Xenharmonic Wiki

Aberschismic temperaments: Difference between revisions

← Older edit
VisualWikitext
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
5,033 edits
m Recategorize
 
(91 intermediate revisions by 11 users not shown)
Line 1: Line 1:
__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 ====
[[Comma list]]: 5120/5103, 235298/234375
Subgroup: 2.3.5.7.11.13
 
Comma list: 352/351, 540/539, 729/728, 1375/1372
 
Mapping: {{mapping| 1 0 -50 -40 32 27 | 0 1 33 27 -18 -21 }}
 
Optimal tunings:
* WE: ~2 = 1199.4772{{c}}, ~3/2 = 702.3379{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.6409{{c}}
 
{{Optimal ET sequence|legend=0| 41, 111, 152f, 415dff }}
 
Badness (Sintel): 1.01
 
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 256/255, 352/351, 540/539, 715/714, 1089/1088
 
Mapping: {{mapping| 1 0 -50 -40 32 27 58 | 0 1 33 27 -18 -21 -34 }}
 
Optimal tunings:
* WE: ~2 = 1199.3537{{c}}, ~3/2 = 702.2850{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.6589{{c}}
 
{{Optimal ET sequence|legend=0| 41, 70, 111, 152fg, 263dfg }}
 
Badness (Sintel): 1.12
 
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 256/255, 352/351, 400/399, 456/455, 715/714, 847/845
 
Mapping: {{mapping| 1 0 -50 -40 32 27 58 -56 | 0 1 33 27 -18 -21 -34 38 }}
 
Optimal tunings:
* WE: ~2 = 1199.3401{{c}}, ~3/2 = 702.2705{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.6548{{c}}
 
{{Optimal ET sequence|legend=0| 41, 70h, 111, 152fg, 263dfgh }}
 
Badness (Sintel): 1.03
 
==== Hemikwai ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 540/539, 676/675, 1375/1372, 5120/5103
 
Mapping: {{mapping| 1 0 -50 -40 32 -51 | 0 2 66 54 -36 69 }}
: mapping generators: ~2, ~26/15
 
Optimal tunings:
* WE: ~2 = 1199.6968{{c}}, ~26/15 = 951.0740{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 951.3123{{c}}
 
{{Optimal ET sequence|legend=0| 82, 111, 193, 304d }}
 
Badness (Sintel): 1.82
 
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 442/441, 540/539, 676/675, 715/714, 5120/5103
 
Mapping: {{mapping| 1 0 -50 -40 32 -51 -30 | 0 2 66 54 -36 69 43 }}
 
Optimal tunings:
* WE: ~2 = 1199.6861{{c}}, ~26/15 = 951.0654{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 951.3120{{c}}
 
{{Optimal ET sequence|legend=0| 82, 111, 193, 304d }}
 
Badness (Sintel): 1.31
 
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 400/399, 442/441, 540/539, 676/675, 715/714, 1445/1444
 
Mapping: {{mapping| 1 0 -50 -40 32 -51 -30 -56 | 0 2 66 54 -36 69 43 76 }}
 
Optimal tunings:
* WE: ~2 = 1199.6718{{c}}, ~26/15 = 951.0526{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 951.3103{{c}}
 
{{Optimal ET sequence|legend=0| 82, 111, 193, 304dh }}
 
Badness (Sintel): 1.16
 
== Ketchup ==
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.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 5120/5103, 1071875/1062882
 
{{Mapping|legend=1| 2 3 4 6 | 0 4 15 -9 }}
: mapping generators: ~1225/864, ~64/63


[[Mapping]]: [&lt;1 0 61 71|, &lt;0 1 -37 -43|]
[[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 }}


[[Wedgie]]: &lt;&lt;1 -37 -43 -61 -71 4||
{{Optimal ET sequence|legend=1| 46, 94, 140 }}


