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Aberschismic temperaments: Difference between revisions

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Temperaments belonging to this category and generated by the fifth are dominant, garibaldi, kwai, undecental, and leapday. Dominant has 5/4 mapped to M3. Garibaldi has 5/4 mapped to d4. Kwai has 5/4 mapped to 4A7. Undecental has 5/4 mapped to 5d7. Leapday has 5/4 mapped to 3A1.  
Temperaments belonging to this category and generated by the fifth are dominant, garibaldi, kwai, undecental, and leapday. Dominant has 5/4 mapped to M3. Garibaldi has 5/4 mapped to d4. Kwai has 5/4 mapped to 4A7. Undecental has 5/4 mapped to 5d7. Leapday has 5/4 mapped to 3A1.  


Diaschismic is generated by the fifth with a semi-octave period. Hemififths has the fifth sliced into two and 5/4 mapped to the hemififth + Pyth. comma. Rodan has the fifth sliced into three as does slendric. Trimot has the twelfth sliced into three as does tricot. Monkey has the fifth sliced into four as does tetracot. Buzzard has the twelfth sliced into four as does vulture. Misty is generated by the fifth with a 1/3-octave period. Supers has the fifth sliced into three with a semi-octave period. Undim is generated by the fifth with a 1/4-octave period. Quinticosiennic and quintakwai have the fourth sliced into five. Amity has the eleventh sliced into five. Countercata has the twelfth sliced into six as does hanson. Warrior has the 6th harmonic sliced into seven as does sensi. Finally, alphaquarter has the fourth sliced into nine as does escapade.  
Diaschismic is generated by the fifth with a semi-octave period. Hemififths has the fifth sliced into two and 5/4 mapped to the hemififth + Pyth. comma. Hemidromeda has the fourth sliced into two and 5/4 mapped to the hemifourth + 3d4. Rodan has the fifth sliced into three as does slendric. Trimot has the twelfth sliced into three as does tricot. Monkey has the fifth sliced into four as does tetracot. Buzzard has the twelfth sliced into four as does vulture. Misty is generated by the fifth with a 1/3-octave period. Supers has the fifth sliced into three with a semi-octave period. Undim is generated by the fifth with a 1/4-octave period. Quinticosiennic and quintakwai have the fourth sliced into five. Amity has the eleventh sliced into five. Countercata has the twelfth sliced into six as does hanson. Warrior has the 6th harmonic sliced into seven as does sensi. Finally, alphaquarter has the fourth sliced into nine as does escapade.  


Temperaments considered below are undecental, leapday, mystery, quanic, septiquarter, countriton, ketchup, and artoneutral. Discussed elsewhere are:
Temperaments considered below are undecental, leapday, hemidromeda, mystery, quanic, septiquarter, countriton, artoneutral and ketchup. Discussed elsewhere are:
* ''[[Dominant]]'' (+36/35) → [[Meantone family #Dominant|Meantone family]]
* ''[[Dominant]]'' (+36/35) → [[Meantone family #Dominant|Meantone family]]
* [[Garibaldi]] (+225/224) → [[Schismatic family #Garibaldi|Schismatic family]]
* [[Garibaldi]] (+225/224) → [[Schismatic family #Garibaldi|Schismatic family]]
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Badness: 0.016067
Badness: 0.016067
== Hemidromeda ==
The name ''hemidromeda'' comes from "hemi-" (Ancient Greek for "one half") and "[[Wikipedia:Andromeda|Andromeda]]", because the generator is 1/2 of the [[Schismatic family #Garibaldi|andromeda]] fourth (~4/3, about 497.6 cents).
[[Subgroup]]: 2.3.5.7
[[Comma list]]: 5120/5103, 52734375/52706752
{{Mapping|legend=1| 1 0 38 48 | 0 2 -45 -57 }}
: Mapping generator: ~2, ~12500/7203
{{Multival|legend=1| 2 -45 -57 -76 -96 -6 }}
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~7203/6250 = 248.581
{{Optimal ET sequence|legend=1| 29, 82cd, 111, 140, 531, 671, 811b, 951b }}
[[Badness]]: 0.115803
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 1331/1323, 1375/1372, 5120/5103
Mapping: {{mapping| 1 0 38 48 32 | 0 2 -45 -57 -36 }}
Optimal tuning (CTE): ~2 = 1\1, ~405/352 = 248.589
Optimal ET sequence: {{Optimal ET sequence| 29, 82cd, 111, 140, 251, 391e }}
Badness: 0.060808
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 676/675, 847/845, 1331/1323
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 ET sequence: {{Optimal ET sequence| 29, 82cdf, 111, 140, 391e, 531e }}
Badness: 0.028632
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
Comma list: 352/351, 442/441, 561/560, 676/675, 715/714
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 ET sequence: {{Optimal ET sequence| 29g, 82cdfg, 111, 140, 251, 391e }}
Badness: 0.019054
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 286/285, 352/351, 363/361, 442/441, 476/475, 561/560
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 ET sequence: {{Optimal ET sequence| 29g, 82cdfgh, 111, 140, 391ehh, 531ehh }}
Badness: 0.016609
=== 23-limit ===
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 253/252, 286/285, 352/351, 363/361, 391/390, 442/441, 460/459
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 ET sequence: {{Optimal ET sequence| 29g, 82cdfgh, 111, 140, 391ehhi, 531ehhii }}
Badness: 0.015361


