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Scales: [[meantone5]], [[meantone7]], [[meantone12]]
Scales: [[meantone5]], [[meantone7]], [[meantone12]]


== Bimeantone ==
== Unidecimal meantone aka Huygens ==
11/8 is mapped to half octave minus the [[meantone diesis]].
{{see also| Meantone vs meanpop }}


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 81/80, 126/125, 245/242
Comma list: 81/80, 126/125, 99/98


Mapping: [{{val| 2 0 -8 -26 -31 }}, {{val| 0 1 4 10 12 }}]
Mapping: [{{val| 1 0 -4 -13 -25 }}, {{val| 0 1 4 10 18 }}]


Mapping generators: ~63/44, ~3
POTE generator: ~3/2 = 696.967


POTE generator: ~3/2 = 696.016
Minimax tuning:  
* [[11-odd-limit]]
: [{{Monzo| 1 0 0 0 0 }}, {{Monzo| 25/16 -1/8 0 0 1/16 }}, {{Monzo| 9/4 -1/2 0 0 1/4 }}, {{Monzo| 21/8 -5/4 0 0 5/8 }}, {{Monzo| 25/8 -9/4 0 0 9/8 }}]
: [[Eigenmonzo]]s: 2, 11/9


{{Val list|legend=1| 12, 26de, 38d, 50 }}
Tuning ranges:
* valid range: [696.774, 700.000] (31 to 12)
* nice range: [691.202, 701.955]
* strict range: [696.774, 700.000]


Badness: 0.0381
Algebraic generator: Traverse, the positive real root of ''x''<sup>4</sup> + 2''x'' - 13, or 696.9529 cents.


=== 13-limit ===
{{Val list|legend=1| 12, 19e, 31, 105, 136b, 167be, 198be }}


Subgroup: 2.3.5.7.11.13
Badness: 0.0170


Comma list: 81/80, 105/104, 126/125, 245/242
; Music
* [http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-74-edo.mp3 Twinkle canon – 74 edo] by [http://soonlabel.com/xenharmonic/archives/573 Claudi Meneghin]


Mapping: [{{val| 2 0 -8 -26 -31 -40 }}, {{val| 0 1 4 10 12 15}}]
=== Tridecimal meantone ===
 
Subgroup: 2.3.5.7.11.13


Mapping generators: ~55/39, ~3
Comma list: 66/65, 81/80, 99/98, 105/104


POTE generator: ~3/2 = 695.836
Mapping: [{{val| 1 0 -4 -13 -25 -20 }}, {{val| 0 1 4 10 18 15 }}]


{{Val list|legend=1| 12f, 26deff, 38df, 50 }}
POTE generator: ~3/2 = 696.642


Badness: 0.0288
{{Val list|legend=1| 12f, 19e, 31 }}


== Unidecimal meantone aka Huygens ==
Badness: 0.0180
{{see also| Meantone vs meanpop }}


Subgroup: 2.3.5.7.11
=== Grosstone ===


Comma list: 81/80, 126/125, 99/98
Subgroup: 2.3.5.7.11.13


Mapping: [{{val| 1 0 -4 -13 -25 }}, {{val| 0 1 4 10 18 }}]
Comma list: 81/80, 99/98, 126/125, 144/143


POTE generator: ~3/2 = 696.967
Mapping: [{{val| 1 0 -4 -13 -25 29 }}, {{val| 0 1 4 10 18 -16 }}]


Minimax tuning:  
POTE generator: ~3/2 = 697.264
* [[11-odd-limit]]
: [{{Monzo| 1 0 0 0 0 }}, {{Monzo| 25/16 -1/8 0 0 1/16 }}, {{Monzo| 9/4 -1/2 0 0 1/4 }}, {{Monzo| 21/8 -5/4 0 0 5/8 }}, {{Monzo| 25/8 -9/4 0 0 9/8 }}]
: [[Eigenmonzo]]s: 2, 11/9


Tuning ranges:  
Tuning ranges:  
Line 137: Line 142:
* strict range: [696.774, 700.000]
* strict range: [696.774, 700.000]


Algebraic generator: Traverse, the positive real root of ''x''<sup>4</sup> + 2''x'' - 13, or 696.9529 cents.
{{Val list|legend=1| 12, 19ef, 31, 43, 74 }}


{{Val list|legend=1| 12, 19e, 31, 105, 136b, 167be, 198be }}
=== Meridetone ===


Badness: 0.0170
Subgroup: 2.3.5.7.11.13


; Music
Comma list: 78/77, 81/80, 99/98, 126/125
* [http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-74-edo.mp3 Twinkle canon – 74 edo] by [http://soonlabel.com/xenharmonic/archives/573 Claudi Meneghin]


=== Tridecimal meantone ===
Mapping: [{{val| 1 0 -4 -13 -25 -39 }}, {{val| 0 1 4 10 18 27 }}]


Subgroup: 2.3.5.7.11.13
POTE generator: ~3/2 = 697.529


Comma list: 66/65, 81/80, 99/98, 105/104
{{Val list|legend=1| 12f, 31f, 43 }}


Mapping: [{{val| 1 0 -4 -13 -25 -20 }}, {{val| 0 1 4 10 18 15 }}]
Badness: 0.0264


POTE generator: ~3/2 = 696.642
=== Hemimeantone ===


{{Val list|legend=1| 12f, 19e, 31 }}
Subgroup: 2.3.5.7.11.13


Badness: 0.0180
Comma list: 81/80, 99/98, 126/125, 169/168


=== Grosstone ===
Mapping: [{{val| 1 0 -4 -13 -25 -5 }}, {{val| 0 2 8 20 36 11 }}]


Subgroup: 2.3.5.7.11.13
Mapping generators: ~2, ~26/15


Comma list: 81/80, 99/98, 126/125, 144/143
POTE generator: ~15/13 = 250.304


Mapping: [{{val| 1 0 -4 -13 -25 29 }}, {{val| 0 1 4 10 18 -16 }}]
{{Val list|legend=1| 19e, 43, 62, 167bef }}


POTE generator: ~3/2 = 697.264
Badness: 0.0314


Tuning ranges:
== Meanpop ==
* valid range: [696.774, 700.000] (31 to 12)
{{see also| Meantone vs meanpop }}
* nice range: [691.202, 701.955]
* strict range: [696.774, 700.000]


{{Val list|legend=1| 12, 19ef, 31, 43, 74 }}
Subgroup: 2.3.5.7.11


=== Meridetone ===
Comma list: 81/80, 126/125, 385/384


Subgroup: 2.3.5.7.11.13
Mapping: [{{val| 1 0 -4 -13 24 }}, {{val| 0 1 4 10 -13 }}]


Comma list: 78/77, 81/80, 99/98, 126/125
Mapping generator: ~2, ~3


Mapping: [{{val| 1 0 -4 -13 -25 -39 }}, {{val| 0 1 4 10 18 27 }}]
POTE generator: ~3/2 = 696.434


POTE generator: ~3/2 = 697.529
Minimax tuning:  
* [[11-odd-limit]]: 1/4 comma
: [{{Monzo| 1 0 0 0 0 }}, {{Monzo| 1 0 1/4 0 0 }}, {{Monzo| 0 0 1 0 0 }}, {{Monzo| -3 0 5/2 0 0 }}, {{Monzo| 11 0 -13/4 0 0 }}]
: [[Eigenmonzo]]s: 2, 5


{{Val list|legend=1| 12f, 31f, 43 }}
Tuning ranges:
* valid range: [694.737, 696.774] (19 to 31)
* nice range: [691.202, 701.955]
* strict range: [694.737, 696.774]


Badness: 0.0264
Algebraic generator: Cybozem; or else Radieubiz, the real root of 3''x''<sup>3</sup> + 6''x'' - 19. Unlike Cybozem, the recurrence for Radieubiz does not converge.


