Gamelismic clan: Difference between revisions

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The 2.3.7 [[Just_intonation_subgroups|subgroup]] comma for the '''gamelismic clan''' is the gamelisma, [[1029/1024]], with monzo {{monzo|-10 1 0 3}}. For any member of the clan, for the rank three [[Gamelismic family #Gamelan|gamelan temperament]] itself, and for the rank two 2.3.7 temperament [[slendric]], this means three [[8/7]] intervals give a fifth, [[3/2]]. In fact, we find that 3/2 = (8/7)<sup>3</sup> × 1029/1024. From this it follows that gamelismic temperaments tend to flatten both the fifth and the 7/4, or if they do not, the other of the pair must be flattened even more. [[36edo]] is a good tuning for gamelismic itself, though if the full 7-limit is desired, [[72edo]], [[77edo]] or [[118edo]] might be preferred.
The 2.3.7 [[Just_intonation_subgroups|subgroup]] comma for the '''gamelismic clan''' is the gamelisma, [[1029/1024]], with monzo {{monzo|-10 1 0 3}}. For any member of the clan, for the rank three [[Gamelismic family #Gamelan|gamelan temperament]] itself, and for the rank two 2.3.7 temperament [[slendric]], this means three [[8/7]] intervals give a fifth, [[3/2]]. In fact, we find that 3/2 = (8/7)<sup>3</sup> × 1029/1024. From this it follows that gamelismic temperaments tend to flatten both the fifth and the 7/4, or if they do not, the other of the pair must be flattened even more. [[36edo|36EDO]] is a good tuning for gamelismic itself, though if the full 7-limit is desired, [[72edo|72EDO]], [[77edo|77EDO]] or [[118edo|118EDO]] might be preferred.


== Slendric ==
== Slendric ==
{{main| Slendric }}
{{main| Slendric }}


Line 22: Line 22:
Scales: [[slendric5]], [[slendric6]], [[slendric11]], [[slendric16]]
Scales: [[slendric5]], [[slendric6]], [[slendric11]], [[slendric16]]


=== Full seven limit extensions ===
=== Full seven limit extensions ===
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 [[blacksmith]], [[mothra]], [[echidnic]], [[trismegistus]], [[hemithirds]], [[gamity]], [[triwell]] and [[heinz]]. The rest are considered below.
Discussed elsewhere are [[blacksmith]], [[mothra]], [[echidnic]], [[trismegistus]], [[hemithirds]], [[gamity]], [[triwell]], [[decades]] and [[heinz]]. The rest are considered below.


=== Subgroup extensions ===
=== Subgroup extensions ===
No-five subgroup extensions of slendric include [[Chromatic pairs #Radon|radon]], the 2.3.7.11 extension that may be viewed as no-five rodan, and baladic, the 2.3.7.13.17 extension, considered below.
No-five subgroup extensions of slendric include [[Chromatic pairs #Radon|radon]], the 2.3.7.11 extension that may be viewed as no-five rodan, and baladic, the 2.3.7.13.17 extension, considered below.


== Miracle ==
== Miracle ==
{{main| Miracle }}
{{main| Miracle }}


Line 61: Line 61:
Scales: [[Miracle 10]], [[Blackjack]]
Scales: [[Miracle 10]], [[Blackjack]]


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 83: Line 83:
Scales: [[Miracle 10]], [[Blackjack]]
Scales: [[Miracle 10]], [[Blackjack]]


==== Miraculous ====
==== Miraculous ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 98: Line 98:
Scales: [[Miracle 10]], [[Blackjack]]
Scales: [[Miracle 10]], [[Blackjack]]


==== Benediction ====
==== Benediction ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 111: Line 111:
Badness: 0.015715
Badness: 0.015715


===== 17-limit =====
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Line 124: Line 124:
Badness: 0.012537
Badness: 0.012537


==== Manna ====
==== Manna ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 137: Line 137:
Badness: 0.017012
Badness: 0.017012


==== Semimiracle ====
==== Semimiracle ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 150: Line 150:
Badness: 0.024622
Badness: 0.024622


===== 17-limit =====
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Line 163: Line 163:
Badness: 0.016130
Badness: 0.016130


==== Hemisecordite ====
==== Hemisecordite ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 176: Line 176:
Badness: 0.025589
Badness: 0.025589


===== 17-limit =====
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Line 189: Line 189:
Badness: 0.022535
Badness: 0.022535


==== Phicordial ====
==== Phicordial ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 202: Line 202:
Badness: 0.033198
Badness: 0.033198


===== 17-limit =====
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Line 215: Line 215:
Badness: 0.024705
Badness: 0.024705


=== Revelation ===
=== Revelation ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 228: Line 228:
Badness: 0.032946
Badness: 0.032946


==== 13-limit ====
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 241: Line 241:
Badness: 0.029452
Badness: 0.029452


=== Hemimiracle ===
=== Hemimiracle ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 254: Line 254:
Badness: 0.059232
Badness: 0.059232


==== 13-limit ====
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 267: Line 267:
Badness: 0.043151
Badness: 0.043151


=== Oracle ===
=== Oracle ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 280: Line 280:
Badness: 0.042687
Badness: 0.042687


== Rodan ==
== Rodan ==
{{main| Rodan }}
{{main| Rodan }}


Line 306: Line 306:
Scales: [[Rodan26opt]], [[Rodan31opt]], [[Rodan41opt]]
Scales: [[Rodan26opt]], [[Rodan31opt]], [[Rodan41opt]]


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 328: Line 328:
Scales: [[Rodan26opt]], [[Rodan31opt]], [[Rodan41opt]]
Scales: [[Rodan26opt]], [[Rodan31opt]], [[Rodan41opt]]


==== 13-limit ====
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 350: Line 350:
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


Line 368: Line 368:
Scales: [[Rodan26opt]], [[Rodan31opt]], [[Rodan41opt]]
Scales: [[Rodan26opt]], [[Rodan31opt]], [[Rodan41opt]]


==== Aerodactyl ====
==== Aerodactyl ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 381: Line 381:
Badness: 0.033986
Badness: 0.033986


=== Aerodino ===
=== Aerodino ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 394: Line 394:
Badness: 0.054294
Badness: 0.054294


==== 13-limit ====
==== 13-limit ====
Comma list: 91/90, 176/175, 245/243, 847/845
Comma list: 91/90, 176/175, 245/243, 847/845


