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Update keys; POTE -> CTE; review comma lists and GPV sequences (1/2)
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{{Main| Meantone }}
{{Main| Meantone }}


Subgroup: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: 81/80
[[Comma list]]: 81/80
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Mapping generators: ~2, ~3
Mapping generators: ~2, ~3


{{multival|legend=1| 1 4 4 }}
{{Multival|legend=1| 1 4 4 }}


[[POTE generator]]: ~3/2 = 696.239
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 697.2143


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[5-odd-limit]]: ~3/2 = {{Monzo| 0 0 1/4 }}
* [[5-odd-limit]]: ~3/2 = {{monzo| 0 0 1/4 }}
: [[Eigenmonzo]]s (unchanged intervals): 2, 5
: [[Eigenmonzo basis]]: 2.5


[[Tuning ranges]]:  
[[Tuning ranges]]:  
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* 5-odd-limit diamond monotone and tradeoff: ~3/2 = [694.786, 701.955]
* 5-odd-limit diamond monotone and tradeoff: ~3/2 = [694.786, 701.955]


{{Val list|legend=1| 5, 7, 12, 19, 31, 50, 81, 131b, 212bb, 293bb }}
{{Val list|legend=1| 5, 7, 12, 19, 31, 50, 81, 131b }}


[[Badness]]: 0.007381
[[Badness]]: 0.007381
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Scales: [[meantone5]], [[meantone7]], [[meantone12]]
Scales: [[meantone5]], [[meantone7]], [[meantone12]]


=== Seven-limit extensions ===
=== Overview to extensions ===
The second comma of the normal comma list defines which [[7-limit]] family member we are looking at.
The second comma of the normal comma list defines which [[7-limit]] family member we are looking at.
* Septimal meantone adds [[Harrison's comma|{{Monzo| -13 10 0 -1 }}]],
* Septimal meantone adds [[Harrison's comma|{{Monzo| -13 10 0 -1 }}]],
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{{See also| No-sevens subgroup temperaments #Mohaha }}
{{See also| No-sevens subgroup temperaments #Mohaha }}


Mohaha is the 2.3.5.11 subgroup temperament with a generator of a neutral third, two of which make up a fifth, and which can be taken to represent 11/9. Mohaha can be thought of, intuitively, as "meantone with quarter tones"; as is the 3/2 generator subdivided in half, so is the 25/24 chromatic semitone divided into two equal ~33/32 quarter tones (in the 2.3.5.11 subgroup). Within this paradigm, mohaha is the temperament that splits the 3/2 into two equal 11/9's, that splits the 6/5 into two equal 11/10's, and that maps four 3/2's to 5/1. It has a 7-note MOS with three larger steps and four smaller ones, going sLsLsLs. Taking septimal meantone mapping of 7 leads to [[#Migration]], flattone mapping of 7 leads to [[#Ptolemy]], and dominant mapping of 7 leads to [[#Neutrominant]].
Mohaha is the 2.3.5.11 subgroup temperament with a generator of a neutral third, two of which make up a fifth, and which can be taken to represent 11/9. Mohaha can be thought of, intuitively, as "meantone with quartertones"; as is the 3/2 generator subdivided in half, so is the [[~]][[25/24]] chromatic semitone divided into two equal ~[[33/32]] quarter tones (in the 2.3.5.11 subgroup). Within this paradigm, mohaha is the temperament that splits the 3/2 into two equal 11/9's, that splits the 6/5 into two equal 11/10~12/11's, and that maps four 3/2's to 5/1. It has a heptatonic mos with three larger steps and four smaller ones, going [[4L 3s|sLsLsLs]]. Taking septimal meantone mapping of 7 leads to [[#Migration]], flattone mapping of 7 leads to [[#Ptolemy]], and dominant mapping of 7 leads to [[#Neutrominant]].


Subgroup: 2.3.5.11
[[Subgroup]]: 2.3.5.11


[[Comma list]]: 81/80, 121/120
[[Comma list]]: 81/80, 121/120
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[[Gencom]]: [2 11/9; 81/80 121/120]
[[Gencom]]: [2 11/9; 81/80 121/120]


[[POTE generator]]: ~11/9 = 348.0938
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~11/9 = 348.8296


{{Val list|legend=1| 7, 17c, 24, 31, 100e, 131bee }}
{{Val list|legend=1| 7, 17c, 24, 31, 69e, 100e, 131bee }}


Scales: [[mohaha7]], [[mohaha10]]
Scales: [[mohaha7]], [[mohaha10]]
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Gencom: [2 11/9; 66/65 81/80 121/120]
Gencom: [2 11/9; 66/65 81/80 121/120]


POTE generator: ~11/9 = 348.9155
Optimal tuning (CTE): ~2 = 1\1, ~11/9 = 348.8794


Optimal GPV sequence: {{Val list| 7, 17c, 24, 31, 55, 86ef, 141ceff }}
Optimal GPV sequence: {{Val list| 7, 17c, 24, 31, 55 }}


Scales: [[mohaha7]], [[mohaha10]]
Scales: [[mohaha7]], [[mohaha10]]
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== Septimal meantone ==
== Septimal meantone ==
<div style="float:right">[[:de:septimal-mitteltönig|Deutsch]]</div>
<div style="float:right">[[:de:septimal-mitteltönig|Deutsch]]</div>
{{see also| Meantone }}
{{Main| Meantone }}
{{Wikipedia|Septimal meantone temperament}}
{{Wikipedia| Septimal meantone temperament }}
The [[7/4]] of septimal meantone is the augmented sixth, C-A#, and other septimal intervals are [[7/6]], C-D#, the augmented second, [[7/5]], C-F#, the augmented fourth, and [[21/16]], C-E#, the augmented third. Septimal meantone tempers out the common 7-limit commas [[126/125]] and [[225/224]] and in fact can be defined as the 7-limit temperament that tempers out any two of 81/80, 126/125 and 225/224.


Subgroup: 2.3.5.7
The [[7/4]] of septimal meantone is the augmented sixth (C-A#), and other septimal intervals are [[7/6]], the augmented second (C-D#), [[7/5]], the augmented fourth (C-F#), and [[21/16]], the augmented third (C-E#). Septimal meantone tempers out the common 7-limit commas [[126/125]] and [[225/224]] and in fact can be defined as the 7-limit temperament that tempers out any two of 81/80, 126/125 and 225/224.
 
