No-threes subgroup temperaments: Difference between revisions

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Classified by focusing on the mapping of 5th harmonic, similar to [[Rank-2 temperaments by mapping of 3]].
Classified by focusing on the mapping of 5th harmonic, similar to [[Rank-2 temperaments by mapping of 3]].
* For no-fives, see [[#No-threes no-fives subgroup temperaments]].
* For no-fives, see [[#No-threes no-fives subgroup temperaments]].
* French decimal and trader have a ~2/1 period and ~5/4 generator. There is a one-to-one correspondence between the 2.5 subgroup and mapped intervals.
* Trader has a ~2/1 period and ~5/4 generator. There is a one-to-one correspondence between the 2.5 subgroup and mapped intervals.
* Ostara, movila and vengeance have variantly expressed generators, three of which give the ~5/2.
* Ostara, movila and vengeance have variantly expressed generators, three of which give the ~5/2.
* Insect has a ~55/32 generator, three of which give the ~5/1.
* Insect has a ~55/32 generator, three of which give the ~5/1.
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* Jubilic ([[50/49]]) → [[Jubilismic clan #Jubilic|Jubilismic clan]]
* Jubilic ([[50/49]]) → [[Jubilismic clan #Jubilic|Jubilismic clan]]
* Didacus ([[3136/3125]]) → [[Hemimean clan #Didacus|Hemimean clan]]
* Didacus ([[3136/3125]]) → [[Hemimean clan #Didacus|Hemimean clan]]
* Mercy ([[823543/819200]]) → [[Quince clan #Mercy|Quince clan]]
* Llywelyn a.k.a. shoe ([[4194304/4117715]]) → [[Llywelynsmic clan #Llywelyn a.k.a. shoe|Llywelynsmic clan]]
* Sidewalk ([[823543/800000]]) → [[2023/2000 #Sidewalk]]
* Sidewalk ([[823543/800000]]) → [[2023/2000 #Sidewalk]]
=== Rainy ===
In rainy, three generators make an [[8/7]]; five generators make a [[5/4]]. It is the no-3's [[restriction]] of [[tertiaseptal]] (and [[valentine]]), notable theoretically as it equates ([[2/1]])/([[5/4]])<sup>3</sup> (128/125, the lesser diesis) with ([[2/1]])/([[8/7]])<sup>5</sup> (the 2.7-subgroup [[cloudy comma]], which is similar to the 2.5-subgroup lesser diesis in that tempering it out tunes the 8/7 about 8.8{{cent}} sharp, while tempering out 128/125 similarly sharpens the 5/4 by about 13.7{{cent}}). By tempering out their difference, stacked 5's and stacked 7's become easier to navigate, using the general-purpose diesis to simplify clusters.
A highly notable tuning of rainy not shown here is [[311edo]], which is 140 + 171 so tuned between them.
[[Subgroup]]: 2.5.7
[[Comma list]]: [[2100875/2097152]]
{{Mapping|legend=2| 1 2 3 | 0 5 -3 }}
{{Mapping|legend=3| 1 0 2 3 | 0 0 5 -3 }}
: mapping generators: ~2, ~256/245
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.0939{{c}}, ~256/245 = 77.2107{{c}}
: [[error map]]: {{val| +0.094 -0.072 -0.176 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~256/245 = 77.2093{{c}}
: error map: {{val| 0.000 -0.267 -0.454 }}
{{Optimal ET sequence|legend=1| 15, 16, 31, 109, 140, 171, 373, 544, 1259, 1803d }}
[[Badness]] (Sintel): 0.156


=== Augment ===
=== Augment ===
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[[Comma list]]: 128/125
[[Comma list]]: 128/125


{{Mapping|legend=2| 3 7 0 | 0 0 1 }}
{{Mapping|legend=3| 3 7 0 | 0 0 1 }}


{{Mapping|legend=3| 3 0 7 0 | 0 0 0 1 }}
{{Mapping|legend=5| 3 0 7 0 | 0 0 0 1 }}
: mapping generators: ~5/4, ~7
: mapping generators: ~5/4, ~7


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Comma list: 56/55, 128/125
Comma list: 56/55, 128/125


Subgroup-val mapping: {{mapping| 3 7 0 2 | 0 0 1 1 }}
{{Mapping|legend=2| 3 7 0 2 | 0 0 1 1 }}