[[POTE_tuning|POTE generator]]: ~3/2 = 703.039
[[Badness]] (Sintel): 2.14


{{Val list|legend=1| 29, 70, 99, 722bc, 821bc, 920bc, 1019bc, 1118bbcc, 1217bbcc, 1316bbccd }}
=== 11-limit ===
Subgroup: 2.3.5.7.11


Badness: 0.094603
Comma list: 385/384, 1331/1323, 2200/2187


= Leapday =
Mapping: {{mapping| 2 3 4 6 7 | 0 4 15 -9 -2 }}
[[Comma]]: 10737418240/10460353203 (trisayo comma)


[[Mapping]]: [&lt;1 0 -31|, &lt;0 1 21|]
Optimal tunings:  
* WE: ~99/70 = 600.0678{{c}}, ~64/63 = 25.6963{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~64/63 = 25.6956{{c}}


[[POTE tuning|POTE generator]]: ~3/2 = 704.179
{{Optimal ET sequence|legend=0| 46, 94, 140 }}


{{Val list|legend=1| 29, 46, 121, 167, 455bc, 622bbc }}
Badness (Sintel): 1.31


[[Badness]]: 0.523182
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


== 7-limit ==
Comma list: 325/324, 352/351, 385/384, 1331/1323
[[Comma list]]: 686/675, 5120/5103


[[Mapping]]: [&lt;1 0 -31 -21|, &lt;0 1 21 15|]
Mapping: {{mapping| 2 3 4 6 7 8 | 0 4 15 -9 -2 -14 }}


[[Wedgie]]: &lt;&lt;1 21 15 31 21 -24||
Optimal tunings:  
* 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]]: ~3/2 = 704.263
{{Optimal ET sequence|legend=0| 46, 94, 140 }}


{{Val list|legend=1| 17c, 29, 46, 167d, 213d, 259cdd, 305bcdd }}
Badness (Sintel): 1.03


[[Badness]]: 0.096123
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17


== 11-limit ==
Comma list: 289/288, 325/324, 352/351, 385/384, 442/441
Comma list: 121/120, 441/440, 686/675


Mapping: [&lt;1 0 -31 -21 -14|, &lt;0 1 21 15 11|]
Mapping: {{mapping| 2 3 4 6 7 8 8 | 0 4 15 -9 -2 -14 4 }}


POTE generator: ~3/2 = 704.250
Optimal tunings:  
* WE: ~17/12 = 600.0896{{c}}, ~66/65 = 25.7048{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~66/65 = 25.7017{{c}}


Vals: {{Val list| 17c, 29, 46, 167de, 213de, 259cdde }}
{{Optimal ET sequence|legend=0| 46, 94, 140 }}


Badness: 0.038624
Badness (Sintel): 0.845


== 13-limit ==
=== 2.3.5.7.11.13.17.23 subgroup ===
Comma list: 91/90, 121/120, 169/168, 352/351
Subgroup: 2.3.5.7.11.13.17.23


Mapping: [&lt;1 0 -31 -21 -14 -9|, &lt;0 1 21 15 11 8|]
Comma list: 253/252, 289/288, 325/324, 352/351, 385/384, 391/390


POTE generator: ~3/2 = 704.214
Mapping: {{mapping| 2 3 4 6 7 8 8 9 | 0 4 15 -9 -2 -14 4 1 }}


Vals: {{Val list| 17c, 29, 46, 121def, 167def, 213deff }}
Optimal tunings:  
* WE: ~17/12 = 600.1139{{c}}, ~66/65 = 25.7053{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~66/65 = 25.7013{{c}}


Badness: 0.024732
{{Optimal ET sequence|legend=0| 46, 94, 140 }}


== 17-limit ==
Badness (Sintel): 0.772
Comma list: 91/90, 121/120, 136/135, 154/153, 169/168


Mapping: [&lt;1 0 -31 -21 -14 -9 -34|, &lt;0 1 21 15 11 8 24|]
== 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> }}.