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 81/80, 126/125
[[Comma list]]: 81/80, 126/125
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{{Multival|legend=1| 1 4 10 4 13 12 }}
{{Multival|legend=1| 1 4 10 4 13 12 }}


[[POTE generator]]: ~3/2 = 696.495
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 696.9521


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~3/2 = {{Monzo| 0 0 1/4 }}
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~3/2 = {{monzo| 0 0 1/4 }}
: [{{Monzo| 1 0 0 0 }}, {{Monzo| 1 0 1/4 0 }}, {{Monzo| 0 0 1 0 }}, {{Monzo| -3 0 5/2 0 }}]
: [{{Monzo| 1 0 0 0 }}, {{monzo| 1 0 1/4 0 }}, {{monzo| 0 0 1 0 }}, {{monzo| -3 0 5/2 0 }}]
: [[Eigenmonzo]]s (unchanged intervals): 2, 5
: [[Eigenmonzo basis]]: 2.5


[[Tuning ranges]]:  
[[Tuning ranges]]:  
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=== Unidecimal meantone aka Huygens ===
=== Unidecimal meantone aka Huygens ===
{{see also| Meantone vs meanpop }}
{{See also| Meantone vs meanpop }}


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
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Mapping: [{{val| 1 0 -4 -13 -25 }}, {{val| 0 1 4 10 18 }}]
Mapping: [{{val| 1 0 -4 -13 -25 }}, {{val| 0 1 4 10 18 }}]


POTE generator: ~3/2 = 696.967
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.1676


Minimax tuning:  
Minimax tuning:  
* [[11-odd-limit]]: ~3/2 = {{Monzo| 9/16 -1/8 0 0 1/16 }}
* 11-odd-limit: ~3/2 = {{Monzo| 9/16 -1/8 0 0 1/16 }}
: [{{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 }}]
: [{{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 }}]
: Eigenmonzos (unchanged intervals): 2, 11/9
: Eigenmonzo basis: 2.11/9


Tuning ranges:  
Tuning ranges:  
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; Music
; 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]
* [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 ====
==== Tridecimal meantone ====
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Mapping: [{{val| 1 0 -4 -13 -25 -20 }}, {{val| 0 1 4 10 18 15 }}]
Mapping: [{{val| 1 0 -4 -13 -25 -20 }}, {{val| 0 1 4 10 18 15 }}]


POTE generator: ~3/2 = 696.642
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.8552


Minimax tuning:  
Minimax tuning:  
* [[13-odd-limit|13-]] and [[15-odd-limit]]: ~3/2 = {{Monzo| 9/16 -1/8 0 0 1/16 }}
* [[13-odd-limit|13-]] and [[15-odd-limit]]: ~3/2 = {{monzo| 9/16 -1/8 0 0 1/16 }}
: Eigenmonzos (unchanged intervals): 2, 11/9
: Eigenmonzo basis: 2.11/9


Optimal GPV sequence: {{Val list| 12f, 19e, 31 }}
Optimal GPV sequence: {{Val list| 12f, 19e, 31 }}
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Comma list: 66/65, 81/80, 99/98, 105/104, 121/119
Comma list: 66/65, 81/80, 99/98, 105/104, 121/119


Mapping: [{{val|1 0 -4 -13 -25 -20 -37}}, {{val|0 1 4 10 18 15 26}}]
Mapping: [{{val| 1 0 -4 -13 -25 -20 -37 }}, {{val| 0 1 4 10 18 15 26 }}]


POTE generator: ~3/2 = 696.377
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.6486


Optimal GPV sequence: {{Val list| 19eg, 31, 50e, 81ee }}
Optimal GPV sequence: {{Val list| 12fg, 19eg, 31, 50e }}


Badness: 0.019037
Badness: 0.019037
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Comma list: 66/65, 77/76, 81/80, 99/98, 105/104, 121/119
Comma list: 66/65, 77/76, 81/80, 99/98, 105/104, 121/119


Mapping: [{{val|1 0 -4 -13 -25 -20 -37 -40}}, {{val|0 1 4 10 18 15 26 28}}]
Mapping: [{{val| 1 0 -4 -13 -25 -20 -37 -40 }}, {{val| 0 1 4 10 18 15 26 28 }}]


POTE generator: ~3/2 = 696.273
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.5551


Optimal GPV sequence: {{Val list| 19egh, 31, 50e, 81ee }}
Optimal GPV sequence: {{Val list| 12fghh, 19egh, 31, 50e }}


Badness: 0.017846
Badness: 0.017846
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Comma list: 51/50, 66/65, 81/80, 85/84, 99/98
Comma list: 51/50, 66/65, 81/80, 85/84, 99/98


Mapping: [{{val|1 0 -4 -13 -25 -20 -7}}, {{val|0 1 4 10 18 15 7}}]
Mapping: [{{val| 1 0 -4 -13 -25 -20 -7 }}, {{val| 0 1 4 10 18 15 7 }}]


POTE generator: ~3/2 = 696.448
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.0360


Optimal GPV sequence: {{Val list| 12f, 19eg, 31g }}
Optimal GPV sequence: {{Val list| 12f, 19eg, 31g }}
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Comma list: 51/50, 57/56, 66/65, 81/80, 85/84, 99/98
Comma list: 51/50, 57/56, 66/65, 81/80, 85/84, 99/98


Mapping: [{{val|1 0 -4 -13 -25 -20 -7 -10}}, {{val|0 1 4 10 18 15 7 9}}]
Mapping: [{{val| 1 0 -4 -13 -25 -20 -7 -10 }}, {{val| 0 1 4 10 18 15 7 9 }}]


POTE generator: ~3/2 = 696.394
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.2161


Optimal GPV sequence: {{Val list| 12f, 19egh, 31gh }}
Optimal GPV sequence: {{Val list| 12f, 19egh, 31gh }}
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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: [{{val|1 0 -4 -13 -25 -20 12}}, {{val|0 1 4 10 18 15 -5}}]
Mapping: [{{val| 1 0 -4 -13 -25 -20 12 }}, {{val| 0 1 4 10 18 15 -5 }}]


