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Meantone family: Difference between revisions

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{{interwiki
| de = Mitteltönig
| en = Meantone family
| es =
| ja =
}}
{{Technical data page}}
{{Technical data page}}
The '''meantone family''' is the family of [[rank-2 temperament]]s that [[tempering out|temper out]] the syntonic comma, [[81/80]], and thus can all be seen as [[extension]]s of [[meantone]].  
The '''meantone family''' is the family of [[rank-2 temperament]]s that [[tempering out|temper out]] the syntonic comma, [[81/80]], and thus can all be seen as [[extension]]s of [[meantone]].  
Line 77: Line 71:
* [[Godzilla]] (+49/48) → [[Semaphoresmic clan #Godzilla|Semaphoresmic clan]]
* [[Godzilla]] (+49/48) → [[Semaphoresmic clan #Godzilla|Semaphoresmic clan]]
* [[Mothra]] (+1029/1024) → [[Gamelismic clan #Mothra|Gamelismic clan]]
* [[Mothra]] (+1029/1024) → [[Gamelismic clan #Mothra|Gamelismic clan]]
* ''[[Mazzard]]'' (+12288/12005) → [[Buzzardsmic clan #Mazzard|Buzzardsmic clan]]
* ''[[Mohaha]]'' (+121/120) → [[Rastmic clan #Mohaha|Rastmic clan]]
* ''[[Mohaha]]'' (+121/120) → [[Rastmic clan #Mohaha|Rastmic clan]]


Line 126: Line 121:
Comma list: 81/80, 99/98, 126/125
Comma list: 81/80, 99/98, 126/125


Mapping: {{mapping| 1 0 -4 -13 -25 | 0 1 4 10 18 }}
{{Mapping|legend=0| 1 0 -4 -13 -25 | 0 1 4 10 18 }}


Optimal tunings:  
Optimal tunings:  
Line 157: Line 152:
Comma list: 81/80, 99/98, 126/125, 144/143
Comma list: 81/80, 99/98, 126/125, 144/143


Mapping: {{mapping| 1 0 -4 -13 -25 29 | 0 1 4 10 18 -16 }}
{{Mapping|legend=0| 1 0 -4 -13 -25 29 | 0 1 4 10 18 -16 }}


Optimal tunings:  
Optimal tunings:  
Line 182: Line 177:
Comma list: 81/80, 99/98, 120/119, 126/125, 144/143
Comma list: 81/80, 99/98, 120/119, 126/125, 144/143


Mapping: {{mapping| 1 0 -4 -13 -25 29 12 | 0 1 4 10 18 -16 -5 }}
{{Mapping|legend=0| 1 0 -4 -13 -25 29 12 | 0 1 4 10 18 -16 -5 }}


Optimal tunings:  
Optimal tunings:  
Line 197: Line 192:
Comma list: 81/80, 96/95, 99/98, 120/119, 126/125, 144/143
Comma list: 81/80, 96/95, 99/98, 120/119, 126/125, 144/143


Mapping: {{mapping| 1 0 -4 -13 -25 29 12 9 | 0 1 4 10 18 -16 -5 -3 }}
{{Mapping|legend=0| 1 0 -4 -13 -25 29 12 9 | 0 1 4 10 18 -16 -5 -3 }}


Optimal tunings:  
Optimal tunings:  
Line 216: Line 211:
Comma list: 66/65, 81/80, 99/98, 105/104
Comma list: 66/65, 81/80, 99/98, 105/104


Mapping: {{mapping| 1 0 -4 -13 -25 -20 | 0 1 4 10 18 15 }}
{{Mapping|legend=0| 1 0 -4 -13 -25 -20 | 0 1 4 10 18 15 }}


Optimal tunings:  
Optimal tunings:  
Line 235: Line 230:
Comma list: 66/65, 81/80, 99/98, 105/104, 120/119
Comma list: 66/65, 81/80, 99/98, 105/104, 120/119


Mapping: {{mapping| 1 0 -4 -13 -25 -20 12 | 0 1 4 10 18 15 -5 }}
{{Mapping|legend=0| 1 0 -4 -13 -25 -20 12 | 0 1 4 10 18 15 -5 }}


Optimal tunings:  
Optimal tunings:  
Line 250: Line 245:
Comma list: 66/65, 81/80, 96/95, 99/98, 105/104, 120/119
Comma list: 66/65, 81/80, 96/95, 99/98, 105/104, 120/119


Mapping: {{mapping| 1 0 -4 -13 -25 -20 12 9 | 0 1 4 10 18 15 -5 -3 }}
{{Mapping|legend=0| 1 0 -4 -13 -25 -20 12 9 | 0 1 4 10 18 15 -5 -3 }}


Optimal tunings:  
Optimal tunings:  
Line 267: Line 262:
Comma list: 78/77, 81/80, 99/98, 126/125
Comma list: 78/77, 81/80, 99/98, 126/125


Mapping: {{mapping| 1 0 -4 -13 -25 -39 | 0 1 4 10 18 27 }}
{{Mapping|legend=0| 1 0 -4 -13 -25 -39 | 0 1 4 10 18 27 }}


Optimal tunings:  
Optimal tunings:  
Line 286: Line 281:
Comma list: 78/77, 81/80, 99/98, 120/119, 126/125
Comma list: 78/77, 81/80, 99/98, 120/119, 126/125


Mapping: {{mapping| 1 0 -4 -13 -25 -39 12 | 0 1 4 10 18 27 -5 }}
{{Mapping|legend=0| 1 0 -4 -13 -25 -39 12 | 0 1 4 10 18 27 -5 }}


Optimal tunings:  
Optimal tunings:  
Line 301: Line 296:
Comma list: 78/77, 81/80, 96/95, 99/98, 120/119, 126/125
Comma list: 78/77, 81/80, 96/95, 99/98, 120/119, 126/125


Mapping: {{mapping| 1 0 -4 -13 -25 -39 12 9 | 0 1 4 10 18 27 -5 -3 }}
{{Mapping|legend=0| 1 0 -4 -13 -25 -39 12 9 | 0 1 4 10 18 27 -5 -3 }}


