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__FORCETOC__
{{Technical data page}}
This is a collection of [[rank-2 temperament|rank-2]] '''aberschismic temperaments''', which [[tempering out|temper out]] the [[aberschisma]] ({{monzo|legend=1| 10 -6 1 -1 }}, [[ratio]]: 5120/5103). These temperaments divide an exact or approximate septimal quartertone, [[36/35]] into two equal steps, each representing [[81/80]][[~]][[64/63]], the syntonic comma or the septimal comma. Therefore, classical and septimal intervals are found by the same [[chain of fifths]] inflected by the syntonic~septimal comma to the opposite sides. In addition we may identify [[10/7]] by the augmented fourth and [[50/49]] by the [[Pythagorean comma]].


The hemifamity temperaments temper out the hemifamity comma, {{monzo| 10 -6 1 -1 }} = [[5120/5103]], dividing an exact or approximate septimal diesis, {{monzo| 2 2 -1 -1 }} = [[36/35]] into two equal steps. Belonging to it and considered below are buzzard, undecental, leapday, mystery, quanic and ketchup. Other hemifamity temperaments are [[Meantone family #Dominant|dominant]], [[Schismatic family #Garibaldi|garibaldi]], [[Breedsmic temperaments #Hemififths|hemififths]], [[Ragismic microtemperaments #Amity|amity]], [[Hemimean clan #Misty|misty]], [[Gamelismic clan #Rodan|rodan]], [[Kleismic family #Countercata|countercata]] and [[Mirkwai clan #Kwai|kwai]].
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.  


=Buzzard=
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. Alphatrimot has the twelfth sliced into three as does alphatricot. 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.
Commas: 1728/1715, 5120/5103


[[POTE_tuning|POTE generator]]: ~320/243 = 475.636
Temperaments discussed elsewhere are:
* [[Dominant (temperament)|Dominant]] (+36/35) → [[Meantone family #Dominant|Meantone family]]
* [[Garibaldi]] (+225/224) → [[Schismatic family #Garibaldi|Schismatic family]]
* [[Leapday]] (+686/675) → [[Sengic temperaments #Leapday|Sengic temperaments]]
* [[Diaschismic]] (+126/125) → [[Diaschismic family #Septimal diaschismic|Diaschismic family]]
* [[Hemififths]] (+2401/2400) → [[Breedsmic temperaments #Hemififths|Breedsmic temperaments]]
* [[Rodan]] (+245/243) → [[Gamelismic clan #Rodan|Gamelismic clan]]
* ''[[Alphatrimot]]'' (+2430/2401) → [[Alphatricot family #Alphatrimot|Alphatricot family]]
* [[Misty]] (+3136/3125) → [[Misty family #Misty|Misty family]]
* [[Monkey]] (+875/864) → [[Tetracot family #Monkey|Tetracot family]]
* [[Buzzard]] (+1728/1715) → [[Buzzardsmic clan #Buzzard|Buzzardsmic clan]]
* ''[[Undim]]'' (+390625/388962) → [[Undim family #Septimal undim|Undim family]]
* ''[[Quinticosiennic]]'' (+395136/390625) → [[Quintaleap family #Quinticosiennic|Quintaleap family]]
* ''[[Quintakwai]]'' (+9765625/9680832) → [[Quindromeda family #Quintakwai|Quindromeda family]]
* [[Amity]] (+4375/4374) → [[Amity family #Septimal amity|Amity family]]
* ''[[Countercata]]'' (+15625/15552) → [[Kleismic family #Countercata|Kleismic family]]
* ''[[Abergravity]]'' (+177147/175000) → [[Gravity family #Abergravity|Gravity family]]
* ''[[Supers]]'' (+118098/117649) → [[Stearnsmic clan #Supers|Stearnsmic clan]]
* ''[[Warrior]]'' (+78732/78125) → [[Sensipent family #Warrior|Sensipent family]]
* ''[[Alphaquarter]]'' (+29360128/29296875) → [[Escapade family #Alphaquarter|Escapade family]]


Map: [<1 0 -6 4|, <0 4 21 -3|]
Considered below are septiquarter, kwai, ketchup, undecental, mystery, hemidromeda, countriton, artoneutral, quanic and jorgensen, in the order of increasing [[TE logflat badness]].


Wedgie: <<4 21 -3 24 -16 -66||
== Septiquarter ==
Septiquarter tempers out [[420175/419904]] and may be described as the {{nowrap| 94 & 99 }} temperament. Its [[ploidacot]] is epsilon-heptacot. [[99edo]] makes for an excellent tuning, and [[292edo]] an even better one. [[94edo]] and [[104edo]] in the 104c val are also among the possibilities.


EDOs: 48, 53, 111, 164d, 275d
[[Subgroup]]: 2.3.5.7


Badness: 0.0480
[[Comma list]]: 5120/5103, 420175/419904


==11-limit==
{{Mapping|legend=1| 1 -4 -28 6 | 0 7 38 -4 }}
Commas: 176/175, 540/539, 5120/5103
: mapping generators: ~2, ~243/140


[[POTE_tuning|POTE generator]]: ~320/243 = 475.700
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.7212{{c}}, ~243/140 = 957.3250{{c}}
: [[error map]]: {{val| -0.279 +0.435 -0.158 +0.201 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~243/140 = 957.5424{{c}}
: error map: {{val| 0.000 +0.842 +0.298 +1.004 }}


Map: [<1 0 -6 4 -12|, <0 4 21 -3 39|]
{{Optimal ET sequence|legend=1| 94, 99, 292, 391, 881bd, 1272bcd }}