POTE generator: ~3/2 = 697.003
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.9080


Optimal GPV sequence: {{Val list| 12f, 19e, 31 }}
Optimal GPV sequence: {{Val list| 12f, 19e, 31 }}
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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: [{{val|1 0 -4 -13 -25 -20 12 9}}, {{val|0 1 4 10 18 15 -5 -3}}]
Mapping: [{{val| 1 0 -4 -13 -25 -20 12 9 }}, {{val| 0 1 4 10 18 15 -5 -3 }}]


POTE generator: ~3/2 = 697.140
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.9308


Optimal GPV sequence: {{Val list| 12f, 19e, 31, 74ffgh, 105ffgh }}
Optimal GPV sequence: {{Val list| 12f, 19e, 31 }}


Badness: 0.018047
Badness: 0.018047
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Mapping: [{{val| 1 0 -4 -13 -25 29 }}, {{val| 0 1 4 10 18 -16 }}]
Mapping: [{{val| 1 0 -4 -13 -25 29 }}, {{val| 0 1 4 10 18 -16 }}]


POTE generator: ~3/2 = 697.264
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.2582


Minimax tuning:  
Minimax tuning:  
* 13- and 15-odd-limit: ~3/2 = {{Monzo| 8/13 0 0 1/26 0 -1/26 }}
* 13- and 15-odd-limit: ~3/2 = {{monzo| 8/13 0 0 1/26 0 -1/26 }}
: Eigenmonzos (unchanged intervals): 2, 14/13
: Eigenmonzo basis: 2.13/7


Tuning ranges:  
Tuning ranges:  
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* 13- and 15-odd-limit diamond monotone and tradeoff: ~3/2 = [696.774, 697.674]
* 13- and 15-odd-limit diamond monotone and tradeoff: ~3/2 = [696.774, 697.674]


Optimal GPV sequence: {{Val list| 12, 19ef, 31, 43, 74 }}
Optimal GPV sequence: {{Val list| 12, 31, 43, 74 }}


Badness: 0.025899
Badness: 0.025899
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Mapping: [{{val| 1 0 -4 -13 -25 29 12 }}, {{val| 0 1 4 10 18 -16 -5 }}]
Mapping: [{{val| 1 0 -4 -13 -25 29 12 }}, {{val| 0 1 4 10 18 -16 -5 }}]


POTE generator: ~3/2 = 697.335
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.2996


Optimal GPV sequence: {{Val list| 12, 19ef, 31, 43, 74g }}
Optimal GPV sequence: {{Val list| 12, 31, 43, 74g }}


Badness: 0.020889
Badness: 0.020889
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Mapping: [{{val| 1 0 -4 -13 -25 29 12 9 }}, {{val| 0 1 4 10 18 -16 -5 -3 }}]
Mapping: [{{val| 1 0 -4 -13 -25 29 12 9 }}, {{val| 0 1 4 10 18 -16 -5 -3 }}]


POTE generator: ~3/2 = 697.380
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.3271


Optimal GPV sequence: {{Val list| 12, 31, 43, 74gh }}
Optimal GPV sequence: {{Val list| 12, 31, 43, 74gh }}
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Mapping: [{{val| 1 0 -4 -13 -25 -39 }}, {{val| 0 1 4 10 18 27 }}]
Mapping: [{{val| 1 0 -4 -13 -25 -39 }}, {{val| 0 1 4 10 18 27 }}]


POTE generator: ~3/2 = 697.529
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.5155


Minimax tuning:  
Minimax tuning:  
* 13- and 15-odd-limit: ~3/2 = {{Monzo| 14/25 -2/25 0 0 0 1/25 }}
* 13- and 15-odd-limit: ~3/2 = {{monzo| 14/25 -2/25 0 0 0 1/25 }}
: Eigenmonzos (unchanged intervals): 2, 18/13
: Eigenmonzo basis: 2.13/9


Optimal GPV sequence: {{Val list| 12f, 31f, 43 }}
Optimal GPV sequence: {{Val list| 12f, 31f, 43 }}
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Comma list: 78/77, 81/80, 99/98, 126/125, 273/272
Comma list: 78/77, 81/80, 99/98, 126/125, 273/272


Mapping: [{{val|1 0 -4 -13 -25 -39 -56}}, {{val|0 1 4 10 18 27 38}}]
Mapping: [{{val| 1 0 -4 -13 -25 -39 -56 }}, {{val| 0 1 4 10 18 27 38 }}]


POTE generator: ~3/2 = 697.514
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.5076


Optimal GPV sequence: {{Val list| 31fg, 43, 117df, 160bdff}}
Optimal GPV sequence: {{Val list| 12fg, 31fg, 43 }}


Badness: 0.027706
Badness: 0.027706
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Comma list: 78/77, 81/80, 99/98, 126/125, 153/152, 273/272
Comma list: 78/77, 81/80, 99/98, 126/125, 153/152, 273/272


Mapping: [{{val|1 0 -4 -13 -25 -39 -56 -59}}, {{val|0 1 4 10 18 27 38 40}}]
Mapping: [{{val| 1 0 -4 -13 -25 -39 -56 -59 }}, {{val| 0 1 4 10 18 27 38 40 }}]


POTE generator: ~3/2 = 697.481
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.4848


Optimal GPV sequence: {{Val list| 31fgh, 43, 74f, 117df, 160bdff }}
Optimal GPV sequence: {{Val list| 12fghh, 31fgh, 43 }}


Badness: 0.025315
Badness: 0.025315
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Comma list: 51/50, 78/77, 81/80, 85/84, 99/98
Comma list: 51/50, 78/77, 81/80, 85/84, 99/98


Mapping: [{{val|1 0 -4 -13 -25 -39 -7}}, {{val|0 1 4 10 18 27 7}}]
Mapping: [{{val| 1 0 -4 -13 -25 -39 -7 }}, {{val| 0 1 4 10 18 27 7 }}]


POTE generator: ~3/2 = 697.376
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.6098


Optimal GPV sequence: {{Val list| 12f, 31fg, 43g, 74fgg }}
Optimal GPV sequence: {{Val list| 12f, 31fg, 43g }}


