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Added a new temperament
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Badness: 0.040182
Badness: 0.040182
== Eris ==
Subgroup: 2.3.5.7
[[Comma list]]: 16875/16807, 65625/65536
[[Mapping]]: [{{val|1 10 0 6}}, {{val|0 -29 8 -11}}]
{{Multival|legend=1|29 -8 11 -80 -64 48}}
[[POTE generator]]: ~60/49 = 348.216
{{Val list|legend=1| 31, 131, 162, 193, 224, 1823cd, 2271cd }}
[[Badness]]: 0.074719
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 540/539, 1375/1372, 65625/65536
Mapping: [{{val|1 10 0 6 20}}, {{val|0 -29 8 -11 -57}}]
POTE generator: ~11/9 = 348.219
Optimal GPV sequence: {{Val list| 31, 193, 224, 703, 927d, 1151cd }}
Badness: 0.027621
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 625/624, 1375/1372, 4096/4095
Mapping: [{{val|1 10 0 6 20 -14}}, {{val|0 -29 8 -11 -57 61}}]
POTE generator: ~11/9 = 348.213
Optimal GPV sequence: {{Val list| 31, 193, 224 }}
Badness: 0.025137


== Mirkat ==
== Mirkat ==
Line 361: Line 320:
Badness: 0.011775
Badness: 0.011775


== Subsemifourth ==
== Eris ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


[[Comma list]]: 16875/16807, 26873856/26796875
[[Comma list]]: 16875/16807, 65625/65536


[[Mapping]]: [{{val|1 -8 -4 -8}}, {{val|0 47 31 53}}]
[[Mapping]]: [{{val|1 10 0 6}}, {{val|0 -29 8 -11}}]


{{Multival|legend=1|47 31 53 -60 -48 36}}
{{Multival|legend=1|29 -8 11 -80 -64 48}}


[[POTE generator]]: ~144/125 = 244.719
[[POTE generator]]: ~60/49 = 348.216


{{Val list|legend=1| 49, 103, 152, 255, 407 }}
{{Val list|legend=1| 31, 131, 162, 193, 224, 1823cd, 2271cd }}


[[Badness]]: 0.135173
[[Badness]]: 0.074719


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


Comma list: 540/539, 1375/1372, 234375/234256
Comma list: 540/539, 1375/1372, 65625/65536


Mapping: [{{val|1 -8 -4 -8 -10}}, {{val|0 47 31 53 66}}]
Mapping: [{{val|1 10 0 6 20}}, {{val|0 -29 8 -11 -57}}]


POTE generator: ~121/105 = 244.719
POTE generator: ~11/9 = 348.219


Optimal GPV sequence: {{Val list| 49, 103, 152, 255, 407, 966d }}
Optimal GPV sequence: {{Val list| 31, 193, 224, 703, 927d, 1151cd }}


Badness: 0.034276
Badness: 0.027621


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


Comma list: 540/539, 847/845, 1375/1372, 1575/1573
Comma list: 540/539, 625/624, 1375/1372, 4096/4095


Mapping: [{{val|1 -8 -4 -8 -10 -12}}, {{val|0 47 31 53 66 77}}]
Mapping: [{{val|1 10 0 6 20 -14}}, {{val|0 -29 8 -11 -57 61}}]


POTE generator: ~15/13 = 244.714
POTE generator: ~11/9 = 348.213


Optimal GPV sequence: {{Val list| 49f, 103, 152f, 255, 407f, 662df }}
Optimal GPV sequence: {{Val list| 31, 193, 224 }}


Badness: 0.028387
Badness: 0.025137
 
== Hemiseptisix ==
The name ''hemiseptisix'' means a half of septimal major sixth ([[12/7]]). The hemiseptisix temperament (103&121) tempers out the mirkwai comma and 95703125/95551488 (''pontiqak'' comma, lazozotritriyo) in the 7-limit. [[224edo|224EDO]] provides an excellent tuning for 7, 11, and 13-limit hemiseptisix.