== Mystery ==
== Mystery ==
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Optimal tuning (POTE): ~2 = 1\1, ~108/77 = 588.545
Optimal tuning (POTE): ~2 = 1\1, ~108/77 = 588.545


{{Optimal ET sequence|legend=1| 53, 104c, 157 }}
Optimal ET sequence: {{Optimal ET sequence| 53, 104c, 157 }}


Badness: 0.084782
Badness: 0.084782
Line 344: Line 428:
Optimal tuning (POTE): ~2 = 1\1, ~108/77 = 588.544
Optimal tuning (POTE): ~2 = 1\1, ~108/77 = 588.544


{{Optimal ET sequence|legend=1| 53, 104c, 157 }}
Optimal ET sequence: {{Optimal ET sequence| 53, 104c, 157 }}


Badness: 0.042321
Badness: 0.042321


== Ketchup ==
== Artoneutral ==
Artoneutral is generated by an artoneutral third of ~11/9 (or a tendoneutral sixth of ~18/11) and can be described as the 87 & 94 temperament. [[181edo]] is a recommendable tuning.
 
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 5120/5103, 1071875/1062882
[[Comma list]]: 5120/5103, 3828125/3779136


{{Mapping|legend=1| 2 3 4 6 | 0 4 15 -9 }}
{{Mapping|legend=1| 1 8 18 -20 | 0 -9 -22 32 }}


{{Multival|legend=1| 8 30 -18 29 -51 -126 }}
: mapping generators: ~2, ~105/64


[[Optimal tuning]] ([[POTE]]): ~1225/864 = 1\2, ~64/63 = 25.719
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~105/64 = 855.2452


{{Optimal ET sequence|legend=1| 46, 94, 140 }}
{{Optimal ET sequence|legend=1| 87, 94, 181 }}


[[Badness]]: 0.084538
[[Badness]]: 0.157120


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


Comma list: 385/384, 1331/1323, 2200/2187
Comma list: 385/384, 2200/2187, 4000/3993


Mapping: {{mapping| 2 3 4 6 7 | 0 4 15 -9 -2 }}
Mapping: {{mapping| 1 8 18 -20 17 | 0 -9 -22 32 -19 }}


Optimal tuning (POTE): ~99/70 = 1\2, ~64/63 = 25.693
Optimal tuning (CTE): ~2 = 1\1, ~18/11 = 855.2397


{{Optimal ET sequence|legend=1| 46, 94, 140 }}
Optimal ET sequence: {{Optimal ET sequence| 87, 181 }}


Badness: 0.039555
Badness: 0.045920


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


Comma list: 325/324, 352/351, 385/384, 1331/1323
Comma list: 325/324, 352/351, 385/384, 1575/1573


Mapping: {{mapping| 2 3 4 6 7 8 | 0 4 15 -9 -2 -14 }}
Mapping: {{mapping| 1 8 18 -20 17 -2 | 0 -9 -22 32 -19 8 }}