=== Hemimeantone ===
{{Val list|legend=1| 12e, 19, 31, 81 }}


Subgroup: 2.3.5.7.11.13
[[Badness]]: 0.0215


Comma list: 81/80, 99/98, 126/125, 169/168
; Music
* [http://soonlabel.com/xenharmonic/archives/607 Scott Joplin's "The Entertainer" tuned into meanpop]{{Dead link}}
* [http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-50-edo.mp3 Twinkle canon – 50 edo] by [http://soonlabel.com/xenharmonic/archives/573 Claudi Meneghin]


Mapping: [{{val| 1 0 -4 -13 -25 -5 }}, {{val| 0 2 8 20 36 11 }}]
=== 13-limit Meanpop ===


Mapping generators: ~2, ~26/15
Subgroup: 2.3.5.7.11.13


POTE generator: ~15/13 = 250.304
Comma list: 81/80, 105/104, 126/125, 144/143


{{Val list|legend=1| 19e, 43, 62, 167bef }}
Mapping: [{{val| 1 0 -4 -13 24 -20 }}, {{val| 0 1 4 10 -13 15 }}]


Badness: 0.0314
Mapping generator: ~2, ~3


== Meanpop ==
POTE generator: ~3/2 = 696.211
{{see also| Meantone vs meanpop }}


Subgroup: 2.3.5.7.11
Tuning ranges:  
* valid range: [694.737, 696.774] (19 to 31)
* nice range: [691.202, 701.955]
* strict range: [694.737, 696.774]


Comma list: 81/80, 126/125, 385/384
{{Val list|legend=1| 12ef, 19, 31, 50, 81, 131bd, 212bbddf }}


Mapping: [{{val| 1 0 -4 -13 24 }}, {{val| 0 1 4 10 -13 }}]
Badness: 0.0209


Mapping generator: ~2, ~3
=== Meanplop ===


POTE generator: ~3/2 = 696.434
Subgroup: 2.3.5.7.11.13


Minimax tuning:  
Comma list: 65/64, 78/77, 81/80, 91/90
* [[11-odd-limit]]: 1/4 comma
: [{{Monzo| 1 0 0 0 0 }}, {{Monzo| 1 0 1/4 0 0 }}, {{Monzo| 0 0 1 0 0 }}, {{Monzo| -3 0 5/2 0 0 }}, {{Monzo| 11 0 -13/4 0 0 }}]
: [[Eigenmonzo]]s: 2, 5


Tuning ranges:
Mapping: [{{val| 1 0 -4 -13 24 10 }}, {{val| 0 1 4 10 -13 -4 }}]
* valid range: [694.737, 696.774] (19 to 31)
* nice range: [691.202, 701.955]
* strict range: [694.737, 696.774]


Algebraic generator: Cybozem; or else Radieubiz, the real root of 3''x''<sup>3</sup> + 6''x'' - 19. Unlike Cybozem, the recurrence for Radieubiz does not converge.
POTE generator: ~3/2 = 696.202


{{Val list|legend=1| 12e, 19, 31, 81 }}
{{Val list|legend=1| 12e, 19, 31f, 50ff, 81fff }}


[[Badness]]: 0.0215
Badness: 0.0277


; Music
== Meanenneadecal ==
* [http://soonlabel.com/xenharmonic/archives/607 Scott Joplin's "The Entertainer" tuned into meanpop]{{Dead link}}
* [http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-50-edo.mp3 Twinkle canon – 50 edo] by [http://soonlabel.com/xenharmonic/archives/573 Claudi Meneghin]


=== 13-limit Meanpop ===
Subgroup: 2.3.5.7.11


Subgroup: 2.3.5.7.11.13
Comma list: 45/44, 56/55, 81/80


Comma list: 81/80, 105/104, 126/125, 144/143
Mapping: [{{val| 1 0 -4 -13 -6 }}, {{val| 0 1 4 10 6 }}]


Mapping: [{{val| 1 0 -4 -13 24 -20 }}, {{val| 0 1 4 10 -13 15 }}]
POTE generator: ~3/2 = 696.250


Mapping generator: ~2, ~3
{{Val list|legend=1| 7d, 12, 19, 31e, 50ee }}


POTE generator: ~3/2 = 696.211
Badness: 0.0214


Tuning ranges:
=== 13-limit ===
* valid range: [694.737, 696.774] (19 to 31)
* nice range: [691.202, 701.955]
* strict range: [694.737, 696.774]


{{Val list|legend=1| 12ef, 19, 31, 50, 81, 131bd, 212bbddf }}
Subgroup: 2.3.5.7.11.13


Badness: 0.0209
Comma list: 45/44, 56/55, 78/77, 81/80


=== Meanplop ===
Mapping: [{{val| 1 0 -4 -13 -6 -20 }}, {{val| 0 1 4 10 6 15 }}]


Subgroup: 2.3.5.7.11.13
POTE generator: ~3/2 = 696.146


Comma list: 65/64, 78/77, 81/80, 91/90
{{Val list|legend=1| 12f, 19, 31e, 50ee }}


Mapping: [{{val| 1 0 -4 -13 24 10 }}, {{val| 0 1 4 10 -13 -4 }}]
Badness: 0.0212


POTE generator: ~3/2 = 696.202
=== Vincenzo ===


{{Val list|legend=1| 12e, 19, 31f, 50ff, 81fff }}
Subgroup: 2.3.5.7.11.13


Badness: 0.0277
Comma list: 45/44, 56/55, 65/64, 81/80


== Meanenneadecal ==
Mapping: [{{val| 1 0 -4 -13 -6 10 }}, {{val| 0 1 4 10 6 -4 }}]


Subgroup: 2.3.5.7.11
POTE generator: ~3/2 = 695.060


Comma list: 45/44, 56/55, 81/80
{{Val list|legend=1| 7d, 12, 19 }}


Mapping: [{{val| 1 0 -4 -13 -6 }}, {{val| 0 1 4 10 6 }}]
Badness: 0.0248


POTE generator: ~3/2 = 696.250
==== 17-limit ====


{{Val list|legend=1| 7d, 12, 19, 31e, 50ee }}
Subgroup: 2.3.5.7.11.13.17


Badness: 0.0214
Comma list: 45/44, 52/51, 56/55, 65/64, 81/80


=== 13-limit ===
Mapping: [{{val| 1 0 -4 -13 -6 10 12 }}, {{val| 0 1 4 10 6 -4 -5 }}]


Subgroup: 2.3.5.7.11.13
POTE generator: ~3/2 = 695.858


Comma list: 45/44, 56/55, 78/77, 81/80
{{Val list|legend=1| 7d, 12, 19 }}


Mapping: [{{val| 1 0 -4 -13 -6 -20 }}, {{val| 0 1 4 10 6 15 }}]
Badness: 0.0255


POTE generator: ~3/2 = 696.146
==== 19-limit ====


{{Val list|legend=1| 12f, 19, 31e, 50ee }}
Subgroup: 2.3.5.7.11.13.17.19


Badness: 0.0212
Comma list: 39/38, 45/44, 52/51, 56/55, 65/64, 81/80


=== Vincenzo ===
Mapping: [{{val| 1 0 -4 -13 -6 10 12 9 }}, {{val| 0 1 4 10 6 -4 -5 -3 }}]


