Xenharmonic Wiki

Aberschismic temperaments: Difference between revisions

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Improve the intros to each temp. Cleanup
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{{Mapping|legend=1| 1 0 61 71 | 0 1 -37 -43 }}
{{Mapping|legend=1| 1 0 61 71 | 0 1 -37 -43 }}
: mapping generators: ~2, ~3


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 703.039
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~3/2 = 703.039{{c}}


{{Optimal ET sequence|legend=1| 29, 70, 99, 722bc, 821bc, 920bc, 1019bc, 1118bbcc, 1217bbcc, 1316bbccd }}
{{Optimal ET sequence|legend=1| 29, 70, 99, 722bc, 821bc, 920bc, 1019bc, 1118bbcc, 1217bbcc, 1316bbccd }}


[[Badness]]: 0.094603
[[Badness]] (Smith): 0.094603


== Leapday ==
== Leapday ==
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{{Mapping|legend=1| 1 0 -31 -21 | 0 1 21 15 }}
{{Mapping|legend=1| 1 0 -31 -21 | 0 1 21 15 }}
: mapping generators: ~2, ~3


Optimal tunings:  
Optimal tunings:  
* [[CTE]]: ~2 = 1\1, ~3/2 = 704.2257
* [[CTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 704.2257{{c}}
* [[POTE]]: ~2 = 1\1, ~3/2 = 704.263
* [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 704.263{{c}}


{{Optimal ET sequence|legend=1| 17c, 29, 46 }}
{{Optimal ET sequence|legend=1| 17c, 29, 46 }}


[[Badness]]: 0.096123
[[Badness]] (Smith): 0.096123


=== 11-limit ===
=== 11-limit ===
Line 71: Line 73:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 704.2625
* CTE: ~2 = 1200.0000{{c}}, ~3/2 = 704.2625{{c}}
* POTE: ~2 = 1\1, ~3/2 = 704.250
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 704.250{{c}}


{{Optimal ET sequence|legend=0| 17c, 29, 46 }}
{{Optimal ET sequence|legend=0| 17c, 29, 46 }}


Badness: 0.038624
Badness (Smith): 0.038624


=== 13-limit ===
=== 13-limit ===
Line 86: Line 88:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 704.2924
* CTE: ~2 = 1200.0000{{c}}, ~3/2 = 704.2924{{c}}
* POTE: ~2 = 1\1, ~3/2 = 704.214
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 704.214{{c}}


{{Optimal ET sequence|legend=0| 17c, 29, 46, 121def }}
{{Optimal ET sequence|legend=0| 17c, 29, 46, 121def }}


Badness: 0.024732
Badness (Smith): 0.024732


=== 17-limit ===
=== 17-limit ===
Line 101: Line 103:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 704.3098
* CTE: ~2 = 1200.0000{{c}}, ~3/2 = 704.3098{{c}}
* POTE: ~2 = 1\1, ~3/2 = 704.229
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 704.229{{c}}


{{Optimal ET sequence|legend=0| 17cg, 29g, 46, 121defg }}
{{Optimal ET sequence|legend=0| 17cg, 29g, 46, 121defg }}


Badness: 0.017863
Badness (Smith): 0.017863


==== 19-limit ====
==== 19-limit ====
Line 116: Line 118:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 704.2990
* CTE: ~2 = 1200.0000{{c}}, ~3/2 = 704.2990{{c}}
* POTE: ~2 = 1\1, ~3/2 = 704.135
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 704.135{{c}}


{{Optimal ET sequence|legend=0| 17cg, 29g, 46, 75dfgh, 121defgh }}
{{Optimal ET sequence|legend=0| 17cg, 29g, 46, 75dfgh, 121defgh }}


Badness: 0.017356
Badness (Smith): 0.017356


===== 23-limit =====
===== 23-limit =====
Line 131: Line 133:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 704.3035
* CTE: ~2 = 1200.0000{{c}}, ~3/2 = 704.3035{{c}}
* POTE: ~2 = 1\1, ~3/2 = 704.141
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 704.141{{c}}