== Subsemifourth ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


[[Comma list]]: 16875/16807, 95703125/95551488
[[Comma list]]: 16875/16807, 26873856/26796875


[[Mapping]]: [{{val|1 -19 -7 -17}}, {{val|0 53 24 51}}]
[[Mapping]]: [{{val|1 -8 -4 -8}}, {{val|0 47 31 53}}]


{{Multival|legend=1|53 24 51 -85 -68 51}}
{{Multival|legend=1|47 31 53 -60 -48 36}}


[[POTE generator]]: ~98/75 = 466.071
[[POTE generator]]: ~144/125 = 244.719


{{Val list|legend=1| 18, 103, 121, 224 }}
{{Val list|legend=1| 49, 103, 152, 255, 407 }}


[[Badness]]: 0.162826
[[Badness]]: 0.135173


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


Comma list: 540/539, 1375/1372, 2734375/2725888
Comma list: 540/539, 1375/1372, 234375/234256


Mapping: [{{val|1 -19 -7 -17 -28}}, {{val|0 53 24 51 81}}]
Mapping: [{{val|1 -8 -4 -8 -10}}, {{val|0 47 31 53 66}}]


POTE generator: ~55/42 = 466.070
POTE generator: ~121/105 = 244.719


Optimal GPV sequence: {{Val list| 103, 121, 224 }}
Optimal GPV sequence: {{Val list| 49, 103, 152, 255, 407, 966d }}


Badness: 0.043381
Badness: 0.034276


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


Comma list: 540/539, 625/624, 1375/1372, 2200/2197
Comma list: 540/539, 847/845, 1375/1372, 1575/1573


Mapping: [{{val|1 -19 -7 -17 -28 -13}}, {{val|0 53 24 51 81 43}}]
Mapping: [{{val|1 -8 -4 -8 -10 -12}}, {{val|0 47 31 53 66 77}}]


POTE generator: ~55/42 = 466.071
POTE generator: ~15/13 = 244.714


Optimal GPV sequence: {{Val list| 103, 121, 224 }}
Optimal GPV sequence: {{Val list| 49f, 103, 152f, 255, 407f, 662df }}