EDOs: 53, 58, 111, 280cd, 391cd
[[Badness]] (Sintel): 1.36


Badness: 0.0345
=== Semiseptiquarter ===
Subgroup: 2.3.5.7.11


==13-limit==
Comma list: 5120/5103, 9801/9800, 14641/14580
Commas: 176/175, 351/350, 540/539, 676/675


[[POTE_tuning|POTE generator]]: ~320/243 = 475.697
Mapping: {{mapping| 2 -8 -56 12 -25 | 0 7 38 -4 20 }}


Map: [<1 0 -6 4 -12 -7|, <0 4 21 -3 39 27|]
Optimal tunings:  
* WE: ~99/70 = 599.8953{{c}}, ~210/121 = 957.3819{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~210/121 = 957.5449{{c}}


EDOs: 53, 58, 111, 280cdf, 391cdf
{{Optimal ET sequence|legend=0| 94, 198, 292, 490 }}


Badness: 0.0188
Badness (Sintel): 2.12


==17-limit==
==== 13-limit ====
Commas: 176/175, 256/255, 351/350, 442/441, 540/539
Subgroup: 2.3.5.7.11.13


[[POTE_tuning|POTE generator]]: ~320/243 = 475.692
Comma list: 352/351, 847/845, 1716/1715, 14641/14580


Map: [<1 0 -6 4 -12 -7 14|, <0 4 21 -3 39 27 -25|]
Mapping: {{mapping| 2 -8 -56 12 -25 9 | 0 7 38 -4 20 -1 }}


EDOs: 53, 58, 111, 321cdfg
Optimal tunings:  
* WE: ~99/70 = 599.8565{{c}}, ~210/121 = 957.3261{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~210/121 = 957.5508{{c}}


Badness: 0.0184
{{Optimal ET sequence|legend=0| 94, 198, 490f }}


==19-limit==
Badness (Sintel): 1.44
Commas: 176/175, 256/255, 286/285, 324/323, 351/350, 540/539


[[POTE_tuning|POTE generator]]: ~320/243 = 475.679
== Kwai ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Kwai]].''


Map: [<1 0 -6 4 -12 -7 14 -12|, <0 4 21 -3 39 27 -25 41|]
Named by [[Gene Ward Smith]] in 2004 for its "bridgeability"<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10766.html Yahoo! Tuning Group | ''Kwai'']</ref>, kwai is generated by a [[3/2|perfect fifth]], and can be described as {{nowrap| 41 & 70 }}.


EDOs: 53, 58h, 111
[[Subgroup]]: 2.3.5.7


Badness: 0.0156
[[Comma list]]: 5120/5103, 16875/16807


==Buteo==
{{Mapping|legend=1| 1 0 -50 -40 | 0 1 33 27 }}
Commas: 99/98, 385/384, 2200/2187
: mapping generators: ~2, ~3


POTE generator: ~21/16 = 475.436
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1199.7337{{c}}, ~3/2 = 702.4600{{c}}
: [[error map]]: {{val| -0.266 +0.239 -0.607 +1.055 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.6085{{c}}
: error map: {{val| 0.000 +0.653 -0.234 +1.603 }}


Map: [&lt;1 0 -6 4 9|, &lt;0 4 21 -3 -14|]
{{Optimal ET sequence|legend=1| 41, 111, 152, 345, 497d }}


EDOs: 5, 48, 53
[[Badness]] (Sintel): 1.38


Badness: 0.0602
=== 11-limit ===
Subgroup: 2.3.5.7.11


===13-limit===
Comma list: 540/539, 1375/1372, 5120/5103
Commas: 99/98, 275/273, 385/384, 572/567


POTE generator: ~21/16 = 475.464
Mapping: {{mapping| 1 0 -50 -40 32 | 0 1 33 27 -18 }}


Map: [&lt;1 0 -6 4 9 -7|, &lt;0 4 21 -3 -14 27|]
Optimal tunings:  
* WE: ~2 = 1199.6672{{c}}, ~3/2 = 702.4282{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.6189{{c}}


EDOs: 5, 53
{{Optimal ET sequence|legend=0| 41, 111, 152, 497de, 649dde }}


Badness: 0.0390
Badness (Sintel): 0.867


=Undecental=
==== 13-limit ====
Commas: 5120/5103, 235298/234375
Subgroup: 2.3.5.7.11.13


[[POTE_tuning|POTE generator]]: ~3/2 = 703.039
Comma list: 352/351, 540/539, 729/728, 1375/1372


Map: [&lt;1 0 61 71|, &lt;0 1 -37 -43|]
Mapping: {{mapping| 1 0 -50 -40 32 27 | 0 1 33 27 -18 -21 }}


Wedgie: &lt;&lt;1 -37 -43 -61 -71 4||
Optimal tunings:  
* WE: ~2 = 1199.4772{{c}}, ~3/2 = 702.3379{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.6409{{c}}


EDOs: 12, 29, 70, 99
{{Optimal ET sequence|legend=0| 41, 111, 152f, 415dff }}


=Leapday=
Badness (Sintel): 1.01
Comma: 10737418240/10460353203


POTE generator: ~3/2 = 704.179
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17


Map: [&lt;1 0 -31|, &lt;0 1 21|]
Comma list: 256/255, 352/351, 540/539, 715/714, 1089/1088


EDOs: 29, 46, 121, 167, 455bc, 622bc
Mapping: {{mapping| 1 0 -50 -40 32 27 58 | 0 1 33 27 -18 -21 -34 }}


Badness: 0.5232
Optimal tunings:  
* WE: ~2 = 1199.3537{{c}}, ~3/2 = 702.2850{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.6589{{c}}


