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'''TODO: add intro and definition (badness < 0.1 ?)'''
{{Technical data page}}
Below are listed some very high accuracy temperaments (Breed's [[Tenney-Euclidean temperament measures|TE error]] < 0.005 cents/octave).


=Rank two temperaments=
= Rank-2 temperaments =
== Kwazy ==
Kwazy ({{nowrap| 118 & 612 }}) tempers out the [[kwazy comma]], {{monzo| -53 10 16 }}. 7-limit extensions of the kwazy temperament include [[marvel temperaments #Gwazy|gwazy]],  [[hemimage temperaments #Bisupermajor|bisupermajor]], and [[ragismic microtemperaments #Crazy|crazy]].


==Astro==
[[Subgroup]]: 2.3.5
Comma: |91 -12 -31&gt;


POTE generator: ~296630859375/274877906944 = 132.1947
[[Comma list]]: {{monzo| -53 10 16 }}


Map: [&lt;1 5 1|, &lt;0 31 -12|]
{{Mapping|legend=1| 2 1 6 | 0 8 -5 }}


EDOs: [[118edo|118]], [[935edo|935]], [[1053edo|1053]], [[1171edo|1171]], [[1289edo|1289]], [[1407edo|1407]], [[2224edo|2224]], [[2460edo|2460]]
: mapping generators: ~94921875/67108864, ~1125/1024


Badness: 0.0628
[[Optimal tuning]]s:  
* [[CTE]]: ~94921875/67108864 = 600.000000, ~1125/1024 = 162.743279
* [[POTE]]: ~94921875/67108864 = 600.000000, ~1125/1024 = 162.742626


==Whoosh==
{{Optimal ET sequence|legend=1| 22, 74, 96, 118, 376, 494, 612, 1342, 3296, 4638, 7934 }}
Comma: |37 25 -33&gt;


POTE generator: ~864/625 = 560.5468
[[Badness]] (Sintel): 0.331


Map: [&lt;1 -16 -11|, &lt;0 33 25|]
== Astro ==
Astro temperament tempers out the [[astro comma]], {{monzo| 91 -12 -31 }}. 7-limit extensions of the astro temperament include [[Horwell temperaments #Kastro|kastro]].


EDOs: [[289edo|289]], [[441edo|441]], [[730edo|730]], [[1171edo|1171]], [[1612edo|1612]], [[1901edo|1901]], [[2631edo|2631]]
[[Subgroup]]: 2.3.5


Badness: 0.0257
[[Comma list]]: {{monzo| 91 -12 -31 }}


==Monzismic==
{{Mapping|legend=1| 1 5 1 | 0 -31 12 }}
Comma: |54 -37 2&gt; = 450359962737049600 / 450283905890997363


POTE generator: ~387420489/335544320 = 249.0184
: mapping generators: ~2, ~{{monzo| -38 5 13 }}


Map: [&lt;1 0 -27|, &lt;0 2 37|]
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000000, ~{{monzo| -38 5 13 }} = 132.194857
* [[POTE]]: ~2 = 1200.000000, ~{{monzo| -38 5 13 }} = 132.194668


EDOs: [[53edo|53]], [[506edo|506]], [[559edo|559]], [[612edo|612]], [[1783edo|1783]], [[2954edo|2954]], [[6520edo|6520]]
{{Optimal ET sequence|legend=1| 9, …, 109, 118, 699, 817, 935, 1053, 1171, 13934, 15105, 16276, 17447, 18618, 19789, 20960, 22131, 23302, 24473, 25644, 26815, 27986c }}


Badness: 0.0104
[[Badness]] (Sintel): 1.47


==Egads==
== Gaster ==
Comma: |-36 -52 51&gt;
{{Main| Gaster temperament }}
{{See also| Mirkwai clan #Gaster }}


POTE generator: ~6/5 = 315.6479
[[Subgroup]]: 2.3.5


Map: [&lt;1 15 16|, &lt;0 -51 -52|]
[[Comma list]]: {{monzo| -70 72 -19 }}


EDOs: [[441edo|441]], [[901edo|901]], [[1342edo|1342]], [[1783edo|1783]], [[2224edo|2224]], [[3125edo|3125]], [[4467edo|4467]], [[4908edo|4908]]
{{Mapping|legend=1| 1 11 38 | 0 -19 -72 }}


Badness: 0.0418
: mapping generators: ~2, ~{{monzo| 19 -19 5 }}


==Fortune==
[[Optimal tuning]]s:
Comma: |-107 47 14&gt;
* [[CTE]]: ~2 = 1200.000000, ~{{monzo| 19 -19 5 }} = 594.634456
* [[POTE]]: ~2 = 1200.000000, ~{{monzo| 19 -19 5 }} = 594.634565