Line 405: Line 405:
Badness: 0.035836
Badness: 0.035836


=== Varan ===
=== Varan ===
Comma list: 100/99, 245/243, 1029/1024
Comma list: 100/99, 245/243, 1029/1024


Line 416: Line 416:
Badness: 0.044937
Badness: 0.044937


==== 13-limit ====
==== 13-limit ====
Comma list: 100/99, 105/104, 245/243, 352/351
Comma list: 100/99, 105/104, 245/243, 352/351


Line 427: Line 427:
Badness: 0.032284
Badness: 0.032284


== Guiron ==
== Guiron ==
{{see also| Schismatic family }}
{{see also| Schismatic family }}


Line 451: Line 451:
[[Badness]]: 0.047544
[[Badness]]: 0.047544


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 471: Line 471:
Badness: 0.026648
Badness: 0.026648


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 486: Line 486:
Badness: 0.028444
Badness: 0.028444


== Valentine ==
== Valentine ==
{{main| Valentine }}
{{main| Valentine }}
{{see also| Starling temperaments #Valentine }}
{{see also| Starling temperaments #Valentine }}
Line 502: Line 502:
[[Badness]]: 0.122765
[[Badness]]: 0.122765


=== 7-limit ===
=== 7-limit ===
 
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 530: Line 529:
[[Badness]]: 0.031056
[[Badness]]: 0.031056


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 552: Line 551:
Badness: 0.016687
Badness: 0.016687


=== Dwynwen ===
=== Dwynwen ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 565: Line 564:
Badness: 0.023461
Badness: 0.023461


=== Lupercalia ===
=== Lupercalia ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 578: Line 577:
Badness: 0.021328
Badness: 0.021328


=== Valentino ===
=== Valentino ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 591: Line 590:
Badness: 0.020665
Badness: 0.020665


=== Semivalentine ===
=== Semivalentine ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 604: Line 603:
Badness: 0.032749
Badness: 0.032749


== Unidec ==
== Unidec ==
{{main| Unidec }}
{{main| Unidec }}


Line 619: Line 618:
{{Val list|legend=1| 26, 46, 72, 118, 2524, 2642, 2760, 2878b, …, 5002bc }}
{{Val list|legend=1| 26, 46, 72, 118, 2524, 2642, 2760, 2878b, …, 5002bc }}


Badness: 0.082423
[[Badness]]: 0.082423


Scales: [[Unidec26]]
Scales: [[Unidec26]]


=== 7-limit ===
=== 7-limit ===
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 650: Line 649:
Scales: [[Unidec26]]
Scales: [[Unidec26]]


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 670: Line 669:
Scales: [[Unidec26]]
Scales: [[Unidec26]]


=== Ekadash ===
=== Ekadash ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 687: Line 686:
Scales: [[Unidec26]]
Scales: [[Unidec26]]


=== Hendec ===
=== Hendec ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 704: Line 703:
Scales: [[Unidec26]]
Scales: [[Unidec26]]


==== 17-limit ====
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Line 721: Line 720:
Scales: [[Unidec26]]
Scales: [[Unidec26]]


== Hemiseven ==
== Hemiseven ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 736: Line 735:
[[Badness]]: 0.056557
[[Badness]]: 0.056557


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 749: Line 748:
Badness: 0.028467
Badness: 0.028467


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 762: Line 761:
Badness: 0.021900
Badness: 0.021900


=== 17-limit ===
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Line 775: Line 774:
Badness: 0.015701
Badness: 0.015701


== Tritikleismic ==
== Tritikleismic ==
{{see also| Kleismic family #Tritikleismic }}
{{see also| Kleismic family #Tritikleismic }}


Line 802: Line 801:
[[Badness]]: 0.056337
[[Badness]]: 0.056337


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 822: Line 821:
Badness: 0.019333
Badness: 0.019333


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 837: Line 836:
Badness: 0.015652
Badness: 0.015652


=== 17-limit ===
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Line 852: Line 851:
Badness: 0.013551
Badness: 0.013551


== Superkleismic ==
== Superkleismic ==
{{see also| Shibboleth family #Superkleismic }}
{{see also| Shibboleth family #Superkleismic }}


Line 869: Line 868:
[[Badness]]: 0.047932
[[Badness]]: 0.047932


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 882: Line 881:
Badness: 0.025659
Badness: 0.025659


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 895: Line 894:
Badness: 0.021478
Badness: 0.021478


== Gorgo ==
== Gorgo ==
In the 5-limit, gorgo tempers out the '''laconic comma''', [[2187/2000]], which is the difference between three [[10/9]]'s and a [[3/2]]. Although a higher-error temperament, it does pop up enough in the low-numbered EDOs to be useful, most notably in [[16edo|16EDO]] and [[21edo|21EDO]]. The only 7-limit extension that makes any sense to use is to add the gamelisma to the comma list.
In the 5-limit, gorgo tempers out the '''laconic comma''', [[2187/2000]], which is the difference between three [[10/9]]'s and a [[3/2]]. Although a higher-error temperament, it does pop up enough in the low-numbered EDOs to be useful, most notably in [[16edo|16EDO]] and [[21edo|21EDO]]. The only 7-limit extension that makes any sense to use is to add the gamelisma to the comma list.


=== 5-limit (laconic) ===
=== 5-limit (laconic) ===
Subgroup: 2.3.5
Subgroup: 2.3.5


Line 913: Line 912:
[[Badness]]: 0.161799
[[Badness]]: 0.161799


=== 7-limit ===
=== 7-limit ===
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 928: Line 927:
[[Badness]]: 0.060663
[[Badness]]: 0.060663


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 941: Line 940:
Badness: 0.049500
Badness: 0.049500


==== 13-limit ====
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 954: Line 953:
Badness: 0.032664
Badness: 0.032664


=== Spartan ===
=== Spartan ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 967: Line 966:
Badness: 0.062683
Badness: 0.062683


==== 13-limit ====
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 980: Line 979:
Badness: 0.047071
Badness: 0.047071


=== Music ===
=== Music ===
* [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/gorgo-example.mp3 Gorgo Example] by [[Herman Miller]]
* [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/gorgo-example.mp3 Gorgo Example] by [[Herman Miller]]