==7-limit==
{{Optimal ET sequence|legend=0| 41, 70, 111, 152fg, 263dfg }}
Commas: 686/675, 5120/5103


[[POTE_tuning|POTE generator]]: ~3/2 = 704.263
Badness (Sintel): 1.12


Map: [&lt;1 0 -31 -21|, &lt;0 1 21 15|]
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19


Wedgie: &lt;&lt;1 21 15 31 21 -24||
Comma list: 256/255, 352/351, 400/399, 456/455, 715/714, 847/845


EDOs: 29, 46, 305
Mapping: {{mapping| 1 0 -50 -40 32 27 58 -56 | 0 1 33 27 -18 -21 -34 38 }}


Badness: 0.0961
Optimal tunings:  
* WE: ~2 = 1199.3401{{c}}, ~3/2 = 702.2705{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.6548{{c}}


==11-limit==
{{Optimal ET sequence|legend=0| 41, 70h, 111, 152fg, 263dfgh }}
Commas: 121/120, 441/440, 686/675


[[POTE_tuning|POTE generator]]: ~3/2 = 704.250
Badness (Sintel): 1.03


Map: [&lt;1 0 -31 -21 -14|, &lt;0 1 21 15 11|]
==== Hemikwai ====
Subgroup: 2.3.5.7.11.13


EDOs: 29, 46, 259
Comma list: 540/539, 676/675, 1375/1372, 5120/5103


Badness: 0.0386
Mapping: {{mapping| 1 0 -50 -40 32 -51 | 0 2 66 54 -36 69 }}
: mapping generators: ~2, ~26/15


==13-limit==
Optimal tunings:
Commas: 91/90, 121/120, 169/168, 441/440
* WE: ~2 = 1199.6968{{c}}, ~26/15 = 951.0740{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 951.3123{{c}}


[[POTE_tuning|POTE generator]]: ~3/2 = 704.214
{{Optimal ET sequence|legend=0| 82, 111, 193, 304d }}


Map: [&lt;1 0 -31 -21 -14 -9|, &lt;0 1 21 15 11 8|]
Badness (Sintel): 1.82


EDOs: 29, 46, 167, 213, 380
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17


Badness: 0.0247
Comma list: 442/441, 540/539, 676/675, 715/714, 5120/5103


==17-limit==
Mapping: {{mapping| 1 0 -50 -40 32 -51 -30 | 0 2 66 54 -36 69 43 }}
Commas: 91/90, 121/120, 136/135, 154/153, 169/168


[[POTE_tuning|POTE generator]]: ~3/2 = 704.229
Optimal tunings:
* WE: ~2 = 1199.6861{{c}}, ~26/15 = 951.0654{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 951.3120{{c}}


[&lt;1 0 -31 -21 -14 -9 -34|, &lt;0 1 21 15 11 8 24|]
{{Optimal ET sequence|legend=0| 82, 111, 193, 304d }}


EDOs: 29g, 46, 121defg, 167defg, 213defg
Badness (Sintel): 1.31


Badness: 0.0179
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19


==19-limit==
Comma list: 400/399, 442/441, 540/539, 676/675, 715/714, 1445/1444
Commas: 91/90, 121/120, 133/132, 136/135, 154/153, 169/168


[[POTE_tuning|POTE generator]]: ~3/2 = 704.135
Mapping: {{mapping| 1 0 -50 -40 32 -51 -30 -56 | 0 2 66 54 -36 69 43 76 }}


Map: [&lt;1 0 -31 -21 -14 -9 -34 9|, &lt;0 1 21 15 11 8 24 -3|]
Optimal tunings:  
* WE: ~2 = 1199.6718{{c}}, ~26/15 = 951.0526{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 951.3103{{c}}


EDOs: 29g, 46, 75dfgh, 121defgh
{{Optimal ET sequence|legend=0| 82, 111, 193, 304dh }}


Badness: 0.0174
Badness (Sintel): 1.16


===Leapling===
== Ketchup ==
Commas: 77/76, 91/90, 121/120, 136/135, 153/152, 169/168
Ketchup may be described as the {{nowrap| 46 & 94 }} temperament. It has a semi-octave period and a generator for a syntonic~septimal comma, four of which plus a period gives the perfect fifth; its [[ploidacot]] is diploid gamma-tetracot. [[140edo]] is an obvious tuning for this temperament.


[[POTE_tuning|POTE generator]]: ~3/2 = 704.123
[[Subgroup]]: 2.3.5.7


Map: [&lt;1 0 -31 -21 -14 -9 -34 -37|, &lt;0 1 21 15 11 8 24 26|]
[[Comma list]]: 5120/5103, 1071875/1062882
 
{{Mapping|legend=1| 2 3 4 6 | 0 4 15 -9 }}
: mapping generators: ~1225/864, ~64/63
 
[[Optimal tuning]]s:
* [[WE]]: ~1225/864 = 599.9685{{c}}, ~64/63 = 25.7181{{c}}
: [[error map]]: {{val| -0.063 +0.823 -0.668 -0.478 }}
* [[CWE]]: ~1225/864 = 600.0000{{c}}, ~64/63 = 25.7181{{c}}
: error map: {{val| 0.000 +0.917 -0.543 -0.288 }}
 
{{Optimal ET sequence|legend=1| 46, 94, 140 }}
 
[[Badness]] (Sintel): 2.14
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 385/384, 1331/1323, 2200/2187
 