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


Optimal tunings:  
Optimal tunings:  
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Badness (Sintel): 0.196
Badness (Sintel): 0.196
=== Mabilic ===
{{Main| Mabilic and trismegistus }}
{{See also| Chromatic pairs #Mabilic }}
Mabilic is the no-3 [[restriction]] of [[mavila family #Armodue|armodue]] (7 & 16), [[magic family #Trismegistus|trismegistus]] (16 & 25), and [[mabila family #Semabila|semabila]] (25 & 34). It is the 7 & 9 temperament in the [[2.5.7 subgroup]], and tempers out [[1071875/1048576]], the mabilisma. [[Weak extension]]s of mabilic include [[archytas clan #Sixix|sixix]] (7 & 25), [[vishnu family #Vishnean|vishnean]] (16 & 34), [[marvel temperaments #Septimin|septimin]] (9 & 41) and [[tetracot family #Monkey|monkey]] (7 & 34).
[[Subgroup]]: 2.5.7
[[Comma list]]: 1071875/1048576
{{Mapping|legend=3| 1 1 5 | 0 3 -5 }}
{{Mapping|legend=5| 1 0 1 5 | 0 0 3 -5 }}
: mapping generators: ~2, ~175/128
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1201.2543{{c}}, ~175/128 = 527.7872{{c}}
: [[error map]]: {{val| +1.254 -1.698 -1.491 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~175/128 = 527.2041{{c}}
: error map: {{val| 0.000 -4.701 -4.846 }}
{{Optimal ET sequence|legend=1| 7, 9, 16, 25, 41, 66, 305ccdd, 371ccddd }}
[[Badness]] (Sintel): 1.70
=== Ostara ===
Ostara is a temperament that is derived from 93 & 524 solar calendar leap rule scale, interpreted in general no-3's 19-limit. It is a weak extension of the unnamed 2.5.7-subgroup 28 & 31 temperament, which tempers out 8589934592/8544921875.
Subgroup: 2.5.7.11
Comma list: 8589934592/8544921875, 30691800524/30517578125
{{Mapping|legend=2| 1 1 20 -49 | 0 3 -39 119 }}
: mapping generators: ~2, ~5120/3773
Optimal tunings:
* WE: ~2 = 1199.9115{{c}}, ~5120/3773 = 528.9650{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5120/3773 = 529.0037{{c}}
{{Optimal ET sequence|legend=0| 93, 245e, 338, 955c, 1386c }}
Badness (Sintel): 11.7
==== 2.5.7.11.13 subgroup ====
Subgroup: 2.5.7.11.13
Comma list: 1001/1000, 34420736/34328125, 5670699008/5661858125
{{Mapping|legend=2| 1 1 20 -49 35 | 0 3 -39 119 -71 }}
Optimal tunings:
* WE: ~2 = 1199.9194{{c}}, ~1664/1225 = 528.9681{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~1664/1225 = 529.0036{{c}}
{{Optimal ET sequence|legend=0| 93, 245e, 338, 431, 1386c }}
Badness (Sintel): 3.42
==== 2.5.7.11.13.17 subgroup ====
Subgroup: 2.5.7.11.13.17
Comma list: 1001/1000, 32768/32725, 147968/147875, 537824/537251
{{Mapping|legend=2| 1 1 20 -49 35 42 | 0 3 -39 119 -71 -86 }}
Optimal tunings:
* WE: ~2 = 1199.9054{{c}}, ~1664/1225 = 528.9628{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~1664/1225 = 529.0046{{c}}
{{Optimal ET sequence|legend=0| 93, 338, 431, 955c, 1386cg }}
Badness (Sintel): 1.99
==== 2.5.7.11.13.17.19 subgroup ====
Subgroup: 2.5.7.11.13.17.19
Comma list: 1001/1000, 2128/2125, 3328/3325, 16807/16796, 147968/147875
{{Mapping|legend=2| 1 1 20 -49 35 42 21 | 0 3 -39 119 -71 -86 -38 }}
Optimal tunings:
* WE: ~2 = 1199.9081{{c}}, ~19/14 = 528.9639{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~19/14 = 529.0045{{c}}
{{Optimal ET sequence|legend=0| 93, 338, 431, 955c, 1386cg }}
Badness (Sintel): 1.29


=== Frostburn ===
=== Frostburn ===
{{Redirect|Frostburn|the software developer|Lumi Pakkanen}}
Frostburn is the common [[restriction]] of [[magic family #Quadrimage|quadrimage]] and [[subgroup temperaments #Baldy|baldy]].  
Frostburn is the common [[restriction]] of [[magic family #Quadrimage|quadrimage]] and [[subgroup temperaments #Baldy|baldy]].  


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[[Comma list]]: 78125/76832
[[Comma list]]: 78125/76832


{{Mapping|legend=2| 1 3 4 | 0 -4 -7 }}
{{Mapping|legend=3| 1 3 4 | 0 -4 -7 }}
: mapping generators: ~2, ~28/25
: mapping generators: ~2, ~28/25


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Comma list: 245/242, 625/616
Comma list: 245/242, 625/616


Subgroup-val mapping: {{mapping| 1 3 4 5 | 0 -4 -7 -9 }}
{{Mapping|legend=2| 1 3 4 5 | 0 -4 -7 -9 }}
: mapping generators: ~2, ~28/25
: mapping generators: ~2, ~28/25


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Badness (Sintel): 0.463
Badness (Sintel): 0.463


=== Mabilic ===
=== Rainy ===
{{Main| Mabilic and trismegistus }}
In rainy, three generators make an [[8/7]]; five generators make a [[5/4]]. It is the no-3's [[restriction]] of [[tertiaseptal]] (and [[valentine]]), notable theoretically as it equates ([[2/1]])/([[5/4]])<sup>3</sup> (128/125, the lesser diesis) with ([[2/1]])/([[8/7]])<sup>5</sup> (the 2.7-subgroup [[cloudy comma]], which is similar to the 2.5-subgroup lesser diesis in that tempering it out tunes the 8/7 about 8.8{{cent}} sharp, while tempering out 128/125 similarly sharpens the 5/4 by about 13.7{{cent}}). By tempering out their difference, stacked 5's and stacked 7's become easier to navigate, using the general-purpose diesis to simplify clusters.
{{See also| Chromatic pairs #Mabilic }}


Mabilic is the no-3 [[restriction]] of [[mavila family #Armodue|armodue]], [[mabila family #Semabila|semabila]], and [[magic family #Trismegistus|trismegistus]]. It is the 7 & 9 temperament in the [[2.5.7 subgroup]], and tempers out [[1071875/1048576]], the mabilisma.
A highly notable tuning of rainy not shown here is [[311edo]], which is 140 + 171 so tuned between them.


[[Subgroup]]: 2.5.7
[[Subgroup]]: 2.5.7


[[Comma list]]: 1071875/1048576
[[Comma list]]: [[2100875/2097152]]


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


{{Mapping|legend=3| 1 0 1 5 | 0 0 3 -5 }}
{{Mapping|legend=5| 1 0 2 3 | 0 0 5 -3 }}
: mapping generators: ~2, ~175/128
: mapping generators: ~2, ~256/245


[[Optimal tuning]]s:
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1201.2543{{c}}, ~175/128 = 527.7872{{c}}
* [[WE]]: ~2 = 1200.0939{{c}}, ~256/245 = 77.2107{{c}}
: [[error map]]: {{val| +1.254 -1.698 -1.491 }}
: [[error map]]: {{val| +0.094 -0.072 -0.176 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~175/128 = 527.2041{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~256/245 = 77.2093{{c}}
: error map: {{val| 0.000 -4.701 -4.846 }}
: error map: {{val| 0.000 -0.267 -0.454 }}


{{Optimal ET sequence|legend=1| 7, 9, 16, 25, 41, 66, 305ccdd, 371ccddd }}
{{Optimal ET sequence|legend=1| 15, 16, 31, 109, 140, 171, 373, 544, 1259, 1803d }}