Badness: 0.027518
Badness: 0.027518
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Comma list: 51/50, 57/56, 78/77, 81/80, 85/84, 99/98
Comma list: 51/50, 57/56, 78/77, 81/80, 85/84, 99/98


Mapping: [{{val|1 0 -4 -13 -25 -39 -7 -10}}, {{val|0 1 4 10 18 27 7 9}}]
Mapping: [{{val| 1 0 -4 -13 -25 -39 -7 -10 }}, {{val| 0 1 4 10 18 27 7 9 }}]


POTE generator: ~3/2 = 697.316
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.7012


Optimal GPV sequence: {{Val list| 12f, 19effgh, 31fgh, 43gh, 74fgghh }}
Optimal GPV sequence: {{Val list| 12f, 19effgh, 31fgh, 43gh }}


Badness: 0.023613
Badness: 0.023613
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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: [{{val|1 0 -4 -13 -25 -39 12}}, {{val|0 1 4 10 18 27 -5}}]
Mapping: [{{val| 1 0 -4 -13 -25 -39 12 }}, {{val| 0 1 4 10 18 27 -5 }}]


POTE generator: ~3/2 = 697.644
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.5384


Optimal GPV sequence: {{Val list| 12f, 31f, 43 }}
Optimal GPV sequence: {{Val list| 12f, 43 }}


Badness: 0.023881
Badness: 0.023881
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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: [{{val|1 0 -4 -13 -25 -39 12 9}}, {{val|0 1 4 10 18 27 -5 -3}}]
Mapping: [{{val| 1 0 -4 -13 -25 -39 12 9 }}, {{val| 0 1 4 10 18 27 -5 -3 }}]


POTE generator: ~3/2 = 697.715
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.5550


Optimal GPV sequence: {{Val list| 12f, 31f, 43 }}
Optimal GPV sequence: {{Val list| 12f, 43 }}


Badness: 0.020540
Badness: 0.020540
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Mapping generators: ~2, ~26/15
Mapping generators: ~2, ~26/15


POTE generator: ~15/13 = 251.535
Optimal tuning (CTE): ~2 = 1\1, ~26/15 = 948.6109


Optimal GPV sequence: {{Val list| 19e, 43, 62, 167bef, 229beeff }}
Optimal GPV sequence: {{Val list| 19e, 43, 62 }}


Badness: 0.031433
Badness: 0.031433
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Mapping: [{{val| 1 0 -4 -13 -25 -5 -22 }}, {{val| 0 2 8 20 36 11 33 }}]
Mapping: [{{val| 1 0 -4 -13 -25 -5 -22 }}, {{val| 0 2 8 20 36 11 33 }}]


POTE generator: ~15/13 = 251.523
Optimal tuning (CTE): ~2 = 1\1, ~26/15 = 948.6173


Optimal GPV sequence: {{Val list| 19eg, 43, 62, 167befg, 229beeffgg }}
Optimal GPV sequence: {{Val list| 19eg, 43, 62 }}


Badness: 0.023380
Badness: 0.023380
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Mapping: [{{val| 1 0 -4 -13 -25 -5 -22 -25 }}, {{val| 0 2 8 20 36 11 33 37 }}]
Mapping: [{{val| 1 0 -4 -13 -25 -5 -22 -25 }}, {{val| 0 2 8 20 36 11 33 37 }}]


POTE generator: ~15/13 = 251.527
Optimal tuning (CTE): ~2 = 1\1, ~26/15 = 948.6088


Optimal GPV sequence: {{Val list| 19egh, 43, 62, 167befg, 229beeffggh }}
Optimal GPV sequence: {{Val list| 19egh, 43, 62 }}


Badness: 0.018952
Badness: 0.018952
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Comma list: 81/80, 99/98, 126/125, 847/845
Comma list: 81/80, 99/98, 126/125, 847/845


Mapping: [{{val|2 0 -8 -26 -50 -59}}, {{val|0 1 4 10 18 21}}]
Mapping: [{{val| 2 0 -8 -26 -50 -59 }}, {{val| 0 1 4 10 18 21 }}]


POTE generator: ~3/2 = 697.005
Mapping generators: ~55/39, ~3


Optimal GPV sequence: {{Val list| 12f, 50eff, 62, 136b, 198bef, 334bbeef }}
Optimal tuning (CTE): ~55/39 = 1\2, ~3/2 = 697.1678
 
Optimal GPV sequence: {{Val list| 12f, 38deefff, 50eff, 62, 136b }}


Badness: 0.040668
Badness: 0.040668
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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: [{{val|2 0 -8 -26 -50 -59 5}}, {{val|0 1 4 10 18 21 1}}]
Mapping: [{{val| 2 0 -8 -26 -50 -59 5 }}, {{val| 0 1 4 10 18 21 1 }}]


POTE generator: ~3/2 = 696.927
Optimal tuning (CTE): ~17/12 = 1\2, ~3/2 = 697.1740


Optimal GPV sequence: {{Val list| 12f, 50eff, 62, 136bg, 198befgg }}
Optimal GPV sequence: {{Val list| 12f, 50eff, 62, 136bg }}


Badness: 0.031491
Badness: 0.031491
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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: [{{val|2 0 -8 -26 -50 -59 5 -1}}, {{val|0 1 4 10 18 21 1 3}}]
Mapping: [{{val| 2 0 -8 -26 -50 -59 5 -1 }}, {{val| 0 1 4 10 18 21 1 3 }}]


POTE generator: ~3/2 = 696.906
Optimal tuning (CTE): ~17/12 = 1\2, ~3/2 = 697.1871


Optimal GPV sequence: {{Val list| 12f, 50eff, 62 }}
Optimal GPV sequence: {{Val list| 12f, 50eff, 62 }}
Line 480: Line 483:


=== Meanpop ===
=== Meanpop ===
{{see also| Meantone vs meanpop }}
{{See also| Meantone vs meanpop }}


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
Line 490: Line 493:
Mapping generator: ~2, ~3
Mapping generator: ~2, ~3


POTE generator: ~3/2 = 696.434
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.5311


Minimax tuning:  
Minimax tuning:  
* 11-odd-limit: ~3/2 = {{Monzo| 0 0 1/4 }}
* 11-odd-limit: ~3/2 = {{monzo| 0 0 1/4 }}
: [{{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 }}]
: [{{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 }}]
: Eigenmonzos (unchanged intervals): 2, 5
: Eigenmonzo basis: 2.5