Optimal tunings:  
Optimal tunings:  
Line 316: Line 311:
Comma list: 81/80, 99/98, 126/125, 169/168
Comma list: 81/80, 99/98, 126/125, 169/168


Mapping: {{mapping| 1 0 -4 -13 -25 -5 | 0 2 8 20 36 11 }}
{{Mapping|legend=0| 1 0 -4 -13 -25 -5 | 0 2 8 20 36 11 }}


: mapping generators: ~2, ~26/15
: mapping generators: ~2, ~26/15
Line 333: Line 328:
Comma list: 81/80, 99/98, 126/125, 169/168, 221/220
Comma list: 81/80, 99/98, 126/125, 169/168, 221/220


Mapping: {{mapping| 1 0 -4 -13 -25 -5 -22 | 0 2 8 20 36 11 33 }}
{{Mapping|legend=0| 1 0 -4 -13 -25 -5 -22 | 0 2 8 20 36 11 33 }}


Optimal tunings:  
Optimal tunings:  
Line 348: Line 343:
Comma list: 81/80, 99/98, 126/125, 153/152, 169/168, 221/220
Comma list: 81/80, 99/98, 126/125, 153/152, 169/168, 221/220


Mapping: {{mapping| 1 0 -4 -13 -25 -5 -22 -25 | 0 2 8 20 36 11 33 37 }}
{{Mapping|legend=0| 1 0 -4 -13 -25 -5 -22 -25 | 0 2 8 20 36 11 33 37 }}


Optimal tunings:  
Optimal tunings:  
Line 363: Line 358:
Comma list: 81/80, 99/98, 126/125, 847/845
Comma list: 81/80, 99/98, 126/125, 847/845


Mapping: {{mapping| 2 0 -8 -26 -50 -59 | 0 1 4 10 18 21 }}
{{Mapping|legend=0| 2 0 -8 -26 -50 -59 | 0 1 4 10 18 21 }}


: mapping generators: ~55/39, ~3
: mapping generators: ~55/39, ~3
Line 380: Line 375:
Comma list: 81/80, 99/98, 126/125, 221/220, 289/288
Comma list: 81/80, 99/98, 126/125, 221/220, 289/288


Mapping: {{mapping| 2 0 -8 -26 -50 -59 5 | 0 1 4 10 18 21 1 }}
{{Mapping|legend=0| 2 0 -8 -26 -50 -59 5 | 0 1 4 10 18 21 1 }}


Optimal tunings:  
Optimal tunings:  
Line 395: Line 390:
Comma list: 81/80, 99/98, 126/125, 153/152, 209/208, 221/220
Comma list: 81/80, 99/98, 126/125, 153/152, 209/208, 221/220


Mapping: {{mapping| 2 0 -8 -26 -50 -59 5 -1 | 0 1 4 10 18 21 1 3 }}
{{Mapping|legend=0| 2 0 -8 -26 -50 -59 5 -1 | 0 1 4 10 18 21 1 3 }}


Optimal tunings:  
Optimal tunings:  
Line 414: Line 409:
Comma list: 81/80, 126/125, 385/384
Comma list: 81/80, 126/125, 385/384


Mapping: {{mapping| 1 0 -4 -13 24 | 0 1 4 10 -13 }}
{{Mapping|legend=0| 1 0 -4 -13 24 | 0 1 4 10 -13 }}


: mapping generator: ~2, ~3
: mapping generator: ~2, ~3
Line 446: Line 441:
Comma list: 81/80, 105/104, 126/125, 144/143
Comma list: 81/80, 105/104, 126/125, 144/143


Mapping: {{mapping| 1 0 -4 -13 24 -20 | 0 1 4 10 -13 15 }}
{{Mapping|legend=0| 1 0 -4 -13 24 -20 | 0 1 4 10 -13 15 }}


Optimal tunings:  
Optimal tunings:  
Line 469: Line 464:
Comma list: 81/80, 105/104, 126/125, 144/143, 273/272
Comma list: 81/80, 105/104, 126/125, 144/143, 273/272


Mapping: {{mapping| 1 0 -4 -13 24 -20 -37 | 0 1 4 10 -13 15 26 }}
{{Mapping|legend=0| 1 0 -4 -13 24 -20 -37 | 0 1 4 10 -13 15 26 }}


Optimal tunings:  
Optimal tunings:  
Line 484: Line 479:
Comma list: 81/80, 105/104, 126/125, 144/143, 153/152, 273/272
Comma list: 81/80, 105/104, 126/125, 144/143, 153/152, 273/272


Mapping: {{mapping| 1 0 -4 -13 24 -20 -37 -40 | 0 1 4 10 -13 15 26 28 }}
{{Mapping|legend=0| 1 0 -4 -13 24 -20 -37 -40 | 0 1 4 10 -13 15 26 28 }}


Optimal tunings:  
Optimal tunings:  
Line 499: Line 494:
Comma list: 81/80, 105/104, 120/119, 126/125, 144/143
Comma list: 81/80, 105/104, 120/119, 126/125, 144/143


Mapping: {{mapping| 1 0 -4 -13 24 -20 12 | 0 1 4 10 -13 15 -5 }}
{{Mapping|legend=0| 1 0 -4 -13 24 -20 12 | 0 1 4 10 -13 15 -5 }}


Optimal tunings:  
Optimal tunings:  
Line 514: Line 509:
Comma list: 77/76, 81/80, 96/95, 105/104, 120/119, 126/125
Comma list: 77/76, 81/80, 96/95, 105/104, 120/119, 126/125


Mapping: {{mapping| 1 0 -4 -13 24 -20 12 9 | 0 1 4 10 -13 15 -5 -3 }}
{{Mapping|legend=0| 1 0 -4 -13 24 -20 12 9 | 0 1 4 10 -13 15 -5 -3 }}


Optimal tunings:  
Optimal tunings:  
Line 529: Line 524:
Comma list: 81/80, 126/125, 385/384, 847/845
Comma list: 81/80, 126/125, 385/384, 847/845


Mapping: {{mapping| 2 0 -8 -26 48 39 | 0 1 4 10 -13 -10 }}
{{Mapping|legend=0| 2 0 -8 -26 48 39 | 0 1 4 10 -13 -10 }}


