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Very high accuracy temperaments: Difference between revisions

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= Rank-2 temperaments =
= Rank-2 temperaments =
== Kwazy ==
== 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]].
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]].


[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5
Line 11: Line 11:


{{Mapping|legend=1| 2 1 6 | 0 8 -5 }}
{{Mapping|legend=1| 2 1 6 | 0 8 -5 }}
: mapping generators: ~94921875/67108864, ~1125/1024
: mapping generators: ~94921875/67108864, ~1125/1024


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~94921875/67108864 = 600.000000, ~1125/1024 = 162.743279
* [[WE]]: ~94921875/67108864 = 600.003398{{c}}, ~1125/1024 = 162.743548{{c}}
* [[POTE]]: ~94921875/67108864 = 600.000000, ~1125/1024 = 162.742626
: [[error map]]: {{val| +0.0068 -0.0032 -0.0111 }}
* [[CWE]]: ~94921875/67108864 = 600.000000{{c}}, ~1125/1024 = 162.742801{{c}}
: error map: {{val| 0.0000 -0.0126 -0.0277 }}


{{Optimal ET sequence|legend=1| 22, 74, 96, 118, 376, 494, 612, 1342, 3296, 4638, 7934 }}
{{Optimal ET sequence|legend=1| 22, 74, 96, 118, 376, 494, 612, 1342, 3296, 4638, 7934 }}
Line 29: Line 30:
[[Comma list]]: {{monzo| 91 -12 -31 }}
[[Comma list]]: {{monzo| 91 -12 -31 }}


{{Mapping|legend=1| 1 5 1 | 0 -31 12 }}
{{Mapping|legend=1| 1 -26 13 | 0 31 -12 }}
 
: mapping generators: ~2, ~{{monzo| 39 -5 -13 }}
: mapping generators: ~2, ~{{monzo| -38 5 13 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000000, ~{{monzo| -38 5 13 }} = 132.194857
* [[WE]]: ~2 = 1199.994636{{c}}, ~{{monzo| 39 -5 -13 }} = 1067.800558{{c}}
* [[POTE]]: ~2 = 1200.000000, ~{{monzo| -38 5 13 }} = 132.194668
: [[error map]]: {{val| -0.0054 +0.0018 +0.0099 }}
* [[CWE]]: ~2 = 1200.000000{{c}}, ~{{monzo| 39 -5 -13 }} = 1067.805278{{c}}
: error map: {{val| 0.0000 +0.0086 +0.0230 }}


{{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 }}
{{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]] (Sintel): 1.47
[[Badness]] (Sintel): 1.473


== Gaster ==
== Gaster ==
Line 49: Line 51:
[[Comma list]]: {{monzo| -70 72 -19 }}
[[Comma list]]: {{monzo| -70 72 -19 }}


{{Mapping|legend=1| 1 11 38 | 0 -19 -72 }}
{{Mapping|legend=1| 1 -8 -34 | 0 19 72 }}
 
: mapping generators: ~2, ~{{monzo| -18 19 -5 }}
: mapping generators: ~2, ~{{monzo| 19 -19 5 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000000, ~{{monzo| 19 -19 5 }} = 594.634456
* [[WE]]: ~2 = 1200.002817{{c}}, ~{{monzo| -18 19 -5 }} = 605.366856{{c}}
* [[POTE]]: ~2 = 1200.000000, ~{{monzo| 19 -19 5 }} = 594.634565
: [[error map]]: {{val| +0.0028 -0.0073 +0.0041 }}
* [[CWE]]: ~2 = 1200.000000{{c}}, ~{{monzo| -18 19 -5 }} = 605.365482{{c}}
: error map: {{val| 0.0000 -0.0108 +0.0010 }}


{{Optimal ET sequence|legend=1| 111, 224, 335, 559, 1342, 1901, 3243, 8387, 11630 }}
{{Optimal ET sequence|legend=1| 111, 224, 335, 559, 1342, 1901, 3243, 8387, 11630 }}


[[Badness]] (Sintel): 2.08
[[Badness]] (Sintel): 2.077


== Whoosh ==
== Whoosh ==
Line 68: Line 71:
[[Comma list]]: {{monzo| 37 25 -33 }}
[[Comma list]]: {{monzo| 37 25 -33 }}


{{Mapping|legend=1| 1 17 14 | 0 -33 -25 }}
{{Mapping|legend=1| 1 -16 -11 | 0 33 25 }}
 
: mapping generators: ~2, ~625/432
: mapping generators: ~2, ~864/625


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000000, ~864/625 = 560.546952
* [[WE]]: ~2 = 1199.997806{{c}}, ~625/432 = 639.452005{{c}}
* [[POTE]]: ~2 = 1200.000000, ~864/625 = 560.546826
: [[error map]]: {{val| -0.0022 -0.0037 +0.0106 }}
* [[CWE]]: ~2 = 1200.000000{{c}}, ~625/432 = 639.453117{{c}}
: error map: {{val| 0.0000 -0.0022 +0.0142 }}


{{Optimal ET sequence|legend=1| 15, …, 122, 137, 152, 289, 441, 730, 1171, 1901, 3072, 4243, 7315, 25017, 32332, 39647c }}
{{Optimal ET sequence|legend=1| 15, …, 122, 137, 152, 289, 441, 730, 1171, 1901, 3072, 4243, 7315, 25017, 32332, 39647c }}
Line 88: Line 92:


