209: | ||
==== 17-limit ==== | ==== 17-limit ==== | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
| Line 212: | Line 223: | ||
== Revelation == | == Revelation == | ||
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 | Subgroup: 2.3.5.7.11.13 | ||
| Line 238: | Line 251: | ||
== Hemimiracle == | == Hemimiracle == | ||
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 | Subgroup: 2.3.5.7.11.13 | ||
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== Oracle == | == Oracle == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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== 11-limit == | == 11-limit == | ||
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 | Subgroup: 2.3.5.7.11.13 | ||
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Scales: [[rodan26opt]], [[rodan31opt]], [[rodan41opt]] | Scales: [[rodan26opt]], [[rodan31opt]], [[rodan41opt]] | ||
=== 17-limit === | ==== 17-limit ==== | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
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=== Aerodactyl === | === Aerodactyl === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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== Aerodino == | == Aerodino == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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=== 13-limit === | === 13-limit === | ||
Comma list: 91/90, 176/175, 245/243, 847/845 | Comma list: 91/90, 176/175, 245/243, 847/845 | ||
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== Varan == | == Varan == | ||
Comma list: 100/99, 245/243, 1029/1024 | Comma list: 100/99, 245/243, 1029/1024 | ||
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=== 13-limit === | === 13-limit === | ||
Comma list: 100/99, 105/104, 245/243, 352/351 | Comma list: 100/99, 105/104, 245/243, 352/351 | ||
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{{main| Valentine }} | {{main| Valentine }} | ||
{{see also| Starling temperaments #Valentine }} | {{see also| Starling temperaments #Valentine }} | ||
== 5-limit == | |||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
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== 7-limit == | == 7-limit == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 463: | Line 490: | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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= Unidec = | = Unidec = | ||
{{main| Unidec }} | {{main| Unidec }} | ||
== 5-limit == | |||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
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== 7-limit == | == 7-limit == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 531: | Line 562: | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 551: | Line 583: | ||
=== Ekadash === | === Ekadash === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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=== Hendec === | === Hendec === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 585: | Line 619: | ||
==== 17-limit ==== | ==== 17-limit ==== | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
| Line 626: | Line 661: | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 644: | Line 680: | ||
== 13-limit == | == 13-limit == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 657: | Line 694: | ||
= Hemiseven = | = Hemiseven = | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 672: | Line 710: | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 685: | Line 724: | ||
== 13-limit == | == 13-limit == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 696: | Line 736: | ||
== 17-limit == | == 17-limit == | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
| Line 732: | Line 773: | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 752: | Line 794: | ||
== 13-limit == | == 13-limit == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 765: | Line 808: | ||
== 17-limit == | == 17-limit == | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
| Line 793: | Line 837: | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 806: | Line 851: | ||
== 13-limit == | == 13-limit == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 822: | Line 868: | ||
== 5-limit (laconic) == | == 5-limit (laconic) == | ||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
| Line 837: | Line 884: | ||
== 7-limit == | == 7-limit == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 852: | Line 900: | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 867: | Line 916: | ||
=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 880: | Line 930: | ||
== Spartan == | == Spartan == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 893: | Line 944: | ||
=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 929: | Line 981: | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 942: | Line 995: | ||
== 13-limit == | == 13-limit == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 958: | Line 1,012: | ||
== 5-limit (university) == | == 5-limit (university) == | ||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
| Line 971: | Line 1,026: | ||
== 7-limit == | == 7-limit == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 999: | Line 1,055: | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,012: | Line 1,069: | ||
= Necromanteion = | = Necromanteion = | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 1,025: | Line 1,083: | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,038: | Line 1,097: | ||
== 13-limit == | == 13-limit == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 1,051: | Line 1,111: | ||
= Widefourth = | = Widefourth = | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 1,066: | Line 1,127: | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,079: | Line 1,141: | ||
== 13-limit == | == 13-limit == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 1,092: | Line 1,155: | ||
= Tritriple = | = Tritriple = | ||
== 5-limit == | |||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
| Line 1,105: | Line 1,170: | ||
== 7-limit == | == 7-limit == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 1,118: | Line 1,184: | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,133: | Line 1,200: | ||
= Restles = | = Restles = | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 1,146: | Line 1,214: | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,159: | Line 1,228: | ||
== 13-limit == | == 13-limit == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||