[[Badness]] (Sintel): 1.70
[[Badness]] (Sintel): 0.156


=== Huntington ===
=== Llywelyn a.k.a. shoe ===
{{See also| Chromatic pairs #Huntington }}
Llywelyn a.k.a. shoe is the common [[restriction]] of [[gamelismic clan #Gorgo|gorgo]] (16 & 21), [[breedsmic temperaments #Gorgik|gorgik]] (21 & 37), and [[gariboh clan #Semaja|semaja]] (16 & 37). It can be described as 16 & 21, and tempers out the [[llywelynsma]]. Its generator is a flattened [[~]][[8/7]] whole tone, seven of which give the interval class of [[5/1|5]]. Its [[ploidacot]] is alpha-heptaseph. [[Weak extension]]s to the full 7-limit include [[marvel temperaments #Misneb|misneb]] (21 & 32), which splits 8/7 into two for [[15/14]]~[[16/15]] each, [[archytas clan #Ultrapyth|ultrapyth]] (32 & 37), which splits [[16/7]] into two for a [[3/2|perfect fifth]], and [[buzzardsmic clan #Septimal buzzard|buzzard]] (53 & 58), which splits 16/7 into three, each for [[21/16]].


Huntington may be described as the 10 & 37 temperament in the 2.5.7.13 subgroup.
; Scales
* [[Shoe5]], [[Shoe6]], [[Shoe11]], [[Shoe16]]


[[Subgroup]]: 2.5.7
[[Subgroup]]: 2.5.7


[[Comma list]]: 40960000/40353607
[[Comma list]]: 4194304/4117715


{{Mapping|legend=2| 1 -4 0 | 0 9 4 }}
{{Mapping|legend=3| 1 1 3 | 0 7 -1 }}


{{Mapping|legend=3| 1 0 -4 0 | 0 0 9 4 }}
{{Mapping|legend=5| 1 0 1 3 | 0 0 7 -1 }}
: mapping generators: ~2, ~80/49
: mapping generators: ~2, ~8/7


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1199.5781{{c}}, ~80/49 = 842.6730{{c}}
* [[WE]]: ~2 = 1199.1974{{c}}, ~8/7 = 226.7586{{c}}
: [[error map]]: {{val| -0.422 -0.569 +1.866 }}
: [[error map]]: {{val| -0.803 +0.194 +2.008 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~80/49 = 842.9136{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/7 = 226.8388{{c}}
: error map: {{val| 0.000 -0.091 +2.828 }}
: error map: {{val| 0.000 +1.558 +4.335 }}
 
{{Optimal ET sequence|legend=1| 5, 11c, 16, 21, 37, 164d }}
 
[[Badness]] (Sintel): 2.06
 
==== 2.5.7.11 subgroup ====
Subgroup: 2.5.7.11
 
Comma list: 176/175, 1310720/1294139
 
{{Mapping|legend=2| 1 1 3 1 | 0 7 -1 13 }}
 
{{Mapping|legend=4| 1 0 1 3 1 | 0 0 7 -1 13 }}
 
Optimal tunings:
* WE: ~2 = 1199.1784{{c}}, ~8/7 = 226.9582{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 227.0438{{c}}


{{Optimal ET sequence|legend=0| 7c, 10, 27, 37, 84, 121 }}
{{Optimal ET sequence|legend=0| 16, 21, 37, 206cd, 243cd, …, 354ccdd }}


Badness (Sintel): 1.87
Badness (Sintel): 0.651


==== 2.5.7.13 subgroup ====
==== 2.5.7.11.13 subgroup ====
Subgroup: 2.5.7.13
Subgroup: 2.5.7.11.13


Comma list: 640/637, 10985/10976
Comma list: 176/175, 640/637, 847/845


Subgroup-val mapping: {{mapping| 1 -4 0 3 | 0 9 4 1 }}
{{Mapping|legend=2| 1 1 3 1 2 | 0 7 -1 13 9 }}


Gencom mapping: {{mapping| 1 0 -4 0 0 3 | 0 0 9 4 0 1 }}
{{Mapping|legend=4| 1 0 1 3 1 2 | 0 0 7 -1 13 9 }}
: mapping generators: ~2, ~13/8


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1199.4788{{c}}, ~13/8 = 842.6318{{c}}
* WE: ~2 = 1199.1643{{c}}, ~8/7 = 226.9495{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~13/8 = 842.9447{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 227.0315{{c}}


{{Optimal ET sequence|legend=0| 7c, 10, 17, 27, 37, 84, 121, 279df, 400ddf }}
{{Optimal ET sequence|legend=0| 16, 21, 37, 206cdf, 243cdf, …, 354ccddff }}


Badness (Sintel): 0.319
Badness (Sintel): 0.319


==== Silver ====
==== 2.5.7.11.13.17 subgroup ====
{{See also| Chromatic pairs #Silver }}
Subgroup: 2.5.7.11.13.17
 
Comma list: 176/175, 221/220, 640/637, 847/845


Silver can be described as the 10 & 37 temperament in the 2.5.7.13.17 subgroup.
{{Mapping|legend=2| 1 1 3 1 2 2 | 0 7 -1 13 9 11 }}


Subgroup: 2.5.7.13.17
{{Mapping|legend=4| 1 0 1 3 1 2 2 | 0 0 7 -1 13 9 11 }}


Comma list: 170/169, 640/637, 5525/5488
Optimal tunings:  
* WE: ~2 = 1199.3162{{c}}, ~8/7 = 227.1125{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 227.1774{{c}}


Subgroup-val mapping: {{mapping| 1 -4 0 3 9 | 0 9 4 1 -7 }}
{{Optimal ET sequence|legend=0| 16, 21, 37, 95 }}


Gencom mapping: {{mapping| 1 0 -4 0 0 3 9 | 0 0 9 4 0 1 -7 }}
Badness (Sintel): 0.458


