Xenharmonic Wiki

Gamelismic clan: Difference between revisions

← Older editNewer edit →
VisualWikitext
Update keys; linking; clarify (1/)
Update keys (2/)
Line 260: Line 260:


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


[[Comma list]]: 2187/2000
[[Comma list]]: 2187/2000


[[Mapping]]: [{{val| 1 1 1 }}, {{val| 0 3 7 }}]
{{Mapping|legend=1| 1 1 1 | 0 3 7 }}


{{Multival|legend=1| 3 7 4 }}
{{Multival|legend=1| 3 7 4 }}


[[POTE generator]]: ~10/9 = 227.426
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~10/9 = 227.426


{{Optimal ET sequence|legend=1| 5, 16, 21, 37b }}
{{Optimal ET sequence|legend=1| 5, 16, 21, 37b }}
Line 278: Line 278:


=== 7-limit ===
=== 7-limit ===
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 36/35, 1029/1024
[[Comma list]]: 36/35, 1029/1024


[[Mapping]]: [{{val| 1 1 1 3 }}, {{val| 0 3 7 -1 }}]
{{Mapping|legend=1| 1 1 1 3 | 0 3 7 -1 }}


{{Multival|legend=1| 3 7 -1 4 -10 -22 }}
{{Multival|legend=1| 3 7 -1 4 -10 -22 }}


[[POTE generator]]: ~8/7 = 228.334
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~8/7 = 228.334


{{Optimal ET sequence|legend=1| 5, 11c, 16, 21 }}
{{Optimal ET sequence|legend=1| 5, 11c, 16, 21 }}
Line 297: Line 297:
Comma list: 36/35, 45/44, 1029/1024
Comma list: 36/35, 45/44, 1029/1024


Mapping: [{{val| 1 1 1 3 1 }}, {{val| 0 3 7 -1 13 }}]
Mapping: {{mapping| 1 1 1 3 1 | 0 3 7 -1 13 }}


POTE generator: ~8/7 = 227.373
Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 227.373


{{Optimal ET sequence|legend=1| 16, 21, 37b }}
{{Optimal ET sequence|legend=1| 16, 21, 37b }}
Line 310: Line 310:
Comma list: 27/26, 36/35, 45/44, 507/500
Comma list: 27/26, 36/35, 45/44, 507/500


Mapping: [{{val| 1 1 1 3 1 2 }}, {{val| 0 3 7 -1 13 9 }}]
Mapping: {{mapping| 1 1 1 3 1 2 | 0 3 7 -1 13 9 }}


POTE generator: ~8/7 = 227.230
Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 227.230


{{Optimal ET sequence|legend=1| 16, 21, 37b }}
{{Optimal ET sequence|legend=1| 16, 21, 37b }}
Line 323: Line 323:
Comma list: 36/35, 56/55, 1029/1024
Comma list: 36/35, 56/55, 1029/1024


Mapping: [{{val| 1 1 1 3 5 }}, {{val| 0 3 7 -1 -8 }}]
Mapping: {{mapping| 1 1 1 3 5 | 0 3 7 -1 -8 }}


POTE generator: ~8/7 = 229.535
Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 229.535


{{Optimal ET sequence|legend=1| 5, 16e, 21, 47c, 68bcce }}
{{Optimal ET sequence|legend=1| 5, 16e, 21, 47c, 68bcce }}
Line 336: Line 336:
Comma list: 27/26, 36/35, 56/55, 507/500
Comma list: 27/26, 36/35, 56/55, 507/500


Mapping: [{{val| 1 1 1 3 5 2 }}, {{val| 0 3 7 -1 -8 9 }}]
Mapping: {{mapping| 1 1 1 3 5 2 | 0 3 7 -1 -8 9 }}


POTE generator: ~8/7 = 229.059
Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 229.059


{{Optimal ET sequence|legend=1| 5, 16e, 21, 68bccef }}
{{Optimal ET sequence|legend=1| 5, 16e, 21, 68bccef }}
Line 345: Line 345:


; 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]]


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


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


[[Comma list]]: 144/125
[[Comma list]]: 144/125


[[Mapping]]: [{{val| 1 1 2 }}, {{val| 0 3 2 }}]
{{Mapping|legend=1| 1 1 2 | 0 3 2 }}


[[POTE generator]]: ~6/5 = 235.4416
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~6/5 = 235.4416