: mapping generators: ~55/39, ~3
: mapping generators: ~55/39, ~3
Line 546: Line 541:
Comma list: 81/80, 126/125, 221/220, 273/272, 289/288
Comma list: 81/80, 126/125, 221/220, 273/272, 289/288


Mapping: {{mapping| 2 0 -8 -26 48 39 5 | 0 1 4 10 -13 -10 1 }}
{{Mapping|legend=0| 2 0 -8 -26 48 39 5 | 0 1 4 10 -13 -10 1 }}


Optimal tunings:  
Optimal tunings:  
Line 561: Line 556:
Comma list: 81/80, 126/125, 153/152, 209/208, 221/220, 273/272
Comma list: 81/80, 126/125, 153/152, 209/208, 221/220, 273/272


Mapping: {{mapping| 2 0 -8 -26 48 39 5 -1 | 0 1 4 10 -13 -10 1 3 }}
{{Mapping|legend=0| 2 0 -8 -26 48 39 5 -1 | 0 1 4 10 -13 -10 1 3 }}


Optimal tunings:  
Optimal tunings:  
Line 578: Line 573:
Comma list: 45/44, 56/55, 81/80
Comma list: 45/44, 56/55, 81/80


Mapping: {{mapping| 1 0 -4 -13 -6 | 0 1 4 10 6 }}
{{Mapping|legend=0| 1 0 -4 -13 -6 | 0 1 4 10 6 }}


Optimal tunings:  
Optimal tunings:  
Line 597: Line 592:
Comma list: 45/44, 56/55, 78/77, 81/80
Comma list: 45/44, 56/55, 78/77, 81/80


Mapping: {{mapping| 1 0 -4 -13 -6 -20 | 0 1 4 10 6 15 }}
{{Mapping|legend=0| 1 0 -4 -13 -6 -20 | 0 1 4 10 6 15 }}


Optimal tunings:  
Optimal tunings:  
Line 612: Line 607:
Comma list: 45/44, 56/55, 78/77, 81/80, 120/119
Comma list: 45/44, 56/55, 78/77, 81/80, 120/119


Mapping: {{mapping| 1 0 -4 -13 -6 -20 12 | 0 1 4 10 6 15 -5 }}
{{Mapping|legend=0| 1 0 -4 -13 -6 -20 12 | 0 1 4 10 6 15 -5 }}


Optimal tunings:  
Optimal tunings:  
Line 627: Line 622:
Comma list: 45/44, 56/55, 78/77, 81/80, 96/95, 120/119
Comma list: 45/44, 56/55, 78/77, 81/80, 96/95, 120/119


Mapping: {{mapping| 1 0 -4 -13 -6 -20 12 9 | 0 1 4 10 6 15 -5 -3 }}
{{Mapping|legend=0| 1 0 -4 -13 -6 -20 12 9 | 0 1 4 10 6 15 -5 -3 }}


Optimal tunings:  
Optimal tunings:  
Line 642: Line 637:
Comma list: 45/44, 56/55, 65/64, 81/80
Comma list: 45/44, 56/55, 65/64, 81/80


Mapping: {{mapping| 1 0 -4 -13 -6 10 | 0 1 4 10 6 -4 }}
{{Mapping|legend=0| 1 0 -4 -13 -6 10 | 0 1 4 10 6 -4 }}


Optimal tunings:  
Optimal tunings:  
Line 657: Line 652:
Comma list: 45/44, 52/51, 56/55, 65/64, 81/80
Comma list: 45/44, 52/51, 56/55, 65/64, 81/80


Mapping: {{mapping| 1 0 -4 -13 -6 10 12 | 0 1 4 10 6 -4 -5 }}
{{Mapping|legend=0| 1 0 -4 -13 -6 10 12 | 0 1 4 10 6 -4 -5 }}


Optimal tunings:  
Optimal tunings:  
Line 672: Line 667:
Comma list: 39/38, 45/44, 52/51, 56/55, 65/64, 81/80
Comma list: 39/38, 45/44, 52/51, 56/55, 65/64, 81/80


Mapping: {{mapping| 1 0 -4 -13 -6 10 12 9 | 0 1 4 10 6 -4 -5 -3 }}
{{Mapping|legend=0| 1 0 -4 -13 -6 10 12 9 | 0 1 4 10 6 -4 -5 -3 }}


Optimal tunings:  
Optimal tunings:  
Line 689: Line 684:
Comma list: 81/80, 126/125, 245/242
Comma list: 81/80, 126/125, 245/242


Mapping: {{mapping| 2 0 -8 -26 -31 | 0 1 4 10 12 }}
{{Mapping|legend=0| 2 0 -8 -26 -31 | 0 1 4 10 12 }}


: mapping generators: ~63/44, ~3
: mapping generators: ~63/44, ~3
Line 706: Line 701:
Comma list: 81/80, 105/104, 126/125, 245/242
Comma list: 81/80, 105/104, 126/125, 245/242


Mapping: {{mapping| 2 0 -8 -26 -31 -40 | 0 1 4 10 12 15 }}
{{Mapping|legend=0| 2 0 -8 -26 -31 -40 | 0 1 4 10 12 15 }}


Optimal tunings:  
Optimal tunings:  
Line 721: Line 716:
Comma list: 81/80, 105/104, 126/125, 189/187, 221/220
Comma list: 81/80, 105/104, 126/125, 189/187, 221/220


Mapping: {{mapping| 2 0 -8 -26 -31 -40 5 | 0 1 4 10 12 15 1 }}
{{Mapping|legend=0| 2 0 -8 -26 -31 -40 5 | 0 1 4 10 12 15 1 }}


Optimal tunings:  
Optimal tunings:  
Line 736: Line 731:
Comma list: 81/80, 105/104, 126/125, 153/152, 189/187, 221/220
Comma list: 81/80, 105/104, 126/125, 153/152, 189/187, 221/220


Mapping: {{mapping| 2 0 -8 -26 -31 -40 5 -1 | 0 1 4 10 12 15 1 3 }}
{{Mapping|legend=0| 2 0 -8 -26 -31 -40 5 -1 | 0 1 4 10 12 15 1 3 }}