Optimal tuning (POTE): ~99/70 = 1\2, ~66/65 = 25.697
Optimal tuning (CTE): ~2 = 1\1, ~18/11 = 855.2369


{{Optimal ET sequence|legend=1| 46, 94, 140 }}
Optimal ET sequence: {{Optimal ET sequence| 87, 181 }}


Badness: 0.024824
Badness: 0.026257


=== 17-limit ===
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Comma list: 289/288, 325/324, 352/351, 385/384, 561/560
Comma list: 325/324, 352/351, 375/374, 385/384, 595/594


Mapping: {{mapping| 2 3 4 6 7 8 8 | 0 4 15 -9 -2 -14 4 }}
Mapping: {{mapping| 1 8 18 -20 17 -2 44 | 0 -9 -22 32 -19 8 -56 }}


Optimal tuning (POTE): ~17/12 = 1\2, ~66/65 = 25.701
Optimal tuning (CTE): ~2 = 1\1, ~18/11 = 855.2495


{{Optimal ET sequence|legend=1| 46, 94, 140 }}
Optimal ET sequence: {{Optimal ET sequence| 87, 94, 181 }}


Badness: 0.016591
Badness: 0.022749


=== 19-limit ===
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.17.19


Comma list: 190/189, 209/208, 289/288, 352/351, 385/384, 561/560
Comma list: 325/324, 352/351, 375/374, 385/384, 400/399, 595/594


Mapping: {{mapping| 2 3 4 6 7 8 8 9 | 0 4 15 -9 -2 -14 4 -12 }}
Mapping: {{mapping| 1 8 18 -20 17 -2 44 52 | 0 -9 -22 32 -19 8 -56 -67 }}


Optimal tuning (POTE): ~17/12 = 1\2, ~66/65 = 25.660
Optimal tuning (CTE): ~2 = 1\1, ~18/11 = 855.2534


{{Optimal ET sequence|legend=1| 46, 94, 140h, 234eh }}
Optimal ET sequence: {{Optimal ET sequence| 87, 94, 181 }}


Badness: 0.018170
Badness: 0.019585


=== 23-limit ===
=== 23-limit ===
Subgroup: 2.3.5.7.11.13.17.19.23
Subgroup: 2.3.5.7.11.13.17.19.23


Comma list: 190/189, 209/208, 253/252, 289/288, 323/322, 352/351, 385/384
Comma list: 300/299, 325/324, 352/351, 375/374, 385/384, 400/399, 484/483


Mapping: {{mapping| 2 3 4 6 7 8 8 9 9 | 0 4 15 -9 -2 -14 4 -12 1 }}
Mapping: {{mapping| 1 8 18 -20 17 -2 44 52 48 | 0 -9 -22 32 -19 8 -56 -67 -61 }}


Optimal tuning (POTE): ~17/12 = 1\2, ~66/65 = 25.661
Optimal tuning (CTE): ~2 = 1\1, ~18/11 = 855.2576
 
{{Optimal ET sequence|legend=1| 46, 94, 140h, 234ehi }}


Badness: 0.014033
Optimal ET sequence: {{Optimal ET sequence| 87, 94, 181 }}


== Artoneutral ==
Badness: 0.016332
Artoneutral is generated by an artoneutral third of ~11/9 (or a tendoneutral sixth of ~18/11) and can be described as the 87 & 94 temperament. [[181edo]] is a recommendable tuning.  


== Ketchup ==
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 5120/5103, 3828125/3779136
[[Comma list]]: 5120/5103, 1071875/1062882


{{Mapping|legend=1| 1 8 18 -20 | 0 -9 -22 32 }}
{{Mapping|legend=1| 2 3 4 6 | 0 4 15 -9 }}


: mapping generators: ~2, ~105/64
{{Multival|legend=1| 8 30 -18 29 -51 -126 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~105/64 = 855.2452
[[Optimal tuning]] ([[POTE]]): ~1225/864 = 1\2, ~64/63 = 25.719


{{Optimal ET sequence|legend=1| 87, 94, 181 }}
{{Optimal ET sequence|legend=1| 46, 94, 140 }}


[[Badness]]: 0.157
[[Badness]]: 0.084538


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


Comma list: 385/384, 2200/2187, 4000/3993
Comma list: 385/384, 1331/1323, 2200/2187