POTE generator: ~3/2 = 704.229
[[Subgroup]]: 2.3.5.7


Vals: {{Val list| 17cg, 29g, 46, 121defg, 167defg, 213deffg }}
[[Comma list]]: 5120/5103, 235298/234375


Badness: 0.017863
{{Mapping|legend=1| 1 0 61 71 | 0 1 -37 -43 }}
: mapping generators: ~2, ~3


== 19-limit ==
[[Optimal tuning]]s:
Comma list: 91/90, 121/120, 133/132, 136/135, 154/153, 169/168
* [[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 }}


Mapping: [&lt;1 0 -31 -21 -14 -9 -34 9|, &lt;0 1 21 15 11 8 24 -3|]
{{Optimal ET sequence|legend=1| 29, 70, 99, 722bc, 821bc, 920bc, 1019bc }}


POTE generator: ~3/2 = 704.135
[[Badness]] (Sintel): 2.39


Vals: {{Val list| 17cg, 29g, 46, 75dfgh, 121defgh }}
== Mystery ==
{{Main| Mystery }}
: ''For the 5-limit version, see [[29th-octave temperaments #Mystery]].''


Badness: 0.017356
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.  


== Leapling ==
[[Subgroup]]: 2.3.5.7
Comma list: 77/76, 91/90, 121/120, 136/135, 153/152, 169/168


Mapping: [&lt;1 0 -31 -21 -14 -9 -34 -37|, &lt;0 1 21 15 11 8 24 26|]
[[Comma list]]: 5120/5103, 50421/50000


POTE generator: ~3/2 = 704.123
{{Mapping|legend=1| 29 46 0 14 | 0 0 1 1 }}
: mapping generators: ~50/49, ~5


Vals: {{Val list| 17cgh, 29g, 46h, 75dfg, 121defghh }}
[[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 }}


Badness: 0.019065
{{Optimal ET sequence|legend=1| 29, 58, 87, 145 }}


=Mystery=
[[Badness]] (Sintel): 2.63
Commas: 5120/5103, 50421/50000


[[POTE_tuning|POTE generator]]: ~5/4 = 388.646
=== 11-limit ===
Subgroup: 2.3.5.7.11


Map: [&lt;29 46 0 14|, &lt;0 0 1 1|]
Comma list: 441/440, 896/891, 3388/3375


Wedgie: &lt;&lt;0 29 29 46 46 -14||
Mapping: {{mapping| 29 46 0 14 33 | 0 0 1 1 1 }}


EDOs: 29, 58, 87, 145
Optimal tunings:  
* WE: ~45/44 = 41.3637{{c}}, ~5/4 = 388.3136{{c}}
* CWE: ~45/44 = 41.3793{{c}}, ~5/4 = 388.0598{{c}}


Badness: 0.1037
{{Optimal ET sequence|legend=0| 29, 58, 87, 145 }}


==11-limit==
Badness (Sintel): 1.13
Commas: 441/440, 896/891, 3388/3375


[[POTE_tuning|POTE generator]]: ~5/4 = 388.460
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


Map: [&lt;29 46 0 14 33|, &lt;0 0 1 1 1|]
Comma list: 196/195, 352/351, 364/363, 676/675


EDOs: 29, 58, 87, 145
Mapping: {{mapping| 29 46 0 14 33 40 | 0 0 1 1 1 1 }}


Badness: 0.0343
Optimal tunings:  
* WE: ~45/44 = 41.3623{{c}}, ~5/4 = 388.1942{{c}}
* CWE: ~40/39 = 41.3793{{c}}, ~5/4 = 387.9017{{c}}


==13-limit==
{{Optimal ET sequence|legend=0| 29, 58, 87, 145, 232 }}
Commas: 196/195, 352/351, 364/363, 676/675


[[POTE_tuning|POTE generator]]: ~5/4 = 388.354
Badness (Sintel): 0.768


Map: [&lt;29 46 0 14 33 40|, &lt;0 0 1 1 1 1|]
== 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.