Tuning ranges:  
Tuning ranges:  
Line 509: Line 512:


; Music
; Music
* [http://soonlabel.com/xenharmonic/archives/607 Scott Joplin's "The Entertainer" tuned into meanpop]{{Dead link}}
* [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]
* [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]


==== Tridecimal meanpop ====
==== Tridecimal meanpop ====
Line 519: Line 522:
Mapping: [{{val| 1 0 -4 -13 24 -20 }}, {{val| 0 1 4 10 -13 15 }}]
Mapping: [{{val| 1 0 -4 -13 24 -20 }}, {{val| 0 1 4 10 -13 15 }}]


Mapping generator: ~2, ~3
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.3563
 
POTE generator: ~3/2 = 696.211


Minimax tuning:  
Minimax tuning:  
* 13- and 15-odd-limit: ~3/2 = {{Monzo| 4/7 0 0 0 -1/28 1/28 }}
* 13- and 15-odd-limit: ~3/2 = {{monzo| 4/7 0 0 0 -1/28 1/28 }}
: Eigenmonzos (unchanged intervals): 2, 13/11
: Eigenmonzo basis: 2.13/11


Tuning ranges:  
Tuning ranges:  
Line 532: Line 533:
* 13- and 15-odd-limit diamond monotone and tradeoff: ~3/2 = [694.737, 696.774]
* 13- and 15-odd-limit diamond monotone and tradeoff: ~3/2 = [694.737, 696.774]


Optimal GPV sequence: {{Val list| 12ef, 19, 31, 50, 81, 131bd, 212bbddf }}
Optimal GPV sequence: {{Val list| 19, 31, 50, 81 }}


Badness: 0.020883
Badness: 0.020883
Line 543: Line 544:
Mapping: [{{val| 1 0 -4 -13 24 -20 -37 }}, {{val| 0 1 4 10 -13 15 26 }}]
Mapping: [{{val| 1 0 -4 -13 24 -20 -37 }}, {{val| 0 1 4 10 -13 15 26 }}]


Mapping generator: ~2, ~3
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.3508
 
POTE generator: ~3/2 = 696.194


Optimal GPV sequence: {{Val list| 19g, 31, 50, 81, 131bd }}
Optimal GPV sequence: {{Val list| 19g, 31, 50, 81, 131bd }}
Line 558: Line 557:
Mapping: [{{val| 1 0 -4 -13 24 -20 -37 -40 }}, {{val| 0 1 4 10 -13 15 26 28 }}]
Mapping: [{{val| 1 0 -4 -13 24 -20 -37 -40 }}, {{val| 0 1 4 10 -13 15 26 28 }}]


Mapping generator: ~2, ~3
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.3471
 
POTE generator: ~3/2 = 696.188


Optimal GPV sequence: {{Val list| 19gh, 31, 50, 81, 131bd }}
Optimal GPV sequence: {{Val list| 19gh, 31, 50, 81 }}


Badness: 0.017791
Badness: 0.017791
Line 571: Line 568:
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: [{{val|1 0 -4 -13 24 -20 12}}, {{val|0 1 4 10 -13 15 -5}}]
Mapping: [{{val| 1 0 -4 -13 24 -20 12 }}, {{val| 0 1 4 10 -13 15 -5 }}]


POTE generator: ~3/2 = 696.408
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.4388


Optimal GPV sequence: {{Val list| 12ef, 19, 31, 81g, 112bfgg }}
Optimal GPV sequence: {{Val list| 19, 31 }}


Badness: 0.022870
Badness: 0.022870
Line 584: Line 581:
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: [{{val|1 0 -4 -13 24 -20 12 9}}, {{val|0 1 4 10 -13 15 -5 -3}}]
Mapping: [{{val| 1 0 -4 -13 24 -20 12 9 }}, {{val| 0 1 4 10 -13 15 -5 -3 }}]


POTE generator: ~4/3 = 503.501
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.4838


Optimal GPV sequence: {{Val list| 12ef, 19, 31, 81gh, 112bfgghh }}
Optimal GPV sequence: {{Val list| 12ef, 19, 31 }}


Badness: 0.020488
Badness: 0.020488
Line 599: Line 596:
Mapping: [{{val| 1 0 -4 -13 24 10 }}, {{val| 0 1 4 10 -13 -4 }}]
Mapping: [{{val| 1 0 -4 -13 24 10 }}, {{val| 0 1 4 10 -13 -4 }}]


POTE generator: ~3/2 = 696.202
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.2827


Minimax tuning:  
Minimax tuning:  
* 13- and 15-odd-limit: ~3/2 = {{Monzo| 11/13 0 0 0 -1/13 }}
* 13- and 15-odd-limit: ~3/2 = {{monzo| 11/13 0 0 0 -1/13 }}
: Eigenmonzos (unchanged intervals): 2, 11
: Eigenmonzo basis: 2.11


Optimal GPV sequence: {{Val list| 12e, 19, 31f, 50ff, 81fff }}
Optimal GPV sequence: {{Val list| 12e, 19, 31f }}


Badness: 0.027666
Badness: 0.027666
Line 614: Line 611:
Comma list: 52/51, 65/64, 78/77, 81/80, 91/90
Comma list: 52/51, 65/64, 78/77, 81/80, 91/90


Mapping: [{{val|1 0 -4 -13 24 10 12}}, {{val|0 1 4 10 -13 -4 -5}}]
Mapping: [{{val| 1 0 -4 -13 24 10 12 }}, {{val| 0 1 4 10 -13 -4 -5 }}]


POTE generator: ~3/2 = 696.414
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.4069


Optimal GPV sequence: {{Val list| 12e, 19, 31f }}
Optimal GPV sequence: {{Val list| 12e, 19 }}


Badness: 0.026836
Badness: 0.026836
Line 627: Line 624:
Comma list: 39/38, 52/51, 65/64, 77/76, 81/80, 91/90
Comma list: 39/38, 52/51, 65/64, 77/76, 81/80, 91/90