POTE generator: ~8388608/7381125 = 221.5679
{{Optimal ET sequence|legend=1| 111, 224, 335, 559, 1342, 1901, 3243, 8387, 11630 }}


Map: [&lt;1 -1 11|, &lt;0 14 -47|]
[[Badness]] (Sintel): 2.08


EDOs: [[612edo|612]], [[1289edo|1289]], [[1901edo|1901]], [[2513edo|2513]], [[3125edo|3125]], [[3737edo|3737]], [[4414edo|4414]], [[5638edo|5638]]
== Whoosh ==
Whoosh ({{nowrap| 152 & 289 }}) tempers out the [[whoosh comma]], {{monzo| 37 25 -33 }}. 7-limit extensions of the whoosh temperament include [[Porwell temperaments #Whoops|whoops]].


Badness: 0.0279
[[Subgroup]]: 2.3.5


===7-limit===
[[Comma list]]: {{monzo| 37 25 -33 }}
Commas: 78125000/78121827, |-52 17 12 -1&gt;


POTE generator: ~8388608/7381125 = 221.5680
{{Mapping|legend=1| 1 17 14 | 0 -33 -25 }}


Map: [&lt;1 -1 11 63|, &lt;0 14 -47 -326|]
: mapping generators: ~2, ~864/625


EDOs: 612, 2513, 3125, 3737, 4349, 5638, 6862, 9987
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000000, ~864/625 = 560.546952
* [[POTE]]: ~2 = 1200.000000, ~864/625 = 560.546826


Badness: 0.0237
{{Optimal ET sequence|legend=1| 15, …, 122, 137, 152, 289, 441, 730, 1171, 1901, 3072, 4243, 7315, 25017, 32332, 39647c }}


===11-limit===
[[Badness]] (Sintel): 0.602
Commas: 151263/151250, 21437500/21434787, 369140625/369098752


POTE generator: ~8388608/7381125 = 221.5681
== Monzismic ==
Monzismic ({{nowrap| 53 & 612 }}) tempers out the [[monzisma]], {{monzo| 54 -37 2 }}. For its 7-limit extension, see [[Ragismic microtemperaments #Monzismic]].


Map: [&lt;1 -1 11 63 134|, &lt;0 14 -47 -326 -707|]
[[Subgroup]]: 2.3.5


EDOs: 612, 2513, 3125, 3737, 4349, 4961, 6862, 8086
[[Comma list]]: {{monzo| 54 -37 2 }}


Badness: 0.0366
{{Mapping|legend=1| 1 0 -27 | 0 2 37 }}


==Senior==
: mapping generators: ~2, ~{{monzo| 27 -18 1 }}
Comma: |-17 62 -35&gt;


POTE generator: ~94143178827/78125000000 = 322.8014
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000000, ~{{monzo| 27 -18 1 }} = 950.981427
* [[POTE]]: ~2 = 1200.000000, ~{{monzo| 27 -18 1 }} = 950.981594


Map: [&lt;1 11 19|, &lt;0 -35 -62|]
{{Optimal ET sequence|legend=1| 53, 347, 400, 453, 506, 559, 612, 1171, 1783, 4737, 6520 }}


EDOs: [[171edo|171]], [[1171edo|1171]], [[1342edo|1342]], [[2513edo|2513]], [[3684edo|3684]], [[3855edo|3855]], [[4855edo|4855]], [[6197edo|6197]]
[[Badness]] (Sintel): 0.244


Badness: 0.0212
== Egads ==
[[Subgroup]]: 2.3.5


==Gross==
[[Comma list]]: {{monzo| -36 -52 51 }}
Comma: |144 -22 -47&gt;


POTE generator: ~1953125000000000/1853020188851841 = 91.5310
{{Mapping|legend=1| 1 15 16 | 0 -51 -52 }}


Map: [&lt;1 -2 4|, &lt;0 47 -22|]
: mapping generators: ~2, ~6/5


EDOs: [[118edo|118]], [[1783edo|1783]], [[1901edo|1901]], [[3684edo|3684]], [[5467edo|5467]], [[5585edo|5585]], [[7250edo|7250]]
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000000, ~6/5 = 315.647899
* [[POTE]]: ~2 = 1200.000000, ~6/5 = 315.647919


Badness: 0.0463
{{Optimal ET sequence|legend=1| 19, …, 365, 384, 403, 422, 441, 901, 1342, 1783, 3125, 4908, 45955, 50863, 55771, 60679, 65587, 70495, 75403, 80311, 85219, 90127 }}


==Raider==
[[Badness]] (Sintel): 0.981
Comma: |71 -99 37&gt;