{{Mapping|legend=1| 1 0 -27 | 0 2 37 }}
{{Mapping|legend=1| 1 0 -27 | 0 2 37 }}
: mapping generators: ~2, ~{{monzo| 27 -18 1 }}
: mapping generators: ~2, ~{{monzo| 27 -18 1 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000000, ~{{monzo| 27 -18 1 }} = 950.981427
* [[WE]]: ~2 = 1199.997524{{c}}, ~{{monzo| 27 -18 1 }} = 950.979631{{c}}
* [[POTE]]: ~2 = 1200.000000, ~{{monzo| 27 -18 1 }} = 950.981594
: [[error map]]: {{val| -0.0025 +0.0043 -0.0005 }}
* [[CWE]]: ~2 = 1200.000000{{c}}, ~{{monzo| 27 -18 1 }} = 950.981535{{c}}
: error map: {{val| 0.0000 +0.0081 +0.0031 }}


{{Optimal ET sequence|legend=1| 53, 347, 400, 453, 506, 559, 612, 1171, 1783, 4737, 6520 }}
{{Optimal ET sequence|legend=1| 53, 347, 400, 453, 506, 559, 612, 1171, 1783, 4737, 6520 }}
Line 104: Line 109:
[[Comma list]]: {{monzo| -36 -52 51 }}
[[Comma list]]: {{monzo| -36 -52 51 }}


{{Mapping|legend=1| 1 15 16 | 0 -51 -52 }}
{{Mapping|legend=1| 1 -36 -36 | 0 51 52 }}
 
: mapping generators: ~2, ~5/3
: mapping generators: ~2, ~6/5


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000000, ~6/5 = 315.647899
* [[WE]]: ~2 = 1200.000553{{c}}, ~5/3 = 884.352488{{c}}
* [[POTE]]: ~2 = 1200.000000, ~6/5 = 315.647919
: [[error map]]: {{val| +0.0006 +0.0020 -0.0042 }}
* [[CWE]]: ~2 = 1200.000000{{c}}, ~5/3 = 844.352090{{c}}
: error map: {{val| 0.0000 +0.0016 -0.0050 }}


{{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 }}
{{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 }}
Line 121: Line 127:
Comma list: 78125000/78121827, {{monzo| -48 0 11 8 }}
Comma list: 78125000/78121827, {{monzo| -48 0 11 8 }}


Mapping: {{mapping| 1 15 16 -16 | 0 -102 -104 143 }}
Mapping: {{mapping| 1 -87 -88 127 | 0 102 104 -143 }}
: mapping generators: ~2, ~67108864/36756909


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000000, ~36756909/33554432 = 157.823952
* WE: ~2 = 1200.000308{{c}}, ~67108864/36756909 = 1042.176313{{c}}
* CWE: ~2 = 1200.000000, ~36756909/33554432 = 157.823954
* CWE: ~2 = 1200.000000{{c}}, ~67108864/36756909 = 1042.176046{{c}}


{{Optimal ET sequence|legend=0| 38, 403, 441, 1802, 2243, 2684, 3125, 6691, 9816, 16507, 75844, 125365c }}
{{Optimal ET sequence|legend=0| 38, 403, 441, 1802, 2243, 2684, 3125, 6691, 9816, 16507, 75844, 125365c }}
Line 134: Line 141:
Subgroup: 2.3.5.13
Subgroup: 2.3.5.13


Comma list: [[140625/140608]], {{monzo|-4 20 -9 0 0 -4}}
Comma list: [[140625/140608]], {{monzo| -4 20 -9 0 0 -4 }}
 
Mapping: {{mapping| 1 -36 -36 -98 | 0 51 52 138 }}


Mapping: {{mapping| 1 15 16 -16 | 0 -51 -52 -138 }}
Optimal tunings:  
* WE: ~2 = 1200.000308{{c}}, ~5/3 = 884.354064{{c}}
* CWE: ~2 = 1200.000000{{c}}, ~5/3 = 884.351835{{c}}


Optimal tunings:
{{Optimal ET sequence|legend=0| 19, …, 441, 460, 901, 1342 }}
* CTE: ~2 = 1200.0031, ~6/5 = 315.6490
* POTE: ~2 = 1200.000000, ~6/5 = 315.6482
{{Optimal ET sequence|legend=0|19, ..., 441, 460, 901, 1342}}


Badness (Sintel): 0.222
Badness (Sintel): 0.222
Line 152: Line 160:
[[Comma list]]: {{monzo| -107 47 14 }}
[[Comma list]]: {{monzo| -107 47 14 }}


{{Mapping|legend=1| 1 13 -36 | 0 -14 47 }}
{{Mapping|legend=1| 1 -1 11 | 0 14 -47 }}
 
: mapping generators: ~2, ~8388608/7381125
: mapping generators: ~2, 7381125/4194304


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000000, ~8388608/7381125 = 221.567861
* [[WE]]: ~2 = 1200.000553{{c}}, ~8388608/7381125 = 221.568202{{c}}
* [[POTE]]: ~2 = 1200.000000, ~8388608/7381125 = 221.567899
: [[error map]]: {{val| +0.0016 -0.0018 -0.0012 }}
* [[CWE]]: ~2 = 1200.000000{{c}}, ~8388608/7381125 = 221.567889{{c}}
: error map: {{val| 0.0000 -0.0046 -0.0045 }}