== Lemba ==
== Lemba ==
{{main| Lemba }}
{{main| Lemba }}
{{see also| Jubilismic clan #Lemba }}
{{see also| Jubilismic clan #Lemba }}
Line 1,003: Line 1,002:
[[Badness]]: 0.062208
[[Badness]]: 0.062208


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 1,016: Line 1,015:
Badness: 0.041563
Badness: 0.041563


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 1,029: Line 1,028:
Badness: 0.025477
Badness: 0.025477


== Gidorah ==
== Gidorah ==
{{main| University temperament }}
{{main| University temperament }}


=== 5-limit (university) ===
=== 5-limit (university) ===
Subgroup: 2.3.5
Subgroup: 2.3.5


Line 1,045: Line 1,044:
[[Badness]]: 0.101806
[[Badness]]: 0.101806


=== 7-limit ===
=== 7-limit ===
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 1,060: Line 1,059:
[[Badness]]: 0.062262
[[Badness]]: 0.062262


== Clyndro ==
== Clyndro ==
{{see also| Pelogic family }}
{{see also| Pelogic family }}


Line 1,077: Line 1,076:
[[Badness]]: 0.159179
[[Badness]]: 0.159179


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 1,090: Line 1,089:
Badness: 0.069703
Badness: 0.069703


== Necromanteion ==
== Necromanteion ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 1,105: Line 1,104:
[[Badness]]: 0.117680
[[Badness]]: 0.117680


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 1,118: Line 1,117:
Badness: 0.053459
Badness: 0.053459


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 1,131: Line 1,130:
Badness: 0.047015
Badness: 0.047015


== Widefourth ==
== Widefourth ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 1,146: Line 1,145:
[[Badness]]: 0.154117
[[Badness]]: 0.154117


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 1,159: Line 1,158:
Badness: 0.040785
Badness: 0.040785


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 1,172: Line 1,171:
Badness: 0.021636
Badness: 0.021636


== Tritriple ==
== Tritriple ==
Subgroup: 2.3.5
Subgroup: 2.3.5


Line 1,185: Line 1,184:
[[Badness]]: 0.283570
[[Badness]]: 0.283570


=== 7-limit ===
=== 7-limit ===
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 1,200: Line 1,199:
[[Badness]]: 0.118640
[[Badness]]: 0.118640


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 1,213: Line 1,212:
Badness: 0.035350
Badness: 0.035350


== Restles ==
== Restles ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 1,228: Line 1,227:
[[Badness]]: 0.108011
[[Badness]]: 0.108011


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 1,241: Line 1,240:
Badness: 0.054655
Badness: 0.054655


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 1,254: Line 1,253:
Badness: 0.028187
Badness: 0.028187


== Quartemka ==
== Quartemka ==
Subgroup: 2.3.5
Subgroup: 2.3.5


Line 1,267: Line 1,266:
[[Badness]]: 1.381216
[[Badness]]: 1.381216


=== 7-limit ===
=== 7-limit ===
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 1,282: Line 1,281:
[[Badness]]: 0.152287
[[Badness]]: 0.152287


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 1,295: Line 1,294:
Badness: 0.057307
Badness: 0.057307


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 1,308: Line 1,307:
Badness: 0.028393
Badness: 0.028393


== Baladic ==
== Baladic ==
{{See also|Subgroup temperaments #No-fives subgroup}}
{{See also|Subgroup temperaments #No-fives subgroup}}


Baladic is a 2.3.7.13.17 subgroup temperament that attempts to approximate the Maqam Sikah Baladi scale. 36edo is an excellent baladic tuning.
Baladic is a 2.3.7.13.17 subgroup temperament that attempts to approximate the Maqam Sikah Baladi scale. 36EDO is an excellent baladic tuning.


[[Comma list]]: 169/168, 273/272, 289/288
[[Comma list]]: 169/168, 273/272, 289/288

Revision as of 12:37, 2 June 2021

The 2.3.7 subgroup comma for the gamelismic clan is the gamelisma, 1029/1024, with monzo [-10 1 0 3⟩. For any member of the clan, for the rank three gamelan temperament itself, and for the rank two 2.3.7 temperament slendric, this means three 8/7 intervals give a fifth, 3/2. In fact, we find that 3/2 = (8/7)3 × 1029/1024. From this it follows that gamelismic temperaments tend to flatten both the fifth and the 7/4, or if they do not, the other of the pair must be flattened even more. 36EDO is a good tuning for gamelismic itself, though if the full 7-limit is desired, 72EDO, 77EDO or 118EDO might be preferred.

Slendric

Main article: Slendric

Subgroup: 2.3.7

Comma list: 1029/1024

Sval mapping: [⟨1 1 3], ⟨0 3 -1]]

Mapping generators: ~2, ~8/7

Gencom mapping: [⟨1 1 0 3], ⟨0 3 0 -1]]

Gencom: [2 8/7; 1029/1024]

POTE generator: ~8/7 = 233.688

Template:Val list

Scales: slendric5, slendric6, slendric11, slendric16

Full seven limit extensions

To the gamelisma itself we need to add the comma which appears next on the modified 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 blacksmith, mothra, echidnic, trismegistus, hemithirds, gamity, triwell, decades and heinz. The rest are considered below.

Subgroup extensions

No-five subgroup extensions of slendric include radon, the 2.3.7.11 extension that may be viewed as no-five rodan, and baladic, the 2.3.7.13.17 extension, considered below.

Miracle

Main article: Miracle

Subgroup: 2.3.5.7

Comma list: 225/224, 1029/1024

Mapping: [⟨1 1 3 3], ⟨0 6 -7 -2]]

Mapping generator: 2, ~15/14

Wedgie: ⟨⟨ 6 -7 -2 -25 -20 15 ]]

POTE generator: ~15/14 = 116.675

Minimax tuning:

[[1 0 0 0⟩, [25/13 6/13 -6/13 0⟩, [25/13 -7/13 7/13 0⟩, [35/13 -2/13 2/13 0⟩]
Eigenmonzos: 2, 6/5
[[1 0 0 0⟩, [25/19 12/19 -6/19 0⟩, [50/19 -14/19 7/19 0⟩, [55/19 -4/19 2/19 0⟩]
Eigenmonzos: 2, 10/9

Algebraic generator: Secor59, positive root of 15x6 - 8x4 - 12

Template:Val list

Badness: 0.016742

Scales: Miracle 10, Blackjack

11-limit

Subgroup: 2.3.5.7.11

Comma list: 225/224, 243/242, 385/384

Mapping: [⟨1 1 3 3 2], ⟨0 6 -7 -2 15]]