{{Optimal ET sequence|legend=1| 5, 31cccc, 36…, 41…, 46…, 51… }}
{{Optimal ET sequence|legend=1| 5, 31cccc, 36…, 41…, 46…, 51… }}
Line 364: Line 364:


=== 7-limit ===
=== 7-limit ===
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 21/20, 144/125
[[Comma list]]: 21/20, 144/125


[[Mapping]]: [{{val| 1 1 2 3 }}, {{val| 0 3 2 -1 }}]
{{Mapping|legend=1| 1 1 2 3 | 0 3 2 -1 }}


{{Multival|legend=1| 3 2 -1 -4 -10 -8 }}
{{Multival|legend=1| 3 2 -1 -4 -10 -8 }}


[[POTE generator]]: ~8/7 = 230.762
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~8/7 = 230.762


{{Optimal ET sequence|legend=1| 5, 16c, 21cc, 26ccc }}
{{Optimal ET sequence|legend=1| 5, 16c, 21cc, 26ccc }}
Line 381: Line 381:
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Oncle]].''
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Oncle]].''


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 1029/1024, 2430/2401
[[Comma list]]: 1029/1024, 2430/2401


[[Mapping]]: [{{Val|1 1 6 3}}, {{Val|0 3 -19 -1}}]
{{Mapping|legend=1| 1 1 6 3 | 0 3 -19 -1 }}


[[POTE generator]]: ~8/7 = 232.498
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~8/7 = 232.498


{{Optimal ET sequence|legend=1| 31, 98c, 129c, 160bc }}
{{Optimal ET sequence|legend=1| 31, 98c, 129c, 160bc }}
Line 396: Line 396:
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Archaeotherium]].''
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Archaeotherium]].''


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 405/392, 1029/1024
[[Comma list]]: 405/392, 1029/1024


[[Mapping]]: [{{Val|1 1 5 3}}, {{Val|0 3 -14 -1}}]
{{Mapping|legend=1| 1 1 5 3 | 0 3 -14 -1 }}


[[POTE generator]]: ~8/7 = 230.258
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~8/7 = 230.258


{{Optimal ET sequence|legend=1| 21, 26, 47, 73bc, 99bc }}
{{Optimal ET sequence|legend=1| 21, 26, 47, 73bc, 99bc }}
Line 409: Line 409:


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


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 135/128, 360/343
[[Comma list]]: 135/128, 360/343


[[Mapping]]: [{{val| 1 1 4 3 }}, {{val| 0 3 -9 -1 }}]
{{Mapping|legend=1| 1 1 4 3 | 0 3 -9 -1 }}


{{Multival|legend=1| 3 -9 -1 -21 -10 23 }}
{{Multival|legend=1| 3 -9 -1 -21 -10 23 }}


[[POTE generator]]: ~8/7 = 226.469
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~8/7 = 226.469


{{Optimal ET sequence|legend=1| 5c, 11, 16 }}
{{Optimal ET sequence|legend=1| 5c, 11, 16 }}
Line 430: Line 430:
Comma list: 33/32, 45/44, 352/343
Comma list: 33/32, 45/44, 352/343


Mapping: [{{val| 1 1 4 3 4 }}, {{val| 0 3 -9 -1 -3 }}]
Mapping: {{mapping| 1 1 4 3 4 | 0 3 -9 -1 -3 }}


POTE generator: ~8/7 = 226.428
Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 226.428


{{Optimal ET sequence|legend=1| 5c, 11, 16 }}
{{Optimal ET sequence|legend=1| 5c, 11, 16 }}
Line 439: Line 439:


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


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 225/224, 1029/1024
[[Comma list]]: 225/224, 1029/1024


[[Mapping]]: [{{val| 1 1 3 3 }}, {{val| 0 6 -7 -2 }}]
{{Mapping|legend=1| 1 1 3 3 | 0 6 -7 -2 }}


Mapping generator: 2, ~15/14
: mapping generator: ~2, ~15/14


{{Multival|legend=1| 6 -7 -2 -25 -20 15 }}
{{Multival|legend=1| 6 -7 -2 -25 -20 15 }}


[[POTE generator]]: ~15/14 = 116.675
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~15/14 = 116.675