{{Optimal ET sequence|legend=1| 65, 352, 417, 482, 547, 612, 1901, 2513, 5638, 8151, 18815, 45781, 64596, 110377, 174973bc }}
{{Optimal ET sequence|legend=1| 65, 352, 417, 482, 547, 612, 1901, 2513, 5638, 8151, 18815, 45781, 64596, 110377, 174973bc }}
Line 169: Line 178:
Comma list: 78125000/78121827, {{monzo| -52 17 12 -1 }}
Comma list: 78125000/78121827, {{monzo| -52 17 12 -1 }}


Mapping: {{mapping| 1 13 -36 -263 | 0 -14 47 326 }}
Mapping: {{mapping| 1 -1 11 63 | 0 14 -47 -326 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000000, ~8388608/7381125 = 221.568013
* WE: ~2 = 1200.001970{{c}}, ~8388608/7381125 = 221.568395{{c}}
* POTE: ~2 = 1200.000000, ~8388608/7381125 = 221.568031
* CWE: ~2 = 1200.000000{{c}}, ~8388608/7381125 = 221.568026{{c}}


{{Optimal ET sequence|legend=0| 612, 1901, 2513, 3125, 6862, 9987, 13112, 36211, 49323 }}
{{Optimal ET sequence|legend=0| 65d, …, 612, 1901, 2513, 3125, 6862, 9987, 13112, 36211, 49323 }}


Badness (Sintel): 0.600
Badness (Sintel): 0.600
Line 184: Line 193:
Comma list: 151263/151250, 21437500/21434787, 369140625/369098752
Comma list: 151263/151250, 21437500/21434787, 369140625/369098752


Mapping: {{mapping| 1 13 -36 -263 -573 | 0 -14 47 326 707 }}
Mapping: {{mapping| 1 -1 11 63 134 | 0 14 -47 -326 -707 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000000, ~8388608/7381125 = 221.568116
* WE: ~2 = 1200.003854{{c}}, ~8388608/7381125 = 221.568850{{c}}
* POTE: ~2 = 1200.000000, ~8388608/7381125 = 221.568139
* CWE: ~2 = 1200.000000{{c}}, ~8388608/7381125 = 221.568133{{c}}


{{Optimal ET sequence|legend=1| 612, 2513, 3125, 3737, 8086, 19909d }}
{{Optimal ET sequence|legend=0| 65dee, …, 612, 2513, 3125, 3737, 8086, 19909d }}


Badness (Sintel): 1.21
Badness (Sintel): 1.211


== Senior ==
== Senior ==
Line 201: Line 210:
[[Comma list]]: {{monzo| -17 62 -35 }}
[[Comma list]]: {{monzo| -17 62 -35 }}


{{Mapping|legend=1| 1 11 19 | 0 -35 -62 }}
{{Mapping|legend=1| 1 -24 -43 | 0 35 62 }}
 
: mapping generators: ~2, ~{{monzo| 7 -23 13 }}
: mapping generators: ~2, ~{{monzo| -6 23 -13 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000000, ~{{monzo| -6 23 -13 }} = 322.801349
* [[WE]]: ~2 = 1200.000236{{c}}, ~{{monzo| 7 -23 13 }} = 877.198814{{c}}
* [[POTE]]: ~2 = 1200.000000, ~{{monzo| -6 23 -13 }} = 322.801358
: [[error map]]: {{val| +0.0002 -0.0022 +0.0026 }}
* [[CWE]]: ~2 = 1200.000000{{c}}, ~{{monzo| 7 -23 13 }} = 877.198647{{c}}
: error map: {{val| 0.0000 -0.0024 -0.0024 }}


{{Optimal ET sequence|legend=1| 26, …, 145, 171, 658, 829, 1000, 1171, 2513, 6197, 39695, 45892, 52089, 58286, 64483, 70680 }}
{{Optimal ET sequence|legend=1| 26, …, 145, 171, 658, 829, 1000, 1171, 2513, 6197, 39695, 45892, 52089, 58286, 64483, 70680 }}
Line 220: Line 230:
[[Comma list]]: {{monzo| 144 -22 -47 }}
[[Comma list]]: {{monzo| 144 -22 -47 }}


{{Mapping|legend=1| 1 45 -18 | 0 -47 22 }}
{{Mapping|legend=1| 1 -2 4 | 0 47 -22 }}
 
: mapping generators: ~2, ~{{monzo| 46 -7 -15 }}
: mapping generators: ~2, ~{{monzo| -45 7 15 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000000, ~{{monzo| 46 -7 -15 }} = 91.530979
* [[WE]]: ~2 = 1199.998956{{c}}, ~{{monzo| 46 -7 -15 }} = 91.530922{{c}}
* [[POTE]]: ~2 = 1200.000000, ~{{monzo| 46 -7 -15 }} = 91.531001
: [[error map]]: {{val| -0.0010 +0.0004 +0.0018 }}
* [[CWE]]: ~2 = 1200.000000{{c}}, ~{{monzo| 46 -7 -15 }} = 91.530995{{c}}
: error map: {{val| 0.0000 +0.0018 +0.0044 }}


{{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 }}
{{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 }}


[[Badness]] (Sintel): 1.09
[[Badness]] (Sintel): 1.086


; Music
; 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
* ''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


== Quectismic ==
== Septarium ==
{{See also| Quectisma }}
Septarium splits the octave in seven, and tempers out the [[septarium comma]], {{monzo| 73 77 -84 }}. It can be described as {{nowrap| 441 & 2513 }} temperament, which tempers out 78125000/78121827 and {{monzo| 47 -7 -7 -7 }} ([[akjaysma]]) in the 7-limit.