POTE generator: ~8000/6561 = 343.2961
=== Hemiegads ===
Subgroup: 2.3.5.7


Map: [&lt;1 -9 -26|, &lt;0 37 99|]
Comma list: 78125000/78121827, {{monzo| -48 0 11 8 }}


EDOs: [[1171edo|1171]], [[1954edo|1954]], [[3125edo|3125]], [[4296edo|4296]], [[5467edo|5467]], [[7421edo|7421]], [[9763edo|9763]], [[14059edo|14059]], [[18355edo|18355]]
Mapping: {{mapping| 1 15 16 -16 | 0 -102 -104 143 }}


Badness: 0.0129
Optimal tunings:  
* CTE: ~2 = 1200.000000, ~36756909/33554432 = 157.823952
* CWE: ~2 = 1200.000000, ~36756909/33554432 = 157.823954


==Pirate==
{{Optimal ET sequence|legend=0| 38, 403, 441, 1802, 2243, 2684, 3125, 6691, 9816, 16507, 75844, 125365c }}
Comma: |-90 -15 49&gt;


POTE generator: ~1358954496/1220703125 = 185.7542
Badness (Sintel): 0.313


Map: [&lt;1 -6 0|, &lt;0 49 15|]
== Fortune ==
Fortune tempers out the [[fortune comma]], {{monzo| -107 47 14 }}. It can be described as {{nowrap| 612 & 2513 }} temperament, which tempers out 78125000/78121827 ([[euzenius comma]]) in the 7-limit; 151263/151250, 21437500/21434787, and 369140625/369098752 in the 11-limit.


EDOs: [[730edo|730]], [[1783edo|1783]], [[2513edo|2513]], [[4296edo|4296]], [[6079edo|6079]], [[6809edo|6809]], [[10375edo|10375]], [[11105edo|11105]]
[[Subgroup]]: 2.3.5


Badness: 0.0057
[[Comma list]]: {{monzo| -107 47 14 }}


==Atomic==
{{Mapping|legend=1| 1 13 -36 | 0 -14 47 }}
Comma: |161 -84 -12&gt;


POTE generator: ~32805/32768 = 1.95516
: mapping generators: ~2, 7381125/4194304


Map: [&lt;12 0 161|, &lt;0 1 -7|]
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000000, ~8388608/7381125 = 221.567861
* [[POTE]]: ~2 = 1200.000000, ~8388608/7381125 = 221.567899


EDOs: [[12edo|12]], [[612edo|612]], [[624edo|624]], [[1236edo|1236]], [[1848edo|1848]], [[2460edo|2460]], [[3072edo|3072]], [[3084edo|3084]], [[3684edo|3684]], [[4296edo|4296]], [[4308edo|4308]], [[4908edo|4908]], [[7980edo|7980]], [[12276edo|12276]], [[16572edo|16572]], [[20868edo|20868]], [[25164edo|25164]], [[29460edo|29460]], [[33756edo|33756]], [[46032edo|46032]]
{{Optimal ET sequence|legend=1| 65, 352, 417, 482, 547, 612, 1901, 2513, 5638, 8151, 18815, 45781, 64596, 110377, 174973bc }}


Badness: 0.0038
[[Badness]] (Sintel): 0.654


===7-limit===
=== 7-limit ===
Commas: 250047/250000, |-55 30 2 1&gt;
Subgroup: 2.3.5.7


POTE generator: ~32805/32768 = 1.94961
Comma list: 78125000/78121827, {{monzo| -52 17 12 -1 }}


Map: [&lt;12 0 161 338|, &lt;0 1 -7 -16|]
Mapping: {{mapping| 1 13 -36 -263 | 0 -14 47 326 }}


EDOs: 12, 612, 624, 1236, 1848, 2460, 3072, 3084, 4308
Optimal tunings:  
* CTE: ~2 = 1200.000000, ~8388608/7381125 = 221.568013
* POTE: ~2 = 1200.000000, ~8388608/7381125 = 221.568031


Badness: 0.0458
{{Optimal ET sequence|legend=0| 612, 1901, 2513, 3125, 6862, 9987, 13112, 36211, 49323 }}


===11-limit===
Badness (Sintel): 0.600
Commas: 9801/9800, 151263/151250, 184549376/184528125


POTE generator: ~32805/32768 = 1.94799
=== 11-limit ===
Subgroup: 2.3.5.7.11


Map: [&lt;12 0 161 338 517|, &lt;0 1 -7 -16 -25|]
Comma list: 151263/151250, 21437500/21434787, 369140625/369098752


EDOs: 12, 612, 624, 1236, 1848, 2460, 3072, 3084, 4308
Mapping: {{mapping| 1 13 -36 -263 -573 | 0 -14 47 326 707 }}