{{Optimal ET sequence|legend=0| 17cg, 29g, 46, 75dfgh, 121defgh }}
{{Optimal ET sequence|legend=0| 17cg, 29g, 46, 75dfgh, 121defgh }}


Badness: 0.014065
Badness (Smith): 0.014065


==== Leapling ====
==== Leapling ====
Line 146: Line 148:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 704.2037
* CTE: ~2 = 1200.0000{{c}}, ~3/2 = 704.2037{{c}}
* POTE: ~2 = 1\1, ~3/2 = 704.123
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 704.123{{c}}


{{Optimal ET sequence|legend=0| 17cgh, 29g, 46h, 75dfg }}
{{Optimal ET sequence|legend=0| 17cgh, 29g, 46h, 75dfg }}


Badness: 0.019065
Badness (Smith): 0.019065


===== 23-limit =====
===== 23-limit =====
Line 161: Line 163:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 704.2082
* CTE: ~2 = 1200.0000{{c}}, ~3/2 = 704.2082{{c}}
* POTE: ~2 = 1\1, ~3/2 = 704.114
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 704.114{{c}}


{{Optimal ET sequence|legend=0| 17cgh, 29g, 46h, 75dfg }}
{{Optimal ET sequence|legend=0| 17cgh, 29g, 46h, 75dfg }}


Badness: 0.016067
Badness (Smith): 0.016067


== Hemidromeda ==
== Hemidromeda ==
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{{Mapping|legend=1| 1 0 38 48 | 0 2 -45 -57 }}
{{Mapping|legend=1| 1 0 38 48 | 0 2 -45 -57 }}
: mapping generator: ~2, ~12500/7203


: Mapping generator: ~2, ~12500/7203
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000{{c}}, ~7203/6250 = 248.581{{c}}
 
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~7203/6250 = 248.581


{{Optimal ET sequence|legend=1| 29, 82cd, 111, 140, 531, 671, 811b, 951b }}
{{Optimal ET sequence|legend=1| 29, 82cd, 111, 140, 531, 671, 811b, 951b }}


[[Badness]]: 0.115803
[[Badness]] (Smith): 0.115803


=== 11-limit ===
=== 11-limit ===
Line 192: Line 193:
Mapping: {{mapping| 1 0 38 48 32 | 0 2 -45 -57 -36 }}
Mapping: {{mapping| 1 0 38 48 32 | 0 2 -45 -57 -36 }}


Optimal tuning (CTE): ~2 = 1\1, ~405/352 = 248.589
Optimal tuning (CTE): ~2 = 1200.000{{c}}, ~405/352 = 248.589{{c}}


{{Optimal ET sequence|legend=0| 29, 82cd, 111, 140, 251, 391e }}
{{Optimal ET sequence|legend=0| 29, 82cd, 111, 140, 251, 391e }}


Badness: 0.060808
Badness (Smith): 0.060808


=== 13-limit ===
=== 13-limit ===
Line 205: Line 206:
Mapping: {{mapping| 1 0 38 48 32 37 | 0 2 -45 -57 -36 -42 }}
Mapping: {{mapping| 1 0 38 48 32 37 | 0 2 -45 -57 -36 -42 }}


Optimal tuning (CTE): ~2 = 1\1, ~15/13 = 248.588
Optimal tuning (CTE): ~2 = 1200.000{{c}}, ~15/13 = 248.588{{c}}


{{Optimal ET sequence|legend=0| 29, 82cdf, 111, 140, 391e, 531e }}
{{Optimal ET sequence|legend=0| 29, 82cdf, 111, 140, 391e, 531e }}


Badness: 0.028632
Badness (Smith): 0.028632


=== 17-limit ===
=== 17-limit ===
Line 218: Line 219:
Mapping: {{mapping| 1 0 38 48 32 37 58 | 0 2 -45 -57 -36 -42 -68 }}
Mapping: {{mapping| 1 0 38 48 32 37 58 | 0 2 -45 -57 -36 -42 -68 }}