Badness: 0.021127
Badness: 0.028387


== Septendesemi ==
== Septendesemi ==
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Badness: 0.020128
Badness: 0.020128
== Gaster ==
Subgroup: 2.3.5.7
[[Comma list]]: 16875/16807, 14348907/14336000
[[Mapping]]: [{{val|1 11 38 37}}, {{val|0 -19 -72 -69}}]
[[POTE generator]]: ~800/567 = 594.64130
{{Optimal GPV sequence|legend=1| 111, 224 }}
[[Badness]]: 0.154521
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 540/539, 1375/1372, 14348907/14336000
Mapping: [{{val|1 11 38 37 -1}}, {{val|0 -19 -72 -69 9}}]
POTE generator: ~512/363 = 594.63909
Optimal GPV sequence: {{Val list| 111, 224, 783d, 1007d, 1231dd }}
Badness: 0.054060
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 729/728, 1375/1372, 2200/2197
Mapping: [{{val|1 11 38 37 -1 26}}, {{val|0 -19 -72 -69 9 -45}}]
POTE generator: ~55/39 = 594.63899
Optimal GPV sequence: {{Val list| 111, 224, 783df, 1007df, 1231ddf }}
Badness: 0.024882
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
Comma list: 540/539, 715/714, 729/728, 936/935, 2200/2197
Mapping: [{{val|1 11 38 37 -1 26 14}}, {{val|0 -19 -72 -69 9 -45 -20}}]
POTE generator: ~24/17 = 594.63553
Optimal GPV sequence: {{Val list| 111, 224, 559dgg }}
Badness: 0.021436
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 324/323, 400/399, 495/494, 540/539, 715/714, 1445/1444
Mapping: [{{val|1 11 38 37 -1 26 14 32}}, {{val|0 -19 -72 -69 9 -45 -20 -56}}]
POTE generator: ~24/17 = 594.63620
Optimal GPV sequence: {{Val list| 111, 224 }}
Badness: 0.018370
=== 23-limit ===
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 324/323, 400/399, 460/459, 495/494, 529/528, 540/539, 715/714
Mapping: [{{val|1 11 38 37 -1 26 14 32 7}}, {{val|0 -19 -72 -69 9 -45 -20 -56 -5}}]
POTE generator: ~24/17 = 594.64147
Optimal GPV sequence: {{Val list| 111, 224 }}
Badness: 0.017619
=== 29-limit ===
Subgroup: 2.3.5.7.11.13.17.19.23.29
Comma list: 290/289, 324/323, 400/399, 460/459, 495/494, 529/528, 540/539, 715/714
Mapping: [{{val|1 11 38 37 -1 26 14 32 7 -11}}, {{val|0 -19 -72 -69 9 -45 -20 -56 -5 32}}]
POTE generator: ~24/17 = 594.64556
Optimal GPV sequence: {{Val list| 111, 113, 224 }}
Badness: 0.016815
=== 31-limit ===
Subgroup: 2.3.5.7.11.13.17.19.23.29.31
Comma list: 290/289, 324/323, 400/399, 435/434, 460/459, 495/494, 528/527, 540/539, 715/714
Mapping: [{{val|1 11 38 37 -1 26 14 32 7 -11 0}}, {{val|0 -19 -72 -69 9 -45 -20 -56 -5 32 10}}]
POTE generator: ~24/17 = 594.64392
Optimal GPV sequence: {{Val list| 111, 113, 224 }}
Badness: 0.014790
=== 37-limit ===
Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37
Comma list: 290/289, 324/323, 400/399, 435/434, 460/459, 495/494, 528/527, 540/539, 667/666, 715/714
Mapping: [{{val|1 11 38 37 -1 26 14 32 7 -11 0 -27}}, {{val|0 -19 -72 -69 9 -45 -20 -56 -5 32 10 65}}]
POTE generator: ~24/17 = 594.64383
Optimal GPV sequence: {{Val list| 111, 113, 224 }}
Badness: 0.014377
=== 41-limit ===
Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37.41
Comma list: 290/289, 324/323, 400/399, 435/434, 460/459, 495/494, 528/527, 533/532, 540/539, 575/574, 667/666
Mapping: [{{val|1 11 38 37 -1 26 14 32 7 -11 0 -27 45}}, {{val|0 -19 -72 -69 9 -45 -20 -56 -5 32 10 65 -80}}]
POTE generator: ~24/17 = 594.64299
Optimal GPV sequence: {{Val list| 111, 113, 224 }}
Badness: 0.012858


== Subsedia ==
== Subsedia ==
Line 569: Line 656:


Badness: 0.017935
Badness: 0.017935
== Hemiseptisix ==
The name ''hemiseptisix'' means a half of septimal major sixth ([[12/7]]). The hemiseptisix temperament (103&121) tempers out the mirkwai comma and 95703125/95551488 (''pontiqak'' comma, lazozotritriyo) in the 7-limit. [[224edo|224EDO]] provides an excellent tuning for 7, 11, and 13-limit hemiseptisix.
Subgroup: 2.3.5.7
[[Comma list]]: 16875/16807, 95703125/95551488
[[Mapping]]: [{{val|1 -19 -7 -17}}, {{val|0 53 24 51}}]
{{Multival|legend=1|53 24 51 -85 -68 51}}
[[POTE generator]]: ~98/75 = 466.071
{{Val list|legend=1| 18, 103, 121, 224 }}
[[Badness]]: 0.162826
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 540/539, 1375/1372, 2734375/2725888
Mapping: [{{val|1 -19 -7 -17 -28}}, {{val|0 53 24 51 81}}]
POTE generator: ~55/42 = 466.070
Optimal GPV sequence: {{Val list| 103, 121, 224 }}
Badness: 0.043381
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 625/624, 1375/1372, 2200/2197
Mapping: [{{val|1 -19 -7 -17 -28 -13}}, {{val|0 53 24 51 81 43}}]
POTE generator: ~55/42 = 466.071
Optimal GPV sequence: {{Val list| 103, 121, 224 }}
Badness: 0.021127


[[Category:Regular temperament theory]]
[[Category:Regular temperament theory]]
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