[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: {{monzo| 554 -351 1 }}
[[Comma list]]: {{monzo| 73 77 -84 }}
 
{{Mapping|legend=1| 1 0 -554 | 0 1 351 }}


: mapping generators: ~2, ~3
{{Mapping|legend=1| 7 1 7 | 0 12 11 }}
: mapping generators: ~{{monzo| 21 22 -24 }}, ~{{monzo| -20 -21 23 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000000, ~3/2 = 701.955310
* [[WE]]: ~{{monzo| 21 22 -24 }} = 171.429{{c}}, ~{{monzo| -20 -21 23 }} = 144.210{{c}}
* [[CWE]]: ~2 = 1200.000000, ~3/2 = 701.955310
* [[CWE]]: ~{{monzo| 21 22 -24 }} = 171.429{{c}}, ~{{monzo| -20 -21 23 }} = 144.210{{c}}


{{Optimal ET sequence|legend=1| 306, 359c, 665, 2301, 2966, 3631, 4296, 46591, 50887, 55183, 59479, 63775, 68071, 72367, 76663, 80959, 85255, 89551 }}
{{Optimal ET sequence|legend=1| 133, 308, 441, 1631, 2072, 2513, 5467, 7980 }}


[[Badness]] (Sintel): 8.74
[[Badness]] (Sintel): 1.395


=== Nanoquectismic ===
=== 7-limit ===
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Comma list: 43046721/43025920, {{monzo| 82 -19 -3 -16 }}
Comma list: 78125000/78121827, 140737488355328/140710042265625


Mapping: {{mapping| 1 0 -554 109 | 0 1 351 -67 }}
Mapping: {{Mapping| 7 1 7 39 | 0 12 11 -23 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000000, ~3/2 = 701.955371
* WE: ~1157625/1048576 = 171.428{{c}}, ~2097152/1929375 = 144.211{{c}}
* CWE: ~2 = 1200.000000, ~3/2 = 701.955457
* CWE: ~1157625/1048576 = 171.429{{c}}, ~2097152/1929375 = 144.212{{c}}
 
{{Optimal ET sequence|legend=0| 133, 308, 441, 1631, 2072, 2513, 2954 }}
 
Badness (Sintel): 0.777
 
== Raider ==
{{See also| Syntonic–chromatic equivalence continuum }}
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| 71 -99 37 }}
 
{{Mapping|legend=1| 1 -9 -26 | 0 37 99 }}
: mapping generators: ~2, ~8000/6561
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.999880537{{c}}, ~8000/6561 = 343.296063356{{c}}
: [[error map]]: {{val| -0.000119 +0.000418 -0.000336 }}
* [[CWE]]: ~2 = 1200.000000000{{c}}, ~8000/6561 = 343.296095985{{c}}
: error map: {{val| 0.000000 +0.000551 -0.000211 }}


{{Optimal ET sequence|legend=1| 306, 665, 1636, 2301, 2966 }}
{{Optimal ET sequence|legend=1| 7, …, 381, 388, 783, 1171, 1954, 3125, 4296, 5467, 7421, 9763, 14059, 18355, 22651, 26947, 31243, 35539, 66782, 102321, 137860 }}


Badness (Sintel): 15.3
[[Badness]] (Sintel): 0.302


=== Conanoquectismic ===
== Pirate ==
Subgroup: 2.3.5.7
{{See also| Hemfiness temperaments #Piracy }}
 
[[Subgroup]]: 2.3.5


Comma list: {{monzo| 33 -26 12 -7 }}, {{monzo| -32 13 17 -10 }}
[[Comma list]]: {{monzo| -90 -15 49 }}


Mapping: {{mapping| 1 0 -554 -945 | 0 1 351 598 }}
{{Mapping|legend=1| 1 -6 0 | 0 49 15 }}
: mapping generators: ~2, ~{{monzo| 24 4 -13 }}


Optimal tunings:  
[[Optimal tuning]]s:  
* CTE: ~2 = 1200.000000, ~3/2 = 701.954810
* [[WE]]: ~2 = 1200.000195604{{c}}, ~{{monzo| 24 4 -13 }} = 185.754209314{{c}}
* CWE: ~2 = 1200.000000, ~3/2 = 701.954771
: [[error map]]: {{val| -0.000196 +0.000418 -0.000336 }}
* [[CWE]]: ~2 = 1200.000000000{{c}}, ~{{monzo| 24 4 -13 }} = 185.754209314{{c}}
: error map: {{val| 0.000000 +0.000082 -0.000574 }}


{{Optimal ET sequence|legend=1| 306d, 359cd, 665 }}
{{Optimal ET sequence|legend=1| 84, 239, 323, 730, 1783, 2513, 4296, 15401, 19697, 23993, 52282, 76275, 128557, 204832 … }}