Optimal tuning (CTE): ~2 = 1\1, ~15/13 = 248.591
Optimal tuning (CTE): ~2 = 1200.000{{c}}, ~15/13 = 248.591{{c}}


{{Optimal ET sequence|legend=0| 29g, 82cdfg, 111, 140, 251, 391e }}
{{Optimal ET sequence|legend=0| 29g, 82cdfg, 111, 140, 251, 391e }}


Badness: 0.019054
Badness (Smith): 0.019054


=== 19-limit ===
=== 19-limit ===
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Mapping: {{mapping| 1 0 38 48 32 37 58 32 | 0 2 -45 -57 -36 -42 -68 -35 }}
Mapping: {{mapping| 1 0 38 48 32 37 58 32 | 0 2 -45 -57 -36 -42 -68 -35 }}


Optimal tuning (CTE): ~2 = 1\1, ~15/13 = 248.587
Optimal tuning (CTE): ~2 = 1200.000{{c}}, ~15/13 = 248.587{{c}}


{{Optimal ET sequence|legend=0| 29g, 82cdfgh, 111, 140, 391ehh, 531ehh }}
{{Optimal ET sequence|legend=0| 29g, 82cdfgh, 111, 140, 391ehh, 531ehh }}


Badness: 0.016609
Badness (Smith): 0.016609


=== 23-limit ===
=== 23-limit ===
Line 244: Line 245:
Mapping: {{mapping| 1 0 38 48 32 37 58 32 18 | 0 2 -45 -57 -36 -42 -68 -35 -17 }}
Mapping: {{mapping| 1 0 38 48 32 37 58 32 18 | 0 2 -45 -57 -36 -42 -68 -35 -17 }}


Optimal tuning (CTE): ~2 = 1\1, ~15/13 = 248.588
Optimal tuning (CTE): ~2 = 1200.000{{c}}, ~15/13 = 248.588{{c}}


{{Optimal ET sequence|legend=0| 29g, 82cdfgh, 111, 140, 391ehhi, 531ehhii }}
{{Optimal ET sequence|legend=0| 29g, 82cdfgh, 111, 140, 391ehhi, 531ehhii }}


Badness: 0.015361
Badness (Smith): 0.015361


== Mystery ==
== Mystery ==
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{{Mapping|legend=1| 29 46 0 14 | 0 0 1 1 }}
{{Mapping|legend=1| 29 46 0 14 | 0 0 1 1 }}
: mapping generators: ~50/49, ~5


[[Optimal tuning]] ([[POTE]]): ~50/49 = 1\29, ~5/4 = 388.646
[[Optimal tuning]] ([[POTE]]): ~50/49 = 41.379{{c}}, ~5/4 = 388.646{{c}}


{{Optimal ET sequence|legend=1| 29, 58, 87, 145 }}
{{Optimal ET sequence|legend=1| 29, 58, 87, 145 }}


[[Badness]]: 0.103734
[[Badness]] (Smith): 0.103734


=== 11-limit ===
=== 11-limit ===
Line 275: Line 277:
Mapping: {{mapping| 29 46 0 14 33 | 0 0 1 1 1 }}
Mapping: {{mapping| 29 46 0 14 33 | 0 0 1 1 1 }}


Optimal tuning (POTE): ~45/44 = 1\29, ~5/4 = 388.460
Optimal tuning (POTE): ~45/44 = 41.379{{c}}, ~5/4 = 388.460{{c}}


{{Optimal ET sequence|legend=0| 29, 58, 87, 145 }}
{{Optimal ET sequence|legend=0| 29, 58, 87, 145 }}


Badness: 0.034291
Badness (Smith): 0.034291


=== 13-limit ===
=== 13-limit ===
Line 288: Line 290:
Mapping: {{mapping| 29 46 0 14 33 40 | 0 0 1 1 1 1 }}
Mapping: {{mapping| 29 46 0 14 33 40 | 0 0 1 1 1 1 }}