Subgroup: 2.3.5.7.11.13
POTE generator: ~3/2 = 696.131


Comma list: 45/44, 56/55, 65/64, 81/80
{{Val list|legend=1| 7d, 12, 19 }}
 
Badness: 0.0223
 
==== 23-limit ====
 
Subgroup: 2.3.5.7.11.13.17.19.23
 
Comma list: 39/38, 45/44, 52/51, 56/55, 65/64, 69/68, 81/80


Mapping: [{{val| 1 0 -4 -13 -6 10 }}, {{val| 0 1 4 10 6 -4 }}]
Mapping: [{{val| 1 0 -4 -13 -6 10 12 9 14 }}, {{val| 0 1 4 10 6 -4 -5 -3 -6 }}]


POTE generator: ~3/2 = 695.060
POTE generator: ~3/2 = 696.044


{{Val list|legend=1| 7d, 12, 19 }}
{{Val list|legend=1| 7d, 12, 19 }}


Badness: 0.0248
Badness: 0.0201


==== 17-limit ====
==== 29-limit ====


Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17.19.23.29


Comma list: 45/44, 52/51, 56/55, 65/64, 81/80
Comma list: 39/38, 45/44, 52/51, 56/55, 58/57, 65/64, 69/68, 81/80


Mapping: [{{val| 1 0 -4 -13 -6 10 12 }}, {{val| 0 1 4 10 6 -4 -5 }}]
Mapping: [{{val| 1 0 -4 -13 -6 10 12 9 14 8 }}, {{val| 0 1 4 10 6 -4 -5 -3 -6 -2 }}]


POTE generator: ~3/2 = 695.858
POTE generator: ~3/2 = 695.913


{{Val list|legend=1| 7d, 12, 19 }}
{{Val list|legend=1| 7d, 12, 19 }}


Badness: 0.0255
Badness: 0.0182


==== 19-limit ====
==== 31-limit ====


Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.17.19.23.29.31


Comma list: 39/38, 45/44, 52/51, 56/55, 65/64, 81/80
Comma list: 39/38, 45/44, 52/51, 56/55, 58/57, 65/64, 69/68, 81/80, 93/92


Mapping: [{{val| 1 0 -4 -13 -6 10 12 9 }}, {{val| 0 1 4 10 6 -4 -5 -3 }}]
Mapping: [{{val| 1 0 -4 -13 -6 10 12 9 14 8 16 }}, {{val| 0 1 4 10 6 -4 -5 -3 -6 -2 -7 }}]


POTE generator: ~3/2 = 696.131
POTE generator: ~3/2 = 695.750


{{Val list|legend=1| 7d, 12, 19 }}
{{Val list|legend=1| 7d, 12, 19 }}


Badness: 0.0223
Badness: 0.0171


==== 23-limit ====
==== 37-limit ====


Subgroup: 2.3.5.7.11.13.17.19.23
Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37


Comma list: 39/38, 45/44, 52/51, 56/55, 65/64, 69/68, 81/80
Comma list: 39/38, 45/44, 52/51, 56/55, 58/57, 65/64, 69/68, 75/74, 81/80, 93/92


Mapping: [{{val| 1 0 -4 -13 -6 10 12 9 14 }}, {{val| 0 1 4 10 6 -4 -5 -3 -6 }}]
Mapping: [{{val| 1 0 -4 -13 -6 10 12 9 14 8 16 -9 }}, {{val| 0 1 4 10 6 -4 -5 -3 -6 -2 -7 9 }}]


POTE generator: ~3/2 = 696.044
POTE generator: ~3/2 = 695.603


{{Val list|legend=1| 7d, 12, 19 }}
{{Val list|legend=1| 7d, 12, 19 }}


Badness: 0.0201
Badness: 0.0161


==== 29-limit ====
==== 41-limit ====


Subgroup: 2.3.5.7.11.13.17.19.23.29
Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37.41


Comma list: 39/38, 45/44, 52/51, 56/55, 58/57, 65/64, 69/68, 81/80
Comma list: 39/38, 45/44, 52/51, 56/55, 58/57, 65/64, 69/68, 75/74, 81/80, 93/92, 124/123


Mapping: [{{val| 1 0 -4 -13 -6 10 12 9 14 8 }}, {{val| 0 1 4 10 6 -4 -5 -3 -6 -2 }}]
Mapping: [{{val| 1 0 -4 -13 -6 10 12 9 14 8 16 -9 18 }}, {{val| 0 1 4 10 6 -4 -5 -3 -6 -2 -7 9 -8 }}]


POTE generator: ~3/2 = 695.913
POTE generator: ~3/2 = 695.696


{{Val list|legend=1| 7d, 12, 19 }}
{{Val list|legend=1| 7d, 12, 19 }}


Badness: 0.0182
Badness: 0.0154


==== 31-limit ====
==== 43-limit ====


Subgroup: 2.3.5.7.11.13.17.19.23.29.31
Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37.41.43


Comma list: 39/38, 45/44, 52/51, 56/55, 58/57, 65/64, 69/68, 81/80, 93/92
Comma list: 39/38, 45/44, 52/51, 56/55, 58/57, 65/64, 69/68, 75/74, 81/80, 86/85, 93/92, 124/123


Mapping: [{{val| 1 0 -4 -13 -6 10 12 9 14 8 16 }}, {{val| 0 1 4 10 6 -4 -5 -3 -6 -2 -7 }}]
Mapping: [{{val| 1 0 -4 -13 -6 10 12 9 14 8 16 -9 18 7 }}, {{val| 0 1 4 10 6 -4 -5 -3 -6 -2 -7 9 -8 -1 }}]


POTE generator: ~3/2 = 695.750
POTE generator: ~3/2 = 695.688


{{Val list|legend=1| 7d, 12, 19 }}
{{Val list|legend=1| 7d, 12, 19 }}


Badness: 0.0171
Badness: 0.0139


==== 37-limit ====
==== 47-limit ====


Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37
Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37.41.43.47


Comma list: 39/38, 45/44, 52/51, 56/55, 58/57, 65/64, 69/68, 75/74, 81/80, 93/92
Comma list: 39/38, 45/44, 52/51, 56/55, 58/57, 65/64, 69/68, 75/74, 81/80, 86/85, 93/92, 95/94, 124/123


Mapping: [{{val| 1 0 -4 -13 -6 10 12 9 14 8 16 -9 }}, {{val| 0 1 4 10 6 -4 -5 -3 -6 -2 -7 9 }}]
Mapping: [{{val| 1 0 -4 -13 -6 10 12 9 14 8 16 -9 18 7 4 }}, {{val| 0 1 4 10 6 -4 -5 -3 -6 -2 -7 9 -8 -1 1 }}]


POTE generator: ~3/2 = 695.603
POTE generator: ~3/2 = 695.676


{{Val list|legend=1| 7d, 12, 19 }}
{{Val list|legend=1| 7d, 12, 19 }}


Badness: 0.0161
Badness: 0.0138


==== 41-limit ====
=== Meanundec ===


Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37.41
Subgroup: 2.3.5.7.11.13


Comma list: 39/38, 45/44, 52/51, 56/55, 58/57, 65/64, 69/68, 75/74, 81/80, 93/92, 124/123
Comma list: 27/26, 40/39, 45/44, 56/55


Mapping: [{{val| 1 0 -4 -13 -6 10 12 9 14 8 16 -9 18 }}, {{val| 0 1 4 10 6 -4 -5 -3 -6 -2 -7 9 -8 }}]
Mapping: [{{val| 1 0 -4 -13 -6 -1 }}, {{val| 0 1 4 10 6 3 }}]


POTE generator: ~3/2 = 695.696
POTE generator: ~3/2 = 697.254


{{Val list|legend=1| 7d, 12, 19 }}
{{Val list|legend=1| 7d, 12f, 19f, 31eff }}


Badness: 0.0154
Badness: 0.0242


==== 43-limit ====
== Meanundeci ==


Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37.41.43
Subgroup: 2.3.5.7.11