Badness (Sintel): 55.0
[[Badness]] (Sintel): 0.133


== Counterquectismic ==
== Counterquectismic ==
Line 292: Line 327:


{{Mapping|legend=1| 1 0 500 | 0 1 -314 }}
{{Mapping|legend=1| 1 0 500 | 0 1 -314 }}
: mapping generators: ~2, ~3
: mapping generators: ~2, ~3


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000000, ~3/2 = 701.954415
* [[WE]]: ~2 = 1200.000184840{{c}}, ~3/2 = 701.954524421{{c}}
* [[CWE]]: ~2 = 1200.000000, ~3/2 = 701.954416
: [[error map]]: {{val| +0.000185 -0.000292 -0.000002 }}
* [[CWE]]: ~2 = 1200.000000000{{c}}, ~3/2 = 701.954415845{{c}}
: error map: {{val| 0.000000 -0.000585 -0.000289 }}


{{Optimal ET sequence|legend=1| 306c, 359, 665, 2354, 3019, 3684, 11717, 15401, 19085, 34486 }}
{{Optimal ET sequence|legend=1| 306c, 359, 665, 2354, 3019, 3684, 11717, 15401, 19085, 34486 }}


[[Badness]] (Sintel): 12.0
[[Badness]] (Sintel): 11.971


== Raider ==
== Quectismic ==
{{See also| Syntonic–chromatic equivalence continuum }}
{{See also| Quectisma }}


[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: {{monzo| 71 -99 37 }}
[[Comma list]]: {{monzo| 554 -351 1 }}
 
{{Mapping|legend=1| 1 0 -554 | 0 1 351 }}
: mapping generators: ~2, ~3
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.999902567{{c}}, ~3/2 = 701.955253373{{c}}
: [[error map]]: {{val| -0.000097 +0.000155 -0.000001 }}
* [[CWE]]: ~2 = 1200.000000000{{c}}, ~3/2 = 701.955310152{{c}}
: error map: {{val| 0.000000 +0.000309 +0.000149 }}


{{Mapping|legend=1| 1 28 73 | 0 -37 -99 }}
{{Optimal ET sequence|legend=1| 306, 359c, 665, 2301, 2966, 3631, 4296, 46591, 50887, 55183, 59479, 63775, 68071, 72367, 76663, 80959, 85255, 89551 }}


: mapping generators: ~2, ~6561/4000
[[Badness]] (Sintel): 8.736


[[Optimal tuning]]s:
=== Nanoquectismic ===
* [[CTE]]: ~2 = 1200.000000, ~8000/6561 = 343.296094
Subgroup: 2.3.5.7
* [[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 }}
Comma list: 43046721/43025920, {{monzo| 82 -19 -3 -16 }}


[[Badness]] (Sintel): 0.581
Mapping: {{mapping| 1 0 -554 109 | 0 1 351 -67 }}


== Pirate ==
Optimal tunings:
{{See also| Hemfiness temperaments #Piracy }}
* WE: ~2 = 1199.979407{{c}}, ~3/2 = 701.943437{{c}}
* CWE: ~2 = 1200.000000{{c}}, ~3/2 = 701.955457{{c}}


[[Subgroup]]: 2.3.5
{{Optimal ET sequence|legend=1| 306, 665, 1636, 2301, 2966 }}


[[Comma list]]: {{monzo| -90 -15 49 }}
Badness (Sintel): 15.285


{{Mapping|legend=1| 1 43 15 | 0 -49 -15 }}
=== Conanoquectismic ===
Subgroup: 2.3.5.7


: Mapping generators: ~2, ~{{monzo| -23 -4 13 }}
Comma list: {{monzo| 33 -26 12 -7 }}, {{monzo| -32 13 17 -10 }}


[[Optimal tuning]]s:  
Mapping: {{mapping| 1 0 -554 -945 | 0 1 351 598 }}
* [[CTE]]: ~2 = 1200.000000, ~{{monzo| 24 4 -13 }} = 185.754186
 
* [[POTE]]: ~2 = 1200.000000, ~{{monzo| 24 4 -13 }} = 185.754179
Optimal tunings:  
* WE: ~2 = 1200.010750{{c}}, ~3/2 = 701.961041{{c}}
* CWE: ~2 = 1200.000000{{c}}, ~3/2 = 701.954771{{c}}


{{Optimal ET sequence|legend=1| 84, 239, 323, 730, 1783, 2513, 4296, 15401, 19697, 23993, 52282, 76275, 128557, 204832 … }}
{{Optimal ET sequence|legend=1| 306d, 359cd, 665 }}


[[Badness]] (Sintel): 0.339
Badness (Sintel): 54.974


== Atomic ==
== Atomic ==
{{See also | Kirnberger's atom }}
: ''For extensions, see [[Landscape microtemperaments #Atomic]].''
 
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]].
Atomic tempers out [[Kirnberger's atom]], the microscopic interval separating eleven [[schisma]]s and a [[syntonic comma]], or twelfth schismas and a [[Pythagorean comma]]. It is a member of the [[schismic–commatic equivalence continuum]] with {{nowrap| ''n'' {{=}} 12 }}. In this extremely accurate temperament, the [[3/2|perfect fifth]] is one [[schisma]] sharp of its [[12edo]] value.  