Optimal tunings:  
Optimal tunings:  
Line 753: Line 748:
Comma list: 81/80, 126/125, 1344/1331
Comma list: 81/80, 126/125, 1344/1331


Mapping: {{mapping| 1 2 4 7 5 | 0 -3 -12 -30 -11 }}
{{Mapping|legend=0| 1 2 4 7 5 | 0 -3 -12 -30 -11 }}


: mapping generators: ~2, ~11/10
: mapping generators: ~2, ~11/10
Line 770: Line 765:
Comma list: 81/80, 126/125, 144/143, 364/363
Comma list: 81/80, 126/125, 144/143, 364/363


Mapping: {{mapping| 1 2 4 7 5 3 | 0 -3 -12 -30 -11 5 }}
{{Mapping|legend=0| 1 2 4 7 5 3 | 0 -3 -12 -30 -11 5 }}


Optimal tunings:  
Optimal tunings:  
Line 785: Line 780:
Comma list: 81/80, 126/125, 144/143, 189/187, 221/220
Comma list: 81/80, 126/125, 144/143, 189/187, 221/220


Mapping: {{mapping| 1 2 4 7 5 3 8 | 0 -3 -12 -30 -11 5 -28 }}
{{Mapping|legend=0| 1 2 4 7 5 3 8 | 0 -3 -12 -30 -11 5 -28 }}


Optimal tunings:  
Optimal tunings:  
Line 841: Line 836:
Comma list: 45/44, 81/80, 385/384
Comma list: 45/44, 81/80, 385/384


Mapping: {{mapping| 1 0 -4 17 -6 | 0 1 4 -9 6 }}
{{Mapping|legend=0| 1 0 -4 17 -6 | 0 1 4 -9 6 }}


Optimal tuning:  
Optimal tuning:  
Line 860: Line 855:
Comma list: 45/44, 65/64, 78/77, 81/80
Comma list: 45/44, 65/64, 78/77, 81/80


Mapping: {{mapping| 1 0 -4 17 -6 10 | 0 1 4 -9 6 -4 }}
{{Mapping|legend=0| 1 0 -4 17 -6 10 | 0 1 4 -9 6 -4 }}


Optimal tunings:  
Optimal tunings:  
Line 911: Line 906:
Comma list: 36/35, 56/55, 64/63
Comma list: 36/35, 56/55, 64/63


Mapping: {{mapping| 1 0 -4 6 13 | 0 1 4 -2 -6 }}
{{Mapping|legend=0| 1 0 -4 6 13 | 0 1 4 -2 -6 }}


Tuning ranges:  
Tuning ranges:  
Line 930: Line 925:
Comma list: 36/35, 56/55, 64/63, 66/65
Comma list: 36/35, 56/55, 64/63, 66/65


Mapping: {{mapping| 1 0 -4 6 13 18 | 0 1 4 -2 -6 -9 }}
{{Mapping|legend=0| 1 0 -4 6 13 18 | 0 1 4 -2 -6 -9 }}


Optimal tunings:  
Optimal tunings:  
Line 949: Line 944:
Comma list: 26/25, 36/35, 56/55, 64/63
Comma list: 26/25, 36/35, 56/55, 64/63


Mapping: {{mapping| 1 0 -4 6 13 -9 | 0 1 4 -2 -6 8 }}
{{Mapping|legend=0| 1 0 -4 6 13 -9 | 0 1 4 -2 -6 8 }}


Optimal tunings:  
Optimal tunings:  
Line 964: Line 959:
Comma list: 36/35, 64/63, 77/75
Comma list: 36/35, 64/63, 77/75


Mapping: {{mapping| 1 0 -4 6 -14 | 0 1 4 -2 11 }}
{{Mapping|legend=0| 1 0 -4 6 -14 | 0 1 4 -2 11 }}


Optimal tunings:  
Optimal tunings:  
Line 979: Line 974:
Comma list: 26/25, 36/35, 64/63, 66/65
Comma list: 26/25, 36/35, 64/63, 66/65


Mapping: {{mapping| 1 0 -4 6 -14 -9 | 0 1 4 -2 11 8 }}
{{Mapping|legend=0| 1 0 -4 6 -14 -9 | 0 1 4 -2 11 8 }}


Optimal tunings:  
Optimal tunings:  
Line 994: Line 989:
Comma list: 36/35, 45/44, 64/63
Comma list: 36/35, 45/44, 64/63


Mapping: {{mapping| 1 0 -4 6 -6 | 0 1 4 -2 6 }}
{{Mapping|legend=0| 1 0 -4 6 -6 | 0 1 4 -2 6 }}


Optimal tunings:  
Optimal tunings:  
Line 1,009: Line 1,004:
Comma list: 22/21, 33/32, 36/35
Comma list: 22/21, 33/32, 36/35


Mapping: {{mapping| 1 0 -4 6 5 | 0 1 4 -2 -1 }}
{{Mapping|legend=0| 1 0 -4 6 5 | 0 1 4 -2 -1 }}


Optimal tunings:  
Optimal tunings:  
Line 1,050: Line 1,045:
Comma list: 45/44, 81/80, 1375/1344
Comma list: 45/44, 81/80, 1375/1344


Mapping: {{mapping| 1 0 -4 -24 -6 | 0 1 4 17 6 }}
{{Mapping|legend=0| 1 0 -4 -24 -6 | 0 1 4 17 6 }}


Optimal tunings:  
Optimal tunings:  
Line 1,091: Line 1,086:
Comma list: 21/20, 28/27, 33/32
Comma list: 21/20, 28/27, 33/32


Mapping: {{mapping| 1 0 -4 -2 5 | 0 1 4 3 -1 }}
{{Mapping|legend=0| 1 0 -4 -2 5 | 0 1 4 3 -1 }}


Optimal tunings:  
Optimal tunings:  
Line 1,212: Line 1,207:
Comma list: 56/55, 81/80, 132/125
Comma list: 56/55, 81/80, 132/125


Mapping: {{mapping| 1 0 -4 -21 -14 | 0 1 4 15 11 }}
{{Mapping|legend=0| 1 0 -4 -21 -14 | 0 1 4 15 11 }}