POTE generator: ~15/14 = 116.633

Minimax tuning:

  • 11-odd-limit
[[1 0 0 0 0⟩, [25/19 12/19 -6/19 0 0⟩, [50/19 -14/19 7/19 0 0⟩, [55/19 -4/19 2/19 0 0⟩, [53/19 30/19 -15/19 0 0⟩]
Eigenmonzos: 2, 10/9

Algebraic generator: Secor59

Vals: Template:Val list

Badness: 0.010684

Scales: Miracle 10, Blackjack

Miraculous

Subgroup: 2.3.5.7.11.13

Comma list: 105/104, 144/143, 196/195, 243/242

Mapping: [⟨1 1 3 3 2 4], ⟨0 6 -7 -2 15 -3]]

POTE generator: ~15/14 = 116.747

Vals: Template:Val list

Badness: 0.018669

Scales: Miracle 10, Blackjack

Benediction

Subgroup: 2.3.5.7.11.13

Comma list: 225/224, 243/242, 351/350, 385/384

Mapping: [⟨1 1 3 3 2 7], ⟨0 6 -7 -2 15 -34]]

POTE generator: ~15/14 = 116.574

Vals: Template:Val list

Badness: 0.015715

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 225/224, 243/242, 273/272, 351/350, 375/374

Mapping: [⟨1 1 3 3 2 7 7], ⟨0 6 -7 -2 15 -34 -30]]

POTE generator: ~15/14 = 116.585

Vals: Template:Val list

Badness: 0.012537

Manna

Subgroup: 2.3.5.7.11.13

Comma list: 225/224, 243/242, 325/324, 385/384

Mapping: [⟨1 1 3 3 2 0], ⟨0 6 -7 -2 15 38]]

POTE generator: ~15/14 = 116.739

Vals: Template:Val list

Badness: 0.017012

Semimiracle

Subgroup: 2.3.5.7.11.13

Comma list: 169/168, 225/224, 243/242, 385/384

Mapping: [⟨2 2 6 6 4 7], ⟨0 6 -7 -2 15 2]]

POTE generator: ~15/14 = 116.624

Vals: Template:Val list

Badness: 0.024622

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 169/168, 221/220, 225/224, 243/242, 273/272

Mapping: [⟨2 2 6 6 4 7 7], ⟨0 6 -7 -2 15 2 6]]

POTE generator: ~15/14 = 116.628

Vals: Template:Val list

Badness: 0.016130

Hemisecordite

Subgroup: 2.3.5.7.11.13

Comma list: 225/224, 243/242, 385/384, 847/845

Mapping: [⟨1 1 3 3 2 2], ⟨0 12 -14 -4 30 35]]

POTE generator: ~27/26 = 58.288

Vals: Template:Val list

Badness: 0.025589

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 225/224, 243/242, 273/272, 385/384, 847/845

Mapping: [⟨1 1 3 3 2 2 2], ⟨0 12 -14 -4 30 35 43]]

POTE generator: ~27/26 = 58.261

Vals: Template:Val list

Badness: 0.022535

Phicordial

Subgroup: 2.3.5.7.11.13

Comma list: 225/224, 243/242, 385/384, 2200/2197

Mapping: [⟨1 7 -4 1 17 4], ⟨0 -18 21 6 -45 -1]]

POTE generator: ~16/13 = 361.121

Vals: Template:Val list

Badness: 0.033198

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 225/224, 243/242, 273/272, 441/440, 2200/2197

Mapping: [⟨1 7 -4 1 17 4 8], ⟨0 -18 21 6 -45 -1 -13]]

POTE generator: ~16/13 = 361.123

Vals: Template:Val list

Badness: 0.024705

Revelation

Subgroup: 2.3.5.7.11

Comma list: 99/98, 176/175, 1029/1024

Mapping: [⟨1 1 3 3 5], ⟨0 6 -7 -2 -16]]

POTE generator: ~15/14 = 116.277

Vals: Template:Val list

Badness: 0.032946

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 66/65, 99/98, 105/104, 512/507

Mapping: [⟨1 1 3 3 5 4], ⟨0 6 -7 -2 -16 -3]]

POTE generator: ~15/14 = 116.268

Vals: Template:Val list

Badness: 0.029452

Hemimiracle

Subgroup: 2.3.5.7.11

Comma list: 225/224, 245/242, 1029/1024

Mapping: [⟨1 1 3 3 4], ⟨0 12 -14 -4 -11]]

POTE generator: ~33/32 = 58.408

Vals: Template:Val list

Badness: 0.059232

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 105/104, 196/195, 245/242, 512/507

Mapping: [⟨1 1 3 3 4 4], ⟨0 12 -14 -4 -11 -6]]

POTE generator: ~33/32 = 58.430

Vals: Template:Val list

Badness: 0.043151

Oracle

Subgroup: 2.3.5.7.11

Comma list: 121/120, 225/224, 1029/1024

Mapping: [⟨1 7 -4 1 3], ⟨0 -12 14 4 1]]

POTE generator: ~11/8 = 541.668

Vals: Template:Val list

Badness: 0.042687

Rodan

Main article: Rodan

Subgroup: 2.3.5.7

Comma list: 245/243, 1029/1024

Mapping: [⟨1 1 -1 3], ⟨0 3 17 -1]]

Wedgie: ⟨⟨ 3 17 -1 20 -10 -50 ]]

POTE generator: ~8/7 = 234.417

Minimax tuning:

[[1 0 0 0⟩, [5/3 0 1/6 -1/6⟩, [25/9 0 17/18 -17/18⟩, [25/9 0 -1/18 1/18⟩]
Eigenmonzos: 2, 7/5

Algebraic generator: larger root of 20x2 - 36x + 15, or (9 + √6)/10.

Template:Val list

Badness: 0.037112

Scales: Rodan26opt, Rodan31opt, Rodan41opt

11-limit

Subgroup: 2.3.5.7.11

Comma list: 245/243, 385/384, 441/440

Mapping: [⟨1 1 -1 3 6], ⟨0 3 17 -1 -13]]

POTE generator: ~8/7 = 234.459

Minimax tuning:

  • 11-odd-limit
[[1 0 0 0 0⟩, [31/19 6/19 0 0 -3/19⟩, [49/19 34/19 0 0 -17/19⟩, [53/19 -2/19 0 0 1/19⟩, [62/19 -26/19 0 0 13/19⟩]
Eigenmonzos: 2, 11/9

Algebraic generator: positive root of x2 + 16x - 31, or √95 - 8.