[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5
Line 353: Line 399:


{{Mapping|legend=1| 12 0 161 | 0 1 -7 }}
{{Mapping|legend=1| 12 0 161 | 0 1 -7 }}
: mapping generators: ~{{monzo| -67 35 5 }}, ~3
: mapping generators: ~{{monzo| -67 35 5 }}, ~3


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~{{monzo| -67 35 5 }} = 100.000000, ~3/2 = 701.955176 (~32805/32768 = 1.955176)
* [[WE]]: ~{{monzo| -67 35 5 }} = 99.999995361{{c}}, ~3/2 = 701.955129505{{c}} (~32805/32768 = 1.955161980{{c}})
* [[POTE]]: ~{{monzo| -67 35 5 }} = 100.000000, ~3/2 = 701.955162 (~32805/32768 = 1.955162)
: [[error map]]: {{val| -0.000056 +0.000072 +0.000022 }}
* [[CWE]]: ~{{monzo| -67 35 5 }} = 100.000000000{{c}}, ~3/2 = 701.955166184{{c}} (~32805/32768 = 1.955166184{{c}})
: error map: {{val| 0.000000 +0.000165 +0.000123 }}


{{Optimal ET sequence|legend=1| 12, …, 576, 588, 600, 612, 2460, 3072, 3684, 4296, 12276, 16572, 20868, 25164, 46032 }}
{{Optimal ET sequence|legend=1| 12, …, 576, 588, 600, 612, 2460, 3072, 3684, 4296, 12276, 16572, 20868, 25164, 46032 }}


[[Badness]] (Sintel): 0.697
[[Badness]] (Sintel): 0.0892


=== 7-limit ===
== Revopentic ==
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 }}
{{See also| Revopentisma }}


Subgroup: 2.3.7
Subgroup: 2.3.7


Comma list: 11399736556781568/11398895185373143
Comma list: {{monzo| 47 4 -19 }}
 
{{Mapping|legend=2| 1 12 5 | 0 -19 -4 }}


: mapping generators: ~2, ~24576/16807
{{Mapping|legend=2| 1 -7 1 | 0 19 4 }}
: mapping generators: ~2, ~16807/12288


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000000, ~24576/16807 = 657.791865
* [[WE]]: ~2 = 1199.998821{{c}}, ~16807/12288 = 542.207710{{c}}
* [[CWE]]: ~2 = 1200.000000, ~24576/16807 = 657.791796
: [[error map]]: {{val| -0.0012 -0.0003 +0.0038 }}
* [[CWE]]: ~2 = 1200.000000{{c}}, ~16807/12288 = 542.208204{{c}}
: error map: {{val| 0.0000 +0.0009 +0.0069 }}


{{Optimal ET sequence|legend=1| 31, 73, 104, 135, 436, 571, 706, 1277, 8233, 9510, 10787, 12064, 13341, 14618, 15895, 33067, 48962, 113819d, 162781d, … }}
{{Optimal ET sequence|legend=1| 31, 73, 104, 135, 436, 571, 706, 1277, 8233, 9510, 10787, 12064, 13341, 14618, 15895, 33067, 48962, 113819d, 162781d, … }}
Line 420: Line 438:
Comma list: 645700815/645657712, {{monzo| 51 -13 -1 -10 }}
Comma list: 645700815/645657712, {{monzo| 51 -13 -1 -10 }}


Mapping: {{mapping| 1 12 -155 5 | 0 -19 287 -4 }}
Mapping: {{mapping| 1 -7 132 1 | 0 19 -287 4 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000000, ~24576/16807 = 657.792032
* WE: ~2 = 1200.000110{{c}}, ~16807/12288 = 542.208018{{c}}
* CWE: ~2 = 1200.000000, ~24576/16807 = 657.792032
* CWE: ~2 = 1200.000000{{c}}, ~16807/12288 = 542.207968{{c}}


{{Optimal ET sequence|legend=0| 135, 436c, 571, 1277, 1848, 3125, 8098, 11223, 25571, 36794, 121605d }}
{{Optimal ET sequence|legend=0| 135, 436c, 571, 1277, 1848, 3125, 8098, 11223, 25571, 36794, 121605d }}
Line 438: Line 456:


{{Mapping|legend=2| 1 0 109 | 0 1 -67 }}
{{Mapping|legend=2| 1 0 109 | 0 1 -67 }}
 
: mapping generators: ~2, ~3
: sval mapping generators: ~2, ~3


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000000, ~3/2 = 701.957820
* [[WE]]: ~2 = 1199.999111{{c}}, ~3/2 = 701.957264{{c}}
* [[POTE]]: ~2 = 1200.000000, ~3/2 = 701.957784
: [[error map]]: {{val| -0.0009 +0.0014 +0.0001 }}
* [[CWE]]: ~2 = 1200.000000{{c}}, ~3/2 = 701.957796{{c}}
: error map: {{val| 0.0000 +0.0028 +0.0018 }}


{{Optimal ET sequence|legend=1| 53, 200, 253, 306, 665, 971, 1277, 6691, 7968, 9245, 10522, 11799, 13076, 40505, 53581, 66657, 79733 }}
{{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
[[Badness]] (Sintel): TBD