Comma list: 39/38, 45/44, 52/51, 56/55, 58/57, 65/64, 69/68, 75/74, 81/80, 86/85, 93/92, 124/123
Comma list: 33/32, 55/54, 77/75


Mapping: [{{val| 1 0 -4 -13 -6 10 12 9 14 8 16 -9 18 7 }}, {{val| 0 1 4 10 6 -4 -5 -3 -6 -2 -7 9 -8 -1 }}]
Mapping: [{{val|1 0 -4 -13 5 }}, {{val| 0 1 4 10 -1 }}]


POTE generator: ~3/2 = 695.688
POTE generator: ~3/2 = 694.689


{{Val list|legend=1| 7d, 12, 19 }}
{{Val list|legend=1| 7d, 12e, 19e }}


Badness: 0.0139
Badness: 0.0315


==== 47-limit ====
=== 13-limit ===


Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37.41.43.47
Subgroup: 2.3.5.7.11.13


Comma list: 39/38, 45/44, 52/51, 56/55, 58/57, 65/64, 69/68, 75/74, 81/80, 86/85, 93/92, 95/94, 124/123
Comma list: 33/32, 55/54, 65/64, 77/75


Mapping: [{{val| 1 0 -4 -13 -6 10 12 9 14 8 16 -9 18 7 4 }}, {{val| 0 1 4 10 6 -4 -5 -3 -6 -2 -7 9 -8 -1 1 }}]
Mapping: [{{val|1 0 -4 -13 5 10 }}, {{val| 0 1 4 10 -1 -4 }}]


POTE generator: ~3/2 = 695.676
POTE generator: ~3/2 = 694.764


{{Val list|legend=1| 7d, 12, 19 }}
{{Val list|legend=1| 7d, 12e, 19e }}


Badness: 0.0138
Badness: 0.0263


=== Meanundec ===
== Bimeantone ==
11/8 is mapped to half octave minus the [[meantone diesis]].


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11


Comma list: 27/26, 40/39, 45/44, 56/55
Comma list: 81/80, 126/125, 245/242


Mapping: [{{val| 1 0 -4 -13 -6 -1 }}, {{val| 0 1 4 10 6 3 }}]
Mapping: [{{val| 2 0 -8 -26 -31 }}, {{val| 0 1 4 10 12 }}]


POTE generator: ~3/2 = 697.254
Mapping generators: ~63/44, ~3


{{Val list|legend=1| 7d, 12f, 19f, 31eff }}
POTE generator: ~3/2 = 696.016


Badness: 0.0242
{{Val list|legend=1| 12, 26de, 38d, 50 }}


== Meanundeci ==
Badness: 0.0381


Subgroup: 2.3.5.7.11
=== 13-limit ===


Comma list: 33/32, 55/54, 77/75
Subgroup: 2.3.5.7.11.13


Mapping: [{{val|1 0 -4 -13 5 }}, {{val| 0 1 4 10 -1 }}]
Comma list: 81/80, 105/104, 126/125, 245/242


POTE generator: ~3/2 = 694.689
Mapping: [{{val| 2 0 -8 -26 -31 -40 }}, {{val| 0 1 4 10 12 15}}]


{{Val list|legend=1| 7d, 12e, 19e }}
Mapping generators: ~55/39, ~3


Badness: 0.0315
POTE generator: ~3/2 = 695.836


=== 13-limit ===
{{Val list|legend=1| 12f, 26deff, 38df, 50 }}


Subgroup: 2.3.5.7.11.13
Badness: 0.0288
 
Comma list: 33/32, 55/54, 65/64, 77/75
 
Mapping: [{{val|1 0 -4 -13 5 10 }}, {{val| 0 1 4 10 -1 -4 }}]
 
POTE generator: ~3/2 = 694.764
 
{{Val list|legend=1| 7d, 12e, 19e }}
 
Badness: 0.0263


= Flattone =
= Flattone =
Line 561: Line 561:
Scales: [[flattone12]]
Scales: [[flattone12]]


= Godzilla =
= Dominant =
<span style="display: block; text-align: right;">[[:de:Semiphor,_Semaphor,_Godzilla|Deutsch]]</span>


{{main| Semaphore and Godzilla }}
The interval class for 7 is obtained from two fourths in succession, so that 7/4 is a minor seventh. The 7/6 interval is, like 6/5, now a minor third, and 7/5 is a diminished fifth. An excellent tuning for dominant is [[12edo]], but it also works well with the Pythagorean tuning of pure [[3/2]] fifths, and with [[29edo]], [[41edo]], or [[53edo]].
 
Godzilla tempers out 49/48, equating 8/7 with 7/6. Two of the step-and-a-quarter intervals these represent give a fourth, and so step-and-a-quarter generators generate godzilla. [[19edo]] is close to being the optimal generator tuning; hence it can be more or less equated with taking 4\19 as a generator. MOS are of 5, 9, or 14 notes.


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


[[Comma list]]: 49/48, 81/80
[[Comma list]]: 36/35, 64/63


[[Mapping]]: [{{val| 1 0 -4 2 }}, {{val| 0 2 8 1 }}]
[[Mapping]]: [{{val| 1 0 -4 6 }}, {{val| 0 1 4 -2 }}]


Mapping generators: ~2, ~7/4
{{Multival|legend=1| 1 4 -2 4 -6 -16 }}


{{Multival|legend=1| 2 8 1 8 -4 -20 }}
[[POTE generator]]: ~3/2 = 701.573
 
[[POTE generator]]: ~8/7 = 252.635


[[Tuning ranges]]:  
[[Tuning ranges]]:  
* valid range: [240.000, 257.143] (5 to 14c)
* valid range: [700.000, 720.000] (12 to 5)
* nice range: [231.174, 266.871]
* nice range: [694.786, 715.587]
* strict range: [240.000, 257.143]
* strict range: [700.000, 715.587]


{{Val list|legend=1| 5, 14c, 19 }}
{{Val list|legend=1| 5, 7, 12, 41cd, 53cdd, 65ccddd }}


[[Badness]]: 0.0267
[[Badness]]: 0.0207


== 11-limit ==
== 11-limit ==
Line 593: Line 588:
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 45/44, 49/48, 81/80
Comma list: 36/35, 56/55, 64/63


Mapping: [{{val| 1 0 -4 2 -6 }}, {{val| 0 2 8 1 12 }}]
Mapping: [{{val| 1 0 -4 6 13 }}, {{val| 0 1 4 -2 -6 }}]


Mapping generators: ~2, ~7/4
Tuning ranges:  
* valid range: [700.000, 705.882] (12 to 17)
* nice range: [691.202, 715.587]
* strict range: [700.000, 705.882]


POTE generator: ~8/7 = 254.027
POTE generator: ~3/2 = 703.254


Tuning ranges:
{{Val list|legend=1| 5, 12, 17c, 29cde }}
* valid range: [252.632, 257.143] (19 to 14c)
* nice range: [231.174, 266.871]
* strict range: [252.632, 257.143]


{{Val list|legend=1| 14c, 19, 33cd, 52cd }}
Badness: 0.0242
 
Badness: 0.0290


=== 13-limit ===
=== 13-limit ===
Line 614: Line 607:
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 45/44, 49/48, 78/77, 81/80
Comma list: 36/35, 56/55, 64/63, 66/65


Mapping: [{{val| 1 0 -4 2 -6 -5 }}, {{val| 0 2 8 1 12 11 }}]
Mapping: [{{val| 1 0 -4 6 13 18 }}, {{val| 0 1 4 -2 -6 -9 }}]


Mapping generators: ~2, ~7/4
POTE generator: ~3/2 = 703.636
 
POTE generator: ~8/7 = 253.603


Tuning ranges:  
Tuning ranges:  
* valid range: 694.737 (19)
* valid range: 705.882 (17)
* nice range: [621.581, 737.652]
* nice range: [691.202, 715.587]
* strict range: 694.737
* strict range: 705.882