[[Minimax tuning]]:
[[Minimax tuning]]:
* [[7-odd-limit]]: ~15/14 = {{monzo| 2/13 1/13 -1/13 }}
* [[7-odd-limit]]: ~15/14 = {{monzo| 2/13 1/13 -1/13 }}
: [{{monzo| 1 0 0 0 }}, {{monzo| 25/13 6/13 -6/13 0 }}, {{monzo| 25/13 -7/13 7/13 0 }}, {{monzo| 35/13 -2/13 2/13 0 }}]
: {{monzo list| 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 }}
: [[Eigenmonzo]]s (unchanged-intervals): 2, 6/5
: [[Eigenmonzo basis|Eigenmonzo (unchanged-interval) basis]]: 2.5/3
* [[9-odd-limit]]: ~15/14 = {{monzo| 1/19 2/19 -1/19 }}
* [[9-odd-limit]]: ~15/14 = {{monzo| 1/19 2/19 -1/19 }}
: [{{monzo| 1 0 0 0 }}, {{monzo| 25/19 12/19 -6/19 0 }}, {{monzo| 50/19 -14/19 7/19 0 }}, {{monzo| 55/19 -4/19 2/19 0 }}]
: {{monzo list| 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 }}
: [[Eigenmonzo]]s (unchanged-intervals): 2, 10/9
: [[Eigenmonzo basis|Eigenmonzo (unchanged-interval) basis]]: 2.9/5


[[Tuning ranges]]:
[[Tuning ranges]]:
Line 468: Line 468:
* 9-odd-limit diamond monotone and tradeoff: ~15/14 = [116.129, 116.993]
* 9-odd-limit diamond monotone and tradeoff: ~15/14 = [116.129, 116.993]


Algebraic generator: Secor59, [[Algebraic number|positive root]] of 15''x''<sup>6</sup> - 8''x''<sup>4</sup> - 12
[[Algebraic generator]]: Secor59, positive root of 15''x''<sup>6</sup> - 8''x''<sup>4</sup> - 12


{{Optimal ET sequence|legend=1| 10, 21, 31, 41, 72 }}
{{Optimal ET sequence|legend=1| 10, 21, 31, 41, 72 }}


[[Badness]]: 0.016742
[[Badness]]: 0.016742
Scales: [[Miracle 10]], [[Blackjack]]


=== 11-limit ===
=== 11-limit ===
Line 481: Line 479:
Comma list: 225/224, 243/242, 385/384
Comma list: 225/224, 243/242, 385/384


Mapping: [{{val| 1 1 3 3 2 }}, {{val| 0 6 -7 -2 15 }}]
Mapping: {{mapping| 1 1 3 3 2 | 0 6 -7 -2 15 }}


POTE generator: ~15/14 = 116.633
Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 116.633


Minimax tuning:
Minimax tuning:
* [[11-odd-limit]]: ~15/14 = {{monzo| 1/19 2/19 -1/19 }}
* 11-odd-limit: ~15/14 = {{monzo| 1/19 2/19 -1/19 }}
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 25/19 12/19 -6/19 0 0 }}, {{monzo| 50/19 -14/19 7/19 0 0 }}, {{monzo| 55/19 -4/19 2/19 0 0 }}, {{monzo| 53/19 30/19 -15/19 0 0 }}]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 25/19 12/19 -6/19 0 0 }}, {{monzo| 50/19 -14/19 7/19 0 0 }}, {{monzo| 55/19 -4/19 2/19 0 0 }}, {{monzo| 53/19 30/19 -15/19 0 0 }}]
: Eigenmonzos (unchanged-intervals): 2, 10/9
: Eigenmonzo (unchanged-interval) basis: 2.9/5


Tuning ranges:
Tuning ranges:
Line 500: Line 498:


Badness: 0.010684
Badness: 0.010684
Scales: [[Miracle 10]], [[Blackjack]]


==== Miraculous ====
==== Miraculous ====
Line 508: Line 504:
Comma list: 105/104, 144/143, 196/195, 243/242
Comma list: 105/104, 144/143, 196/195, 243/242


Mapping: [{{val| 1 1 3 3 2 4 }}, {{val| 0 6 -7 -2 15 -3 }}]
Mapping: {{mapping| 1 1 3 3 2 4 | 0 6 -7 -2 15 -3 }}


POTE generator: ~14/13 = 116.747
Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 116.747


{{Optimal ET sequence|legend=1| 10, 21e, 31, 41, 72f, 113f, 185cff }}
{{Optimal ET sequence|legend=1| 10, 21e, 31, 41, 72f, 113f, 185cff }}


Badness: 0.018669
Badness: 0.018669
Scales: [[Miracle 10]], [[Blackjack]]