Optimal tunings:  
Optimal tunings:  
Line 1,227: Line 1,222:
Comma list: 26/25, 56/55, 66/65, 81/80
Comma list: 26/25, 56/55, 66/65, 81/80


Mapping: {{mapping| 1 0 -4 -21 -14 -9 | 0 1 4 15 11 8 }}
{{Mapping|legend=0| 1 0 -4 -21 -14 -9 | 0 1 4 15 11 8 }}


Optimal tunings:  
Optimal tunings:  
Line 1,279: Line 1,274:
Comma list: 81/80, 121/120, 176/175
Comma list: 81/80, 121/120, 176/175


Mapping: {{mapping| 1 1 0 6 2 | 0 2 8 -11 5 }}
{{Mapping|legend=0| 1 1 0 6 2 | 0 2 8 -11 5 }}


Optimal tunings:  
Optimal tunings:  
Line 1,305: Line 1,300:
Comma list: 66/65, 81/80, 105/104, 121/120
Comma list: 66/65, 81/80, 105/104, 121/120


Mapping: {{mapping| 1 1 0 6 2 4 | 0 2 8 -11 5 -1 }}
{{Mapping|legend=0| 1 1 0 6 2 4 | 0 2 8 -11 5 -1 }}


Optimal tunings:  
Optimal tunings:  
Line 1,322: Line 1,317:
Comma list: 66/65, 81/80, 105/104, 121/120, 154/153
Comma list: 66/65, 81/80, 105/104, 121/120, 154/153


Mapping: {{mapping| 1 1 0 6 2 4 7 | 0 2 8 -11 5 -1 -10 }}
{{Mapping|legend=0| 1 1 0 6 2 4 7 | 0 2 8 -11 5 -1 -10 }}


Optimal tunings:  
Optimal tunings:  
Line 1,339: Line 1,334:
Comma list: 66/65, 77/76, 81/80, 96/95, 105/104, 153/152
Comma list: 66/65, 77/76, 81/80, 96/95, 105/104, 153/152


Mapping: {{mapping| 1 1 0 6 2 4 7 6 | 0 2 8 -11 5 -1 -10 -6 }}
{{Mapping|legend=0| 1 1 0 6 2 4 7 6 | 0 2 8 -11 5 -1 -10 -6 }}


Optimal tunings:  
Optimal tunings:  
Line 1,379: Line 1,374:
Comma list: 56/55, 77/75, 243/242
Comma list: 56/55, 77/75, 243/242


Mapping: {{mapping| 1 1 0 -1 2 | 0 2 8 13 5 }}
{{Mapping|legend=0| 1 1 0 -1 2 | 0 2 8 13 5 }}


Optimal tunings:  
Optimal tunings:  
Line 1,396: Line 1,391:
Comma list: 56/55, 66/65, 77/75, 243/242
Comma list: 56/55, 66/65, 77/75, 243/242


Mapping: {{mapping| 1 1 0 -1 2 4 | 0 2 8 13 5 -1 }}
{{Mapping|legend=0| 1 1 0 -1 2 4 | 0 2 8 13 5 -1 }}


Optimal tunings:  
Optimal tunings:  
Line 1,443: Line 1,438:
Comma list: 56/55, 81/80, 540/539
Comma list: 56/55, 81/80, 540/539


Mapping: {{mapping| 1 0 -4 -3 4 | 0 3 12 11 -1 }}
{{Mapping|legend=0| 1 0 -4 -3 4 | 0 3 12 11 -1 }}


Optimal tunings:  
Optimal tunings:  
Line 1,458: Line 1,453:
Comma list: 56/55, 78/77, 81/80, 91/90
Comma list: 56/55, 78/77, 81/80, 91/90


Mapping: {{mapping| 1 0 -4 -3 4 0 | 0 3 12 11 -1 7 }}
{{Mapping|legend=0| 1 0 -4 -3 4 0 | 0 3 12 11 -1 7 }}


Optimal tunings:  
Optimal tunings:  
Line 1,473: Line 1,468:
Comma list: 77/75, 81/80, 99/98
Comma list: 77/75, 81/80, 99/98


Mapping: {{mapping| 1 0 -4 -3 -5 | 0 3 12 11 16 }}
{{Mapping|legend=0| 1 0 -4 -3 -5 | 0 3 12 11 16 }}


Optimal tunings:  
Optimal tunings:  
Line 1,488: Line 1,483:
Comma list: 66/65, 77/75, 81/80, 99/98
Comma list: 66/65, 77/75, 81/80, 99/98


Mapping: {{mapping| 1 0 -4 -3 -5 0 | 0 3 12 11 16 7 }}
{{Mapping|legend=0| 1 0 -4 -3 -5 0 | 0 3 12 11 16 7 }}


Optimal tunings:  
Optimal tunings:  
Line 1,503: Line 1,498:
Comma list: 45/44, 81/80, 343/330
Comma list: 45/44, 81/80, 343/330


Mapping: {{mapping| 1 0 -4 -3 -6 | 0 3 12 11 18 }}
{{Mapping|legend=0| 1 0 -4 -3 -6 | 0 3 12 11 18 }}


Optimal tunings:  
Optimal tunings:  
Line 1,518: Line 1,513:
Comma list: 45/44, 81/80, 91/88, 147/143
Comma list: 45/44, 81/80, 91/88, 147/143


Mapping: {{mapping| 1 0 -4 -3 -6 0 | 0 3 12 11 18 7 }}
{{Mapping|legend=0| 1 0 -4 -3 -6 0 | 0 3 12 11 18 7 }}


Optimal tunings:  
Optimal tunings:  
Line 1,554: Line 1,549:
Comma list: 81/80, 176/175, 864/847
Comma list: 81/80, 176/175, 864/847


Mapping: {{mapping| 1 2 4 1 5 | 0 -3 -12 13 -11 }}
{{Mapping|legend=0| 1 2 4 1 5 | 0 -3 -12 13 -11 }}


Optimal tunings:  
Optimal tunings:  
Line 1,569: Line 1,564:
Comma list: 78/77, 81/80, 144/143, 176/175
Comma list: 78/77, 81/80, 144/143, 176/175