EDOs: 29, 58, 87, 145, 232, 377
[[Subgroup]]: 2.3.5.7


Badness: 0.0186
[[Comma list]]: 5120/5103, 52734375/52706752


=Quanic=
{{Mapping|legend=1| 1 0 38 48 | 0 2 -45 -57 }}
Commas: 5120/5103, 5832000/5764801
: mapping generator: ~2, ~12500/7203


POTE generator: ~160/147 = 140.493
[[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 }}


Map: [&lt;1 1 -4 0|, &lt;0 5 54 24|]
{{Optimal ET sequence|legend=1| 29, 82cd, 111, 140, 251, 391, 1424bbcdd }}


EDOs: 94, 111, 205
[[Badness]] (Sintel): 2.93


Badness: 0.1795
=== 11-limit ===
Subgroup: 2.3.5.7.11


==11-limit==
Comma list: 1331/1323, 1375/1372, 5120/5103
Commas: 540/539, 1331/1323, 5120/5103


POTE generator: ~88/81 = 140.489
Mapping: {{mapping| 1 0 38 48 32 | 0 2 -45 -57 -36 }}


Map: [&lt;1 1 -4 0 1|, &lt;0 5 54 24 21|]
Optimal tunings:  
* WE: ~2 = 1199.8767{{c}}, ~400/231 = 951.3065{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~400/231 = 951.4063{{c}}


EDOs: 94, 111, 205
{{Optimal ET sequence|legend=0| 29, 82cd, 111, 140, 251, 391e }}


Badness: 0.0587
Badness (Sintel): 2.01


==13-limit==
=== 13-limit ===
Commas: 352/351, 540/539, 729/728, 1331/1323
Subgroup: 2.3.5.7.11.13


POTE generator: ~13/12 = 140.496
Comma list: 352/351, 676/675, 847/845, 1331/1323


Map: [&lt;1 1 -4 0 1 3|, &lt;0 5 54 24 21 6|]
Mapping: {{mapping| 1 0 38 48 32 37 | 0 2 -45 -57 -36 -42 }}


EDOs: 94, 111, 205
Optimal tunings:  
* WE: ~2 = 1199.8753{{c}}, ~26/15 = 951.3054{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 951.4064{{c}}


Badness: 0.0325
{{Optimal ET sequence|legend=0| 29, 82cdf, 111, 140, 251, 391e }}


==17-limit==
Badness (Sintel): 1.18
Commas: 352/351, 442/441, 540/539, 715/714, 847/845


POTE generator: ~13/12 = 140.497
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17


Map: [&lt;1 1 -4 0 1 3 -2|, &lt;0 5 54 24 21 6 52|]
Comma list: 352/351, 442/441, 561/560, 676/675, 715/714


EDOs: 94, 111, 205
Mapping: {{mapping| 1 0 38 48 32 37 58 | 0 2 -45 -57 -36 -42 -68 }}


Badness: 0.0211
Optimal tunings:  
* WE: ~2 = 1199.8770{{c}}, ~26/15 = 951.3039{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 951.4035{{c}}


==19-limit==
{{Optimal ET sequence|legend=0| 29g, 82cdfg, 111, 140, 251, 391e }}
Commas: 352/351, 400/399, 442/441, 456/455, 495/494, 715/714


POTE generator: ~13/12 = 140.496
Badness (Sintel): 0.971


Map: [&lt;1 1 -4 0 1 3 -2 -5|, &lt;0 5 54 24 21 6 52 79|]
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19


EDOs: 94, 111, 205
Comma list: 286/285, 352/351, 363/361, 442/441, 476/475, 561/560


Badness: 0.0173
Mapping: {{mapping| 1 0 38 48 32 37 58 32 | 0 2 -45 -57 -36 -42 -68 -35 }}


=Supers=
Optimal tunings:
Commas: 5120/5103, 118098/117649
* WE: ~2 = 1199.7534{{c}}, ~26/15 = 951.2024{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 951.4020{{c}}