{{Val list|legend=1| 14cf, 19, 33cdff, 52cdf }}
{{Val list|legend=1| 12f, 17c, 29cdef }}


Badness: 0.0225
Badness: 0.0241


== Semafour ==
=== Dominion ===


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11.13


Comma list: 33/32, 49/48, 55/54
Comma list: 26/25, 36/35, 56/55, 64/63


Mapping: [{{val| 1 0 -4 2 5 }}, {{val| 0 2 8 1 -2 }}]
Mapping: [{{val| 1 0 -4 6 13 -9 }}, {{val| 0 1 4 -2 -6 8 }}]


Mapping generators: ~2, ~7/4
{{Val list|legend=1| 5, 12, 17c, 46cde }}


POTE generator: ~8/7 = 254.042
POTE generator: ~3/2 = 704.905


{{Val list|legend=1| 14c, 19e, 33cdee }}
Badness: 0.0273


Badness: 0.0285
== Domineering ==
 
== Varan ==


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 49/48, 77/75, 81/80
Comma list: 36/35, 45/44, 64/63


Mapping: [{{val| 1 0 -4 2 -10 }}, {{val| 0 2 8 1 17 }}]
Mapping: [{{val| 1 0 -4 6 -6 }}, {{val| 0 1 4 -2 6 }}]


Mapping generators: ~2, ~7/4
POTE generator: ~3/2 = 698.776


POTE generator: ~8/7 = 251.079
{{Val list|legend=1| 5e, 7, 12, 19d, 43de }}


{{Val list|legend=1| 19e, 24, 43de }}
Badness: 0.0220
 
Badness: 0.0396


=== 13-limit ===
=== 13-limit ===
Line 667: Line 654:
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 49/48, 66/65, 77/75, 81/80
Comma list: 36/35, 45/44, 52/49, 64/63


Mapping: [{{val| 1 0 -4 2 -10 -5 }}, {{val| 0 2 8 1 17 11 }}]
Mapping: [{{val| 1 0 -4 6 -6 10 }}, {{val| 0 1 4 -2 6 -4 }}]


Mapping generators: ~2, ~7/4
POTE generator: ~3/2 = 695.762


POTE generator: ~8/7 = 251.165
{{Val list|legend=1| 5ef, 7, 12, 19d, 31def }}


{{Val list|legend=1| 19e, 24, 43de }}
Badness: 0.0270


Badness: 0.0257
==== 17-limit ====


== Baragon ==
Subgroup: 2.3.5.7.11.13.17


Subgroup: 2.3.5.7.11
Comma list: 36/35, 45/44, 51/49, 52/49, 64/63


Comma list: 49/48, 56/55, 81/80
Mapping: [{{val| 1 0 -4 6 -6 10 12 }}, {{val| 0 1 4 -2 6 -4 -5 }}]


Mapping: [{{val| 1 0 -4 2 9 }}, {{val| 0 2 8 1 -7 }}]
POTE generator: ~3/2 = 696.115


Mapping generators: ~2, ~7/4
{{Val list|legend=1| 5ef, 7, 12, 19d, 31def }}


POTE generator: ~8/7 = 251.173
Badness: 0.0245


{{Val list|legend=1| 19, 24, 43d }}
==== 19-limit ====


Badness: 0.0357
Subgroup: 2.3.5.7.11.13.17.19


= Dominant =
Comma list: 36/35, 39/38, 45/44, 51/49, 52/49, 57/56


The interval class for 7 is obtained from two fourths in succession, so that 7/4 is a minor seventh. The 7/6 interval is, like 6/5, now a minor third, and 7/5 is a diminished fifth. An excellent tuning for dominant is [[12edo]], but it also works well with the Pythagorean tuning of pure [[3/2]] fifths, and with [[29edo]], [[41edo]], or [[53edo]].
Mapping: [{{val| 1 0 -4 6 -6 10 12 9 }}, {{val| 0 1 4 -2 6 -4 -5 -3 }}]


Subgroup: 2.3.5.7
POTE generator: ~3/2 = 696.217
 
{{Val list|legend=1| 5ef, 7, 12, 19d, 31def }}


[[Comma list]]: 36/35, 64/63
Badness: 0.0204


[[Mapping]]: [{{val| 1 0 -4 6 }}, {{val| 0 1 4 -2 }}]
=== Dominatrix ===


{{Multival|legend=1| 1 4 -2 4 -6 -16 }}
Subgroup: 2.3.5.7.11.13


[[POTE generator]]: ~3/2 = 701.573
Comma list: 27/26, 36/35, 45/44, 64/63


[[Tuning ranges]]:
Mapping: [{{val| 1 0 -4 6 -6 -1 }}, {{val| 0 1 4 -2 6 3 }}]
* valid range: [700.000, 720.000] (12 to 5)
* nice range: [694.786, 715.587]
* strict range: [700.000, 715.587]


{{Val list|legend=1| 5, 7, 12, 41cd, 53cdd, 65ccddd }}
POTE generator: ~3/2 = 698.544


[[Badness]]: 0.0207
{{Val list|legend=1| 5e, 7, 12f, 19df }}


== 11-limit ==
== Domination ==


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 36/35, 56/55, 64/63
Comma list: 36/35, 64/63, 77/75
 
Mapping: [{{val| 1 0 -4 6 -14 }}, {{val| 0 1 4 -2 11 }}]


Mapping: [{{val| 1 0 -4 6 13 }}, {{val| 0 1 4 -2 -6 }}]
POTE generator: ~3/2 = 705.004


Tuning ranges:
{{Val list|legend=1| 5e, 12e, 17c, 46cd }}
* valid range: [700.000, 705.882] (12 to 17)
* nice range: [691.202, 715.587]
* strict range: [700.000, 705.882]


POTE generator: ~3/2 = 703.254
Badness: 0.0366
 
{{Val list|legend=1| 5, 12, 17c, 29cde }}
 
Badness: 0.0242


=== 13-limit ===
=== 13-limit ===
Line 741: Line 722:
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 36/35, 56/55, 64/63, 66/65
Comma list: 26/25, 36/35, 64/63, 66/65


Mapping: [{{val| 1 0 -4 6 13 18 }}, {{val| 0 1 4 -2 -6 -9 }}]
Mapping: [{{val| 1 0 -4 6 -14 -9 }}, {{val| 0 1 4 -2 11 8 }}]


POTE generator: ~3/2 = 703.636
POTE generator: ~3/2 = 705.496


Tuning ranges:
{{Val list|legend=1| 5e, 12e, 17c }}
* valid range: 705.882 (17)
* nice range: [691.202, 715.587]
* strict range: 705.882


{{Val list|legend=1| 12f, 17c, 29cdef }}
Badness: 0.0274


Badness: 0.0241
== Arnold ==


=== Dominion ===
Subgroup: 2.3.5.7.11


Subgroup: 2.3.5.7.11.13
Comma list: 22/21, 33/32, 36/35


Comma list: 26/25, 36/35, 56/55, 64/63
Mapping: [{{val| 1 0 -4 6 5 }}, {{val| 0 1 4 -2 -1 }}]


Mapping: [{{val| 1 0 -4 6 13 -9 }}, {{val| 0 1 4 -2 -6 8 }}]
POTE generator: ~3/2 = 698.491