Mapping: {{mapping| 2 3 4 6 7 | 0 4 15 -9 -2 }}
 
Optimal tunings:
* WE: ~99/70 = 600.0678{{c}}, ~64/63 = 25.6963{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~64/63 = 25.6956{{c}}
 
{{Optimal ET sequence|legend=0| 46, 94, 140 }}
 
Badness (Sintel): 1.31
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


EDOs: 29g, 46h, 75dfg
Comma list: 325/324, 352/351, 385/384, 1331/1323


Badness: 0.0191
Mapping: {{mapping| 2 3 4 6 7 8 | 0 4 15 -9 -2 -14 }}


=Mystery=
Optimal tunings:
Commas: 5120/5103, 50421/50000
* WE: ~99/70 = 600.0612{{c}}, ~66/65 = 25.7000{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~66/65 = 25.6978{{c}}


[[POTE_tuning|POTE generator]]: ~5/4 = 388.646
{{Optimal ET sequence|legend=0| 46, 94, 140 }}


Map: [&lt;29 46 0 14|, &lt;0 0 1 1|]
Badness (Sintel): 1.03


Wedgie: &lt;&lt;0 29 29 46 46 -14||
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17


EDOs: 29, 58, 87, 145
Comma list: 289/288, 325/324, 352/351, 385/384, 442/441


Badness: 0.1037
Mapping: {{mapping| 2 3 4 6 7 8 8 | 0 4 15 -9 -2 -14 4 }}


==11-limit==
Optimal tunings:
Commas: 441/440, 896/891, 3388/3375
* WE: ~17/12 = 600.0896{{c}}, ~66/65 = 25.7048{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~66/65 = 25.7017{{c}}


[[POTE_tuning|POTE generator]]: ~5/4 = 388.460
{{Optimal ET sequence|legend=0| 46, 94, 140 }}


Map: [&lt;29 46 0 14 33|, &lt;0 0 1 1 1|]
Badness (Sintel): 0.845


EDOs: 29, 58, 87, 145
=== 2.3.5.7.11.13.17.23 subgroup ===
Subgroup: 2.3.5.7.11.13.17.23


Badness: 0.0343
Comma list: 253/252, 289/288, 325/324, 352/351, 385/384, 391/390


==13-limit==
Mapping: {{mapping| 2 3 4 6 7 8 8 9 | 0 4 15 -9 -2 -14 4 1 }}
Commas: 196/195, 352/351, 364/363, 676/675


[[POTE_tuning|POTE generator]]: ~5/4 = 388.354
Optimal tunings:  
* WE: ~17/12 = 600.1139{{c}}, ~66/65 = 25.7053{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~66/65 = 25.7013{{c}}


Map: [&lt;29 46 0 14 33 40|, &lt;0 0 1 1 1 1|]
{{Optimal ET sequence|legend=0| 46, 94, 140 }}


EDOs: 29, 58, 87, 145, 232, 377
Badness (Sintel): 0.772


Badness: 0.0186
== Undecental ==
Undecental adds the triwellisma to the comma list and may be described as the {{nowrap| 29 & 70 }} temperament. 5/4 is mapped to the quintuple-diminished seventh or equivalently the perfect fourth minus three [[diesis (scale theory)|dieses]]. [[99edo|58\99]] is an almost perfect generator, just as the name suggests. Another interesting tuning choice is the argent fifth, {{nowrap| 2<sup>(2 - sqrt (2))</sup> }}.  


=Quanic=
[[Subgroup]]: 2.3.5.7
Commas: 5120/5103, 5832000/5764801


POTE generator: ~160/147 = 140.493
[[Comma list]]: 5120/5103, 235298/234375


Map: [&lt;1 1 -4 0|, &lt;0 5 54 24|]
{{Mapping|legend=1| 1 0 61 71 | 0 1 -37 -43 }}
: mapping generators: ~2, ~3


EDOs: 94, 111, 205
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1199.6543{{c}}, ~3/2 = 702.8370{{c}}
: [[error map]]: {{val| -0.346 +0.536 +0.423 -0.494 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.0465{{c}}
: error map: {{val| 0.000 +1.092 +0.966 +0.175 }}


Badness: 0.1795
{{Optimal ET sequence|legend=1| 29, 70, 99, 722bc, 821bc, 920bc, 1019bc }}


==11-limit==
[[Badness]] (Sintel): 2.39
Commas: 540/539, 1331/1323, 5120/5103


POTE generator: ~88/81 = 140.489
== Mystery ==
{{Main| Mystery }}
: ''For the 5-limit version, see [[29th-octave temperaments #Mystery]].''


Map: [&lt;1 1 -4 0 1|, &lt;0 5 54 24 21|]
Mystery tempers out [[50421/50000]] and may be described as the {{nowrap| 29 & 58 }} temperament. It has a 1\29 period and primes 5, 7, 11 and 13 are all reached by one generator step; its ploidacot is 29-ploid acot. [[145edo]] or [[232edo]] are good candidates for tunings.