POTE generator: ~9/7 = 434.218
{{Optimal ET sequence|legend=0| 29g, 82cdfgh, 111, 140 }}


Map: [&lt;2 1 -12 2|, &lt;0 3 23 5|]
Badness (Sintel): 1.01


Wedgie: &lt;&lt;6 46 10 59 -1 -106||
=== 23-limit ===
Subgroup: 2.3.5.7.11.13.17.19.23


EDOs: {{EDOs|58, 94, 152}}
Comma list: 253/252, 286/285, 352/351, 363/361, 391/390, 442/441, 460/459


Badness: 0.092748
Mapping: {{mapping| 1 0 38 48 32 37 58 32 18 | 0 2 -45 -57 -36 -42 -68 -35 -17 }}


==11-limit==
Optimal tunings:
Commas: 540/539, 4000/3993, 5120/5103
* WE: ~2 = 1199.9128{{c}}, ~26/15 = 951.3371{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 951.4076{{c}}


POTE generator: ~9/7 = 434.217
{{Optimal ET sequence|legend=0| 29g, 82cdfgh, 111, 140 }}


Map: [&lt;2 1 -12 2 -9|, &lt;0 3 23 5 22|]
Badness (Sintel): 1.10


EDOs: {{EDOs|58, 94, 152}}
== Countriton ==
: ''For the 5-limit version, see [[Schismic–Mercator equivalence continuum #Countritonic]].''


Badness: 0.028240
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.  


==13-limit==
Countriton was named by [[Xenllium]] in 2022 as a counterpart of [[untriton]].
Commas: 352/351, 540/539, 729/728, 1575/1573


POTE generator: ~9/7 = 434.221
[[Subgroup]]: 2.3.5.7


Map: [&lt;2 1 -12 2 -9 -2|, &lt;0 3 23 5 22 13|]
[[Comma list]]: 5120/5103, 7558272/7503125


EDOs: {{EDOs|58, 94, 152f}}
{{Mapping|legend=1| 1 -3 -15 13 | 0 9 34 -20 }}
: mapping generators: ~2, ~1225/864


Badness: 0.021645
[[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 }}


==17-limit==
{{Optimal ET sequence|legend=1| 51c, 53, 157, 210, 473cdd }}
Commas: 170/169, 289/288, 352/351, 442/441, 561/560


POTE generator: ~9/7 = 434.181
[[Badness]] (Sintel): 3.32


Map: [&lt;2 1 -12 2 -9 -2 6|, &lt;0 3 23 5 22 13 3|]
=== 11-limit ===
Subgroup: 2.3.5.7.11


EDOs: {{EDOs|58, 94, 152f}}
Comma list: 176/175, 5120/5103, 41503/41472


Badness: 0.021316
Mapping: {{mapping| 1 -3 -15 13 -21 | 0 9 34 -20 48 }}


=Alphaquarter=
Optimal tunings:
Commas: 5120/5103, 29360128/29296875
* WE: ~2 = 1199.5178{{c}}, ~77/54 = 611.2097{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~77/54 = 611.4495{{c}}


POTE generator: ~16128/15625 = 55.243
{{Optimal ET sequence|legend=0| 51ce, 53, 104c, 157 }}


Map: [&lt;1 2 2 0|, &lt;0 -9 7 61|]
Badness (Sintel): 2.80


Wedgie: &lt;&lt;9 -7 -61 -32 -122 -122||
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


EDOs: 87, 152, 239, 391
Comma list: 176/175, 351/350, 847/845, 2197/2187


Badness: 0.1166
Mapping: {{mapping| 1 -3 -15 13 -21 -7 | 0 9 34 -20 48 21 }}


==11-limit==
Optimal tunings:
Commas: 3025/3024, 4000/3993, 5120/5103
* WE: ~2 = 1199.5944{{c}}, ~77/54 = 611.2491{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~77/54 = 611.4506{{c}}


POTE generator: ~33/32 = 55.243
{{Optimal ET sequence|legend=0| 51ce, 53, 104c, 157 }}


Map: [&lt;1 2 2 0 3|, &lt;0 -9 7 61 10|]
Badness (Sintel): 1.75


EDOs: 87, 152, 239, 391
== Artoneutral ==
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.