Mapping: {{mapping| 1 2 4 1 5 3 | 0 -3 -12 13 -11 5 }}
{{Mapping|legend=0| 1 2 4 1 5 3 | 0 -3 -12 13 -11 5 }}


Optimal tunings:  
Optimal tunings:  
Line 1,637: Line 1,632:
Comma list: 81/80, 99/98, 121/120
Comma list: 81/80, 99/98, 121/120


Mapping: {{mapping| 1 -1 -8 -3 -3 | 0 4 16 9 10 }}
{{Mapping|legend=0| 1 -1 -8 -3 -3 | 0 4 16 9 10 }}


Optimal tunings:  
Optimal tunings:  
Line 1,652: Line 1,647:
Comma list: 66/65, 81/80, 99/98, 121/120
Comma list: 66/65, 81/80, 99/98, 121/120


Mapping: {{mapping| 1 -1 -8 -3 -3 5 | 0 4 16 9 10 -2 }}
{{Mapping|legend=0| 1 -1 -8 -3 -3 5 | 0 4 16 9 10 -2 }}


Optimal tunings:  
Optimal tunings:  
Line 1,667: Line 1,662:
Comma list: 78/77, 81/80, 91/90, 99/98
Comma list: 78/77, 81/80, 91/90, 99/98


Mapping: {{mapping| 1 -1 -8 -3 -3 -6 | 0 4 16 9 10 15 }}
{{Mapping|legend=0| 1 -1 -8 -3 -3 -6 | 0 4 16 9 10 15 }}


Optimal tunings:  
Optimal tunings:  
Line 1,682: Line 1,677:
Comma list: 81/80, 99/98, 105/104, 121/120
Comma list: 81/80, 99/98, 105/104, 121/120


Mapping: {{mapping| 1 -1 -8 -3 -3 -15 | 0 4 16 9 10 29 }}
{{Mapping|legend=0| 1 -1 -8 -3 -3 -15 | 0 4 16 9 10 29 }}


Optimal tunings:  
Optimal tunings:  
Line 1,697: Line 1,692:
Comma list: 81/80, 99/98, 105/104, 120/119, 121/119
Comma list: 81/80, 99/98, 105/104, 120/119, 121/119


Mapping: {{mapping| 1 -1 -8 -3 -3 -15 -3 | 0 4 16 9 10 29 11 }}
{{Mapping|legend=0| 1 -1 -8 -3 -3 -15 -3 | 0 4 16 9 10 29 11 }}


Optimal tunings:  
Optimal tunings:  
Line 1,712: Line 1,707:
Comma list: 77/76, 81/80, 99/98, 105/104, 120/119, 121/119
Comma list: 77/76, 81/80, 99/98, 105/104, 120/119, 121/119


Mapping: {{mapping| 1 -1 -8 -3 -3 -15 -3 -8 | 0 4 16 9 10 29 11 19 }}
{{Mapping|legend=0| 1 -1 -8 -3 -3 -15 -3 -8 | 0 4 16 9 10 29 11 19 }}


Optimal tunings:  
Optimal tunings:  
Line 1,727: Line 1,722:
Comma list: 81/80, 385/384, 1375/1372
Comma list: 81/80, 385/384, 1375/1372


Mapping: {{mapping| 1 -1 -8 -3 17 | 0 4 16 9 -21 }}
{{Mapping|legend=0| 1 -1 -8 -3 17 | 0 4 16 9 -21 }}


Optimal tunings:  
Optimal tunings:  
Line 1,738: Line 1,733:


== Jerome ==
== Jerome ==
Jerome is related to [[20ed5|Hieronymus' tuning]]; the Hieronymus generator is 5<sup>1/20</sup>, or 139.316 cents. It may be described as {{nowrap| 17c & 26 }}; its ploidacot is pentacot. While the generator represents both 13/12 and 12/11, the CTE/CWE and Hieronymus generators are close to 13/12 in size.
Jerome is related to [[20ed5|Hieronymus' tuning]]; the Hieronymus generator is 5<sup>1/20</sup>, or 139.316 cents. It may be described as {{nowrap| 17c & 26 }}; its ploidacot is pentacot. Related temperaments include [[progression]] and [[secund]], which only differ by the mapping of 5. While the generator represents both 13/12 and 12/11, the CTE/CWE and Hieronymus generators are close to 13/12 in size.


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 1,763: Line 1,758:
Comma list: 81/80, 99/98, 864/847
Comma list: 81/80, 99/98, 864/847


Mapping: {{mapping| 1 1 0 2 3 | 0 5 20 7 4 }}
{{Mapping|legend=0| 1 1 0 2 3 | 0 5 20 7 4 }}


Optimal tunings:  
Optimal tunings:  
Line 1,778: Line 1,773:
Comma list: 78/77, 81/80, 99/98, 144/143
Comma list: 78/77, 81/80, 99/98, 144/143


Mapping: {{mapping| 1 1 0 2 3 3 | 0 5 20 7 4 6 }}
{{Mapping|legend=0| 1 1 0 2 3 3 | 0 5 20 7 4 6 }}


Optimal tunings:  
Optimal tunings:  
Line 1,793: Line 1,788:
Comma list: 78/77, 81/80, 99/98, 144/143, 189/187
Comma list: 78/77, 81/80, 99/98, 144/143, 189/187


Mapping: {{mapping| 1 1 0 2 3 3 2 | 0 5 20 7 4 6 18 }}
{{Mapping|legend=0| 1 1 0 2 3 3 2 | 0 5 20 7 4 6 18 }}


Optimal tunings:  
Optimal tunings:  
Line 1,808: Line 1,803:
Comma list: 78/77, 81/80, 99/98, 120/119, 135/133, 144/143
Comma list: 78/77, 81/80, 99/98, 120/119, 135/133, 144/143


Mapping: {{mapping| 1 1 0 2 3 3 2 1 | 0 5 20 7 4 6 18 28 }}
{{Mapping|legend=0| 1 1 0 2 3 3 2 1 | 0 5 20 7 4 6 18 28 }}