Badness: 0.0160
Optimal tunings:  
* CTE: ~2 = 1200.000000, ~8388608/7381125 = 221.568116
* POTE: ~2 = 1200.000000, ~8388608/7381125 = 221.568139


{{Optimal ET sequence|legend=1| 612, 2513, 3125, 3737, 8086, 19909d }}


=Rank three temperaments=
Badness (Sintel): 1.21
==171 &amp; 1106 &amp; 3566==
Comma: 282475249000/282429536481


Map: [&lt;1 0 9 -3|, &lt;0 1 8 0|, &lt;0 0 10 -3|]
== Senior ==
Senior ({{nowrap| 171 & 1171 }}) tempers out the [[senior comma]], {{monzo| -17 62 -35 }}. 7-limit extensions of the senior temperament include [[Ragismic microtemperaments #Seniority|seniority]].


EDOs: 171, 935, 1106, 1277, 2289, 2460, 3395, 3566, 3737
[[Subgroup]]: 2.3.5


Badness: 0.000281
[[Comma list]]: {{monzo| -17 62 -35 }}


==171 &amp; 2019 &amp; 3566==
{{Mapping|legend=1| 1 11 19 | 0 -35 -62 }}
Comma: 13841287201/13839609375


Map: [&lt;1 0 0 0|, &lt;0 1 7 5|, &lt;0 0 12 7|]
: mapping generators: ~2, ~{{monzo| -6 23 -13 }}


EDOs: 171, 1547, 1677, 1718, 1848, 2019, 3395, 3566, 3737
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000000, ~{{monzo| -6 23 -13 }} = 322.801349
* [[POTE]]: ~2 = 1200.000000, ~{{monzo| -6 23 -13 }} = 322.801358


Badness: 0.000135
{{Optimal ET sequence|legend=1| 26, …, 145, 171, 658, 829, 1000, 1171, 2513, 6197, 39695, 45892, 52089, 58286, 64483, 70680 }}


==171 &amp; 441 &amp; 4973==
[[Badness]] (Sintel): 0.498
Comma: |-7 19 -16 5&gt; = 19534128475869/19531250000000


Map: [&lt;1 0 3 11|, &lt;0 1 4 9|, &lt;0 0 5 16|]
== Gross ==
Gross ({{nowrap| 118 & 1783 }}) tempers out the gross comma, {{monzo| 144 -22 -47 }}, by which a stack of 22 [[3/1|3rd harmonics]] and 47 [[5/1|5th harmonics]] falls short of 144 (gross) octaves.


EDOs: 171, 270, 441, 612, 783, 4802, 4973, 5144
[[Subgroup]]: 2.3.5


Badness: 0.000297
[[Comma list]]: {{monzo| 144 -22 -47 }}


==171 &amp; 1547 &amp; 3125==
{{Mapping|legend=1| 1 45 -18 | 0 -47 22 }}
Comma: 3955078125/3954653486


Map: [&lt;1 3 0 1|, &lt;0 11 0 4|, &lt;0 0 1 1|]
: mapping generators: ~2, ~{{monzo| -45 7 15 }}


EDOs: 171, 1407, 1547, 1578, 1718, 2783, 2954, 3125, 3296
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000000, ~{{monzo| 46 -7 -15 }} = 91.530979
* [[POTE]]: ~2 = 1200.000000, ~{{monzo| 46 -7 -15 }} = 91.531001


Badness: 0.000114
{{Optimal ET sequence|legend=1| 118, 957, 1075, 1193, 1311, 1429, 1547, 1665, 1783, 3684, 5467, 36486, 41953, 47420, 52887, 63821, 69288, 74755, 144043c, 218798c }}


==Starscape==
[[Badness]] (Sintel): 1.09
Comma: 645700815/645657712


Map: [&lt;1 0 4 0|, &lt;0 1 1 2|, &lt;0 0 9 1|]
; Music
* ''Gross temperament EP'' (2023) by [[User:Francium|Francium]] – [https://open.spotify.com/album/02Fz6IIJ2x9k7bEvFylZ2A Spotify] | [https://francium223.bandcamp.com/album/gross-temperament-ep Bandcamp] | [https://youtube.com/playlist?list=PLLZE7hMjEXRZy_JWYbZxbsxPsXahiEJA2&si=RttlCFpkeN4Rl7Tj YouTube] – 2-piece extended play


EDOs: 171, 1848, 2019, 2783, 2954, 3125, 3296, 4973, 5144
== Quectismic ==
{{See also| Quectisma }}


Badness: 0.000545
[[Subgroup]]: 2.3.5


==171 &amp; 3566 &amp; 4973==
[[Comma list]]: {{monzo| 554 -351 1 }}
Comma: 6104007655641/6103515625000