Mapping: {{mapping| 1 8 18 -20 17 | 0 -9 -22 32 -19 }}
Mapping: {{mapping| 2 3 4 6 7 | 0 4 15 -9 -2 }}


Optimal tuning (CTE): ~2 = 1\1, ~18/11 = 855.2397
Optimal tuning (POTE): ~99/70 = 1\2, ~64/63 = 25.693


{{Optimal ET sequence|legend=1| 87, 181 }}
Optimal ET sequence: {{Optimal ET sequence| 46, 94, 140 }}


Badness: 0.0459
Badness: 0.039555


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


Comma list: 325/324, 352/351, 385/384, 1575/1573
Comma list: 325/324, 352/351, 385/384, 1331/1323


Mapping: {{mapping| 1 8 18 -20 17 -2 | 0 -9 -22 32 -19 8 }}
Mapping: {{mapping| 2 3 4 6 7 8 | 0 4 15 -9 -2 -14 }}


Optimal tuning (CTE): ~2 = 1\1, ~18/11 = 855.2369
Optimal tuning (POTE): ~99/70 = 1\2, ~66/65 = 25.697


{{Optimal ET sequence|legend=1| 87, 181 }}
Optimal ET sequence: {{Optimal ET sequence| 46, 94, 140 }}


Badness: 0.0263
Badness: 0.024824


=== 17-limit ===
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Comma list: 325/324, 352/351, 375/374, 385/384, 595/594
Comma list: 289/288, 325/324, 352/351, 385/384, 561/560


Mapping: {{mapping| 1 8 18 -20 17 -2 44 | 0 -9 -22 32 -19 8 -56 }}
Mapping: {{mapping| 2 3 4 6 7 8 8 | 0 4 15 -9 -2 -14 4 }}


Optimal tuning (CTE): ~2 = 1\1, ~18/11 = 855.2495
Optimal tuning (POTE): ~17/12 = 1\2, ~66/65 = 25.701


{{Optimal ET sequence|legend=1| 87, 94, 181 }}
Optimal ET sequence: {{Optimal ET sequence| 46, 94, 140 }}


Badness: 0.0227
Badness: 0.016591


=== 19-limit ===
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.17.19


Comma list: 325/324, 352/351, 375/374, 385/384, 400/399, 595/594
Comma list: 190/189, 209/208, 289/288, 352/351, 385/384, 561/560


Mapping: {{mapping| 1 8 18 -20 17 -2 44 52 | 0 -9 -22 32 -19 8 -56 -67 }}
Mapping: {{mapping| 2 3 4 6 7 8 8 9 | 0 4 15 -9 -2 -14 4 -12 }}


Optimal tuning (CTE): ~2 = 1\1, ~18/11 = 855.2534
Optimal tuning (POTE): ~17/12 = 1\2, ~66/65 = 25.660


{{Optimal ET sequence|legend=1| 87, 94, 181 }}
Optimal ET sequence: {{Optimal ET sequence| 46, 94, 140h, 234eh }}


Badness: 0.0196
Badness: 0.018170


=== 23-limit ===
=== 23-limit ===
Subgroup: 2.3.5.7.11.13.17.19.23
Subgroup: 2.3.5.7.11.13.17.19.23


Comma list: 300/299, 325/324, 352/351, 375/374, 385/384, 400/399, 484/483
Comma list: 190/189, 209/208, 253/252, 289/288, 323/322, 352/351, 385/384


Mapping: {{mapping| 1 8 18 -20 17 -2 44 52 48 | 0 -9 -22 32 -19 8 -56 -67 -61 }}
Mapping: {{mapping| 2 3 4 6 7 8 8 9 9 | 0 4 15 -9 -2 -14 4 -12 1 }}


Optimal tuning (CTE): ~2 = 1\1, ~18/11 = 855.2576
Optimal tuning (POTE): ~17/12 = 1\2, ~66/65 = 25.661


{{Optimal ET sequence|legend=1| 87, 94, 181 }}
Optimal ET sequence: {{Optimal ET sequence| 46, 94, 140h, 234ehi }}


Badness: 0.0163
Badness: 0.014033


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