===== 17-limit =====
===== 17-limit =====
Line 523: Line 517:
Comma list: 105/104, 120/119, 144/143, 154/153, 170/169
Comma list: 105/104, 120/119, 144/143, 154/153, 170/169


Mapping: [{{val| 1 1 3 3 2 4 4 }}, {{val| 0 6 -7 -2 15 -3 1 }}]
Mapping: {{mapping| 1 1 3 3 2 4 4 | 0 6 -7 -2 15 -3 1 }}


POTE generator: ~14/13 = 116.769
Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 116.769


{{Optimal ET sequence|legend=1| 10, 21e, 31, 41, 72fg, 113fgg }}
{{Optimal ET sequence|legend=1| 10, 21e, 31, 41, 72fg, 113fgg }}
Line 536: Line 530:
Comma list: 225/224, 243/242, 351/350, 385/384
Comma list: 225/224, 243/242, 351/350, 385/384


Mapping: [{{val| 1 1 3 3 2 7 }}, {{val| 0 6 -7 -2 15 -34 }}]
Mapping: {{mapping| 1 1 3 3 2 7 | 0 6 -7 -2 15 -34 }}


POTE generator: ~15/14 = 116.574
Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 116.574


{{Optimal ET sequence|legend=1| 31, 72, 103, 175f }}
{{Optimal ET sequence|legend=1| 31, 72, 103, 175f }}
Line 549: Line 543:
Comma list: 225/224, 243/242, 273/272, 351/350, 375/374
Comma list: 225/224, 243/242, 273/272, 351/350, 375/374


Mapping: [{{val| 1 1 3 3 2 7 7 }}, {{val| 0 6 -7 -2 15 -34 -30 }}]
Mapping: {{mapping| 1 1 3 3 2 7 7 | 0 6 -7 -2 15 -34 -30 }}


POTE generator: ~15/14 = 116.585
Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 116.585


{{Optimal ET sequence|legend=1| 31, 72, 103, 175f }}
{{Optimal ET sequence|legend=1| 31, 72, 103, 175f }}
Line 562: Line 556:
Comma list: 225/224, 243/242, 325/324, 385/384
Comma list: 225/224, 243/242, 325/324, 385/384


Mapping: [{{val| 1 1 3 3 2 0 }}, {{val| 0 6 -7 -2 15 38 }}]
Mapping: {{mapping| 1 1 3 3 2 0 | 0 6 -7 -2 15 38 }}


POTE generator: ~15/14 = 116.739
Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 116.739


{{Optimal ET sequence|legend=1| 31f, 41, 72, 185cf, 257cff }}
{{Optimal ET sequence|legend=1| 31f, 41, 72, 185cf, 257cff }}
Line 575: Line 569:
Comma list: 225/224, 243/242, 273/272, 325/324, 385/384
Comma list: 225/224, 243/242, 273/272, 325/324, 385/384


Mapping: [{{val| 1 1 3 3 2 0 0 }}, {{val| 0 6 -7 -2 15 38 42 }}]
Mapping: {{mapping| 1 1 3 3 2 0 0 | 0 6 -7 -2 15 38 42 }}


POTE generator: ~15/14 = 116.727
Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 116.727


{{Optimal ET sequence|legend=1| 31fg, 41, 72, 185cf, 257cff }}
{{Optimal ET sequence|legend=1| 31fg, 41, 72, 185cf, 257cff }}
Line 588: Line 582:
Comma list: 169/168, 225/224, 243/242, 385/384
Comma list: 169/168, 225/224, 243/242, 385/384


Mapping: [{{val| 2 2 6 6 4 7 }}, {{val| 0 6 -7 -2 15 2 }}]
Mapping: {{mapping| 2 2 6 6 4 7 | 0 6 -7 -2 15 2 }}


POTE generator: ~15/14 = 116.624
Optimal tuning (POTE): ~99/70 = 1\2, ~15/14 = 116.624


{{Optimal ET sequence|legend=1| 10, 62, 72 }}
{{Optimal ET sequence|legend=1| 10, 62, 72 }}
Line 601: Line 595:
Comma list: 169/168, 221/220, 225/224, 243/242, 273/272
Comma list: 169/168, 221/220, 225/224, 243/242, 273/272


Mapping: [{{val| 2 2 6 6 4 7 7 }}, {{val| 0 6 -7 -2 15 2 6 }}]
Mapping: {{mapping| 2 2 6 6 4 7 7 | 0 6 -7 -2 15 2 6 }}