Mapping: [{{val|1 0 -4 -13 24 10 12 9}}, {{val|0 1 4 10 -13 -4 -5 -3}}]
Mapping: [{{val| 1 0 -4 -13 24 10 12 9 }}, {{val| 0 1 4 10 -13 -4 -5 -3 }}]


POTE generator: ~3/2 = 696.497
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.4731


Optimal GPV sequence: {{Val list| 12e, 19, 31f }}
Optimal GPV sequence: {{Val list| 12e, 19 }}


Badness: 0.023540
Badness: 0.023540
Line 640: Line 637:
Comma list: 51/50, 65/64, 78/77, 81/80, 85/84
Comma list: 51/50, 65/64, 78/77, 81/80, 85/84


Mapping: [{{val|1 0 -4 -13 24 10 -7}}, {{val|0 1 4 10 -13 -4 7}}]
Mapping: [{{val| 1 0 -4 -13 24 10 -7 }}, {{val| 0 1 4 10 -13 -4 7 }}]


POTE generator: ~3/2 = 696.415
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.6614


Optimal GPV sequence: {{Val list| 12e, 19g, 31fg }}
Optimal GPV sequence: {{Val list| 12e, 19g, 31fg }}
Line 653: Line 650:
Comma list: 51/50, 57/56, 65/64, 76/75, 78/77, 81/80
Comma list: 51/50, 57/56, 65/64, 76/75, 78/77, 81/80


Mapping: [{{val|1 0 -4 -13 24 10 -7 -10}}, {{val|0 1 4 10 -13 -4 7 9}}]
Mapping: [{{val| 1 0 -4 -13 24 10 -7 -10 }}, {{val| 0 1 4 10 -13 -4 7 9 }}]


POTE generator: ~3/2 = 696.583
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.0160


Optimal GPV sequence: {{Val list| 12e, 19gh, 31fgh }}
Optimal GPV sequence: {{Val list| 12e, 19gh, 31fgh }}
Line 668: Line 665:
Mapping: [{{val| 1 0 -4 -13 -6 }}, {{val| 0 1 4 10 6 }}]
Mapping: [{{val| 1 0 -4 -13 -6 }}, {{val| 0 1 4 10 6 }}]


POTE generator: ~3/2 = 696.250
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.1527


Tuning ranges:  
Tuning ranges:  
Line 675: Line 672:
* 11-odd-limit diamond monotone and tradeoff: ~3/2 = [694.737, 700.000]
* 11-odd-limit diamond monotone and tradeoff: ~3/2 = [694.737, 700.000]


Optimal GPV sequence: {{Val list| 7d, 12, 19, 31e, 50ee }}
Optimal GPV sequence: {{Val list| 7d, 12, 19, 31e }}


Badness: 0.021423
Badness: 0.021423
Line 686: Line 683:
Mapping: [{{val| 1 0 -4 -13 -6 -20 }}, {{val| 0 1 4 10 6 15 }}]
Mapping: [{{val| 1 0 -4 -13 -6 -20 }}, {{val| 0 1 4 10 6 15 }}]


POTE generator: ~3/2 = 696.146
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.0983


Optimal GPV sequence: {{Val list| 7df, 12f, 19, 31e, 50ee }}
Optimal GPV sequence: {{Val list| 7df, 12f, 19, 31e }}


Badness: 0.021182
Badness: 0.021182
Line 699: Line 696:
Mapping: [{{val| 1 0 -4 -13 -6 -20 12 }}, {{val| 0 1 4 10 6 15 -5 }}]
Mapping: [{{val| 1 0 -4 -13 -6 -20 12 }}, {{val| 0 1 4 10 6 15 -5 }}]


POTE generator: ~3/2 = 696.575
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.2161


Optimal GPV sequence: {{Val list| 7df, 12f, 19, 31e }}
Optimal GPV sequence: {{Val list| 12f, 19, 31e }}


Badness: 0.022980
Badness: 0.022980
Line 712: Line 709:
Mapping: [{{val| 1 0 -4 -13 -6 -20 12 9 }}, {{val| 0 1 4 10 6 15 -5 -3 }}]
Mapping: [{{val| 1 0 -4 -13 -6 -20 12 9 }}, {{val| 0 1 4 10 6 15 -5 -3 }}]


POTE generator: ~3/2 = 696.706
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.2774


Optimal GPV sequence: {{Val list| 7df, 12f, 19, 31e }}
Optimal GPV sequence: {{Val list| 12f, 19, 31e }}


Badness: 0.020293
Badness: 0.020293
Line 723: Line 720:
Comma list: 34/33, 45/44, 51/50, 56/55, 78/77
Comma list: 34/33, 45/44, 51/50, 56/55, 78/77


Mapping: [{{val|1 0 -4 -13 -6 -20 -7}}, {{val|0 1 4 10 6 15 7}}]
Mapping: [{{val| 1 0 -4 -13 -6 -20 -7 }}, {{val| 0 1 4 10 6 15 7 }}]


POTE generator: ~3/2 = 696.025
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.4501


Optimal GPV sequence: {{Val list| 7dfg, 12f, 19g, 31eg, 50eegg }}
Optimal GPV sequence: {{Val list| 7dfg, 12f, 19g }}


Badness: 0.020171
Badness: 0.020171
Line 736: Line 733:
Comma list: 34/33, 45/44, 51/50, 56/55, 57/55, 78/77
Comma list: 34/33, 45/44, 51/50, 56/55, 57/55, 78/77


Mapping: [{{val|1 0 -4 -13 -6 -20 -7 -10}}, {{val|0 1 4 10 6 15 7 9}}]
Mapping: [{{val| 1 0 -4 -13 -6 -20 -7 -10 }}, {{val| 0 1 4 10 6 15 7 9 }}]


POTE generator: ~3/2 = 696.121
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.121


Optimal GPV sequence: {{Val list| 7dfgh, 12f, 19gh, 31egh, 50eegghh }}
Optimal GPV sequence: {{Val list| 7dfgh, 12f, 19gh }}


Badness: 0.018045
Badness: 0.018045
Line 751: Line 748:
Mapping: [{{val| 1 0 -4 -13 -6 10 }}, {{val| 0 1 4 10 6 -4 }}]
Mapping: [{{val| 1 0 -4 -13 -6 10 }}, {{val| 0 1 4 10 6 -4 }}]