Optimal tunings:  
Optimal tunings:  
Line 1,844: Line 1,839:
Comma list: 81/80, 99/98, 2541/2500
Comma list: 81/80, 99/98, 2541/2500


Mapping: {{mapping| 1 -1 -8 -7 -11 | 0 5 20 19 28 }}
{{Mapping|legend=0| 1 -1 -8 -7 -11 | 0 5 20 19 28 }}


Optimal tunings:  
Optimal tunings:  
Line 1,890: Line 1,885:
Comma list: 45/44, 50/49, 81/80
Comma list: 45/44, 50/49, 81/80


Mapping: {{mapping| 2 0 -8 -7 -12 | 0 1 4 4 6 }}
{{Mapping|legend=0| 2 0 -8 -7 -12 | 0 1 4 4 6 }}


Optimal tunings:  
Optimal tunings:  
Line 1,909: Line 1,904:
Comma list: 45/44, 50/49, 78/77, 81/80
Comma list: 45/44, 50/49, 78/77, 81/80


Mapping: {{mapping| 2 0 -8 -7 -12 -21 | 0 1 4 4 6 9 }}
{{Mapping|legend=0| 2 0 -8 -7 -12 -21 | 0 1 4 4 6 9 }}


Optimal tunings:  
Optimal tunings:  
Line 1,928: Line 1,923:
Comma list: 45/44, 50/49, 78/77, 81/80, 85/84
Comma list: 45/44, 50/49, 78/77, 81/80, 85/84


Mapping: {{mapping| 2 0 -8 -7 -12 -21 5 | 0 1 4 4 6 9 1 }}
{{Mapping|legend=0| 2 0 -8 -7 -12 -21 5 | 0 1 4 4 6 9 1 }}


Optimal tunings:  
Optimal tunings:  
Line 1,943: Line 1,938:
Comma list: 45/44, 50/49, 57/56, 78/77, 81/80, 85/84
Comma list: 45/44, 50/49, 57/56, 78/77, 81/80, 85/84


Mapping: {{mapping| 2 0 -8 -7 -12 -21 5 -1 | 0 1 4 4 6 9 1 3 }}
{{Mapping|legend=0| 2 0 -8 -7 -12 -21 5 -1 | 0 1 4 4 6 9 1 3 }}


Optimal tunings:  
Optimal tunings:  
Line 1,958: Line 1,953:
Comma list: 27/26, 40/39, 45/44, 50/49
Comma list: 27/26, 40/39, 45/44, 50/49


Mapping: {{mapping| 2 0 -8 -7 -12 -2 | 0 1 4 4 6 3 }}
{{Mapping|legend=0| 2 0 -8 -7 -12 -2 | 0 1 4 4 6 3 }}


Optimal tunings:  
Optimal tunings:  
Line 1,973: Line 1,968:
Comma list: 33/32, 50/49, 55/54
Comma list: 33/32, 50/49, 55/54


Mapping: {{mapping| 2 0 -8 -7 10 | 0 1 4 4 -1 }}
{{Mapping|legend=0| 2 0 -8 -7 10 | 0 1 4 4 -1 }}


Optimal tunings:  
Optimal tunings:  
Line 1,988: Line 1,983:
Comma list: 50/49, 56/55, 81/77
Comma list: 50/49, 56/55, 81/77


Mapping: {{mapping| 2 0 -8 -7 7 | 0 1 4 4 0 }}
{{Mapping|legend=0| 2 0 -8 -7 7 | 0 1 4 4 0 }}


Optimal tunings:  
Optimal tunings:  
Line 2,007: Line 2,002:
Comma list: 50/49, 81/80, 864/847
Comma list: 50/49, 81/80, 864/847


Mapping: {{mapping| 2 1 -4 -3 8 | 0 2 8 8 -1 }}
{{Mapping|legend=0| 2 1 -4 -3 8 | 0 2 8 8 -1 }}


: mapping generators: ~7/5, ~16/11
: mapping generators: ~7/5, ~16/11
Line 2,024: Line 2,019:
Comma list: 50/49, 78/77, 81/80, 144/143
Comma list: 50/49, 78/77, 81/80, 144/143


Mapping: {{mapping| 2 1 -4 -3 8 2 | 0 2 8 8 -1 5 }}
{{Mapping|legend=0| 2 1 -4 -3 8 2 | 0 2 8 8 -1 5 }}


Optimal tunings:  
Optimal tunings:  
Line 2,039: Line 2,034:
Comma list: 50/49, 78/77, 81/80, 85/84, 144/143
Comma list: 50/49, 78/77, 81/80, 85/84, 144/143


Mapping: {{mapping| 2 1 -4 -3 8 2 6 | 0 2 8 8 -1 5 2 }}
{{Mapping|legend=0| 2 1 -4 -3 8 2 6 | 0 2 8 8 -1 5 2 }}


Optimal tunings:  
Optimal tunings:  
Line 2,054: Line 2,049:
Comma list: 50/49, 57/56, 78/77, 81/80, 85/84, 144/143
Comma list: 50/49, 57/56, 78/77, 81/80, 85/84, 144/143


Mapping: {{mapping| 2 1 -4 -3 8 2 6 2 | 0 2 8 8 -1 5 2 6 }}
{{Mapping|legend=0| 2 1 -4 -3 8 2 6 2 | 0 2 8 8 -1 5 2 6 }}


Optimal tunings:  
Optimal tunings:  
Line 2,090: Line 2,085:
Comma list: 81/80, 245/242, 385/384
Comma list: 81/80, 245/242, 385/384


Mapping: {{mapping| 2 1 -4 11 8 | 0 2 8 -5 -1 }}
{{Mapping|legend=0| 2 1 -4 11 8 | 0 2 8 -5 -1 }}


Optimal tunings:  
Optimal tunings:  
Line 2,105: Line 2,100:
Comma list: 81/80, 105/104, 144/143, 245/242
Comma list: 81/80, 105/104, 144/143, 245/242


Mapping: {{mapping| 2 1 -4 11 8 2 | 0 2 8 -5 -1 5 }}
{{Mapping|legend=0| 2 1 -4 11 8 2 | 0 2 8 -5 -1 5 }}