Vals: Template:Val list

Badness: 0.023093

Scales: Rodan26opt, Rodan31opt, Rodan41opt

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 196/195, 245/243, 352/351, 364/363

Mapping: [⟨1 1 -1 3 6 8], ⟨0 3 17 -1 -13 -22]]

POTE generator: ~8/7 = 234.482

Minimax tuning:

  • 13- and 15-odd-limit
[[1 0 0 0 0 0⟩, [23/14 3/14 0 0 0 -3/28⟩, [37/14 17/14 0 0 0 -17/28⟩, [39/14 -1/14 0 0 0 1/28⟩, [45/14 -13/14 0 0 0 13/28⟩, [23/7 -11/7 0 0 0 11/14⟩]
Eigenmonzos: 2, 13/9

Algebraic generator: Gatetone, positive root of 4x6 - 7x - 1. Recurrence converges slowly.

Vals: Template:Val list

Badness: 0.018448

Scales: Rodan26opt, Rodan31opt, Rodan41opt

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 154/153, 196/195, 245/243, 256/255, 273/272

Mapping: [⟨1 1 -1 3 6 8 8], ⟨0 3 17 -1 -13 -22 -20]]

POTE generator: ~8/7 = 234.524

Minimax tuning:

  • 17-odd-limit eigenmonzos: 2, 18/17

Vals: Template:Val list

Badness: 0.016743

Scales: Rodan26opt, Rodan31opt, Rodan41opt

Aerodactyl

Subgroup: 2.3.5.7.11.13

Comma list: 91/90, 245/243, 385/384, 441/440

Mapping: [⟨1 1 -1 3 6 -1], ⟨0 3 17 -1 -13 24]]

POTE generator: ~8/7 = 234.639

Vals: Template:Val list

Badness: 0.033986

Aerodino

Subgroup: 2.3.5.7.11

Comma list: 176/175, 245/243, 1029/1024

Mapping: [⟨1 1 -1 3 -3], ⟨0 3 17 -1 33]]

POTE generator: ~8/7 = 234.728

Vals: Template:Val list

Badness: 0.054294

13-limit

Comma list: 91/90, 176/175, 245/243, 847/845

Mapping: [⟨1 1 -1 3 -3 -1], ⟨0 3 17 -1 33 24]]

POTE generator: ~8/7 = 234.782

Vals: Template:Val list

Badness: 0.035836

Varan

Comma list: 100/99, 245/243, 1029/1024

Mapping: [⟨1 1 -1 3 -2], ⟨0 3 17 -1 28]]

POTE generator: ~8/7 = 234.145

Vals: Template:Val list

Badness: 0.044937

13-limit

Comma list: 100/99, 105/104, 245/243, 352/351

Mapping: [⟨1 1 -1 3 -2 0], ⟨0 3 17 -1 28 19]]

POTE generator: ~8/7 = 234.089

Vals: Template:Val list

Badness: 0.032284

Guiron

See also: Schismatic family

Subgroup: 2.3.5.7

Comma list: 1029/1024, 10976/10935

Mapping: [⟨1 1 7 3], ⟨0 3 -24 -1]]

Mapping generators: ~2, ~8/7

Wedgie: ⟨⟨ 3 -24 -1 -45 -10 65 ]]

POTE generator: ~8/7 = 233.930

Minimax tuning:

[[1 0 0 0⟩, [15/8 0 -1/8 0⟩, [0 0 1 0⟩, [65/24 0 1/24 0⟩]
Eigenmonzos: 2, 5/4

Template:Val list

Badness: 0.047544

11-limit

Subgroup: 2.3.5.7.11

Comma list: 385/384, 441/440, 10976/10935

Mapping: [⟨1 1 7 3 -2], ⟨0 3 -24 -1 28]]

Mapping generators: ~2, ~8/7

POTE generator: ~8/7 = 233.931

Minimax tuning:

  • 11-odd-limit
[[1 0 0 0 0⟩, [15/8 0 -1/8 0 0⟩, [0 0 1 0 0⟩, [65/24 0 1/24 0 0⟩, [37/6 0 -7/6 0 0⟩]
Eigenmonzos: 2, 5/4

Vals: Template:Val list

Badness: 0.026648

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 196/195, 352/351, 385/384, 729/728

Mapping: [⟨1 1 7 3 -2 0], ⟨0 3 -24 -1 28 19]]

Mapping generators: ~2, ~8/7

POTE generator: ~8/7 = 233.890

Vals: Template:Val list

Badness: 0.028444

Valentine

Main article: Valentine
See also: Starling temperaments § Valentine

Subgroup: 2.3.5

Comma list: 1990656/1953125

Mapping: [⟨1 1 2], ⟨0 9 5]]

POTE generator: ~25/24 = 78.039

Template:Val list

Badness: 0.122765

7-limit

Subgroup: 2.3.5.7

Comma list: 126/125, 1029/1024

Mapping: [⟨1 1 2 3], ⟨0 9 5 -3]]

Mapping generators: ~2, ~21/20

Wedgie: ⟨⟨ 9 5 -3 -13 -30 -21 ]]

POTE generator: ~21/20 = 77.864

Minimax tuning:

[[1 0 0 0⟩, [5/2 3/4 0 -3/4⟩, [17/6 5/12 0 -5/12⟩, [5/2 -1/4 0 1/4⟩]
Eigenmonzos: 2, 7/6
[[1 0 0 0⟩, [10/7 6/7 0 -3/7⟩, [47/21 10/21 0 -5/21⟩, [20/7 -2/7 0 1/7⟩]
Eigenmonzos: 2, 9/7

Algebraic generator: smaller root of x2 - 89x + 92, or (89 - sqrt (7553))/2, at 77.8616 cents.