EDOs: 94, 111, 205
[[Subgroup]]: 2.3.5.7


Badness: 0.0587
[[Comma list]]: 5120/5103, 50421/50000


==13-limit==
{{Mapping|legend=1| 29 46 0 14 | 0 0 1 1 }}
Commas: 352/351, 540/539, 729/728, 1331/1323
: mapping generators: ~50/49, ~5


POTE generator: ~13/12 = 140.496
[[Optimal tuning]]s:
* [[WE]]: ~50/49 = 41.3652{{c}}, ~5/4 = 388.5128{{c}}
: [[error map]]: {{val| -0.410 +0.842 +1.378 -2.022 }}
* [[CWE]]: ~50/49 = 41.3793{{c}}, ~5/4 = 388.3030{{c}}
: error map: {{val| 0.000 +1.493 +1.989 -1.213 }}


Map: [&lt;1 1 -4 0 1 3|, &lt;0 5 54 24 21 6|]
{{Optimal ET sequence|legend=1| 29, 58, 87, 145 }}


EDOs: 94, 111, 205
[[Badness]] (Sintel): 2.63


Badness: 0.0325
=== 11-limit ===
Subgroup: 2.3.5.7.11


==17-limit==
Comma list: 441/440, 896/891, 3388/3375
Commas: 352/351, 442/441, 540/539, 715/714, 847/845


POTE generator: ~13/12 = 140.497
Mapping: {{mapping| 29 46 0 14 33 | 0 0 1 1 1 }}


Map: [&lt;1 1 -4 0 1 3 -2|, &lt;0 5 54 24 21 6 52|]
Optimal tunings:  
* WE: ~45/44 = 41.3637{{c}}, ~5/4 = 388.3136{{c}}
* CWE: ~45/44 = 41.3793{{c}}, ~5/4 = 388.0598{{c}}


EDOs: 94, 111, 205
{{Optimal ET sequence|legend=0| 29, 58, 87, 145 }}


Badness: 0.0211
Badness (Sintel): 1.13


==19-limit==
=== 13-limit ===
Commas: 352/351, 400/399, 442/441, 456/455, 495/494, 715/714
Subgroup: 2.3.5.7.11.13


POTE generator: ~13/12 = 140.496
Comma list: 196/195, 352/351, 364/363, 676/675


Map: [&lt;1 1 -4 0 1 3 -2 -5|, &lt;0 5 54 24 21 6 52 79|]
Mapping: {{mapping| 29 46 0 14 33 40 | 0 0 1 1 1 1 }}


EDOs: 94, 111, 205
Optimal tunings:  
* WE: ~45/44 = 41.3623{{c}}, ~5/4 = 388.1942{{c}}
* CWE: ~40/39 = 41.3793{{c}}, ~5/4 = 387.9017{{c}}


Badness: 0.0173
{{Optimal ET sequence|legend=0| 29, 58, 87, 145, 232 }}


=Supers=
Badness (Sintel): 0.768
Commas: 5120/5103, 118098/117649


POTE generator: ~9/7 = 434.218
== Hemidromeda ==
Hemidromeda may be described as the {{nowrap| 29 & 111 }} temperament. Named by [[Xenllium]] in 2023, ''hemidromeda'' comes from ''hemi-'' (Ancient Greek for "one half") and ''[[andromeda]]'', because the generator is 1/2 of andromeda's perfect twelfth (~3/1, about 1902.4 cents); the ploidacot for this temperament is alpha-dicot.  


Map: [&lt;2 1 -12 2|, &lt;0 3 23 5|]
[[Subgroup]]: 2.3.5.7


Wedgie: &lt;&lt;6 46 10 59 -1 -106||
[[Comma list]]: 5120/5103, 52734375/52706752


EDOs: {{EDOs|58, 94, 152}}
{{Mapping|legend=1| 1 0 38 48 | 0 2 -45 -57 }}
: mapping generator: ~2, ~12500/7203


Badness: 0.092748
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1199.7236{{c}}, ~12500/7203 = 951.1864{{c}}
: [[error map]]: {{val| -0.276 +0.418 -0.205 +0.282 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~12500/7203 = 951.4098{{c}}
: error map: {{val| 0.000 +0.865 +0.243 +0.813 }}


==11-limit==
{{Optimal ET sequence|legend=1| 29, 82cd, 111, 140, 251, 391, 1424bbcdd }}
Commas: 540/539, 4000/3993, 5120/5103


POTE generator: ~9/7 = 434.217
[[Badness]] (Sintel): 2.93


Map: [&lt;2 1 -12 2 -9|, &lt;0 3 23 5 22|]
=== 11-limit ===
Subgroup: 2.3.5.7.11


EDOs: {{EDOs|58, 94, 152}}
Comma list: 1331/1323, 1375/1372, 5120/5103


Badness: 0.028240
Mapping: {{mapping| 1 0 38 48 32 | 0 2 -45 -57 -36 }}


==13-limit==
Optimal tunings:
Commas: 352/351, 540/539, 729/728, 1575/1573
* WE: ~2 = 1199.8767{{c}}, ~400/231 = 951.3065{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~400/231 = 951.4063{{c}}


POTE generator: ~9/7 = 434.221
{{Optimal ET sequence|legend=0| 29, 82cd, 111, 140, 251, 391e }}


Map: [&lt;2 1 -12 2 -9 -2|, &lt;0 3 23 5 22 13|]
Badness (Sintel): 2.01


EDOs: {{EDOs|58, 94, 152f}}
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


Badness: 0.021645
Comma list: 352/351, 676/675, 847/845, 1331/1323


==17-limit==
Mapping: {{mapping| 1 0 38 48 32 37 | 0 2 -45 -57 -36 -42 }}
Commas: 170/169, 289/288, 352/351, 442/441, 561/560


POTE generator: ~9/7 = 434.181
Optimal tunings:  
* WE: ~2 = 1199.8753{{c}}, ~26/15 = 951.3054{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 951.4064{{c}}


Map: [&lt;2 1 -12 2 -9 -2 6|, &lt;0 3 23 5 22 13 3|]
{{Optimal ET sequence|legend=0| 29, 82cdf, 111, 140, 251, 391e }}


EDOs: {{EDOs|58, 94, 152f}}
Badness (Sintel): 1.18


Badness: 0.021316
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17


=Alphaquarter=
Comma list: 352/351, 442/441, 561/560, 676/675, 715/714
Commas: 5120/5103, 29360128/29296875