Optimal tuning (POTE): ~45/44 = 1\29, ~5/4 = 388.354
Optimal tuning (POTE): ~45/44 = 41.379{{c}}, ~5/4 = 388.354{{c}}


{{Optimal ET sequence|legend=0| 29, 58, 87, 145, 232, 377cef }}
{{Optimal ET sequence|legend=0| 29, 58, 87, 145, 232, 377cef }}


Badness: 0.018591
Badness (Smith): 0.018591


== Quanic ==
== Quanic ==
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{{Mapping|legend=1| 1 1 -4 0 | 0 5 54 24 }}
{{Mapping|legend=1| 1 1 -4 0 | 0 5 54 24 }}
: mapping generators: ~2, ~160/147


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~160/147 = 140.493
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~160/147 = 140.493{{c}}


{{Optimal ET sequence|legend=1| 94, 111, 205 }}
{{Optimal ET sequence|legend=1| 94, 111, 205 }}


[[Badness]]: 0.179475
[[Badness]] (Smith): 0.179475


=== 11-limit ===
=== 11-limit ===
Line 314: Line 317:
Mapping: {{mapping| 1 1 -4 0 1 | 0 5 54 24 21 }}
Mapping: {{mapping| 1 1 -4 0 1 | 0 5 54 24 21 }}


Optimal tuning (POTE): ~2 = 1\1, ~88/81 = 140.489
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~88/81 = 140.489{{c}}


{{Optimal ET sequence|legend=0| 94, 111, 205 }}
{{Optimal ET sequence|legend=0| 94, 111, 205 }}


Badness: 0.058678
Badness (Smith): 0.058678


=== 13-limit ===
=== 13-limit ===
Line 327: Line 330:
Mapping: {{mapping| 1 1 -4 0 1 3 | 0 5 54 24 21 6 }}
Mapping: {{mapping| 1 1 -4 0 1 3 | 0 5 54 24 21 6 }}


Optimal tuning (POTE): ~2 = 1\1, ~13/12 = 140.496
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~13/12 = 140.496{{c}}


{{Optimal ET sequence|legend=0| 94, 111, 205 }}
{{Optimal ET sequence|legend=0| 94, 111, 205 }}


Badness: 0.032481
Badness (Smith): 0.032481


=== 17-limit ===
=== 17-limit ===
Line 340: Line 343:
Mapping: {{mapping| 1 1 -4 0 1 3 -2 | 0 5 54 24 21 6 52 }}
Mapping: {{mapping| 1 1 -4 0 1 3 -2 | 0 5 54 24 21 6 52 }}


Optimal tuning (POTE): ~2 = 1\1, ~13/12 = 140.497
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~13/12 = 140.497{{c}}


{{Optimal ET sequence|legend=0| 94, 111, 205 }}
{{Optimal ET sequence|legend=0| 94, 111, 205 }}


Badness: 0.021112
Badness (Smith): 0.021112


=== 19-limit ===
=== 19-limit ===
Line 353: Line 356:
Mapping: {{mapping| 1 1 -4 0 1 3 -2 -5 | 0 5 54 24 21 6 52 79 }}
Mapping: {{mapping| 1 1 -4 0 1 3 -2 -5 | 0 5 54 24 21 6 52 79 }}


Optimal tuning (POTE): ~2 = 1\1, ~13/12 = 140.496
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~13/12 = 140.496{{c}}


{{Optimal ET sequence|legend=0| 94, 111, 205 }}
{{Optimal ET sequence|legend=0| 94, 111, 205 }}


Badness: 0.017273
Badness (Smith): 0.017273


== Septiquarter ==
== Septiquarter ==
Line 365: Line 368:


{{Mapping|legend=1| 1 3 10 2 | 0 -7 -38 4 }}
{{Mapping|legend=1| 1 3 10 2 | 0 -7 -38 4 }}
: mapping generators: ~2, ~147/128


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~147/128 = 242.453
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~147/128 = 242.453{{c}}