Optimal tunings:
=== Mercy ===
* WE: ~2 = 1200.0932{{c}}, ~13/8 = 842.7764{{c}}
Named by {{u|KingHyperio}} in 2021, mercy is the common restriction of [[gamelismic clan #Miracle|miracle]] and [[porwell temperaments #Countermiracle|countermiracle]]. It tempers out the [[quince comma]]. In this temperament, two generators make [[~]][[8/7]], five make ~[[7/5]], and seven make ~[[8/5]]. The [[ploidacot]] for this temperament is omega-heptaseph. [[Weak extension]]s of this temperament include [[starling temperaments #Cassablanca|cassablanca]], [[octagar temperaments #Slendi|slendi]], [[ragismic microtemperaments #Quincy|quincy]], [[septischismic clan #Cotoneum|cotoneum]], and [[varunismic temperaments #Octowerck|octowerck]].  
* CWE: ~2 = 1200.0000{{c}}, ~13/8 = 842.7143{{c}}


{{Optimal ET sequence|legend=0| 10, 27, 37, 47, 84, 131, 178g }}
[[Subgroup]]: 2.5.7


Badness (Sintel): 0.504
[[Comma list]]: 823543/819200


=== Ostara ===
{{Mapping|legend=3| 1 3 3 | 0 -7 -2 }}
Ostara is a temperament that is derived from 93 & 524 solar calendar leap rule scale, interpreted in general no-3's 19-limit. It is a weak extension of the unnamed 2.5.7-subgroup 28 & 31 temperament, which tempers out 8589934592/8544921875.


Subgroup: 2.5.7.11
{{Mapping|legend=5| 1 0 3 3 | 0 0 -7 -2 }}
: mapping generators: ~2, ~343/320


Comma list: 8589934592/8544921875, 30691800524/30517578125
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1200.2169{{c}}, ~343/320 = 116.3116{{c}}
: [[error map]]: {{val| +0.217 +0.156 -0.798 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~343/320 = 116.2576{{c}}
: error map: {{val| 0.000 -0.117 -1.341 }}


Subgroup-val mapping: {{mapping| 1 1 20 -49 | 0 3 -39 119 }}
{{Optimal ET sequence|legend=1| 10, 21, 31, 134, 165, 196, 227, 485d, 712d, 1197dd }}
: mapping generators: ~2, ~5120/3773


Optimal tunings:  
[[Badness]] (Sintel): 0.428
* WE: ~2 = 1199.9115{{c}}, ~5120/3773 = 528.9650{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5120/3773 = 529.0037{{c}}


{{Optimal ET sequence|legend=0| 93, 245e, 338, 955c, 1386c }}
==== 2.5.7.13 subgroup ====
Presented here is a low-accuracy extension, which may be thought of as a way to conceptualize the 2.5.7.13.17.19 subgroup of [[31edo]].


Badness (Sintel): 11.7
Subgroup: 2.5.7.13


==== 2.5.7.11.13 subgroup ====
Comma list: 343/338, 640/637
Subgroup: 2.5.7.11.13


Comma list: 1001/1000, 34420736/34328125, 5670699008/5661858125
{{Mapping|legend=2| 1 3 3 4 | 0 -7 -2 -3 }}


Subgroup-val mapping: {{mapping| 1 1 20 -49 35 | 0 3 -39 119 -71 }}
{{Mapping|legend=4| 1 0 3 3 0 4 | 0 0 -7 -2 0 -3 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1199.9194{{c}}, ~1664/1225 = 528.9681{{c}}
* WE: ~2 = 1199.2166{{c}}, ~14/13 = 116.0181{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~1664/1225 = 529.0036{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 116.2099{{c}}
 
{{Optimal ET sequence|legend=0| 10, 21, 31 }}


{{Optimal ET sequence|legend=0| 93, 245e, 338, 431, 1386c }}
Badness (Sintel): 0.546


Badness (Sintel): 3.42
==== 2.5.7.13.17 subgroup ====
Subgroup: 2.5.7.13.17


==== 2.5.7.11.13.17 subgroup ====
Comma list: 170/169, 224/221, 343/338
Subgroup: 2.5.7.11.13.17


Comma list: 1001/1000, 32768/32725, 147968/147875, 537824/537251
{{Mapping|legend=2| 1 3 3 4 4 | 0 -7 -2 -3 1 }}


Subgroup-val mapping: {{mapping| 1 1 20 -49 35 42 | 0 3 -39 119 -71 -86 }}
{{Mapping|legend=4| 1 0 3 3 0 4 4 | 0 0 -7 -2 0 -3 1 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1199.9054{{c}}, ~1664/1225 = 528.9628{{c}}
* WE: ~2 = 1198.5476{{c}}, ~14/13 = 115.6294{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~1664/1225 = 529.0046{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 115.9132{{c}}
 
{{Optimal ET sequence|legend=0| 10, 21, 31, 83fg }}


{{Optimal ET sequence|legend=0| 93, 338, 431, 955c, 1386cg }}
Badness (Sintel): 0.451


Badness (Sintel): 1.99
==== 2.5.7.13.17.19 subgroup ====
Subgroup: 2.5.7.13.17.19


==== 2.5.7.11.13.17.19 subgroup ====
Comma list: 170/169, 224/221, 343/338, 476/475
Subgroup: 2.5.7.11.13.17.19


Comma list: 1001/1000, 2128/2125, 3328/3325, 16807/16796, 147968/147875
{{Mapping|legend=2| 1 3 3 4 4 3 | 0 -7 -2 -3 1 13 }}


Subgroup-val mapping: {{mapping| 1 1 20 -49 35 42 21 | 0 3 -39 119 -71 -86 -38 }}
{{Mapping|legend=4| 1 0 3 3 0 4 4 3 | 0 0 -7 -2 0 -3 1 13 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1199.9081{{c}}, ~19/14 = 528.9639{{c}}
* WE: ~2 = 1198.4839{{c}}, ~14/13 = 115.5700{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~19/14 = 529.0045{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 115.7299{{c}}
 
{{Optimal ET sequence|legend=0| 10h, 21, 31, 52f, 83fg }}


{{Optimal ET sequence|legend=0| 93, 338, 431, 955c, 1386cg }}
Badness (Sintel): 0.759


Badness (Sintel): 1.29
=== Huntington ===
{{See also| Chromatic pairs #Huntington }}


=== French decimal ===
Huntington may be described as the 10 & 37 temperament in the 2.5.7.13 subgroup.  
French decimal is conceived upon the fact that 1789edo has an excellent 5/4, and uses it as the generator. This rings particularly true for the French attempts to decimalize a lot more things than we are used to today. Using the maximal evenness method of finding rank-2 temperaments, a 1525 & 1789 temperament is obtained.