Template:Val list

Badness: 0.031056

11-limit

Subgroup: 2.3.5.7.11

Comma list: 121/120, 126/125, 176/175

Mapping: [⟨1 1 2 3 3], ⟨0 9 5 -3 7]]

Mapping generators: ~2, ~21/20

POTE generator: ~21/20 = 77.881

Minimax tuning:

  • 11-odd-limit
[[1 0 0 0 0⟩, [1 0 0 -9/10 9/10⟩, [2 0 0 -1/2 1/2⟩, [3 0 0 3/10 -3/10⟩, [3 0 0 -7/10 7/10⟩]
Eigenmonzos: 2, 11/7

Algebraic generator: positive root of 4x3 + 15x2 - 21, or else Gontrand2, the smallest positive root of 4x7 - 8x6 + 5.

Vals: Template:Val list

Badness: 0.016687

Dwynwen

Subgroup: 2.3.5.7.11.13

Comma list: 91/90, 121/120, 126/125, 176/175

Mapping: [⟨1 1 2 3 3 2], ⟨0 9 5 -3 7 26]]

POTE generator: ~21/20 = 78.219

Vals: Template:Val list

Badness: 0.023461

Lupercalia

Subgroup: 2.3.5.7.11.13

Comma list: 66/65, 105/104, 121/120, 126/125

Mapping: [⟨1 1 2 3 3 3], ⟨0 9 5 -3 7 11]]

POTE generator: ~21/20 = 77.709

Vals: Template:Val list

Badness: 0.021328

Valentino

Subgroup: 2.3.5.7.11.13

Comma list: 121/120, 126/125, 176/175, 196/195

Mapping: [⟨1 1 2 3 3 5], ⟨0 9 5 -3 7 -20]]

POTE generator: ~21/20 = 77.958

Vals: Template:Val list

Badness: 0.020665

Semivalentine

Subgroup: 2.3.5.7.11.13

Comma list: 121/120, 126/125, 169/168, 176/175

Mapping: [⟨2 2 4 6 6 7], ⟨0 9 5 -3 7 3]]

POTE generator: ~21/20 = 77.839

Vals: Template:Val list

Badness: 0.032749

Unidec

Main article: Unidec

Subgroup: 2.3.5

Comma list: 31381059609/31250000000

Mapping: [⟨2 5 8], ⟨0 -6 -11]]

Mapping generators: ~177147/125000, ~10/9

POTE generator: ~10/9 = 183.047

Template:Val list

Badness: 0.082423

Scales: Unidec26

7-limit

Subgroup: 2.3.5.7

Comma list: 1029/1024, 4375/4374

Mapping: [⟨2 5 8 5], ⟨0 -6 -11 2]]

Mapping generators: ~1225/864, ~10/9

Wedgie: ⟨⟨ 12 22 -4 7 -40 -71 ]]

POTE generator: ~10/9 = 183.161

Minimax tuning:

[[1 0 0 0⟩, [47/26 0 6/13 -6/13⟩, [71/26 0 11/13 -11/13⟩, [71/26 0 -2/13 2/13⟩]
Eigenmonzos: 2, 7/5
[[1 0 0 0⟩, [10/7 6/7 0 -3/7⟩, [57/28 11/7 0 -11/14⟩, [20/7 -2/7 0 1/7⟩]
Eigenmonzos: 2, 9/7

Template:Val list

Badness: 0.038393

Scales: Unidec26

11-limit

Subgroup: 2.3.5.7.11

Comma list: 385/384, 441/440, 4375/4374

Mapping: [⟨2 5 8 5 6], ⟨0 -6 -11 2 3]]

Mapping generators: ~99/70, ~10/9

Minimax tuning:

  • 11-odd-limit
[[1 0 0 0 0⟩, [10/7 6/7 0 -3/7 0⟩, [57/28 11/7 0 -11/14 0⟩, [20/7 -2/7 0 1/7 0⟩, [99/28 -3/7 0 3/14 0⟩]
Eigenmonzos: 2, 9/7

Vals: Template:Val list

Badness: 0.015479

Scales: Unidec26

Ekadash

Subgroup: 2.3.5.7.11.13

Comma list: 385/384, 441/440, 625/624, 729/728

Mapping: [⟨2 5 8 5 6 19], ⟨0 -6 -11 2 3 -38]]

Mapping generators: ~99/70, ~10/9

POTE generator: ~10/9 = 183.187

Vals: Template:Val list

Badness: 0.020381

Scales: Unidec26

Hendec

Subgroup: 2.3.5.7.11.13

Comma list: 169/168, 325/324, 364/363, 385/384

Mapping: [⟨2 5 8 5 6 8], ⟨0 -6 -11 2 3 -2]]

Mapping generators: ~91/64, ~10/9

POTE generator: ~10/9 = 183.198

Vals: Template:Val list

Badness: 0.017707

Scales: Unidec26

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 169/168, 221/220, 273/272, 325/324, 364/363

Mapping: [⟨2 5 8 5 6 8 10], ⟨0 -6 -11 2 3 -2 -6]]

Mapping generators: ~17/12, ~10/9

POTE generator: ~10/9 = 183.196

Vals: Template:Val list

Badness: 0.011676

Scales: Unidec26

Hemiseven

Subgroup: 2.3.5.7

Comma list: 1029/1024, 19683/19600

Mapping: [⟨1 4 14 2], ⟨0 -6 -29 2]]

Wedgie: ⟨⟨ 6 29 -2 32 -20 -86 ]]

POTE generator: ~320/243 = 483.267

Template:Val list

Badness: 0.056557

11-limit

Subgroup: 2.3.5.7.11

Comma list: 385/384, 441/440, 19683/19600

Mapping: [⟨1 4 14 2 -5], ⟨0 -6 -29 2 21]]

POTE generator: ~320/243 = 483.276

Vals: Template:Val list

Badness: 0.028467

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 351/350, 385/384, 441/440, 676/675

Mapping: [⟨1 4 14 2 -5 19], ⟨0 -6 -29 2 21 -38]]

POTE generator: ~120/91 = 483.256

Vals: Template:Val list

Badness: 0.021900

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 273/272, 351/350, 385/384, 441/440, 676/675

Mapping: [⟨1 4 14 2 -5 19 21], ⟨0 -6 -29 2 21 -38 -42]]

POTE generator: ~45/34 = 483.261

Vals: Template:Val list

Badness: 0.015701

Tritikleismic

See also: Kleismic family § Tritikleismic

Subgroup: 2.3.5.7

Comma list: 1029/1024, 15625/15552

Mapping: [⟨3 0 3 10], ⟨0 6 5 -2]]