{{Optimal ET sequence|legend=1| 94, 99, 292, 391, 881bd, 1272bcd }}
{{Optimal ET sequence|legend=1| 94, 99, 292, 391, 881bd, 1272bcd }}


[[Badness]]: 0.053760
[[Badness]] (Smith): 0.053760


=== Semiseptiquarter ===
=== Semiseptiquarter ===
Line 379: Line 383:
Mapping: {{mapping| 2 6 20 4 15 | 0 -7 -38 4 -20 }}
Mapping: {{mapping| 2 6 20 4 15 | 0 -7 -38 4 -20 }}


Optimal tuning (POTE): ~2 = 1\1, ~121/105 = 242.4511
Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~121/105 = 242.4511{{c}}


{{Optimal ET sequence|legend=0| 94, 198, 292, 490 }}
{{Optimal ET sequence|legend=0| 94, 198, 292, 490 }}


Badness: 0.064160
Badness (Smith): 0.064160


==== 13-limit ====
==== 13-limit ====
Line 392: Line 396:
Mapping: {{mapping| 2 6 20 4 15 7 | 0 -7 -38 4 -20 1 }}
Mapping: {{mapping| 2 6 20 4 15 7 | 0 -7 -38 4 -20 1 }}


Optimal tuning (POTE): ~2 = 1\1, ~121/105 = 242.4448
Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~121/105 = 242.4448{{c}}


{{Optimal ET sequence|legend=0| 94, 198, 490f }}
{{Optimal ET sequence|legend=0| 94, 198, 490f }}


Badness: 0.034834
Badness (Smith): 0.034834


== Countriton ==
== Countriton ==
Line 406: Line 410:


{{Mapping|legend=1| 1 6 19 -7 | 0 -9 -34 20 }}
{{Mapping|legend=1| 1 6 19 -7 | 0 -9 -34 20 }}
: mapping generators: ~2, ~1728/1225


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~1728/1225 = 588.582
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~1728/1225 = 588.582{{c}}


{{Optimal ET sequence|legend=1| 53, 157, 210 }}
{{Optimal ET sequence|legend=1| 53, 157, 210 }}


[[Badness]]: 0.131191
[[Badness]] (Smith): 0.131191


=== 11-limit ===
=== 11-limit ===
Line 420: Line 425:
Mapping: {{mapping| 1 6 19 -7 27 | 0 -9 -34 20 -48 }}
Mapping: {{mapping| 1 6 19 -7 27 | 0 -9 -34 20 -48 }}


Optimal tuning (POTE): ~2 = 1\1, ~108/77 = 588.545
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~108/77 = 588.545{{c}}


{{Optimal ET sequence|legend=0| 53, 104c, 157 }}
{{Optimal ET sequence|legend=0| 53, 104c, 157 }}


Badness: 0.084782
Badness (Smith): 0.084782


=== 13-limit ===
=== 13-limit ===
Line 433: Line 438:
Mapping: {{mapping| 1 6 19 -7 27 14 | 0 -9 -34 20 -48 -21 }}
Mapping: {{mapping| 1 6 19 -7 27 14 | 0 -9 -34 20 -48 -21 }}


Optimal tuning (POTE): ~2 = 1\1, ~108/77 = 588.544
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~108/77 = 588.544{{c}}


{{Optimal ET sequence|legend=0| 53, 104c, 157 }}
{{Optimal ET sequence|legend=0| 53, 104c, 157 }}


Badness: 0.042321
Badness (Smith): 0.042321


== Artoneutral ==
== Artoneutral ==
Line 447: Line 452:


{{Mapping|legend=1| 1 8 18 -20 | 0 -9 -22 32 }}
{{Mapping|legend=1| 1 8 18 -20 | 0 -9 -22 32 }}
: mapping generators: ~2, ~105/64
: mapping generators: ~2, ~105/64


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~105/64 = 855.2452
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~105/64 = 855.2452{{c}}


{{Optimal ET sequence|legend=1| 87, 94, 181 }}
{{Optimal ET sequence|legend=1| 87, 94, 181 }}