[[Subgroup]]: 2.5.7
[[Subgroup]]: 2.5.7


[[Comma list]]: {{monzo| 372 -159 -1 }}
[[Comma list]]: 40960000/40353607
 
{{Mapping|legend=3| 1 -4 0 | 0 9 4 }}


{{Mapping|legend=2| 1 0 372 | 0 1 -159 }}
{{Mapping|legend=5| 1 0 -4 0 | 0 0 9 4 }}
: mapping generators: ~2, ~5
: mapping generators: ~2, ~80/49


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1199.9901{{c}}, ~5/4 = 386.3562{{c}}
* [[WE]]: ~2 = 1199.5781{{c}}, ~80/49 = 842.6730{{c}}
: [[error map]]: {{val| -0.010 +0.023 +0.000 }}
: [[error map]]: {{val| -0.422 -0.569 +1.866 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/4 = 386.3595{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~80/49 = 842.9136{{c}}
: error map: {{val| 0.000 +0.046 +0.019 }}
: error map: {{val| 0.000 -0.091 +2.828 }}


{{Optimal ET sequence|legend=1| 205, 264, 733, 997, 2258, 3255, 7507, 10762 }}
{{Optimal ET sequence|legend=0| 7c, 10, 27, 37, 84, 121 }}


[[Badness]] (Sintel): 148
Badness (Sintel): 1.87


==== 2.5.7.11 subgroup ====
==== 2.5.7.13 subgroup ====
Subgroup: 2.5.7.11
Subgroup: 2.5.7.13
 
Comma list: 640/637, 10985/10976


Comma list: {{monzo| -49 8 17 -5 }}, {{monzo| 45 -27 10 -3 }}
{{Mapping|legend=2| 1 -4 0 3 | 0 9 4 1 }}


Subgroup-val mapping: {{mapping| 1 0 372 1255 | 0 1 -159 -539 }}
{{Mapping|legend=4| 1 0 -4 0 0 3 | 0 0 9 4 0 1 }}
: mapping generators: ~2, ~13/8


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1200.0130{{c}}, ~5/4 = 386.3653{{c}}
* WE: ~2 = 1199.4788{{c}}, ~13/8 = 842.6318{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 386.3611{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~13/8 = 842.9447{{c}}
 
{{Optimal ET sequence|legend=0| 7c, 10, 17, 27, 37, 84, 121, 279df, 400ddf }}
 
Badness (Sintel): 0.319
 
==== Silver ====
{{See also| Chromatic pairs #Silver }}


{{Optimal ET sequence|legend=0| 264, 997e, 1261e, 1525, 1789 }}
Silver can be described as the 10 & 37 temperament in the 2.5.7.13.17 subgroup.


Badness (Sintel): 52.2
Subgroup: 2.5.7.13.17


==== 2.5.7.11.13 subgroup ====
Comma list: 170/169, 640/637, 5525/5488
Subgroup: 2.5.7.11.13


Comma basis: 28824005/28792192, 200126927/200000000, 6106906624/6103515625
{{Mapping|legend=2| 1 -4 0 3 9 | 0 9 4 1 -7 }}


Subgroup-val mapping: {{mapping| 1 0 372 1255 -398 | 0 1 -159 -539 173 }}
{{Mapping|legend=4| 1 0 -4 0 0 3 9 | 0 0 9 4 0 1 -7 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1200.0137{{c}}, ~5/4 = 386.3655{{c}}
* WE: ~2 = 1200.0932{{c}}, ~13/8 = 842.7764{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 386.3611{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~13/8 = 842.7143{{c}}


{{Optimal ET sequence|legend=0| 261, 1261e, 1525, 1789 }}
{{Optimal ET sequence|legend=0| 10, 27, 37, 47, 84, 131, 178g }}


Badness (Sintel): 10.5
Badness (Sintel): 0.504


=== Bastille ===
=== Bastille ===
Line 330: Line 431:
[[Comma list]]: {{monzo| 1426 -596 -15 }}
[[Comma list]]: {{monzo| 1426 -596 -15 }}


{{Mapping|legend=2| 1 -4 254 | 0 15 -596 }}
{{Mapping|legend=3| 1 -4 254 | 0 15 -596 }}
: mapping generators: ~2, ~{{monzo| -380 159 4 }}
: mapping generators: ~2, ~{{monzo| -380 159 4 }}


Line 353: Line 454:
[[Comma list]]: 5021863/5000000
[[Comma list]]: 5021863/5000000


{{Mapping|legend=2| 1 0 -2 3 | 0 1 1 1 | 0 0 4 -3 }}
{{Mapping|legend=3| 1 0 -2 3 | 0 1 1 1 | 0 0 4 -3 }}
: mapping generators: ~2, ~5, ~77/50
: mapping generators: ~2, ~5, ~77/50


Line 371: Line 472:
Comma list: 847/845, 1001/1000
Comma list: 847/845, 1001/1000


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


Optimal tunings:  
Optimal tunings:  
Line 386: Line 487:
Comma list: 170/169, 221/220, 847/845
Comma list: 170/169, 221/220, 847/845