POTE generator: ~16128/15625 = 55.243
Mapping: {{mapping| 1 0 38 48 32 37 58 | 0 2 -45 -57 -36 -42 -68 }}


Map: [&lt;1 2 2 0|, &lt;0 -9 7 61|]
Optimal tunings:  
* WE: ~2 = 1199.8770{{c}}, ~26/15 = 951.3039{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 951.4035{{c}}


Wedgie: &lt;&lt;9 -7 -61 -32 -122 -122||
{{Optimal ET sequence|legend=0| 29g, 82cdfg, 111, 140, 251, 391e }}


EDOs: 87, 152, 239, 391
Badness (Sintel): 0.971


Badness: 0.1166
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19


==11-limit==
Comma list: 286/285, 352/351, 363/361, 442/441, 476/475, 561/560
Commas: 3025/3024, 4000/3993, 5120/5103


POTE generator: ~33/32 = 55.243
Mapping: {{mapping| 1 0 38 48 32 37 58 32 | 0 2 -45 -57 -36 -42 -68 -35 }}


Map: [&lt;1 2 2 0 3|, &lt;0 -9 7 61 10|]
Optimal tunings:  
* WE: ~2 = 1199.7534{{c}}, ~26/15 = 951.2024{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 951.4020{{c}}


EDOs: 87, 152, 239, 391
{{Optimal ET sequence|legend=0| 29g, 82cdfgh, 111, 140 }}


Badness: 0.0296
Badness (Sintel): 1.01


= Septiquarter =
=== 23-limit ===
Commas: 5120/5103, 420175/419904
Subgroup: 2.3.5.7.11.13.17.19.23


POTE generator: ~147/128 = 242.453
Comma list: 253/252, 286/285, 352/351, 363/361, 391/390, 442/441, 460/459


Map: [&lt;1 3 10 2|, &lt;0 -7 -38 4|]
Mapping: {{mapping| 1 0 38 48 32 37 58 32 18 | 0 2 -45 -57 -36 -42 -68 -35 -17 }}


Wedgie: &lt;&lt;7 38 -4 44 -26 -116||
Optimal tunings:  
* WE: ~2 = 1199.9128{{c}}, ~26/15 = 951.3371{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 951.4076{{c}}


EDOs: {{EDOs|94, 99, 292, 391, 881bd, 1272bcd}}
{{Optimal ET sequence|legend=0| 29g, 82cdfgh, 111, 140 }}


Badness: 0.0538
Badness (Sintel): 1.10


== Semiseptiquarter ==
== Countriton ==
Commas: 5120/5103, 9801/9800, 14641/14580
: ''For the 5-limit version, see [[Schismic–Mercator equivalence continuum #Countritonic]].''


POTE generators: ~121/105 = 242.4511
Countriton may be described as the {{nowrap| 51c & 53 }} temperament. It splits the [[24/1|24th harmonic]] into nine tritone generators; its ploidacot is thus delta-enneacot. Among the possible tunings are [[157edo]] and [[210edo]], as well as [[104edo]] in the 104c val.  


Map: [<2 6 20 4 15|, <0 -7 -38 4 -20|]
Countriton was named by [[Xenllium]] in 2022 as a counterpart of [[untriton]].


EDOs: {{EDOs|94, 198, 292, 490}}
[[Subgroup]]: 2.3.5.7


Badness: 0.0642
[[Comma list]]: 5120/5103, 7558272/7503125
 
{{Mapping|legend=1| 1 -3 -15 13 | 0 9 34 -20 }}
: mapping generators: ~2, ~1225/864
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.4179{{c}}, ~1225/864 = 611.1213{{c}}
: [[error map]]: {{val| -0.582 -0.117 +0.541 +1.181 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~1225/864 = 611.4120{{c}}
: error map: {{val| 0.000 +0.753 +1.695 +2.934 }}
 
{{Optimal ET sequence|legend=1| 51c, 53, 157, 210, 473cdd }}
 
[[Badness]] (Sintel): 3.32
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 176/175, 5120/5103, 41503/41472
 
Mapping: {{mapping| 1 -3 -15 13 -21 | 0 9 34 -20 48 }}
 
Optimal tunings:
* WE: ~2 = 1199.5178{{c}}, ~77/54 = 611.2097{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~77/54 = 611.4495{{c}}
 
{{Optimal ET sequence|legend=0| 51ce, 53, 104c, 157 }}
 
Badness (Sintel): 2.80


=== 13-limit ===
=== 13-limit ===
Commas: 352/351, 847/845, 1716/1715, 14641/14580
Subgroup: 2.3.5.7.11.13
 
Comma list: 176/175, 351/350, 847/845, 2197/2187


POTE generators: ~121/105 = 242.4448
Mapping: {{mapping| 1 -3 -15 13 -21 -7 | 0 9 34 -20 48 21 }}


Map: [<2 6 20 4 15 7|, <0 -7 -38 4 -20 1|]
Optimal tunings:  
* WE: ~2 = 1199.5944{{c}}, ~77/54 = 611.2491{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~77/54 = 611.4506{{c}}


EDOs: {{EDOs|94, 198, 490f}}
{{Optimal ET sequence|legend=0| 51ce, 53, 104c, 157 }}


Badness: 0.0348
Badness (Sintel): 1.75


= Tricot (aka Trimot) =
== Artoneutral ==
{{see also|Tricot family}}
Artoneutral can be described as the {{nowrap| 87 & 94 }} temperament. It is generated by an artoneutral third of ~11/9 (or a tendoneutral sixth of ~18/11), nine of which make the [[12/1|12th harmonic]]; its ploidacot is thus beta-enneacot. [[181edo]] may be recommended as a tuning.