[[Badness]]: 0.157120
[[Badness]] (Smith): 0.157120


=== 11-limit ===
=== 11-limit ===
Line 463: Line 467:
Mapping: {{mapping| 1 8 18 -20 17 | 0 -9 -22 32 -19 }}
Mapping: {{mapping| 1 8 18 -20 17 | 0 -9 -22 32 -19 }}


Optimal tuning (CTE): ~2 = 1\1, ~18/11 = 855.2397
Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~18/11 = 855.2397{{c}}


{{Optimal ET sequence|legend=0| 87, 181 }}
{{Optimal ET sequence|legend=0| 87, 181 }}


Badness: 0.045920
Badness (Smith): 0.045920


=== 13-limit ===
=== 13-limit ===
Line 476: Line 480:
Mapping: {{mapping| 1 8 18 -20 17 -2 | 0 -9 -22 32 -19 8 }}
Mapping: {{mapping| 1 8 18 -20 17 -2 | 0 -9 -22 32 -19 8 }}


Optimal tuning (CTE): ~2 = 1\1, ~18/11 = 855.2369
Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~18/11 = 855.2369{{c}}


{{Optimal ET sequence|legend=0| 87, 181 }}
{{Optimal ET sequence|legend=0| 87, 181 }}


Badness: 0.026257
Badness (Smith): 0.026257


=== 17-limit ===
=== 17-limit ===
Line 489: Line 493:
Mapping: {{mapping| 1 8 18 -20 17 -2 44 | 0 -9 -22 32 -19 8 -56 }}
Mapping: {{mapping| 1 8 18 -20 17 -2 44 | 0 -9 -22 32 -19 8 -56 }}


Optimal tuning (CTE): ~2 = 1\1, ~18/11 = 855.2495
Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~18/11 = 855.2495{{c}}


{{Optimal ET sequence|legend=0| 87, 94, 181 }}
{{Optimal ET sequence|legend=0| 87, 94, 181 }}


Badness: 0.022749
Badness (Smith): 0.022749


=== 19-limit ===
=== 19-limit ===
Line 502: Line 506:
Mapping: {{mapping| 1 8 18 -20 17 -2 44 52 | 0 -9 -22 32 -19 8 -56 -67 }}
Mapping: {{mapping| 1 8 18 -20 17 -2 44 52 | 0 -9 -22 32 -19 8 -56 -67 }}


Optimal tuning (CTE): ~2 = 1\1, ~18/11 = 855.2534
Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~18/11 = 855.2534{{c}}


{{Optimal ET sequence|legend=0| 87, 94, 181 }}
{{Optimal ET sequence|legend=0| 87, 94, 181 }}


Badness: 0.019585
Badness (Smith): 0.019585


=== 23-limit ===
=== 23-limit ===
Line 515: Line 519:
Mapping: {{mapping| 1 8 18 -20 17 -2 44 52 48 | 0 -9 -22 32 -19 8 -56 -67 -61 }}
Mapping: {{mapping| 1 8 18 -20 17 -2 44 52 48 | 0 -9 -22 32 -19 8 -56 -67 -61 }}


Optimal tuning (CTE): ~2 = 1\1, ~18/11 = 855.2576
Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~18/11 = 855.2576{{c}}


{{Optimal ET sequence|legend=0| 87, 94, 181 }}
{{Optimal ET sequence|legend=0| 87, 94, 181 }}


Badness: 0.016332
Badness (Smith): 0.016332


== Ketchup ==
== Ketchup ==
Line 528: Line 532:
{{Mapping|legend=1| 2 3 4 6 | 0 4 15 -9 }}
{{Mapping|legend=1| 2 3 4 6 | 0 4 15 -9 }}


[[Optimal tuning]] ([[POTE]]): ~1225/864 = 1\2, ~64/63 = 25.719
[[Optimal tuning]] ([[POTE]]): ~1225/864 = 600.000{{c}}, ~64/63 = 25.719{{c}}
: mapping generators: ~1225/864, ~64/63