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


Optimal tunings:  
Optimal tunings:  
Line 399: Line 500:
Temperaments discussed elsewhere include:
Temperaments discussed elsewhere include:
* Jacobin superfamily ([[6656/6655]]) → [[The Jacobins]]
* Jacobin superfamily ([[6656/6655]]) → [[The Jacobins]]
=== Sephiroth ===
{{See also| Chromatic pairs #Sephiroth }}
Sephiroth is the common [[restriction]] of [[magic family #Muggles|muggles]] and [[avicennmic temperaments #Submerged|submerged]].
[[Subgroup]]: 2.5.11
[[Comma list]]: 34375/32768
{{Mapping|legend=3| 1 0 15 | 0 1 -5 }}
{{Mapping|legend=5| 1 0 0 0 15 | 0 0 1 0 -5 }}
: mapping generators: ~2, ~5
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1203.3290{{c}}, ~5/4 = 373.6097{{c}}
: [[error map]]: {{val| +3.329 -6.046 -2.722 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/4 = 372.1586{{c}}
: error map: {{val| 0.000 -14.155 -12.111 }}
{{Optimal ET sequence|legend=0| 3, 10, 13, 16, 29, 132cceee }}
[[Badness]] (Sintel): 1.85
==== 2.5.11.13 subgroup ====
Subgroup: 2.5.11.13
Comma list: 65/64, 6875/6656
{{Mapping|legend=2| 1 0 15 6 | 0 1 -5 -1 }}
{{Mapping|legend=4| 1 0 0 0 15 6 | 0 0 1 0 -5 -1 }}
Optimal tunings:
* WE: ~2 = 1203.3825{{c}}, ~5/4 = 373.6318{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 372.1519{{c}}
{{Optimal ET sequence|legend=0| 3, 10, 13, 16, 29, 132cceeeff }}
Badness (Sintel): 0.410
==== 2.5.11.13.17 subgroup ====
Subgroup: 2.5.11.13.17
Comma list: 65/64, 170/169, 221/220
{{Mapping|legend=2| 1 0 15 6 11 | 0 1 -5 -1 -3 }}
{{Mapping|legend=4| 1 0 0 0 15 6 11 | 0 0 1 0 -5 -1 -3 }}
Optimal tunings:
* WE: ~2 = 1203.6741{{c}}, ~5/4 = 373.3775{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 371.6773{{c}}
{{Optimal ET sequence|legend=0| 3, 10, 13, 16, 29g, 129ccceeffgggg }}
Badness (Sintel): 0.299


=== Wizz ===
=== Wizz ===
{{See also| Chromatic pairs #Wizz }}
{{See also| Chromatic pairs #Wizz }}


Wizz, the 6 & 16 temperament in the 2.5.11 subgroup, tempers out [[15625/15488]], and is the common [[restriction]] of [[astrology]] and [[wizard]].  
Wizz, the 6 & 16 temperament in the 2.5.11 subgroup, tempers out [[15625/15488]], and is the common [[restriction]] of [[jubilismic clan #Astrology|astrology]] and [[stearnsmic clan #Wizard|wizard]].  


[[Subgroup]]: 2.5.11
[[Subgroup]]: 2.5.11
Line 409: Line 568:
[[Comma list]]: 15625/15488
[[Comma list]]: 15625/15488


{{Mapping|legend=2| 2 0 -7 | 0 1 3 }}
{{Mapping|legend=3| 2 0 -7 | 0 1 3 }}


{{Mapping|legend=3| 2 0 4 0 5 | 0 0 1 0 3 }}
{{Mapping|legend=5| 2 0 4 0 5 | 0 0 1 0 3 }}
: mapping generators: ~125/88, ~5/4
: mapping generators: ~125/88, ~5/4


Line 429: Line 588:
[[Comma list]]: 33275/32768
[[Comma list]]: 33275/32768


{{Mapping|legend=2| 1 0 5 | 0 3 -2 }}
{{Mapping|legend=3| 1 0 5 | 0 3 -2 }}
: mapping generators, ~2, ~55/32
: mapping generators, ~2, ~55/32


Line 443: Line 602:


=== Movila ===
=== Movila ===
This temperament has a structure very similar to [[mavila]] but is somewhat more accurate because the generator is a flat [[11/8]] rather than a sharp [[4/3]]. The major third is still ~[[5/4]], but the minor third is now ~[[64/55]] instead of ~[[6/5]].
This temperament has a structure very similar to [[mavila family #Mavila|mavila]] but is somewhat more accurate because the generator is a flat [[11/8]] rather than a sharp [[4/3]]. The major third is still ~[[5/4]], but the minor third is now ~[[64/55]] instead of ~[[6/5]].


[[Subgroup]]: 2.5.11
[[Subgroup]]: 2.5.11
Line 449: Line 608:
[[Comma list]]: 1331/1280
[[Comma list]]: 1331/1280


{{Mapping|legend=2| 1 1 3 | 0 3 1 }}
{{Mapping|legend=3| 1 1 3 | 0 3 1 }}
: mapping generators: ~2, ~11/8
: mapping generators: ~2, ~11/8


Line 461: Line 620:


[[Badness]] (Sintel): 0.718
[[Badness]] (Sintel): 0.718
=== Sephiroth ===
{{See also| Chromatic pairs #Sephiroth }}
Sephiroth is the no-7 [[restriction]] of [[muggles]].
[[Subgroup]]: 2.5.11
[[Comma list]]: 34375/32768
{{Mapping|legend=2| 1 0 15 | 0 1 -5 }}
{{Mapping|legend=3| 1 0 0 0 15 | 0 0 1 0 -5 }}
: mapping generators: ~2, ~5
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1203.3290{{c}}, ~5/4 = 373.6097{{c}}
: [[error map]]: {{val| +3.329 -6.046 -2.722 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/4 = 372.1586{{c}}
: error map: {{val| 0.000 -14.155 -12.111 }}
{{Optimal ET sequence|legend=0| 3, 10, 13, 16, 29, 132cceee }}
[[Badness]] (Sintel): 1.85
==== 2.5.11.13 subgroup ====
Subgroup: 2.5.11.13
Comma list: 65/64, 6875/6656
Subgroup-val mapping: {{mapping| 1 0 15 6 | 0 1 -5 -1 }}
Gencom mapping: {{mapping| 1 0 0 0 15 6 | 0 0 1 0 -5 -1 }}
Optimal tunings:
* WE: ~2 = 1203.3825{{c}}, ~5/4 = 373.6318{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 372.1519{{c}}
{{Optimal ET sequence|legend=0| 3, 10, 13, 16, 29, 132cceeeff }}
Badness (Sintel): 0.410
==== 2.5.11.13.17 subgroup ====
Subgroup: 2.5.11.13.17
Comma list: 65/64, 170/169, 221/220
Subgroup-val mapping: {{mapping| 1 0 15 6 11 | 0 1 -5 -1 -3 }}
Gencom mapping: {{mapping| 1 0 0 0 15 6 11 | 0 0 1 0 -5 -1 -3 }}
Optimal tunings:
* WE: ~2 = 1203.6741{{c}}, ~5/4 = 373.3775{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 371.6773{{c}}
{{Optimal ET sequence|legend=0| 3, 10, 13, 16, 29g, 129ccceeffgggg }}
Badness (Sintel): 0.299