== Icarus ==
== Icarus ==
Line 456: Line 475:
[[Comma list]]: {{monzo| -32 -64 71 }}
[[Comma list]]: {{monzo| -32 -64 71 }}


{{Mapping|legend=1| 1 35 32 | 0 -71 -64 }}
{{Mapping|legend=2| 1 -36 -32 | 0 71 64 }}
: mapping generators: ~3, ~{{monzo| -4 -9 10 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~3 = 1901.955, ~{{monzo| 5 9 -10 }} = 898.340
* [[WE]]: ~3 = 1901.955003{{c}}, ~{{monzo| -4 -9 10 }} = 1003.615406{{c}}
* [[CWE]]: ~3 = 1901.955, ~{{monzo| 5 9 -10 }} = 898.340
: [[error map]]: {{val| +0.0000 +0.0000 -0.0000 }}
* [[CWE]]: ~3 = 1901.955001{{c}}, ~{{monzo| -4 -9 10 }} = 1003.615405{{c}}
: error map: {{val| 0.0000 -0.0000 -0.0000 }}


[[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]]
[[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): 0.360
[[Badness]] (Sintel): TBD


= Rank-3 temperaments =
= Rank-3 temperaments =
== Akjaysmic ==
{{See also| Akjaysma }}
[[Subgroup]]: 2.3.5.7
[[Comma list]]: {{monzo| 47 -7 -7 -7 }}
{{Mapping|legend=1| 7 0 0 47 | 0 1 0 -1 | 0 0 1 -1 }}
: mapping generators: ~1157625/1048576, ~3, ~5
[[Optimal tuning]]s:
* [[WE]]: ~1157625/1048576 = 171.427811{{c}}, ~3/2 = 701.962313{{c}}, ~5/4 = 386.328628{{c}}
: [[error map]]: {{val| -0.0053 +0.0020 +0.0043 +0.0062 }}
* [[CWE]]: ~1157625/1048576 = 171.428571{{c}}, ~3/2 = 701.964859{{c}}, ~5/4 = 386.330310{{c}}
: error map: {{val| 0.0000 +0.0099 +0.0166 +0.0218 }}
{{Optimal ET sequence|legend=1| 140, 217, 224, 301, 441, 966, 1106, 1407, 1547, 1848, 2513, 2954, 6349, 9303, 11151, 14105, 17500, 20454 }}
[[Badness]] (Sintel): 2.22
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 184549376/184528125, 199297406/199290375
Mapping: {{mapping| 7 0 0 47 -168 | 0 1 0 -1 10 | 0 0 1 -1 5 }}
: mapping generators: ~29160/26411, ~3, ~5
Optimal tunings:
* WE: ~29160/26411 = 171.427802{{c}}, ~3/2 = 701.964561{{c}}, ~5/4 = 386.329837{{c}}
* CWE: ~29160/26411 = 171.428571{{c}}, ~3/2 = 701.967291{{c}}, ~5/4 = 386.331624{{c}}
{{Optimal ET sequence|legend=0| 301, 441, 665e, 742, 1106, 1547, 1848, 3395, 4501, 5243, 6349, 17941, 24290, 30639, 45185cde, 63126bcde, 69475bccdde, 75824bccddee }}
Badness (Sintel): 1.32
== Sasaquinbizo-atriyo (171 & 1106 & 3566) ==
== Sasaquinbizo-atriyo (171 & 1106 & 3566) ==
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 474: Line 532:
{{Mapping|legend=1| 1 0 9 -3 | 0 1 8 0 | 0 0 10 -3 }}
{{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 tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 701.9624{{c}}, ~6561/3430 = 1122.9387{{c}}


{{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 }}
{{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 }}
Line 480: Line 538:
[[Badness]] (Sintel): 1.24
[[Badness]] (Sintel): 1.24


== Saquadtrizo-asepgu (171 & 2019 & 3566) ==
== Izarismic ==
This temperament is identical to the [[izar]] in the no-twos subgroup, but has an independent generator for prime 2. It can be described as {{nowrap| 41 & 49 & 130 }} temperament, and tempers out the [[izar comma]], {{monzo| 0 -11 -7 12 }}.
 
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: {{monzo| 0 -11 -7 12 }} (13841287201/13839609375)
[[Comma list]]: 13841287201/13839609375


{{Mapping|legend=1| 1 0 0 0 | 0 1 7 5 | 0 0 -12 -7 }}
{{Mapping|legend=1| 1 0 0 0 | 0 1 7 5 | 0 0 -12 -7 }}
: mapping generators: ~2, ~3, ~16807/10125


[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9584, ~16807/10125 = 877.2825
[[Optimal tuning]]s:
* [[TE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9584{{c}}, ~16807/10125 = 877.2825{{c}}
* [[WE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9584{{c}}, ~16807/10125 = 877.2825{{c}}


{{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 }}
{{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 }}
Line 500: Line 563:
{{Mapping|legend=1| 1 0 3 11 | 0 1 4 9 | 0 0 5 16 }}
{{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 tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 701.9501{{c}}, ~250/189 = 484.2956{{c}}


{{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 }}
{{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 }}
Line 513: Line 576:
{{Mapping|legend=1| 1 3 0 1 | 0 -11 0 -4 | 0 0 1 1 }}
{{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 tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~375/343 = 154.3678{{c}}, ~5/4 = 386.3070{{c}}