The generator for tricot is the real cube root of third harmonic, 3<sup>1/3</sup>, tuned between 63/44 and 13/9. Tricot can be described as 53&amp;70 temperament (also known as ''trimot''), tempering out the [[tricot comma]], {{monzo| 39 -29 3 }} in the 5-limit, 2430/2401 (nuwell comma) and 5120/5103 in the 7-limit, 99/98 and 121/120 in the 11-limit, 169/168, 352/351, 640/637, and 729/728 in the 13-limit.
Artoneutral was named by [[Flora Canou]] in 2023 for its generator's quality.  


[[Comma list]]: 2430/2401, 5120/5103
[[Subgroup]]: 2.3.5.7


[[Mapping]]: [&lt;1 0 -13 -3|, &lt;0 3 29 11|]
[[Comma list]]: 5120/5103, 3828125/3779136


[[Wedgie]]: &lt;&lt;3 29 11 39 9 -56||
{{Mapping|legend=1| 1 -1 -4 12 | 0 9 22 -32 }}
: mapping generators: ~2, ~128/105


[[POTE tuning|POTE generator]]: ~81/56 = 634.026
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.1400{{c}}, ~128/105 = 344.7929{{c}}
: [[error map]]: {{val| +0.140 +1.041 -1.430 -0.518 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~128/105 = 344.7531{{c}}
: error map: {{val| 0.000 +0.823 -1.746 -0.925 }}


{{Val list|legend=1| 17c, 36c, 53, 229dd, 282dd }}
{{Optimal ET sequence|legend=1| 87, 94, 181 }}


[[Badness]]: 0.100127
[[Badness]] (Sintel): 3.98


== 11-limit ==
=== 11-limit ===
Comma list: 99/98, 121/120, 5120/5103
Subgroup: 2.3.5.7.11


Mapping: [&lt;1 0 -13 -3 -5|, &lt;0 3 29 11 16|]
Comma list: 385/384, 2200/2187, 4000/3993


POTE generator: ~63/44 = 634.027
Mapping: {{mapping| 1 -1 -4 12 -2 | 0 9 22 -32 19 }}


Vals: {{Val list| 17c, 36ce, 53, 70, 123de }}
Optimal tunings:  
* WE: ~2 = 1200.1668{{c}}, ~11/9 = 344.8027{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 344.7557{{c}}


Badness: 0.056134
{{Optimal ET sequence|legend=0| 87, 181 }}


== 13-limit ==
Badness (Sintel): 1.52
Comma list: 99/98, 121/120, 169/168, 352/351


Mapping: [&lt;1 0 -13 -3 -5 0|, &lt;0 3 29 11 16 7|]
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


POTE generator: ~13/9 = 634.012
Comma list: 325/324, 352/351, 385/384, 1575/1573


Vals: {{Val list| 17c, 36ce, 53, 70, 123de }}
Mapping: {{mapping| 1 -1 -4 12 -2 6 | 0 9 22 -32 19 -8 }}


Badness: 0.032102
Optimal tunings:  
* WE: ~2 = 1200.0662{{c}}, ~11/9 = 344.7804{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 344.7617{{c}}


= Ketchup =
{{Optimal ET sequence|legend=0| 87, 181 }}
[[Comma list]]: 5120/5103, 1071875/1062882
 
Badness (Sintel): 1.08
 
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 325/324, 352/351, 375/374, 385/384, 595/594
 
Mapping: {{mapping| 1 -1 -4 12 -2 6 -12 | 0 9 22 -32 19 -8 56 }}
 
Optimal tunings:
* WE: ~2 = 1200.0346{{c}}, ~11/9 = 344.7589{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 344.7492{{c}}
 
{{Optimal ET sequence|legend=0| 87, 94, 181 }}
 
Badness (Sintel): 1.16
 
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 325/324, 352/351, 375/374, 385/384, 400/399, 595/594
 
Mapping: {{mapping| 1 -1 -4 12 -2 6 -12 -15 | 0 9 22 -32 19 -8 56 67 }}
 
Optimal tunings:
* WE: ~2 = 1200.0282{{c}}, ~11/9 = 344.7532{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 344.7453{{c}}
 
{{Optimal ET sequence|legend=0| 87, 94, 181 }}
 
Badness (Sintel): 1.19
 
=== 23-limit ===
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
 
Mapping: {{mapping| 1 -1 -4 12 -2 6 -12 -15 -13 | 0 9 22 -32 19 -8 56 67 61 }}
 
Optimal tunings:
* WE: ~2 = 1200.0163{{c}}, ~11/9 = 344.7461{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 344.7416{{c}}
 
{{Optimal ET sequence|legend=0| 87, 94, 181 }}
 
Badness (Sintel): 1.17
 
== Quanic ==
Quanic may be described as the {{nowrap| 94 & 111 }} temperament. It splits the perfect fifth into five generators which in the 13-limit extension may be taken as ~13/12; its ploidacot is thus pentacot. [[205edo]] may be recommended as a tuning.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 5120/5103, 5832000/5764801
 
{{Mapping|legend=1| 1 1 -4 0 | 0 5 54 24 }}
: mapping generators: ~2, ~160/147
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.6159{{c}}, ~160/147 = 140.4483{{c}}
: [[error map]]: {{val| -0.384 -0.098 -0.570 +1.933 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~160/147 = 140.4862{{c}}
: error map: {{val| 0.000 +0.476 -0.061 +2.842 }}
 