POTE generator: ~3/2 = 695.060
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.7897


Optimal GPV sequence: {{Val list| 7d, 12, 19 }}
Optimal GPV sequence: {{Val list| 7d, 12, 19 }}
Line 764: Line 761:
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 }}, {{val| 0 1 4 10 6 -4 -5 }}]


POTE generator: ~3/2 = 695.858
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.0114


Optimal GPV sequence: {{Val list| 7d, 12, 19 }}
Optimal GPV sequence: {{Val list| 12, 19 }}


Badness: 0.025535
Badness: 0.025535
Line 777: Line 774:
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 }}, {{val| 0 1 4 10 6 -4 -5 -3 }}]


POTE generator: ~3/2 = 696.131
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.1196


Optimal GPV sequence: {{Val list| 7d, 12, 19 }}
Optimal GPV sequence: {{Val list| 12, 19 }}


Badness: 0.022302
Badness: 0.022302
Line 790: Line 787:
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 }}, {{val| 0 1 4 10 6 -4 -5 -3 -6 }}]


POTE generator: ~3/2 = 696.044
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.0585


Optimal GPV sequence: {{Val list| 7d, 12, 19 }}
Optimal GPV sequence: {{Val list| 12, 19 }}


Badness: 0.020139
Badness: 0.020139
Line 803: Line 800:
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 }}, {{val| 0 1 4 10 6 -4 -5 -3 -6 -2 }}]


POTE generator: ~3/2 = 695.913
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.9824


Optimal GPV sequence: {{Val list| 7d, 12, 19 }}
Optimal GPV sequence: {{Val list| 12, 19 }}


Badness: 0.018168
Badness: 0.018168
Line 816: Line 813:
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 }}, {{val| 0 1 4 10 6 -4 -5 -3 -6 -2 -7 }}]


POTE generator: ~3/2 = 695.750
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.7980


Optimal GPV sequence: {{Val list| 7d, 12, 19 }}
Optimal GPV sequence: {{Val list| 12, 19 }}


Badness: 0.017069
Badness: 0.017069
Line 829: Line 826:
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 }}, {{val| 0 1 4 10 6 -4 -5 -3 -6 -2 -7 9 }}]


POTE generator: ~3/2 = 695.603
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.6746


Optimal GPV sequence: {{Val list| 7d, 12, 19 }}
Optimal GPV sequence: {{Val list| 12, 19 }}


Badness: 0.016129
Badness: 0.016129
Line 842: Line 839:
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 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 = 695.696
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.7239


Optimal GPV sequence: {{Val list| 7d, 12, 19 }}
Optimal GPV sequence: {{Val list| 12, 19 }}


Badness: 0.015356
Badness: 0.015356
Line 855: Line 852:
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 -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 = 695.688
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.7160


Optimal GPV sequence: {{Val list| 7d, 12, 19 }}
Optimal GPV sequence: {{Val list| 12, 19 }}


Badness: 0.013906
Badness: 0.013906
Line 868: Line 865:
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 -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 = 695.676
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.6849


Optimal GPV sequence: {{Val list| 7d, 12, 19 }}
Optimal GPV sequence: {{Val list| 12, 19 }}


Badness: 0.013818
Badness: 0.013818
Line 879: Line 876:
Comma list: 34/33, 45/44, 51/50, 56/55, 65/64
Comma list: 34/33, 45/44, 51/50, 56/55, 65/64


Mapping: [{{val|1 0 -4 -13 -6 10 -7}}, {{val|0 1 4 10 6 -4 7}}]
Mapping: [{{val| 1 0 -4 -13 -6 10 -7 }}, {{val| 0 1 4 10 6 -4 7 }}]


POTE generator: ~3/2 = 695.358
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.4125


Optimal GPV sequence: {{Val list| 7dg, 12, 19g }}
Optimal GPV sequence: {{Val list| 7dg, 12, 19g }}
Line 892: Line 889:
Comma list: 34/33, 45/44, 51/50, 56/55, 57/55, 65/64
Comma list: 34/33, 45/44, 51/50, 56/55, 57/55, 65/64


Mapping: [{{val|1 0 -4 -13 -6 10 -7 -10}}, {{val|0 1 4 10 6 -4 7 9}}]
Mapping: [{{val| 1 0 -4 -13 -6 10 -7 -10 }}, {{val| 0 1 4 10 6 -4 7 9 }}]


POTE generator: ~3/2 = 695.725
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.9500


Optimal GPV sequence: {{Val list| 7dgh, 12, 19gh, 50eeffgghh }}
Optimal GPV sequence: {{Val list| 7dgh, 12, 19gh }}


Badness: 0.019904
Badness: 0.019904
Line 907: Line 904:
Mapping: [{{val| 1 0 -4 -13 -6 -1 }}, {{val| 0 1 4 10 6 3 }}]
Mapping: [{{val| 1 0 -4 -13 -6 -1 }}, {{val| 0 1 4 10 6 3 }}]


POTE generator: ~3/2 = 697.254
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.6202


Optimal GPV sequence: {{Val list| 7d, 12f, 19f, 31eff }}
Optimal GPV sequence: {{Val list| 7d, 12f, 19f }}


Badness: 0.024243
Badness: 0.024243
Line 920: Line 917:
Mapping: [{{val| 1 0 -4 -13 -6 -1 -7 }}, {{val| 0 1 4 10 6 3 7 }}]
Mapping: [{{val| 1 0 -4 -13 -6 -1 -7 }}, {{val| 0 1 4 10 6 3 7 }}]


POTE generator: ~3/2 = 697.586
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.2789


Optimal GPV sequence: {{Val list| 7dg, 12f, 19fg, 31effg }}
Optimal GPV sequence: {{Val list| 7dg, 12f }}


Badness: 0.021400
Badness: 0.021400
Line 933: Line 930:
Mapping: [{{val| 1 0 -4 -13 -6 -1 -7 -10 }}, {{val| 0 1 4 10 6 3 7 9 }}]
Mapping: [{{val| 1 0 -4 -13 -6 -1 -7 -10 }}, {{val| 0 1 4 10 6 3 7 9 }}]


POTE generator: ~3/2 = 698.118
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.8486