{{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 }}
{{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 }}
Line 519: Line 582:
[[Badness]] (Sintel): 0.501
[[Badness]] (Sintel): 0.501


== Starscape or Latritriru-ayo ==
== Starscape ==
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


Line 526: Line 589:
{{Mapping|legend=1| 1 0 4 0 | 0 1 1 2 | 0 0 -9 -1 }}
{{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 tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 701.9514{{c}}, ~9/7 = 435.0709{{c}}


{{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 }}
{{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 }}
Line 539: Line 602:
{{Mapping|legend=1| 1 0 13 16 | 0 1 10 12 | 0 0 -14 -17 }}
{{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 tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 701.9548{{c}}, ~31250/16807 = 1073.8021{{c}}


{{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 }}
{{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 }}
Line 545: Line 608:
[[Badness]] (Sintel): 0.982
[[Badness]] (Sintel): 0.982


== Euzenius or Sabiruquinyo ==
== Euzenius ==
{{See also| Euzenius comma }}
{{See also| Euzenius comma }}


Line 554: Line 617:
{{Mapping|legend=1| 1 1 0 -5 | 0 2 0 -13 | 0 0 1 5 }}
{{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 tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~6250/5103 = 350.9787{{c}}, ~5/4 = 386.3099{{c}}


{{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 }}
{{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 }}
Line 560: Line 623:
[[Badness]] (Sintel): 0.0902
[[Badness]] (Sintel): 0.0902


== Nommismic or Quinla-zoyoyo ==
== Nommismic ==
{{See also| Nommisma }}
{{See also| Nommisma }}


Line 569: Line 632:
{{Mapping|legend=1| 1 0 0 55 | 0 1 0 -30 | 0 0 1 -2 }}
{{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 tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 701.9516{{c}}, ~5/4 = 386.3132{{c}}


{{Optimal ET sequence|legend=1| 612, 1236, 1277, 1848, 2513, 3125, 6862, 8098, 8710, 11835, 14960, 26795, 195663b, }} …
{{Optimal ET sequence|legend=1| 612, 1236, 1277, 1848, 2513, 3125, 6862, 8098, 8710, 11835, 14960, 26795, 195663b, }} …
Line 582: Line 645:
{{Mapping|legend=1| 1 0 9 7 | 0 1 3 3 | 0 0 -23 -18 }}
{{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 tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 701.9551{{c}}, ~56953125/40353607 = 596.5022{{c}}


{{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, }} …
{{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, }} …
Line 588: Line 651:
[[Badness]] (Sintel): 0.505
[[Badness]] (Sintel): 0.505


== Technologismic or Trisa-quinbiru-agu ==
== Technologismic ==
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


Line 595: Line 658:
{{Mapping|legend=1| 1 0 1 5 | 0 1 7 -2 | 0 0 -10 1 }}
{{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 tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 701.9553{{c}}, ~63/32 = 1172.7374{{c}}


{{Optimal ET sequence|legend=1| 441, 966, 1277, 1407, 1718, 1848, 2684, 3125, 6691, 9816, 11664, 14789, 18355, 33144, 51499, 124478, 175977, }} …
{{Optimal ET sequence|legend=1| 441, 966, 1277, 1407, 1718, 1848, 2684, 3125, 6691, 9816, 11664, 14789, 18355, 33144, 51499, 124478, 175977, }} …
Line 601: Line 664:
[[Badness]] (Sintel): 0.116
[[Badness]] (Sintel): 0.116


== Quinbisa-quinbizo-alegu (1848 & 11664 & 21480) ==
== Quinbisa-quinbizo-alegu (1848 & 3737 & 6079) ==
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


Line 608: Line 671:
{{Mapping|legend=1| 1 0 0 -11 | 0 1 9 17 | 0 0 -10 -11 }}
{{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 tuning]] ([[CTE]]): ~2 = 1200.000{{c}}, ~3/2 = 701.955{{c}}, ~32805/28672 = 233.128{{c}}


{{Optimal ET sequence|legend=1| 1848, 3737, 5585, 6079, 7927, 9816, 11664, 21480, 33144, 54624, 70025, 81689, 103169, }} …
{{Optimal ET sequence|legend=1| 1848, 3737, 5585, 6079, 7927, 9816, 11664, 21480, 33144, 54624, 70025, 81689, 103169, }} …


[[Badness]] (Sintel): 0.538
[[Badness]] (Sintel): 0.538
== Septrongismic ==
{{See also| Septrongisma }}
[[Subgroup]]: 2.3.5.7
[[Comma list]]: {{monzo| -7 30 -9 -7 }} = 205891132094649/205885750000000
{{Mapping|legend=1| 1 0 0 -1 | 0 1 1 3 | 0 0 7 -9 }}
[[Optimal tuning]] ([[CWE]]): ~2 = 1200.000{{c}}, ~3/2 = 701.954{{c}}, ~1715000/1594323 = 126.337{{c}}
{{Optimal ET sequence|legend=1| 171, 2783, 2954, 3125, 8539, 11664, 14789, }} …
[[Badness]] (Sintel): 0.320


[[Category:Temperament collections]]
[[Category:Temperament collections]]
[[Category:Pages with mostly numerical content]]
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