Optimal tunings:  
Optimal tunings:  
Line 2,120: Line 2,115:
Comma list: 81/80, 105/104, 144/143, 245/242, 273/272
Comma list: 81/80, 105/104, 144/143, 245/242, 273/272


Mapping: {{mapping| 2 1 -4 11 8 2 6 | 0 2 8 -5 -1 5 2 }}
{{Mapping|legend=0| 2 1 -4 11 8 2 6 | 0 2 8 -5 -1 5 2 }}


Optimal tunings:  
Optimal tunings:  
Line 2,135: Line 2,130:
Comma list: 81/80, 105/104, 133/132, 144/143, 171/170, 210/209
Comma list: 81/80, 105/104, 133/132, 144/143, 171/170, 210/209


Mapping: {{mapping| 2 1 -4 11 8 2 6 2 | 0 2 8 -5 -1 5 2 6 }}
{{Mapping|legend=0| 2 1 -4 11 8 2 6 2 | 0 2 8 -5 -1 5 2 6 }}


Optimal tunings:  
Optimal tunings:  
Line 2,171: Line 2,166:
Comma list: 81/80, 99/98, 73728/73205
Comma list: 81/80, 99/98, 73728/73205


Mapping: {{mapping| 2 1 -4 4 8 | 0 4 16 3 -2 }}
{{Mapping|legend=0| 2 1 -4 4 8 | 0 4 16 3 -2 }}


Optimal tunings:  
Optimal tunings:  
Line 2,186: Line 2,181:
Comma list: 81/80, 99/98, 144/143, 2200/2197
Comma list: 81/80, 99/98, 144/143, 2200/2197


Mapping: {{mapping| 2 1 -4 4 8 2 | 0 4 16 3 -2 10 }}
{{Mapping|legend=0| 2 1 -4 4 8 2 | 0 4 16 3 -2 10 }}


Optimal tunings:  
Optimal tunings:  
Line 2,222: Line 2,217:
Comma list: 81/80, 385/384, 2401/2376
Comma list: 81/80, 385/384, 2401/2376


Mapping: {{mapping| 5 0 -20 14 41 | 0 1 4 0 -3 }}
{{Mapping|legend=0| 5 0 -20 14 41 | 0 1 4 0 -3 }}


Optimal tunings:  
Optimal tunings:  
Line 2,237: Line 2,232:
Comma list: 81/80, 105/104, 144/143, 2401/2376
Comma list: 81/80, 105/104, 144/143, 2401/2376


Mapping: {{mapping| 5 0 -20 14 41 -21 | 0 1 4 0 -3 5 }}
{{Mapping|legend=0| 5 0 -20 14 41 -21 | 0 1 4 0 -3 5 }}


Optimal tunings:  
Optimal tunings:  
Line 2,253: Line 2,248:
[[Comma list]]: 81/80, 96/95
[[Comma list]]: 81/80, 96/95


{{Mapping|legend=2| 1 0 -4 9 | 0 1 4 -3 }}
{{Mapping|legend=3| 1 0 -4 9 | 0 1 4 -3 }}


{{Mapping|legend=3| 1 0 -4 0 0 0 0 9 | 0 1 4 0 0 0 0 -3 }}
{{Mapping|legend=5| 1 0 -4 0 0 0 0 9 | 0 1 4 0 0 0 0 -3 }}


: mapping generators: ~2, ~3
: mapping generators: ~2, ~3
Line 2,276: Line 2,271:
[[Comma list]]: 45/44, 81/80
[[Comma list]]: 45/44, 81/80


{{Mapping|legend=2| 1 0 -4 -6 | 0 1 4 6 }}
{{Mapping|legend=3| 1 0 -4 -6 | 0 1 4 6 }}


{{Mapping|legend=3| 1 0 -4 0 -6 | 0 1 4 0 6 }}
{{Mapping|legend=5| 1 0 -4 0 -6 | 0 1 4 0 6 }}


: mapping generators: ~2, ~3
: mapping generators: ~2, ~3
Line 2,297: Line 2,292:
Comma list: 45/44, 65/64, 81/80
Comma list: 45/44, 65/64, 81/80


Subgroup-val mapping: {{mapping| 1 0 -4 -6 10 | 0 1 4 6 -4 }}
{{Mapping|legend=2| 1 0 -4 -6 10 | 0 1 4 6 -4 }}


Gencom mapping: {{mapping| 1 0 -4 0 -6 10 | 0 1 4 0 6 -4 }}
{{Mapping|legend=4| 1 0 -4 0 -6 10 | 0 1 4 0 6 -4 }}


Optimal tunings:  
Optimal tunings:  
Line 2,314: Line 2,309:
[[Comma list]]: 33/32, 55/54
[[Comma list]]: 33/32, 55/54


{{Mapping|legend=2| 1 0 -4 5 | 0 1 4 -1 }}
{{Mapping|legend=3| 1 0 -4 5 | 0 1 4 -1 }}


{{Mapping|legend=3| 1 0 -4 0 5 | 0 1 4 0 -1 }}
{{Mapping|legend=5| 1 0 -4 0 5 | 0 1 4 0 -1 }}


: mapping generators: ~2, ~3
: mapping generators: ~2, ~3
Line 2,335: Line 2,330:
Comma list: 33/32, 55/54, 975/968
Comma list: 33/32, 55/54, 975/968


Subgroup-val mapping: {{mapping| 1 0 -4 5 21 | 0 1 4 -1 -11 }}
{{Mapping|legend=2| 1 0 -4 5 21 | 0 1 4 -1 -11 }}


Gencom mapping: {{mapping| 1 0 -4 0 5 21 | 0 1 4 0 -1 -11 }}
{{Mapping|legend=4| 1 0 -4 0 5 21 | 0 1 4 0 -1 -11 }}


Optimal tunings:  
Optimal tunings:  
Line 2,350: Line 2,345:
<references/>
<references/>


[[Category:Temperament families]
[[Category:Meantone family| ]] <!-- main article -->
[[Category:Meantone family| ]] <!-- main article -->
[[Category:Meantone| ]] <!-- key article -->
[[Category:Meantone| ]] <!-- key article -->
Retrieved from "https://en.xen.wiki/w/Meantone_family"