Map: [&lt;1 0 13 16|, &lt;0 1 10 12|, &lt;0 0 14 17|]
{{Mapping|legend=1| 1 0 -554 | 0 1 351 }}


EDOs: 171, 1236, 1407, 3566, 3737, 3908, 4802, 4973, 8539, 8710
: mapping generators: ~2, ~3


Badness: 0.000223
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000000, ~3/2 = 701.955310
* [[CWE]]: ~2 = 1200.000000, ~3/2 = 701.955310


==Euzenius==
{{Optimal ET sequence|legend=1| 306, 359c, 665, 2301, 2966, 3631, 4296, 46591, 50887, 55183, 59479, 63775, 68071, 72367, 76663, 80959, 85255, 89551 }}
Comma: 78125000/78121827


Map: [&lt;1 0 0 -5|, &lt;0 2 0 -13|, &lt;0 0 1 5|]
[[Badness]] (Sintel): 8.74


EDOs: 171, 441, 612, 2954, 3125, 3566, 3737, 6520, 6691
=== Nanoquectismic ===
Subgroup: 2.3.5.7


Badness: 0.000205
Comma list: 43046721/43025920, {{monzo| 82 -19 -3 -16 }}


==612 &amp; 1848 &amp; 3125==
Mapping: {{mapping| 1 0 -554 109 | 0 1 351 -67 }}
Comma: |-55 30 2 1&gt;


Map: [&lt;1 0 0 55|, &lt;0 1 0 -30|, &lt;0 0 1 -2|]
Optimal tunings:  
* CTE: ~2 = 1200.000000, ~3/2 = 701.955371
* CWE: ~2 = 1200.000000, ~3/2 = 701.955457


EDOs: 612, 665, 1236, 1277, 1848, 1889, 2460, 2513, 3125, 3737, 4973, 5585, 6862, 8098, 8710, 11835, 14960
{{Optimal ET sequence|legend=1| 306, 665, 1636, 2301, 2966 }}


Badness: 0.000366
Badness (Sintel): 15.3


==171 &amp; 1547 &amp; 4973==
=== Conanoquectismic ===
Comma: |1 -15 -18 23&gt;
Subgroup: 2.3.5.7


Map: [&lt;1 0 9 7|, &lt;0 1 3 3|, &lt;0 0 23 18|]
Comma list: {{monzo| 33 -26 12 -7 }}, {{monzo| -32 13 17 -10 }}


EDOs: 171, 1547, 4802, 4973, 5144, 6520, 6691, 6862, 11493, 11664, 11835, 18184, 18355, 18526, 25046, 30019, 30190, 48545
Mapping: {{mapping| 1 0 -554 -945 | 0 1 351 598 }}


Badness: 0.000114
Optimal tunings:  
* CTE: ~2 = 1200.000000, ~3/2 = 701.954810
* CWE: ~2 = 1200.000000, ~3/2 = 701.954771


==441 &amp; 1848 &amp; 3125==
{{Optimal ET sequence|legend=1| 306d, 359cd, 665 }}
Comma: |51 -13 -1 -10&gt;


Map: [&lt;1 0 1 5|, &lt;0 1 7 -2|, &lt;0 0 10 -1|]
Badness (Sintel): 55.0


EDOs: 441, 1848, 3125, 3566, 4973, 6691, 8098, 8539, 9816, 11664, 14789, 15230, 18355, 21480, 30019, 33144, 39835, 51499
== Counterquectismic ==
{{See also| Counterquectisma }}


Badness: 0.000263
[[Subgroup]]: 2.3.5


[[category:todo:add definition]]
[[Comma list]]: {{monzo| -500 314 1 }}
[[category:todo:intro]]
 
{{Mapping|legend=1| 1 0 500 | 0 1 -314 }}
 
: mapping generators: ~2, ~3
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000000, ~3/2 = 701.954415
* [[CWE]]: ~2 = 1200.000000, ~3/2 = 701.954416
 
{{Optimal ET sequence|legend=1| 306c, 359, 665, 2354, 3019, 3684, 11717, 15401, 19085, 34486 }}
 
[[Badness]] (Sintel): 12.0
 
== Raider ==
{{See also| Syntonic–chromatic equivalence continuum }}
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| 71 -99 37 }}
 
{{Mapping|legend=1| 1 28 73 | 0 -37 -99 }}
 
: mapping generators: ~2, ~6561/4000
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000000, ~8000/6561 = 343.296094
* [[POTE]]: ~2 = 1200.000000, ~8000/6561 = 343.296098
 