{{Val list|legend=1| 5, 12, 17c, 46cde }}
{{Val list|legend=1| 5, 7, 12e }}


POTE generator: ~3/2 = 704.905
Badness: 0.0261


Badness: 0.0273
=== 13-limit ===


== Domineering ==
Subgroup: 2.3.5.7.11.13


Subgroup: 2.3.5.7.11
Comma list: 22/21, 27/26, 33/32, 36/35


Comma list: 36/35, 45/44, 64/63
Mapping: [{{val| 1 0 -4 6 5 -1 }}, {{val| 0 1 4 -2 3 }}]


Mapping: [{{val| 1 0 -4 6 -6 }}, {{val| 0 1 4 -2 6 }}]
POTE generator: ~3/2 = 696.743


POTE generator: ~3/2 = 698.776
{{Val list|legend=1| 5, 7, 12ef, 19def }}


{{Val list|legend=1| 5e, 7, 12, 19d, 43de }}
Badness: 0.0233


Badness: 0.0220
=== 17-limit ===


=== 13-limit ===
Subgroup: 2.3.5.7.11.13.17


Subgroup: 2.3.5.7.11.13
Comma list: 22/21, 27/26, 33/32, 36/35, 51/49


Comma list: 36/35, 45/44, 52/49, 64/63
Mapping: [{{val| 1 0 -4 6 5 -1 12 }}, {{val| 0 1 4 -2 3 -5 }}]


Mapping: [{{val| 1 0 -4 6 -6 10 }}, {{val| 0 1 4 -2 6 -4 }}]
POTE generator: ~3/2 = 696.978


POTE generator: ~3/2 = 695.762
{{Val list|legend=1| 5, 7, 12ef, 19def }}


{{Val list|legend=1| 5ef, 7, 12, 19d, 31def }}
Badness: 0.0245


Badness: 0.0270
=== 19-limit ===


==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17.19


Subgroup: 2.3.5.7.11.13.17
Comma list: 22/21, 27/26, 33/32, 36/35, 51/49, 57/56


Comma list: 36/35, 45/44, 51/49, 52/49, 64/63
Mapping: [{{val| 1 0 -4 6 5 -1 12 9 }}, {{val| 0 1 4 -2 3 -5 -3 }}]


Mapping: [{{val| 1 0 -4 6 -6 10 12 }}, {{val| 0 1 4 -2 6 -4 -5 }}]
POTE generator: ~3/2 = 697.068


POTE generator: ~3/2 = 696.115
{{Val list|legend=1| 5, 7, 12ef, 19def }}


{{Val list|legend=1| 5ef, 7, 12, 19d, 31def }}
Badness: 0.0211


Badness: 0.0245
= Sharptone =


==== 19-limit ====
Sharptone is a low-accuracy temperament tempering out 21/20 and 28/27. In sharptone, a 7/4 is a major sixth, a 7/6 a whole tone, and a 7/5 a fourth. Genuinely septimal sounding harmony therefore cannot be expected, but it can be used to translate, more or less, 7-limit JI into 5-limit meantone. [[12edo]] tuning does sharptone about as well as such a thing can be done, of course not in its patent val.


Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7


Comma list: 36/35, 39/38, 45/44, 51/49, 52/49, 57/56
[[Comma list]]: 21/20, 28/27


Mapping: [{{val| 1 0 -4 6 -6 10 12 9 }}, {{val| 0 1 4 -2 6 -4 -5 -3 }}]
[[Mapping]]: [{{val| 1 0 -4 -2 }}, {{val| 0 1 4 3 }}]


POTE generator: ~3/2 = 696.217
{{Multival|legend=1| 1 4 3 4 2 -4 }}


{{Val list|legend=1| 5ef, 7, 12, 19d, 31def }}
[[POTE generator]]: ~3/2 = 700.140


Badness: 0.0204
{{Val list|legend=1| 5, 7d, 12d }}


=== Dominatrix ===
[[Badness]]: 0.0248


Subgroup: 2.3.5.7.11.13
== Meanertone ==


Comma list: 27/26, 36/35, 45/44, 64/63
Subgroup: 2.3.5.7.11


Mapping: [{{val| 1 0 -4 6 -6 -1 }}, {{val| 0 1 4 -2 6 3 }}]
Comma list: 21/20, 28/27, 33/32


POTE generator: ~3/2 = 698.544
Mapping: [{{val| 1 0 -4 -2 5 }}, {{val| 0 1 4 3 -1 }}]


{{Val list|legend=1| 5e, 7, 12f, 19df }}
POTE generator: ~3/2 = 696.615


== Domination ==
{{Val list|legend=1| 5, 7d, 12de }}


Subgroup: 2.3.5.7.11
Badness: 0.0252


Comma list: 36/35, 64/63, 77/75
= Plutus =


Mapping: [{{val| 1 0 -4 6 -14 }}, {{val| 0 1 4 -2 11 }}]
Subgroup: 2.3.5.7


POTE generator: ~3/2 = 705.004
[[Comma list]]: 15/14, 81/80


{{Val list|legend=1| 5e, 12e, 17c, 46cd }}
[[Mapping]]: [{{val| 1 0 -4 -5 }}, {{val| 0 1 4 5 }}]


Badness: 0.0366
{{Multival|legend=1| 1 4 5 4 5 0 }}


=== 13-limit ===
[[POTE generator]]: ~3/2 = 682.895


Subgroup: 2.3.5.7.11.13
{{Val list|legend=1| 7, 37bcccdd, 44bccccdd }}


Comma list: 26/25, 36/35, 64/63, 66/65
[[Badness]]: 0.0453


Mapping: [{{val| 1 0 -4 6 -14 -9 }}, {{val| 0 1 4 -2 11 8 }}]
== 11-limit ==


POTE generator: ~3/2 = 705.496
Subgroup: 2.3.5.7.11


{{Val list|legend=1| 5e, 12e, 17c }}
Comma list: 15/14, 22/21, 81/80


Badness: 0.0274
Mapping: [{{val| 1 0 -4 -5 -6 }}, {{val| 0 1 4 5 6 }}]


== Arnold ==
POTE generator: ~3/2 = 685.234


Subgroup: 2.3.5.7.11
{{Val list|legend=1| 5de, 7 }}


Comma list: 22/21, 33/32, 36/35
Badness: 0.0325


Mapping: [{{val| 1 0 -4 6 5 }}, {{val| 0 1 4 -2 -1 }}]
= Supermean =


POTE generator: ~3/2 = 698.491
Subgroup: 2.3.5.7


{{Val list|legend=1| 5, 7, 12e }}
[[Comma list]]: 81/80, 672/625


Badness: 0.0261
[[Mapping]]: [{{val| 1 0 -4 -21 }}, {{val| 0 1 4 15 }}]


=== 13-limit ===
[[POTE generator]]: ~3/2 = 704.889


Subgroup: 2.3.5.7.11.13
{{Val list|legend=1| 5d, 12d, 17c, 29c }}


Comma list: 22/21, 27/26, 33/32, 36/35
[[Badness]]: 0.1342


Mapping: [{{val| 1 0 -4 6 5 -1 }}, {{val| 0 1 4 -2 3 }}]
== 11-limit ==


POTE generator: ~3/2 = 696.743
Subgroup: 2.3.5.7.11


{{Val list|legend=1| 5, 7, 12ef, 19def }}
Comma list: 56/55, 81/80, 132/125


Badness: 0.0233
Mapping: [{{val| 1 0 -4 -21 -14 }}, {{val| 0 1 4 15 11 }}]


=== 17-limit ===
POTE generator: ~3/2 = 705.096


Subgroup: 2.3.5.7.11.13.17
{{Val list|legend=1| 5de, 12de, 17c, 29c }}


Comma list: 22/21, 27/26, 33/32, 36/35, 51/49
Badness: 0.0633


Mapping: [{{val| 1 0 -4 6 5 -1 12 }}, {{val| 0 1 4 -2 3 -5 }}]
== 13-limit ==


POTE generator: ~3/2 = 696.978
Subgroup: 2.3.5.7.11.13


{{Val list|legend=1| 5, 7, 12ef, 19def }}
Comma list: 26/25, 56/55, 66/65, 81/80


Badness: 0.0245
Mapping: [{{val| 1 0 -4 -21 -14 -9 }}, {{val| 0 1 4 15 11 8 }}]