Mapping generators: ~63/50, ~6/5

Wedgie: ⟨⟨ 18 15 -6 -18 -60 -56 ]]

POTE generator: ~6/5 = 316.872

Minimax tuning:

[[1 0 0 0⟩, [2 0 6/7 -6/7⟩, [8/3 0 5/7 -5/7⟩, [8/3 0 -2/7 2/7⟩]
Eigenmonzos: 2, 7/5
[[1 0 0 0⟩, [10/7 6/7 0 -3/7⟩, [46/21 5/7 0 -5/14⟩, [20/7 -2/7 0 1/7⟩]
Eigenmonzos: 2, 9/7

Template:Val list

Badness: 0.056337

11-limit

Subgroup: 2.3.5.7.11

Comma list: 385/384, 441/440, 4000/3993

Mapping: [⟨3 0 3 10 8], ⟨0 6 5 -2 3]]

Mapping generators: ~44/35, ~6/5

POTE generator: ~6/5 = 316.881

Minimax tuning:

  • 11-odd-limit
[[1 0 0 0 0⟩, [10/7 6/7 0 -3/7 0⟩, [46/21 5/7 0 -5/14 0⟩, [20/7 -2/7 0 1/7 0⟩, [71/21 3/7 0 -3/14 0⟩]
Eigenmonzos: 2, 9/7

Vals: Template:Val list

Badness: 0.019333

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 325/324, 364/363, 385/384, 625/624

Mapping: [⟨3 0 3 10 8 0], ⟨0 6 5 -2 3 14]]

Mapping generators: ~44/35, ~6/5

POTE generator: ~6/5 = 316.9585

Vals: Template:Val list

Badness: 0.015652

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 273/272, 325/324, 364/363, 375/374, 385/384

Mapping: [⟨3 0 3 10 8 0 -2], ⟨0 6 5 -2 3 14 18]]

Mapping generators: ~34/27, ~6/5

POTE generator: ~6/5 = 316.9082

Vals: Template:Val list

Badness: 0.013551

Superkleismic

See also: Shibboleth family § Superkleismic

Subgroup: 2.3.5.7

Comma list: 875/864, 1029/1024

Mapping: [⟨1 4 5 2], ⟨0 -9 -10 3]]

Wedgie: ⟨⟨ 9 10 -3 -5 -30 -35 ]]

POTE generator: ~6/5 = 321.930

Template:Val list

Badness: 0.047932

11-limit

Subgroup: 2.3.5.7.11

Comma list: 100/99, 245/242, 385/384

Mapping: [⟨1 4 5 2 4], ⟨0 -9 -10 3 -2]]

POTE generator: ~6/5 = 321.847

Vals: Template:Val list

Badness: 0.025659

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 100/99, 105/104, 245/243, 1188/1183

Mapping: [⟨1 4 5 2 4 8], ⟨0 -9 -10 3 -2 -16]]

POTE generator: ~6/5 = 321.994

Vals: Template:Val list

Badness: 0.021478

Gorgo

In the 5-limit, gorgo tempers out the laconic comma, 2187/2000, which is the difference between three 10/9's and a 3/2. Although a higher-error temperament, it does pop up enough in the low-numbered EDOs to be useful, most notably in 16EDO and 21EDO. The only 7-limit extension that makes any sense to use is to add the gamelisma to the comma list.

5-limit (laconic)

Subgroup: 2.3.5

Comma list: 2187/2000

Mapping: [⟨1 1 1], ⟨0 3 7]]

Wedgie: ⟨⟨ 3 7 4 ]]

POTE generator: ~10/9 = 227.426

Template:Val list

Badness: 0.161799

7-limit

Subgroup: 2.3.5.7

Comma list: 36/35, 1029/1024

Mapping: [⟨1 1 1 3], ⟨0 3 7 -1]]

Wedgie: ⟨⟨ 3 7 -1 4 -10 -22 ]]

POTE generator: ~8/7 = 228.334

Template:Val list

Badness: 0.060663

11-limit

Subgroup: 2.3.5.7.11

Comma list: 36/35, 45/44, 1029/1024

Mapping: [⟨1 1 1 3 1], ⟨0 3 7 -1 13]]

POTE generator: ~8/7 = 227.373

Vals: Template:Val list

Badness: 0.049500

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 27/26, 36/35, 45/44, 507/500

Mapping: [⟨1 1 1 3 1 2], ⟨0 3 7 -1 13 9]]

POTE generator: ~8/7 = 227.230

Vals: Template:Val list

Badness: 0.032664

Spartan

Subgroup: 2.3.5.7.11

Comma list: 36/35, 56/55, 1029/1024

Mapping: [⟨1 1 1 3 5], ⟨0 3 7 -1 -8]]

POTE generator: ~8/7 = 229.535

Vals: Template:Val list

Badness: 0.062683

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 27/26, 36/35, 56/55, 507/500

Mapping: [⟨1 1 1 3 5 2], ⟨0 3 7 -1 -8 9]]

POTE generator: ~8/7 = 229.059

Template:Val list

Badness: 0.047071

Music

Lemba

Main article: Lemba
See also: Jubilismic clan § Lemba

Subgroup: 2.3.5.7

Comma list: 50/49, 525/512

Mapping: [⟨2 2 5 6], ⟨0 3 -1 -1]]

Mapping generators: ~7/5, ~8/7

Wedgie: ⟨⟨ 6 -2 -2 -17 -20 1 ]]

POTE generator: ~8/7 = 232.089

Template:Val list

Badness: 0.062208

11-limit

Subgroup: 2.3.5.7.11

Comma list: 45/44, 50/49, 385/384

Mapping: [⟨2 2 5 6 5], ⟨0 3 -1 -1 5]]

POTE generator: ~8/7 = 230.974

Vals: Template:Val list

Badness: 0.041563

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 45/44, 50/49, 65/64, 78/77

Mapping: [⟨2 2 5 6 5 7], ⟨0 3 -1 -1 5 1]]

POTE generator: ~8/7 = 230.966

Vals: Template:Val list

Badness: 0.025477

Gidorah

Main article: University temperament

5-limit (university)

Subgroup: 2.3.5

Comma list: 144/125

Mapping: [⟨1 1 2], ⟨0 3 2]]