{{Optimal ET sequence|legend=1| 388, 783, 1171, 1954, 3125, 4296, 5467, 7421, 9763, 14059, 18355, 22651, 26947, 31243, 35539, 66782, 102321, 137860 }}
 
[[Badness]] (Sintel): 0.302
 
== Pirate ==
{{See also| Hemfiness temperaments #Piracy }}
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| -90 -15 49 }}
 
{{Mapping|legend=1| 1 43 15 | 0 -49 -15 }}
 
: Mapping generators: ~2, ~{{monzo| -23 -4 13 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000000, ~{{monzo| 24 4 -13 }} = 185.754186
* [[POTE]]: ~2 = 1200.000000, ~{{monzo| 24 4 -13 }} = 185.754179
 
{{Optimal ET sequence|legend=1| 84, 239, 323, 730, 1783, 2513, 4296, 15401, 19697, 23993, 52282, 76275, 128557, 204832 … }}
 
[[Badness]] (Sintel): 0.133
 
== Atomic ==
{{See also | Kirnberger's atom }}
 
Atomic observes the [[schisma]], and the 3/2 is one schisma sharp of its [[12edo]] value. In atomic, since twelve fifths are sharp of seven octaves by twelve schismas, the [[Pythagorean comma]] is twelve schismas, and hence [[81/80]], the Didymus comma, is eleven schismas. In fact eleven schismas is sharp of 81/80, and twelve schismas of the Pythaorean comma, by the microscopic interval of the atom, which atomic tempers out. Extremely accurate.
 
Atomic extensions discussed elsewhere include [[minutes]] and [[72nd-octave temperaments#Hafnium|hafnium]].
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| 161 -84 -12 }}
 
{{Mapping|legend=1| 12 0 161 | 0 1 -7 }}
 
: mapping generators: ~{{monzo| -67 35 5 }}, ~3
 
[[Optimal tuning]]s:
* [[CTE]]: ~{{monzo| -67 35 5 }} = 100.000000, ~3/2 = 701.955176 (~32805/32768 = 1.955176)
* [[POTE]]: ~{{monzo| -67 35 5 }} = 100.000000, ~3/2 = 701.955162 (~32805/32768 = 1.955162)
 
{{Optimal ET sequence|legend=1| 12, …, 576, 588, 600, 612, 2460, 3072, 3684, 4296, 12276, 16572, 20868, 25164, 46032 }}
 
[[Badness]] (Sintel): 0.0892
 
=== 7-limit ===
Subgroup: 2.3.5.7
 
Comma list: 250047/250000, {{monzo| -55 30 2 1 }}
 
Mapping: {{mapping| 12 0 161 338 | 0 1 -7 -16 }}
 
Optimal tunings:
* CTE: ~30375/28672 = 100.000000, ~3/2 = 701.949917 (or ~32805/32768 = 1.949917)
* POTE: ~30375/28672 = 100.000000, ~3/2 = 701.949608 (or ~32805/32768 = 1.949608)
 
{{Optimal ET sequence|legend=0| 12, …, 600, 612, 1236, 1848, 4308, 10464, 14772, 25236c, 40008ccd }}
 
Badness (Sintel): 1.16
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 9801/9800, 151263/151250, 184549376/184528125
 
Mapping: {{mapping| 12 0 161 338 517 | 0 1 -7 -16 -25 }}
 
Optimal tunings:
* CTE: ~30375/28672 = 100.000000, ~3/2 = 701.948456 (or ~32805/32768 = 1.948456)
* POTE: ~30375/28672 = 100.000000, ~3/2 = 701.947988 (or ~32805/32768 = 1.947988)
 
{{Optimal ET sequence|legend=0| 12, …, 600e, 612, 1236, 1848 }}
 
Badness (Sintel): 0.530
 
== Revopentic (2.3.7) ==
{{See also| Revopentisma }}
 
Subgroup: 2.3.7
 
Comma list: 11399736556781568/11398895185373143
 
{{Mapping|legend=2| 1 12 5 | 0 -19 -4 }}
 
: mapping generators: ~2, ~24576/16807
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000000, ~24576/16807 = 657.791865
* [[CWE]]: ~2 = 1200.000000, ~24576/16807 = 657.791796
 
{{Optimal ET sequence|legend=1| 31, 73, 104, 135, 436, 571, 706, 1277, 8233, 9510, 10787, 12064, 13341, 14618, 15895, 33067, 48962, 113819d, 162781d, … }}
 
[[Badness]] (Sintel): 0.0704
 
=== Revopent ===
Revopent can be described as the {{nowrap| 1848 & 3125 }} temperament.
 