=== 19-limit ===
POTE generator: ~3/2 = 705.094


Subgroup: 2.3.5.7.11.13.17.19
{{Val list|legend=1| 5de, 12de, 17c, 29c }}


Comma list: 22/21, 27/26, 33/32, 36/35, 51/49, 57/56
= Godzilla =
<span style="display: block; text-align: right;">[[:de:Semiphor,_Semaphor,_Godzilla|Deutsch]]</span>


Mapping: [{{val| 1 0 -4 6 5 -1 12 9 }}, {{val| 0 1 4 -2 3 -5 -3 }}]
{{main| Semaphore and Godzilla }}


POTE generator: ~3/2 = 697.068
Godzilla tempers out 49/48, equating 8/7 with 7/6. Two of the step-and-a-quarter intervals these represent give a fourth, and so step-and-a-quarter generators generate godzilla. [[19edo]] is close to being the optimal generator tuning; hence it can be more or less equated with taking 4\19 as a generator. MOS are of 5, 9, or 14 notes.


{{Val list|legend=1| 5, 7, 12ef, 19def }}
Subgroup: 2.3.5.7


Badness: 0.0211
[[Comma list]]: 49/48, 81/80


= Sharptone =
[[Mapping]]: [{{val| 1 0 -4 2 }}, {{val| 0 2 8 1 }}]


Sharptone is a low-accuracy temperament tempering out 21/20 and 28/27. In sharptone, a 7/4 is a major sixth, a 7/6 a whole tone, and a 7/5 a fourth. Genuinely septimal sounding harmony therefore cannot be expected, but it can be used to translate, more or less, 7-limit JI into 5-limit meantone. [[12edo]] tuning does sharptone about as well as such a thing can be done, of course not in its patent val.
Mapping generators: ~2, ~7/4


Subgroup: 2.3.5.7
{{Multival|legend=1| 2 8 1 8 -4 -20 }}


[[Comma list]]: 21/20, 28/27
[[POTE generator]]: ~8/7 = 252.635


[[Mapping]]: [{{val| 1 0 -4 -2 }}, {{val| 0 1 4 3 }}]
[[Tuning ranges]]:
* valid range: [240.000, 257.143] (5 to 14c)
* nice range: [231.174, 266.871]
* strict range: [240.000, 257.143]


{{Multival|legend=1| 1 4 3 4 2 -4 }}
{{Val list|legend=1| 5, 14c, 19 }}


[[POTE generator]]: ~3/2 = 700.140
[[Badness]]: 0.0267


{{Val list|legend=1| 5, 7d, 12d }}
== 11-limit ==


[[Badness]]: 0.0248
Subgroup: 2.3.5.7.11


== Meanertone ==
Comma list: 45/44, 49/48, 81/80


Subgroup: 2.3.5.7.11
Mapping: [{{val| 1 0 -4 2 -6 }}, {{val| 0 2 8 1 12 }}]


Comma list: 21/20, 28/27, 33/32
Mapping generators: ~2, ~7/4


Mapping: [{{val| 1 0 -4 -2 5 }}, {{val| 0 1 4 3 -1 }}]
POTE generator: ~8/7 = 254.027


POTE generator: ~3/2 = 696.615
Tuning ranges:  
* valid range: [252.632, 257.143] (19 to 14c)
* nice range: [231.174, 266.871]
* strict range: [252.632, 257.143]


{{Val list|legend=1| 5, 7d, 12de }}
{{Val list|legend=1| 14c, 19, 33cd, 52cd }}


Badness: 0.0252
Badness: 0.0290


= Plutus =
=== 13-limit ===


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7.11.13


[[Comma list]]: 15/14, 81/80
Comma list: 45/44, 49/48, 78/77, 81/80


[[Mapping]]: [{{val| 1 0 -4 -5 }}, {{val| 0 1 4 5 }}]
Mapping: [{{val| 1 0 -4 2 -6 -5 }}, {{val| 0 2 8 1 12 11 }}]


{{Multival|legend=1| 1 4 5 4 5 0 }}
Mapping generators: ~2, ~7/4


[[POTE generator]]: ~3/2 = 682.895
POTE generator: ~8/7 = 253.603
 
Tuning ranges:
* valid range: 694.737 (19)
* nice range: [621.581, 737.652]
* strict range: 694.737


{{Val list|legend=1| 7, 37bcccdd, 44bccccdd }}
{{Val list|legend=1| 14cf, 19, 33cdff, 52cdf }}


[[Badness]]: 0.0453
Badness: 0.0225


== 11-limit ==
== Semafour ==


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 15/14, 22/21, 81/80
Comma list: 33/32, 49/48, 55/54


Mapping: [{{val| 1 0 -4 -5 -6 }}, {{val| 0 1 4 5 6 }}]
Mapping: [{{val| 1 0 -4 2 5 }}, {{val| 0 2 8 1 -2 }}]


POTE generator: ~3/2 = 685.234
Mapping generators: ~2, ~7/4


{{Val list|legend=1| 5de, 7 }}
POTE generator: ~8/7 = 254.042


Badness: 0.0325
{{Val list|legend=1| 14c, 19e, 33cdee }}


= Supermean =
Badness: 0.0285


Subgroup: 2.3.5.7
== Varan ==


[[Comma list]]: 81/80, 672/625
Subgroup: 2.3.5.7.11


[[Mapping]]: [{{val| 1 0 -4 -21 }}, {{val| 0 1 4 15 }}]
Comma list: 49/48, 77/75, 81/80


[[POTE generator]]: ~3/2 = 704.889
Mapping: [{{val| 1 0 -4 2 -10 }}, {{val| 0 2 8 1 17 }}]


{{Val list|legend=1| 5d, 12d, 17c, 29c }}
Mapping generators: ~2, ~7/4


[[Badness]]: 0.1342
POTE generator: ~8/7 = 251.079


== 11-limit ==
{{Val list|legend=1| 19e, 24, 43de }}


Subgroup: 2.3.5.7.11
Badness: 0.0396


Comma list: 56/55, 81/80, 132/125
=== 13-limit ===


Mapping: [{{val| 1 0 -4 -21 -14 }}, {{val| 0 1 4 15 11 }}]
Subgroup: 2.3.5.7.11.13


POTE generator: ~3/2 = 705.096
Comma list: 49/48, 66/65, 77/75, 81/80


{{Val list|legend=1| 5de, 12de, 17c, 29c }}
Mapping: [{{val| 1 0 -4 2 -10 -5 }}, {{val| 0 2 8 1 17 11 }}]


Badness: 0.0633
Mapping generators: ~2, ~7/4


== 13-limit ==
POTE generator: ~8/7 = 251.165


Subgroup: 2.3.5.7.11.13
{{Val list|legend=1| 19e, 24, 43de }}


Comma list: 26/25, 56/55, 66/65, 81/80
Badness: 0.0257


Mapping: [{{val| 1 0 -4 -21 -14 -9 }}, {{val| 0 1 4 15 11 8 }}]
== Baragon ==


POTE generator: ~3/2 = 705.094
Subgroup: 2.3.5.7.11


{{Val list|legend=1| 5de, 12de, 17c, 29c }}
Comma list: 49/48, 56/55, 81/80
 
Mapping: [{{val| 1 0 -4 2 9 }}, {{val| 0 2 8 1 -7 }}]
 
Mapping generators: ~2, ~7/4
 
POTE generator: ~8/7 = 251.173
 
{{Val list|legend=1| 19, 24, 43d }}
 
Badness: 0.0357


= Injera =
= Injera =
Line 1,950: Line 1,950:
Badness: 0.0182
Badness: 0.0182


= Meanmag =
= Cloudtone =
The ''cloudtone'' temperament (5&amp;50, named by [[User:Xenllium|Xenllium]]) tempers out the [[cloudy comma]], 16807/16384 and the [[81/80|syntonic comma]], 81/80 in the 7-limit. It can be extended to the 11- and 13-limit by adding 385/384 and 105/104 to the comma list in this order.
 