{{Optimal ET sequence|legend=1| 46, 94, 140 }}
{{Optimal ET sequence|legend=1| 46, 94, 140 }}


[[Badness]]: 0.084538
[[Badness]] (Smith): 0.084538


=== 11-limit ===
=== 11-limit ===
Line 541: Line 546:
Mapping: {{mapping| 2 3 4 6 7 | 0 4 15 -9 -2 }}
Mapping: {{mapping| 2 3 4 6 7 | 0 4 15 -9 -2 }}


Optimal tuning (POTE): ~99/70 = 1\2, ~64/63 = 25.693
Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~64/63 = 25.693{{c}}


{{Optimal ET sequence|legend=0| 46, 94, 140 }}
{{Optimal ET sequence|legend=0| 46, 94, 140 }}


Badness: 0.039555
Badness (Smith): 0.039555


=== 13-limit ===
=== 13-limit ===
Line 554: Line 559:
Mapping: {{mapping| 2 3 4 6 7 8 | 0 4 15 -9 -2 -14 }}
Mapping: {{mapping| 2 3 4 6 7 8 | 0 4 15 -9 -2 -14 }}


Optimal tuning (POTE): ~99/70 = 1\2, ~66/65 = 25.697
Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~66/65 = 25.697{{c}}


{{Optimal ET sequence|legend=0| 46, 94, 140 }}
{{Optimal ET sequence|legend=0| 46, 94, 140 }}


Badness: 0.024824
Badness (Smith): 0.024824


=== 17-limit ===
=== 17-limit ===
Line 567: Line 572:
Mapping: {{mapping| 2 3 4 6 7 8 8 | 0 4 15 -9 -2 -14 4 }}
Mapping: {{mapping| 2 3 4 6 7 8 8 | 0 4 15 -9 -2 -14 4 }}


Optimal tuning (POTE): ~17/12 = 1\2, ~66/65 = 25.701
Optimal tuning (POTE): ~17/12 = 600.000{{c}}, ~66/65 = 25.701{{c}}


{{Optimal ET sequence|legend=0| 46, 94, 140 }}
{{Optimal ET sequence|legend=0| 46, 94, 140 }}


Badness: 0.016591
Badness (Smith): 0.016591


=== 19-limit ===
=== 19-limit ===
Line 580: Line 585:
Mapping: {{mapping| 2 3 4 6 7 8 8 9 | 0 4 15 -9 -2 -14 4 -12 }}
Mapping: {{mapping| 2 3 4 6 7 8 8 9 | 0 4 15 -9 -2 -14 4 -12 }}


Optimal tuning (POTE): ~17/12 = 1\2, ~66/65 = 25.660
Optimal tuning (POTE): ~17/12 = 600.000{{c}}, ~66/65 = 25.660{{c}}


{{Optimal ET sequence|legend=0| 46, 94, 140h, 234eh }}
{{Optimal ET sequence|legend=0| 46, 94, 140h, 234eh }}


Badness: 0.018170
Badness (Smith): 0.018170


=== 23-limit ===
=== 23-limit ===
Line 593: Line 598:
Mapping: {{mapping| 2 3 4 6 7 8 8 9 9 | 0 4 15 -9 -2 -14 4 -12 1 }}
Mapping: {{mapping| 2 3 4 6 7 8 8 9 9 | 0 4 15 -9 -2 -14 4 -12 1 }}


Optimal tuning (POTE): ~17/12 = 1\2, ~66/65 = 25.661
Optimal tuning (POTE): ~17/12 = 600.000{{c}}, ~66/65 = 25.661{{c}}


{{Optimal ET sequence|legend=0| 46, 94, 140h, 234ehi }}
{{Optimal ET sequence|legend=0| 46, 94, 140h, 234ehi }}


Badness: 0.014033
Badness (Smith): 0.014033


[[Category:Temperament collections]]
[[Category:Temperament collections]]
Retrieved from "https://en.xen.wiki/w/Aberschismic_temperaments"