POTE generator: ~15/14 = 116.628
Optimal tuning (POTE): ~2 = 17\12, ~15/14 = 116.628


{{Optimal ET sequence|legend=1| 10, 62, 72 }}
{{Optimal ET sequence|legend=1| 10, 62, 72 }}
Line 614: Line 608:
Comma list: 225/224, 243/242, 385/384, 847/845
Comma list: 225/224, 243/242, 385/384, 847/845


Mapping: [{{val| 1 1 3 3 2 2 }}, {{val| 0 12 -14 -4 30 35 }}]
Mapping: {{mapping| 1 1 3 3 2 2 | 0 12 -14 -4 30 35 }}


POTE generator: ~27/26 = 58.288
Optimal tuning (POTE): ~2 = 1\1, ~27/26 = 58.288


{{Optimal ET sequence|legend=1| 41, 62, 103, 247c, 350bcde }}
{{Optimal ET sequence|legend=1| 41, 62, 103, 247c, 350bcde }}
Line 627: Line 621:
Comma list: 225/224, 243/242, 273/272, 385/384, 847/845
Comma list: 225/224, 243/242, 273/272, 385/384, 847/845


Mapping: [{{val| 1 1 3 3 2 2 2 }}, {{val| 0 12 -14 -4 30 35 43 }}]
Mapping: {{mapping| 1 1 3 3 2 2 2 | 0 12 -14 -4 30 35 43 }}


POTE generator: ~27/26 = 58.261
Optimal tuning (POTE): ~2 = 1\1, ~27/26 = 58.261


{{Optimal ET sequence|legend=1| 41, 62, 103 }}
{{Optimal ET sequence|legend=1| 41, 62, 103 }}
Line 640: Line 634:
Comma list: 225/224, 243/242, 289/288, 385/384, 847/845
Comma list: 225/224, 243/242, 289/288, 385/384, 847/845


Mapping: [{{val| 2 2 6 6 4 4 7 }}, {{val| 0 12 -14 -4 30 35 12 }}]
Mapping: {{mapping| 2 2 6 6 4 4 7 | 0 12 -14 -4 30 35 12 }}


POTE generator: ~27/26 = 58.288
Optimal tuning (POTE): ~17/12 = 1\2, ~27/26 = 58.288


{{Optimal ET sequence|legend=1| 62, 144g, 206begg, 350bcdeggg }}
{{Optimal ET sequence|legend=1| 62, 144g, 206begg, 350bcdeggg }}
Line 653: Line 647:
Comma list: 209/208, 225/224, 243/242, 289/288, 361/360, 385/384
Comma list: 209/208, 225/224, 243/242, 289/288, 361/360, 385/384


Mapping: [{{val| 2 2 6 6 4 4 7 8 }}, {{val| 0 12 -14 -4 30 35 12 5 }}]
Mapping: {{mapping| 2 2 6 6 4 4 7 8 | 0 12 -14 -4 30 35 12 5 }}


POTE generator: ~27/26 = 58.283
Optimal tuning (POTE): ~17/12 = 1\2, ~27/26 = 58.283


{{Optimal ET sequence|legend=1| 62, 144gh, 206begghh }}
{{Optimal ET sequence|legend=1| 62, 144gh, 206begghh }}
Line 666: Line 660:
Comma list: 209/208, 225/224, 243/242, 289/288, 323/322, 361/360, 385/384
Comma list: 209/208, 225/224, 243/242, 289/288, 323/322, 361/360, 385/384


Mapping: [{{val| 2 2 6 6 4 4 7 8 7 }}, {{val| 0 12 -14 -4 30 35 12 5 21 }}]
Mapping: {{mapping| 2 2 6 6 4 4 7 8 7 | 0 12 -14 -4 30 35 12 5 21 }}


POTE generator: ~27/26 = 58.283
Optimal tuning (POTE): ~17/12 = 1\2, ~27/26 = 58.283


{{Optimal ET sequence|legend=1| 62, 144gh, 206begghhi }}
{{Optimal ET sequence|legend=1| 62, 144gh, 206begghhi }}
Line 679: Line 673:
Comma list: 225/224, 243/242, 385/384, 2200/2197
Comma list: 225/224, 243/242, 385/384, 2200/2197


Mapping: [{{val| 1 7 -4 1 17 4 }}, {{val| 0 -18 21 6 -45 -1 }}]
Mapping: {{mapping| 1 7 -4 1 17 4 | 0 -18 21 6 -45 -1 }}