=== Trader ===
=== Trader ===
Line 525: Line 626:
[[Comma list]]: 26/25
[[Comma list]]: 26/25


{{Mapping|legend=2| 1 2 3 | 0 1 2 }}
{{Mapping|legend=3| 1 0 -1 | 0 1 2 }}
: mapping generators, ~2, ~5/4
: mapping generators, ~2, ~5


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
Line 543: Line 644:
[[Comma list]]: 64000000/62748517
[[Comma list]]: 64000000/62748517


{{Mapping|legend=2| 1 -2 0 | 0 7 6 }}
{{Mapping|legend=3| 1 -2 0 | 0 7 6 }}
: mapping generators, ~2, ~20/13
: mapping generators, ~2, ~20/13


Line 573: Line 674:
[[Comma list]]: 5767168/5764801
[[Comma list]]: 5767168/5764801


{{Mapping|legend=2| 1 0 -19 | 0 1 8 }}
{{Mapping|legend=3| 1 0 -19 | 0 1 8 }}
: mapping generators: ~2, ~7
: mapping generators: ~2, ~7


Line 587: Line 688:


=== Argument ===
=== Argument ===
Argument tempers out [[1372/1331]] in the 2.7.11 subgroup. It is the no-3 [[restriction]] of [[#Augment|augment]].  
Argument tempers out [[1372/1331]] in the 2.7.11 subgroup, equating [[14/11]] to a step of [[3edo]]. It is the no-3 [[restriction]] of [[#Augment|augment]].  


[[Subgroup]]: 2.7.11
[[Subgroup]]: 2.7.11
Line 593: Line 694:
[[Comma list]]: 1372/1331
[[Comma list]]: 1372/1331


{{Mapping|legend=2| 3 0 2 | 0 1 1 }}
{{Mapping|legend=3| 3 0 2 | 0 1 1 }}
: mapping generators: ~14/11, ~7
: mapping generators: ~14/11, ~7


Line 606: Line 707:
[[Badness]] (Sintel): 0.475
[[Badness]] (Sintel): 0.475


=== Score ===
=== Scaevola ===
Scaevola is the 2.7.11-subgroup temperament tempering out 14641/14336, with a generator of [[11/8]] and mapping +4 generators to [[7/4]]. Two strong extensions are [[#Score|score]] to 2.7.11.13 and [[subgroup temperaments #Joan|joan]] to 2.9.7.11.
 
Scaevola has a structure that is very similar to [[mavila family #Mavila|mavila]], but whereas mavila has a "fifth" of [[3/2]], "major third" of [[5/4]], and "minor third" of [[6/5]], scaevola has a "fifth" of [[16/11]], "major third" of [[14/11]], and "minor third" of [[8/7]], substituting mavila's 4:5:6 for 11:14:16. Essentially, Scaevola can be seen as a counterpart of mavila for fifths even flatter than [[9edo]], such as [[11edo]]'s fifth.
 
It was named by [[CompactStar]] in 2026, referring to ''{{w|Scaevola}}'' (the genus of flowering plants), which is meant to sound reminiscent of ''score'' and ''mavila'' (the score and joan temperaments were actually named prior to this temperament).
 
[[Subgroup]]: 2.7.11
 
[[Comma list]]: 14641/14336
 
{{Mapping|legend=3| 1 1 3 | 0 4 1 }}
 
{{Mapping|legend=5| 1 0 0 1 3 | 0 0 0 4 1 }}
: mapping generators: ~2, ~11/8
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1201.2479{{c}}, ~11/8 = 542.1162{{c}}
: [[error map]]: {{val| +1.248 +0.887 -5.458 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/8 = 541.9403{{c}}
: error map: {{val| 0.000 -1.065 -9.378 }}
 
{{Optimal ET sequence|legend=1| 2, 7d, 9, 11, 20, 31, 51, 82e, 113e, 195eee }}
 
[[Badness]] (Sintel): 0.578
 
==== Score ====
{{See also| Chromatic pairs #Score }}
{{See also| Chromatic pairs #Score }}


Score is a low-accuracy [[extension]] of the unnamed 2.7.11-subgroup temperament tempering out 14641/14336.  
Score is an extension of scaevola that maps [[13/8]] to +6 generators.


[[Subgroup]]: 2.7.11.13
Subgroup: 2.7.11.13


[[Comma list]]: 343/338, 847/832
Comma list: 343/338, 847/832


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


{{Mapping|legend=3| 1 0 0 1 3 1 | 0 0 0 4 1 6 }}
{{Mapping|legend=4| 1 0 0 1 3 1 | 0 0 0 4 1 6 }}
: mapping generators: ~2, ~11/8


[[Optimal tuning]]s:  
Optimal tunings:  
* [[WE]]: ~2 = 1201.5484{{c}}, ~11/8 = 540.7963{{c}}
* WE: ~2 = 1201.5484{{c}}, ~11/8 = 540.7963{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/8 = 540.5091{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 540.5091{{c}}


{{Optimal ET sequence|legend=1| 9, 11, 20 }}
{{Optimal ET sequence|legend=0| 9, 11, 20 }}


[[Badness]] (Sintel): 0.368
Badness (Sintel): 0.368


=== Bossier ===
=== Bossier ===
Line 637: Line 763:
[[Comma list]]: 214358881/210827008
[[Comma list]]: 214358881/210827008