== 7-limit ==
 
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


[[Comma list]]: 81/80, 3125/3072
[[Comma list]]: 81/80, 16807/16384


[[Mapping]]: [{{val| 19 30 44 0 }}, {{val| 0 0 0 1 }}]
[[Mapping]]: [{{val| 5 0 -20 14 }}, {{val| 0 1 4 0 }}]


Mapping generators: ~25/24, ~7
Mapping generators: ~8/7, ~3


[[Wedgie]]: {{wedgie| 0 0 19 0 30 44 }}
{{Multival|legend=1| 5 20 0 20 -14 -56 }}


[[POTE generator]]: ~8/7 = 238.396
[[POTE generator]]: ~3/2 = 695.720


{{Val list|legend=1| 19, 38, 57, 76, 95bc }}
{{Val list|legend=1| 5, 45, 50, 95bcd, 145bcdd, 195bbcdd }}


[[Badness]]: 0.077023
[[Badness]]: 0.102256


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


Comma list: 81/80, 385/384, 625/616
Comma list: 81/80, 385/384, 2401/2376


Mapping: [{{val| 19 30 44 0 119 }}, {{val| 0 0 0 1 -1 }}]
Mapping: [{{val| 5 0 -20 14 41 }}, {{val| 0 1 4 0 -3 }}]


Mapping generators: ~25/24, ~7
Mapping generators: ~8/7, ~3


POTE generator: ~8/7 = 233.486
POTE generator: ~3/2 = 696.536


{{Val list|legend=1| 19, 38, 57, 76 }}
{{Val list|legend=1| 5, 50, 55, 105d, 155bdd, 205bddd }}


Badness: 0.066829
Badness: 0.070378


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


Comma list: 81/80, 105/104, 144/143, 625/616
Comma list: 81/80, 105/104, 144/143, 2401/2376


Mapping: [{{val| 19 30 44 0 119 17 }}, {{val| 0 0 0 1 -1 1 }}]
Mapping: [{{val| 5 0 -20 14 41 -21 }}, {{val| 0 1 4 0 -3 5 }}]


Mapping generators: ~25/24, ~7
Mapping generators: ~8/7, ~3


POTE generator: ~8/7 = 234.890
POTE generator: ~3/2 = 696.162


{{Val list|legend=1| 19, 38, 57, 76 }}
{{Val list|legend=1| 5, 45f, 50, 55 }}


Badness: 0.045844
Badness: 0.048829


= Undevigintone =
= Meanmag =
Subgroup: 2.3.5.7


Subgroup: 2.3.5.7.11
[[Comma list]]: 81/80, 3125/3072


[[Comma list]]: 49/48, 81/80, 126/125
[[Mapping]]: [{{val| 19 30 44 0 }}, {{val| 0 0 0 1 }}]


[[Mapping]]: [{{val| 19 30 44 53 0 }}, {{val| 0 0 0 0 1 }}]
Mapping generators: ~25/24, ~7


Mapping generators: ~21/20, ~11
[[Wedgie]]: {{wedgie| 0 0 19 0 30 44 }}


[[POTE generator]]: ~11/8 = 538.047
[[POTE generator]]: ~8/7 = 238.396


{{Val list|legend=1| 19, 38d }}
{{Val list|legend=1| 19, 38, 57, 76, 95bc }}


Badness: 0.0364
[[Badness]]: 0.077023


== 13-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11


Subgroup: 2.3.5.7.11.13
Comma list: 81/80, 385/384, 625/616


Comma list: 49/48, 65/64, 81/80, 126/125
Mapping: [{{val| 19 30 44 0 119 }}, {{val| 0 0 0 1 -1 }}]


Mapping: [{{val| 19 30 44 53 0 70 }}, {{val| 0 0 0 0 1 0 }}]
Mapping generators: ~25/24, ~7


Mapping generators: ~21/20, ~11
POTE generator: ~8/7 = 233.486


POTE generator: ~11/8 = 537.061
{{Val list|legend=1| 19, 38, 57, 76 }}


{{Val list|legend=1| 19, 38d }}
Badness: 0.066829


Badness: 0.0229
== 13-limit ==
Subgroup: 2.3.5.7.11.13


= Cloudtone =
Comma list: 81/80, 105/104, 144/143, 625/616
The ''cloudtone'' temperament (5&amp;50, named by [[User:Xenllium|Xenllium]]) tempers out the [[cloudy comma]], 16807/16384 and the [[81/80|syntonic comma]], 81/80 in the 7-limit. It can be extended to the 11- and 13-limit by adding 385/384 and 105/104 to the comma list in this order.


== 7-limit ==
Mapping: [{{val| 19 30 44 0 119 17 }}, {{val| 0 0 0 1 -1 1 }}]


Subgroup: 2.3.5.7
Mapping generators: ~25/24, ~7


[[Comma list]]: 81/80, 16807/16384
POTE generator: ~8/7 = 234.890


[[Mapping]]: [{{val| 5 0 -20 14 }}, {{val| 0 1 4 0 }}]
{{Val list|legend=1| 19, 38, 57, 76 }}


Mapping generators: ~8/7, ~3
Badness: 0.045844


{{Multival|legend=1| 5 20 0 20 -14 -56 }}
= Undevigintone =
 
[[POTE generator]]: ~3/2 = 695.720
 
{{Val list|legend=1| 5, 45, 50, 95bcd, 145bcdd, 195bbcdd }}
 
[[Badness]]: 0.102256
 
== 11-limit ==


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 81/80, 385/384, 2401/2376
[[Comma list]]: 49/48, 81/80, 126/125


Mapping: [{{val| 5 0 -20 14 41 }}, {{val| 0 1 4 0 -3 }}]
[[Mapping]]: [{{val| 19 30 44 53 0 }}, {{val| 0 0 0 0 1 }}]


Mapping generators: ~8/7, ~3
Mapping generators: ~21/20, ~11


POTE generator: ~3/2 = 696.536
[[POTE generator]]: ~11/8 = 538.047


{{Val list|legend=1| 5, 50, 55, 105d, 155bdd, 205bddd }}
{{Val list|legend=1| 19, 38d }}


Badness: 0.070378
Badness: 0.0364


== 13-limit ==
== 13-limit ==
Line 2,070: Line 2,070:
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 81/80, 105/104, 144/143, 2401/2376
Comma list: 49/48, 65/64, 81/80, 126/125


Mapping: [{{val| 5 0 -20 14 41 -21 }}, {{val| 0 1 4 0 -3 5 }}]
Mapping: [{{val| 19 30 44 53 0 70 }}, {{val| 0 0 0 0 1 0 }}]


Mapping generators: ~8/7, ~3
Mapping generators: ~21/20, ~11


POTE generator: ~3/2 = 696.162
POTE generator: ~11/8 = 537.061


{{Val list|legend=1| 5, 45f, 50, 55 }}
{{Val list|legend=1| 19, 38d }}


Badness: 0.048829
Badness: 0.0229


[[Category:Theory]]
[[Category:Theory]]
Retrieved from "https://en.xen.wiki/w/Meantone_family"