Subgroup: 2.3.5.7
 
Comma list: 645700815/645657712, {{monzo| 51 -13 -1 -10 }}
 
Mapping: {{mapping| 1 12 -155 5 | 0 -19 287 -4 }}
 
Optimal tunings:
* CTE: ~2 = 1200.000000, ~24576/16807 = 657.792032
* CWE: ~2 = 1200.000000, ~24576/16807 = 657.792032
 
{{Optimal ET sequence|legend=0| 135, 436c, 571, 1277, 1848, 3125, 8098, 11223, 25571, 36794, 121605d }}
 
Badness (Sintel): 0.665
 
== Nanic ==
{{See also| Nanisma }}
 
[[Subgroup]]: 2.3.7
 
[[Comma list]]: {{monzo| 109 -67 -1 }}
 
{{Mapping|legend=2| 1 0 109 | 0 1 -67 }}
 
: sval mapping generators: ~2, ~3
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000000, ~3/2 = 701.957820
* [[POTE]]: ~2 = 1200.000000, ~3/2 = 701.957784
 
{{Optimal ET sequence|legend=1| 53, 200, 253, 306, 665, 971, 1277, 6691, 7968, 9245, 10522, 11799, 13076, 40505, 53581, 66657, 79733 }}
 
[[Badness]] (Sintel): 0.474
 
== Icarus ==
This temperament is named after a very distant star. Curiously, the names of two even more distant stars coincide with named temperaments, those being [[godzilla]] and [[mothra]].
 
[[Subgroup]]: 3.5.7
 
[[Comma list]]: {{monzo| -32 -64 71 }}
 
{{Mapping|legend=1| 1 35 32 | 0 -71 -64 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~3 = 1901.955, ~{{monzo| 5 9 -10 }} = 898.340
* [[CWE]]: ~3 = 1901.955, ~{{monzo| 5 9 -10 }} = 898.340
 
[[Optimal ET sequence]]: [[163edt|b163cd]], [[199edt|b199c]], [[235edt|b235]], [[271edt|b271]], [[4643edt|b4643]], [[4914edt|b4914]], …, [[8708edt|b8708]], [[8979edt|b8979]], [[18229edt|b18229]], [[27208edt|b27208]], [[99853edt|b99853]], [[127061edt|b127061]], [[154269edt|b154269]], [[181477edt|b181477]], [[208685edt|b208685]], [[390162edt|b390162]]
 
[[Badness]] (Sintel): 0.00493
 
= Rank-3 temperaments =
== Sasaquinbizo-atriyo (171 & 1106 & 3566) ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: {{monzo| 3 -24 3 10 }} (282475249000/282429536481)
 
{{Mapping|legend=1| 1 0 9 -3 | 0 1 8 0 | 0 0 10 -3 }}
 
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9624, ~6561/3430 = 1122.9387
 
{{Optimal ET sequence|legend=1| 171, 764, 935, 1106, 1277, 2118, 2289, 2460, 3224, 3395, 3566, 26068, 26239, 29634, 29805, 33200, 33371, 36937, 40503, 44069 }}
 
[[Badness]] (Sintel): 1.24
 
== Saquadtrizo-asepgu (171 & 2019 & 3566) ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: {{monzo| 0 -11 -7 12 }} (13841287201/13839609375)
 
{{Mapping|legend=1| 1 0 0 0 | 0 1 7 5 | 0 0 -12 -7 }}
 
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9584, ~16807/10125 = 877.2825
 
{{Optimal ET sequence|legend=1| 171, 814, 985, 1034, 1205, 1376, 1547, 1718, 1848, 2019, 3224, 3395, 3566, 8980, 9151, 12717, 47131, 50697, 59848d, 63414d, 76131d }}
 
[[Badness]] (Sintel): 0.595
 
== Laquinzo-aquadquadgu (171 & 441 & 4973) ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: {{monzo| -7 19 -16 5 }} (19534128475869/19531250000000)
 
{{Mapping|legend=1| 1 0 3 11 | 0 1 4 9 | 0 0 5 16 }}
 
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9501, ~250/189 = 484.2956
 
{{Optimal ET sequence|legend=1| 171, 441, 612, 2696, 2795, 2867, 2966, 3137, 3308, 3407, 3479, 3578, 3749, 3920, 4091, 4190, 4361, 4532, 4703, 4802, 4973, 5144, 10117, 10558, 15531, 15702, 52079, 62637, 67781, 78339 }}
 
[[Badness]] (Sintel): 1.31
 
== Laleruyo (171 & 1547 & 3125) ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: {{monzo| -1 4 11 -11 }} (3955078125/3954653486)
 
{{Mapping|legend=1| 1 3 0 1 | 0 -11 0 -4 | 0 0 1 1 }}
 
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~375/343 = 154.3678, ~5/4 = 386.3070
 