{{Mapping|legend=2| 1 0 1 | 0 8 7 }}
{{Mapping|legend=3| 1 0 1 | 0 8 7 }}


{{Mapping|legend=3| 1 0 0 0 1 | 0 0 0 8 7 }}
{{Mapping|legend=5| 1 0 0 0 1 | 0 0 0 8 7 }}
: mapping generators: ~2, ~14/11
: mapping generators: ~2, ~14/11


Line 657: Line 783:
Comma list: 1573/1568, 15488/15379
Comma list: 1573/1568, 15488/15379


Subgroup-val mapping: {{mapping| 1 0 1 3 | 0 8 7 2 }}
{{Mapping|legend=2| 1 0 1 3 | 0 8 7 2 }}


Gencom mapping: {{mapping|| 1 0 0 0 1 3 | 0 0 0 8 7 2 }}
{{Mapping|legend=4| 1 0 0 0 1 3 | 0 0 0 8 7 2 }}


Optimal tunings:  
Optimal tunings:  
Line 676: Line 802:
[[Comma list]]: 28672/28561
[[Comma list]]: 28672/28561


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


{{Mapping|legend=3| 1 0 0 0 0 3 | 0 0 0 4 0 1 }}
{{Mapping|legend=5| 1 0 0 0 0 3 | 0 0 0 4 0 1 }}
: mapping generators: ~2, ~13
: mapping generators: ~2, ~13


Line 696: Line 822:
[[Comma list]]: 4913/4802
[[Comma list]]: 4913/4802


{{Mapping|legend=2| 1 2 3 | 0 3 4 }}
{{Mapping|legend=3| 1 2 3 | 0 3 4 }}
: mapping generators, ~2, ~17/14
: mapping generators, ~2, ~17/14


Line 714: Line 840:
[[Comma list]]: 2024782584832/2015993900449
[[Comma list]]: 2024782584832/2015993900449


{{Mapping|legend=2| 1 0 1 | 0 10 11 }}
{{Mapping|legend=3| 1 0 1 | 0 10 11 }}
: mapping generators, ~2, ~17/14
: mapping generators, ~2, ~17/14


Line 732: Line 858:
[[Comma list]]: 1048576/1042139
[[Comma list]]: 1048576/1042139


{{Mapping|legend=2| 1 0 6 | 0 3 -1 }}]
{{Mapping|legend=3| 1 0 6 | 0 3 -1 }}]
: mapping generators, ~2, ~64/53
: mapping generators, ~2, ~64/53


Line 754: Line 880:
[[Comma list]]: 1352/1331
[[Comma list]]: 1352/1331


{{Mapping|legend=2| 1 3 3 | 0 2 3 }}
{{Mapping|legend=3| 1 1 0 | 0 2 3 }}


{{Mapping|legend=3| 1 0 0 0 3 3 | 0 0 0 0 2 3 }}
{{Mapping|legend=5| 1 0 0 0 1 0 | 0 0 0 0 2 3 }}
: mapping generators, ~2, ~13/11
: mapping generators: ~2, ~26/11


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
Line 777: Line 903:
[[Comma list]]: 265837/262144
[[Comma list]]: 265837/262144


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


{{Mapping|legend=3| 1 0 0 0 3 4 | 0 0 0 0 3 -2 }}
{{Mapping|legend=5| 1 0 0 0 3 4 | 0 0 0 0 3 -2 }}
: mapping generators, ~2, ~143/128
: mapping generators, ~2, ~143/128


Line 801: Line 927:
[[Comma list]]: 29282/28561
[[Comma list]]: 29282/28561


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


{{Mapping|legend=3| 4 0 0 0 12 13 | 0 0 0 0 1 1 }}
{{Mapping|legend=5| 4 0 0 0 12 13 | 0 0 0 0 1 1 }}
: mapping generators, ~13/11, ~11
: mapping generators, ~13/11, ~11


Line 823: Line 949:
[[Comma list]]: 209/208, 2057/2048, 83521/83486
[[Comma list]]: 209/208, 2057/2048, 83521/83486


{{Mapping|legend=2| 1 1 8 9 11 | 0 4 -7 -8 -11 }}
{{Mapping|legend=3| 1 1 8 9 11 | 0 4 -7 -8 -11 }}
: mapping generators: ~2, ~26/17
: mapping generators: ~2, ~26/17


Line 841: Line 967:
[[Comma list]]: 2432/2431, 7086244/7054567, 33698267/33554432
[[Comma list]]: 2432/2431, 7086244/7054567, 33698267/33554432


{{Mapping|legend=2| 33 0 8 249 26 | 0 1 1 -1 1 }}
{{Mapping|legend=3| 33 0 8 249 26 | 0 1 1 -1 1 }}
: mapping generators: ~247/242, ~11
: mapping generators: ~247/242, ~11


Line 861: Line 987:
[[Comma list]]: 1874161/1874048
[[Comma list]]: 1874161/1874048


{{Mapping|legend=2| 4 0 7 | 0 1 1 }}
{{Mapping|legend=3| 4 0 7 | 0 1 1 }}
: mapping generators: ~44/37, ~11
: mapping generators: ~44/37, ~11


Line 879: Line 1,005:
[[Comma list]]: 47525504/47045881
[[Comma list]]: 47525504/47045881


{{Mapping|legend=2| 1 1 2 | 0 6 5 }}
{{Mapping|legend=3| 1 1 2 | 0 6 5 }}
: mapping generators: ~2, ~26/19
: mapping generators: ~2, ~26/19


Line 897: Line 1,023:
[[Comma list]]: 209/208, 2057/2048
[[Comma list]]: 209/208, 2057/2048


{{Mapping|legend=2| 1 0 0 11 4 | 0 1 0 -2 -1 | 0 0 1 0 1 }}
{{Mapping|legend=3| 1 0 0 11 4 | 0 1 0 -2 -1 | 0 0 1 0 1 }}
: mapping generators: ~2, ~11, ~13
: mapping generators: ~2, ~11, ~13


Line 908: Line 1,034:
[[Badness]] (Sintel): 0.106
[[Badness]] (Sintel): 0.106


[[Category:Temperament collections]]
[[Category:Catalogs of subgroup temperaments]]
[[Category:Subgroup temperaments]]
[[Category:Catalogs of rank-2 temperaments]]