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]], [[ | Discussed elsewhere are [[Archytas clan #Blacksmith|blacksmith]], [[Diaschismic family|echidnic]], [[Meantone family #Mothra|mothra]], [[Schismatic family #Guiron|guiron]], [[Semicomma family|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 | ||
| Line 83: | Line 82: | ||
=== Miraculous === | === Miraculous === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 99: | Line 97: | ||
=== Benediction === | === Benediction === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 113: | Line 110: | ||
==== 17-limit ==== | ==== 17-limit ==== | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
| Line 125: | Line 121: | ||
=== 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 153: | Line 147: | ||
==== 17-limit ==== | ==== 17-limit ==== | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
| Line 167: | Line 160: | ||
=== Hemisecordite === | === Hemisecordite === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 181: | Line 173: | ||
==== 17-limit ==== | ==== 17-limit ==== | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
| Line 195: | Line 186: | ||
=== Phicordial === | === Phicordial === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 209: | Line 199: | ||
==== 17-limit ==== | ==== 17-limit ==== | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
| Line 223: | Line 212: | ||
== Revelation == | == Revelation == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 237: | Line 225: | ||
=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 251: | Line 238: | ||
== Hemimiracle == | == Hemimiracle == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 265: | Line 251: | ||
=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 279: | Line 264: | ||
== Oracle == | == Oracle == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 317: | Line 301: | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 340: | Line 323: | ||
=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 362: | Line 344: | ||
Scales: [[rodan26opt]], [[rodan31opt]], [[rodan41opt]] | Scales: [[rodan26opt]], [[rodan31opt]], [[rodan41opt]] | ||
=== 17-limit === | |||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
| Line 382: | Line 363: | ||
=== 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 | ||
| Line 434: | Line 411: | ||
=== 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 }} | ||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
| Line 464: | Line 438: | ||
== 7-limit == | == 7-limit == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 490: | Line 463: | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 514: | Line 486: | ||
= Unidec = | = Unidec = | ||
{{main| Unidec }} | {{main| Unidec }} | ||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
| Line 534: | Line 504: | ||
== 7-limit == | == 7-limit == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 562: | Line 531: | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 583: | Line 551: | ||
=== Ekadash === | === Ekadash === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 601: | Line 568: | ||
=== Hendec === | === Hendec === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 619: | Line 585: | ||
==== 17-limit ==== | ==== 17-limit ==== | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
| Line 661: | Line 626: | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 680: | Line 644: | ||
== 13-limit == | == 13-limit == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 694: | Line 657: | ||
= Hemiseven = | = Hemiseven = | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 710: | Line 672: | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 724: | Line 685: | ||
== 13-limit == | == 13-limit == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 736: | Line 696: | ||
== 17-limit == | == 17-limit == | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
| Line 773: | Line 732: | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 794: | Line 752: | ||
== 13-limit == | == 13-limit == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 808: | Line 765: | ||
== 17-limit == | == 17-limit == | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
| Line 837: | Line 793: | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 851: | Line 806: | ||
== 13-limit == | == 13-limit == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 868: | Line 822: | ||
== 5-limit (laconic) == | == 5-limit (laconic) == | ||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
| Line 884: | Line 837: | ||
== 7-limit == | == 7-limit == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 900: | Line 852: | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 916: | Line 867: | ||
=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 930: | Line 880: | ||
== Spartan == | == Spartan == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 944: | Line 893: | ||
=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 981: | Line 929: | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 995: | Line 942: | ||
== 13-limit == | == 13-limit == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 1,012: | Line 958: | ||
== 5-limit (university) == | == 5-limit (university) == | ||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
| Line 1,026: | Line 971: | ||
== 7-limit == | == 7-limit == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 1,055: | Line 999: | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,069: | Line 1,012: | ||
= Necromanteion = | = Necromanteion = | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 1,083: | Line 1,025: | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,097: | Line 1,038: | ||
== 13-limit == | == 13-limit == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 1,111: | Line 1,051: | ||
= Widefourth = | = Widefourth = | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 1,127: | Line 1,066: | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,141: | Line 1,079: | ||
== 13-limit == | == 13-limit == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 1,155: | Line 1,092: | ||
= Tritriple = | = Tritriple = | ||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
| Line 1,170: | Line 1,105: | ||
== 7-limit == | == 7-limit == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 1,184: | Line 1,118: | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,200: | Line 1,133: | ||
= Restles = | = Restles = | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 1,214: | Line 1,146: | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,228: | Line 1,159: | ||
== 13-limit == | == 13-limit == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||