POTE generator: ~6/5 = 235.4416

Template:Val list

Badness: 0.101806

7-limit

Subgroup: 2.3.5.7

Comma list: 21/20, 144/125

Mapping: [⟨1 1 2 3], ⟨0 3 2 -1]]

Wedgie: ⟨⟨ 3 2 -1 -4 -10 -8 ]]

POTE generator: ~8/7 = 230.762

Template:Val list

Badness: 0.062262

Clyndro

See also: Pelogic family

Subgroup: 2.3.5.7

Comma list: 135/128, 360/343

Mapping: [⟨1 1 4 3], ⟨0 3 -9 -1]]

Wedgie: ⟨⟨ 3 -9 -1 -21 -10 23 ]]

POTE generator: ~8/7 = 226.469

Template:Val list

Badness: 0.159179

11-limit

Subgroup: 2.3.5.7.11

Comma list: 33/32, 45/44, 352/343

Mapping: [⟨1 1 4 3 4], ⟨0 3 -9 -1 -3]]

POTE generator: ~8/7 = 226.428

Vals: Template:Val list

Badness: 0.069703

Necromanteion

Subgroup: 2.3.5.7

Comma list: 1029/1024, 5103/5000

Mapping: [⟨1 7 10 1], ⟨0 -12 -17 4]]

Wedgie: ⟨⟨ 12 17 -4 -1 -40 -57 ]]

POTE generator: ~48/35 = 541.779

Template:Val list

Badness: 0.117680

11-limit

Subgroup: 2.3.5.7.11

Comma list: 176/175, 243/242, 1029/1024

Mapping: [⟨1 7 10 1 17], ⟨0 -12 -17 4 -30]]

POTE generator: ~15/11 = 541.729

Vals: Template:Val list

Badness: 0.053459

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 144/143, 176/175, 243/242, 343/338

Mapping: [⟨1 7 10 1 17 1], ⟨0 -12 -17 4 -30 6]]

POTE generator: ~15/11 = 541.606

Vals: Template:Val list

Badness: 0.047015

Widefourth

Subgroup: 2.3.5.7

Comma list: 1029/1024, 48828125/48771072

Mapping: [⟨1 16 8 -2], ⟨0 -33 -13 11]]

Wedgie: ⟨⟨ 33 13 -11 -56 -110 -62 ]]

POTE generator: ~3125/2304 = 524.210

Template:Val list

Badness: 0.154117

11-limit

Subgroup: 2.3.5.7.11

Comma list: 385/384, 441/440, 234375/234256

Mapping: [⟨1 16 8 -2 17], ⟨0 -33 -13 11 -31]]

POTE generator: ~847/625 = 524.210

Vals: Template:Val list

Badness: 0.040785

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 385/384, 441/440, 625/624, 847/845

Mapping: [⟨1 16 8 -2 17 12], ⟨0 -33 -13 11 -31 -19]]

POTE generator: ~65/48 = 524.209

Vals: Template:Val list

Badness: 0.021636

Tritriple

Subgroup: 2.3.5

Comma list: [31 20 -27⟩

Mapping: [⟨1 -11 -7], ⟨0 27 20]]

POTE generator: ~864/625 = 559.332

Template:Val list

Badness: 0.283570

7-limit

Subgroup: 2.3.5.7

Comma list: 1029/1024, 1959552/1953125

Mapping: [⟨1 -11 -7 7], ⟨0 27 20 -9]]

Wedgie: ⟨⟨ 27 20 -9 -31 -90 -77 ]]

POTE generator: ~864/625 = 559.295

Template:Val list

Badness: 0.118640

11-limit

Subgroup: 2.3.5.7.11

Comma list: 385/384, 441/440, 43923/43750

Mapping: [⟨1 -11 -7 7 -4], ⟨0 27 20 -9 16]]

POTE generator: ~242/175 = 559.293

Vals: Template:Val list

Badness: 0.035350

Restles

Subgroup: 2.3.5.7

Comma list: 1029/1024, 153664/151875

Mapping: [⟨1 -2 8 4], ⟨0 12 -19 -4]]

Wedgie: ⟨⟨ 12 -19 -4 -58 -40 44 ]]

POTE generator: ~315/256 = 358.5485

Template:Val list

Badness: 0.108011

11-limit

Subgroup: 2.3.5.7.11

Comma list: 385/384, 441/440, 153664/151875

Mapping: [⟨1 -2 8 4 -7], ⟨0 12 -19 -4 35]]

POTE generator: ~27/22 = 358.5713

Vals: Template:Val list

Badness: 0.054655

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 196/195, 352/351, 385/384, 676/675

Mapping: [⟨1 -2 8 4 -7 4], ⟨0 12 -19 -4 35 -1]]

POTE generator: ~16/13 = 358.5739

Vals: Template:Val list

Badness: 0.028187

Quartemka

Subgroup: 2.3.5

Comma list: [2 -32 11⟩

Mapping: [⟨1 4 6], ⟨0 -21 -32]]

POTE generator: ~27/25 = 137.962

Template:Val list

Badness: 1.381216

7-limit

Subgroup: 2.3.5.7

Comma list: 1029/1024, 1250000/1240029

Mapping: [⟨1 4 6 2], ⟨0 -21 -32 7]]

Wedgie: ⟨⟨ 21 32 -7 2 -70 -106 ]]

POTE generator: ~27/25 = 138.006

Template:Val list

Badness: 0.152287

11-limit

Subgroup: 2.3.5.7.11

Comma list: 385/384, 441/440, 800000/793881

Mapping: [⟨1 4 6 2 3], ⟨0 -21 -32 7 4]]

POTE generator: ~27/25 = 137.990

Vals: Template:Val list

Badness: 0.057307

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 325/324, 364/363, 385/384, 2200/2197

Mapping: [⟨1 4 6 2 3 6], ⟨0 -21 -32 7 4 -20]]

POTE generator: ~13/12 = 137.990

Vals: Template:Val list

Badness: 0.028393

Baladic

See also: Subgroup temperaments § No-fives subgroup

Baladic is a 2.3.7.13.17 subgroup temperament that attempts to approximate the Maqam Sikah Baladi scale. 36EDO is an excellent baladic tuning.

Comma list: 169/168, 273/272, 289/288

Sval mapping: [⟨2 2 6 7 7], ⟨0 3 -1 1 3]]

Mapping generators: ~17/12, ~8/7

POTE generator: ~8/7 = 233.6155

Template:Val list

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