{{Optimal ET sequence|legend=1| 94, 111, 205 }}
 
[[Badness]] (Sintel): 4.54
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 540/539, 1331/1323, 5120/5103
 
Mapping: {{mapping| 1 1 -4 0 1 | 0 5 54 24 21 }}
 
Optimal tunings:
* WE: ~2 = 1199.7834{{c}}, ~88/81 = 140.4635{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~88/81 = 140.4850{{c}}


[[Mapping]]: [&lt;2 3 4 6|, &lt;0 4 15 -9|]
{{Optimal ET sequence|legend=0| 94, 111, 205 }}


[[Wedgie]]: &lt;&lt;8 30 -18 29 -51 -126||
Badness (Sintel): 1.94


[[POTE tuning|POTE generator]]: ~64/63 = ~81/80 = 25.719
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


{{Val list|legend=1| 46, 94, 140 }}
Comma list: 352/351, 540/539, 729/728, 1331/1323


[[Badness]]: 0.084538
Mapping: {{mapping| 1 1 -4 0 1 3 | 0 5 54 24 21 6 }}


== 11-limit ==
Optimal tunings:
Comma list: 385/384, 1331/1323, 2200/2187
* WE: ~2 = 1199.6639{{c}}, ~13/12 = 140.4562{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 140.4904{{c}}


Mapping: [&lt;2 3 4 6 7|, &lt;0 4 15 -9 -2|]
{{Optimal ET sequence|legend=0| 94, 111, 205 }}


POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.693
Badness (Sintel): 1.34


Vals: {{Val list| 46, 94, 140 }}
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17


Badness: 0.039555
Comma list: 352/351, 442/441, 540/539, 715/714, 847/845


== 13-limit ==
Mapping: {{mapping| 1 1 -4 0 1 3 -2 | 0 5 54 24 21 6 52 }}
Comma list: 325/324, 352/351, 847/845, 1331/1323


Mapping: [&lt;2 3 4 6 7 8|, &lt;0 4 15 -9 -2 -14|]
Optimal tunings:  
* WE: ~2 = 1199.6699{{c}}, ~13/12 = 140.4586{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 140.4920{{c}}


POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.697
{{Optimal ET sequence|legend=0| 94, 111, 205 }}


Vals: {{Val list| 46, 94, 140 }}
Badness (Sintel): 1.08


Badness: 0.024824
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19


== 17-limit ==
Comma list: 352/351, 400/399, 442/441, 456/455, 495/494, 715/714
Comma list: 289/288, 325/324, 352/351, 385/384, 561/560


Map: [&lt;2 3 4 6 7 8 8|, &lt;0 4 15 -9 -2 -14 4|]
Mapping: {{mapping| 1 1 -4 0 1 3 -2 -5 | 0 5 54 24 21 6 52 79 }}


POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.701
Optimal tunings:  
* WE: ~2 = 1199.6745{{c}}, ~13/12 = 140.4574{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 140.4908{{c}}


Vals: {{Val list| 46, 94, 140 }}
{{Optimal ET sequence|legend=0| 94, 111, 205 }}


Badness: 0.016591
Badness (Sintel): 1.05


== 19-limit ==
== Jorgensen ==
Comma list: 190/189, 209/208, 289/288, 352/351, 385/384, 561/560
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Jorgensen]].''


Mapping: [&lt;2 3 4 6 7 8 8 9|, &lt;0 4 15 -9 -2 -14 4 -12|]
Jorgensen tempers out the [[linus comma]] in addition to the aberschisma, and may be described as the {{nowrap| 70 & 140 }} temperament, with a 70th-octave period. Its ploidacot is 70-ploid acot.


POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.660
It is the natural 7-limit extension of the 5-limit temperament tempering out the 70-comma, named by [[Mike Battaglia]] in 2012 for historical interests<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_103982.html Yahoo! Tuning Group | ''Jorgensen Temperament'']</ref>.  


Vals: {{Val list| 46, 94, 140h, 234eh }}
[[Subgroup]]: 2.3.5.7


Badness: 0.018170
[[Comma list]]: 5120/5103, 578509309952/576650390625


== 23-limit ==
{{Mapping|legend=1| 70 111 0 34 | 0 0 1 1 }}
Commas: 190/189, 209/208, 253/252, 289/288, 323/322, 352/351, 385/384
: mapping generators: ~50421/50000, ~5


Mapping: [&lt;2 3 4 6 7 8 8 9 9|, &lt;0 4 15 -9 -2 -14 4 -12 1|]
[[Optimal tuning]]s:  
* [[WE]]: ~50421/50000 = 17.1387{{c}}, ~5/4 = 386.8071{{c}}
: [[error map]]: {{val| -0.288 +0.445 -0.084 +0.121 }}
* [[CWE]]: ~50421/50000 = 17.1429{{c}}, ~5/4 = 386.6593{{c}}
: error map: {{val| 0.000 +0.902 +0.346 +0.690 }}


POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.661
{{Optimal ET sequence|legend=1| 70, 140, 350, 490 }}


Vals: {{Val list| 46, 94, 140h, 234ehi }}
[[Badness]] (Sintel): 5.40


Badness: 0.014033
== References ==


[[Category:Temperament]]
[[Category:Aberschismic temperaments| ]] <!-- main article -->
[[Category:Hemifamity]]
[[Category:Temperament collections]]
[[Category:Rank 2]]
[[Category:Catalogs of rank-2 temperaments]]
Retrieved from "https://en.xen.wiki/w/Aberschismic_temperaments"