{{Optimal ET sequence|legend=1| 171, 863, 894, 1034, 1065, 1205, 1236, 1376, 1407, 1547, 1578, 1718, 2612, 2783, 2954, 3125, 12329, 15454, 18579, 21704, 40283, 61987 }}
 
[[Badness]] (Sintel): 0.501
 
== Starscape or Latritriru-ayo ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 645700815/645657712
 
{{Mapping|legend=1| 1 0 4 0 | 0 1 1 2 | 0 0 -9 -1 }}
 
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9514, ~9/7 = 435.0709
 
{{Optimal ET sequence|legend=1| 171, 742, 764, 935, 1106, 1277, 1677, 1848, 2019, 2783, 2954, 3125, 8098, 11223, 25571, 33840, 36794, 45063, 48188, 59411, 70634 }}
 
[[Badness]] (Sintel): 0.240
 
== Sepbizo-asegu (171 & 3566 & 4973) ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: {{monzo| -3 2 -17 14 }} (6104007655641/6103515625000)
 
{{Mapping|legend=1| 1 0 13 16 | 0 1 10 12 | 0 0 -14 -17 }}
 
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9548, ~31250/16807 = 1073.8021
 
{{Optimal ET sequence|legend=1| 171, 894, 1065, 1236, 1407, 1578, 3053, 3224, 3395, 3566, 5144, 8368, 8539, 8710, 17249, 20815, 29525, 38064, 67589, 105653 }}
 
[[Badness]] (Sintel): 0.982
 
== Euzenius or Sabiruquinyo ==
{{See also| Euzenius comma }}
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 78125000/78121827
 
{{Mapping|legend=1| 1 1 0 -5 | 0 2 0 -13 | 0 0 1 5 }}
 
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~6250/5103 = 350.9787, ~5/4 = 386.3099
 
{{Optimal ET sequence|legend=1| 171, 441, 612, 1730, 1901, 2072, 2171, 2342, 2513, 2684, 2783, 2954, 3125, 6520, 6691, 9816, 16336, 16507, 23027, 26152, 32843, 42659, 58995, 68811, 101654 }}
 
[[Badness]] (Sintel): 0.0902
 
== Nommismic or Quinla-zoyoyo ==
{{See also| Nommisma }}
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: {{monzo| -55 30 2 1 }}
 
{{Mapping|legend=1| 1 0 0 55 | 0 1 0 -30 | 0 0 1 -2 }}
 
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9516, ~5/4 = 386.3132
 
{{Optimal ET sequence|legend=1| 612, 1236, 1277, 1848, 2513, 3125, 6862, 8098, 8710, 11835, 14960, 26795, 195663b, }} …
 
[[Badness]] (Sintel): 1.62
 
== Satwethezo-atritribigu (171 & 1547 & 4973)  ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: {{monzo| 1 -15 -18 23 }}
 
{{Mapping|legend=1| 1 0 9 7 | 0 1 3 3 | 0 0 -23 -18 }}
 
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9551, ~56953125/40353607 = 596.5022
 
{{Optimal ET sequence|legend=1| 171, 863, 1034, 1205, 1376, 1547, 1718, 3255, 3426, 3597, 4460, 4631, 4802, 4973, 5144, 6520, 6691, 11664, 18355, 48374, 48545, 66900, 145464, }} …
 
[[Badness]] (Sintel): 0.505
 
== Technologismic or Trisa-quinbiru-agu ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: {{monzo| 51 -13 -1 -10 }}
 
{{Mapping|legend=1| 1 0 1 5 | 0 1 7 -2 | 0 0 -10 1 }}
 
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9553, ~63/32 = 1172.7374
 
{{Optimal ET sequence|legend=1| 441, 966, 1277, 1407, 1718, 1848, 2684, 3125, 6691, 9816, 11664, 14789, 18355, 33144, 51499, 124478, 175977, }} …
 
[[Badness]] (Sintel): 0.116
 
== Quinbisa-quinbizo-alegu (1848 & 11664 & 21480) ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: {{monzo| 110 -71 -11 10 }}
 
{{Mapping|legend=1| 1 0 0 -11 | 0 1 9 17 | 0 0 -10 -11 }}
 
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.955, ~32805/28672 = 233.128
 
{{Optimal ET sequence|legend=1| 1848, 3737, 5585, 6079, 7927, 9816, 11664, 21480, 33144, 54624, 70025, 81689, 103169, }} …
 
[[Badness]] (Sintel): 0.538
 
[[Category:Temperament collections]]
[[Category:Pages with mostly numerical content]]
Retrieved from "https://en.xen.wiki/w/Very_high_accuracy_temperaments"