POTE generator: ~16/13 = 361.121
Optimal tuning (POTE): ~2 = 1\1, ~16/13 = 361.121


{{Optimal ET sequence|legend=1| 103, 113, 216c }}
{{Optimal ET sequence|legend=1| 103, 113, 216c }}
Line 692: Line 686:
Comma list: 225/224, 243/242, 273/272, 441/440, 2200/2197
Comma list: 225/224, 243/242, 273/272, 441/440, 2200/2197


Mapping: [{{val| 1 7 -4 1 17 4 8 }}, {{val| 0 -18 21 6 -45 -1 -13 }}]
Mapping: {{mapping| 1 7 -4 1 17 4 8 | 0 -18 21 6 -45 -1 -13 }}


POTE generator: ~16/13 = 361.123
Optimal tuning (POTE): ~2 = 1\1, ~16/13 = 361.123


{{Optimal ET sequence|legend=1| 103, 113, 216c }}
{{Optimal ET sequence|legend=1| 103, 113, 216c }}
Line 705: Line 699:
Comma list: 99/98, 176/175, 1029/1024
Comma list: 99/98, 176/175, 1029/1024


Mapping: [{{val| 1 1 3 3 5 }}, {{val| 0 6 -7 -2 -16 }}]
Mapping: {{mapping| 1 1 3 3 5 | 0 6 -7 -2 -16 }}


POTE generator: ~15/14 = 116.277
Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 116.277


{{Optimal ET sequence|legend=1| 10e, 21, 31 }}
{{Optimal ET sequence|legend=1| 10e, 21, 31 }}
Line 718: Line 712:
Comma list: 66/65, 99/98, 105/104, 512/507
Comma list: 66/65, 99/98, 105/104, 512/507


Mapping: [{{val| 1 1 3 3 5 4 }}, {{val| 0 6 -7 -2 -16 -3 }}]
Mapping: {{mapping| 1 1 3 3 5 4 | 0 6 -7 -2 -16 -3 }}


POTE generator: ~15/14 = 116.268
Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 116.268


{{Optimal ET sequence|legend=1| 10e, 21, 31 }}
{{Optimal ET sequence|legend=1| 10e, 21, 31 }}
Line 731: Line 725:
Comma list: 225/224, 245/242, 1029/1024
Comma list: 225/224, 245/242, 1029/1024


Mapping: [{{val| 1 1 3 3 4 }}, {{val| 0 12 -14 -4 -11 }}]
Mapping: {{mapping| 1 1 3 3 4 | 0 12 -14 -4 -11 }}


POTE generator: ~33/32 = 58.408
Optimal tuning (POTE): ~2 = 1\1, ~33/32 = 58.408


{{Optimal ET sequence|legend=1| 20, 21, 41, 144e, 185cee, 226cee }}
{{Optimal ET sequence|legend=1| 20, 21, 41, 144e, 185cee, 226cee }}
Line 744: Line 738:
Comma list: 105/104, 196/195, 245/242, 512/507
Comma list: 105/104, 196/195, 245/242, 512/507


Mapping: [{{val| 1 1 3 3 4 4 }}, {{val| 0 12 -14 -4 -11 -6 }}]
Mapping: {{mapping| 1 1 3 3 4 4 | 0 12 -14 -4 -11 -6 }}


POTE generator: ~33/32 = 58.430
Optimal tuning (POTE): ~2 = 1\1, ~33/32 = 58.430


{{Optimal ET sequence|legend=1| 20, 21, 41, 144eff, 185ceeff }}
{{Optimal ET sequence|legend=1| 20, 21, 41, 144eff, 185ceeff }}
Line 757: Line 751:
Comma list: 121/120, 225/224, 1029/1024
Comma list: 121/120, 225/224, 1029/1024


Mapping: [{{val| 1 7 -4 1 3 }}, {{val| 0 -12 14 4 1 }}]
Mapping: {{mapping| 1 7 -4 1 3 | 0 -12 14 4 1 }}


POTE generator: ~11/8 = 541.668
Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 541.668


{{Optimal ET sequence|legend=1| 11, 20, 31, 82e, 113e, 144ee }}
{{Optimal ET sequence|legend=1| 11, 20, 31, 82e, 113e, 144ee }}
Retrieved from "https://en.xen.wiki/w/Gamelismic_clan"