Optimal GPV sequence: {{Val list| 7dgh, 12f, 19fgh, 31effgh }}
Optimal GPV sequence: {{Val list| 7dgh, 12f }}


Badness: 0.018996
Badness: 0.018996
Line 944: Line 941:
Comma list: 33/32, 55/54, 77/75
Comma list: 33/32, 55/54, 77/75


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


POTE generator: ~3/2 = 694.689
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.7022


Optimal GPV sequence: {{Val list| 7d, 12e, 19e }}
Optimal GPV sequence: {{Val list| 7d, 12e, 19e }}
Line 957: Line 954:
Comma list: 33/32, 55/54, 65/64, 77/75
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 }}]
Mapping: [{{val| 1 0 -4 -13 5 10 }}, {{val| 0 1 4 10 -1 -4 }}]


POTE generator: ~3/2 = 694.764
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.2408


Optimal GPV sequence: {{Val list| 7d, 12e, 19e }}
Optimal GPV sequence: {{Val list| 7d, 12e, 19e }}
Line 974: Line 971:
Mapping generators: ~2, ~11/9
Mapping generators: ~2, ~11/9


POTE generator: ~11/9 = 348.182
Optimal tuning (CTE): ~2 = 1\1, ~11/9 = 348.5324


Optimal GPV sequence: {{Val list| 7d, 24d, 31, 100de, 131bdee, 162bdee }}
Optimal GPV sequence: {{Val list| 7d, 24d, 31, 100de, 131bdee, 162bdee }}
Line 987: Line 984:
Mapping: [{{val| 1 1 0 -3 2 4 }}, {{val| 0 2 8 20 5 -1 }}]
Mapping: [{{val| 1 1 0 -3 2 4 }}, {{val| 0 2 8 20 5 -1 }}]


Mapping generators: ~2, ~11/9
Optimal tuning (CTE): ~2 = 1\1, ~11/9 = 348.5444
 
POTE generator: ~11/9 = 348.490


Optimal GPV sequence: {{Val list| 7d, 24d, 31, 55d }}
Optimal GPV sequence: {{Val list| 7d, 24d, 31 }}


Badness: 0.028071
Badness: 0.028071
Line 1,006: Line 1,001:
Mapping generators: ~63/44, ~3
Mapping generators: ~63/44, ~3


POTE generator: ~3/2 = 696.016
Optimal tuning (CTE): ~63/44 = 1\2, ~3/2 = 696.5199


Optimal GPV sequence: {{Val list| 12, 26de, 38d, 50 }}
Optimal GPV sequence: {{Val list| 12, 26de, 38d, 50 }}
Line 1,019: Line 1,014:
Mapping: [{{val| 2 0 -8 -26 -31 -40 }}, {{val| 0 1 4 10 12 15 }}]
Mapping: [{{val| 2 0 -8 -26 -31 -40 }}, {{val| 0 1 4 10 12 15 }}]


Mapping generators: ~55/39, ~3
Optimal tuning (CTE): ~55/39 = 1\2, ~3/2 = 696.3410
 
POTE generator: ~3/2 = 695.836


Optimal GPV sequence: {{Val list| 12f, 26deff, 38df, 50 }}
Optimal GPV sequence: {{Val list| 12f, 26deff, 38df, 50 }}
Line 1,034: Line 1,027:
Mapping: [{{val| 2 0 -8 -26 -31 -40 5 }}, {{val| 0 1 4 10 12 15 1 }}]
Mapping: [{{val| 2 0 -8 -26 -31 -40 5 }}, {{val| 0 1 4 10 12 15 1 }}]


Mapping generators: ~17/12, ~3
Optimal tuning (CTE): ~17/12 = 1\2, ~3/2 = 696.3526
 
POTE generator: ~3/2 = 695.783


Optimal GPV sequence: {{Val list| 12f, 26deff, 38df, 50 }}
Optimal GPV sequence: {{Val list| 12f, 38df, 50 }}


Badness: 0.022666
Badness: 0.022666
Line 1,049: Line 1,040:
Mapping: [{{val| 2 0 -8 -26 -31 -40 5 -1 }}, {{val| 0 1 4 10 12 15 1 3 }}]
Mapping: [{{val| 2 0 -8 -26 -31 -40 5 -1 }}, {{val| 0 1 4 10 12 15 1 3 }}]


Mapping generators: ~17/12, ~3
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.3837
 
POTE generator: ~3/2 = 695.752


Optimal GPV sequence: {{Val list| 12f, 26deff, 38df, 50 }}
Optimal GPV sequence: {{Val list| 12f, 26deff, 38df, 50 }}
Line 1,064: Line 1,053:
Mapping: [{{val| 1 2 4 7 5 }}, {{val| 0 -3 -12 -30 -11 }}]
Mapping: [{{val| 1 2 4 7 5 }}, {{val| 0 -3 -12 -30 -11 }}]


POTE generator: ~11/10 = 167.805
Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 167.7074


Optimal GPV sequence: {{Val list| 43, 50, 93, 143b, 236bbde }}
Optimal GPV sequence: {{Val list| 43, 50, 93 }}


Badness: 0.050729
Badness: 0.050729
Line 1,077: Line 1,066:
Mapping: [{{val| 1 2 4 7 5 3 }}, {{val| 0 -3 -12 -30 -11 5 }}]
Mapping: [{{val| 1 2 4 7 5 3 }}, {{val| 0 -3 -12 -30 -11 5 }}]


POTE generator: ~11/10 = 167.790
Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 167.7121


Optimal GPV sequence: {{Val list| 43, 50, 93, 143b, 236bbde }}
Optimal GPV sequence: {{Val list| 43, 50, 93 }}


Badness: 0.035445
Badness: 0.035445
Line 1,090: Line 1,079:
Mapping: [{{val| 1 2 4 7 5 3 8 }}, {{val| 0 -3 -12 -30 -11 5 -28 }}]
Mapping: [{{val| 1 2 4 7 5 3 8 }}, {{val| 0 -3 -12 -30 -11 5 -28 }}]


POTE generator: ~11/10 = 167.786
Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 167.7047


Optimal GPV sequence: {{Val list| 43, 50, 93, 236bbdeg }}
Optimal GPV sequence: {{Val list| 43, 50, 93 }}


Badness: 0.025221
Badness: 0.025221
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