Badness: 0.0296
Artoneutral was named by [[Flora Canou]] in 2023 for its generator's quality.  


= Septiquarter =
[[Subgroup]]: 2.3.5.7
Commas: 5120/5103, 420175/419904


POTE generator: ~147/128 = 242.453
[[Comma list]]: 5120/5103, 3828125/3779136


Map: [&lt;1 3 10 2|, &lt;0 -7 -38 4|]
{{Mapping|legend=1| 1 -1 -4 12 | 0 9 22 -32 }}
: mapping generators: ~2, ~128/105


Wedgie: &lt;&lt;7 38 -4 44 -26 -116||
[[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 }}


EDOs: {{EDOs|94, 99, 292, 391, 881bd, 1272bcd}}
{{Optimal ET sequence|legend=1| 87, 94, 181 }}


Badness: 0.0538
[[Badness]] (Sintel): 3.98


== Semiseptiquarter ==
=== 11-limit ===
Commas: 5120/5103, 9801/9800, 14641/14580
Subgroup: 2.3.5.7.11


POTE generators: ~121/105 = 242.4511
Comma list: 385/384, 2200/2187, 4000/3993


Map: [<2 6 20 4 15|, <0 -7 -38 4 -20|]
Mapping: {{mapping| 1 -1 -4 12 -2 | 0 9 22 -32 19 }}


EDOs: {{EDOs|94, 198, 292, 490}}
Optimal tunings:  
* WE: ~2 = 1200.1668{{c}}, ~11/9 = 344.8027{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 344.7557{{c}}


Badness: 0.0642
{{Optimal ET sequence|legend=0| 87, 181 }}
 
Badness (Sintel): 1.52


=== 13-limit ===
=== 13-limit ===
Commas: 352/351, 847/845, 1716/1715, 14641/14580
Subgroup: 2.3.5.7.11.13
 
Comma list: 325/324, 352/351, 385/384, 1575/1573
 
Mapping: {{mapping| 1 -1 -4 12 -2 6 | 0 9 22 -32 19 -8 }}
 
Optimal tunings:
* WE: ~2 = 1200.0662{{c}}, ~11/9 = 344.7804{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 344.7617{{c}}
 
{{Optimal ET sequence|legend=0| 87, 181 }}
 
Badness (Sintel): 1.08
 
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17


POTE generators: ~121/105 = 242.4448
Comma list: 325/324, 352/351, 375/374, 385/384, 595/594


Map: [<2 6 20 4 15 7|, <0 -7 -38 4 -20 1|]
Mapping: {{mapping| 1 -1 -4 12 -2 6 -12 | 0 9 22 -32 19 -8 56 }}


EDOs: {{EDOs|94, 198, 490f}}
Optimal tunings:  
* WE: ~2 = 1200.0346{{c}}, ~11/9 = 344.7589{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 344.7492{{c}}


Badness: 0.0348
{{Optimal ET sequence|legend=0| 87, 94, 181 }}


= Tricot (aka Trimot) =
Badness (Sintel): 1.16
{{see also|Tricot family}}


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


[[Comma list]]: 2430/2401, 5120/5103
Comma list: 325/324, 352/351, 375/374, 385/384, 400/399, 595/594


[[Mapping]]: [&lt;1 0 -13 -3|, &lt;0 3 29 11|]
Mapping: {{mapping| 1 -1 -4 12 -2 6 -12 -15 | 0 9 22 -32 19 -8 56 67 }}


[[Wedgie]]: &lt;&lt;3 29 11 39 9 -56||
Optimal tunings:  
* WE: ~2 = 1200.0282{{c}}, ~11/9 = 344.7532{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 344.7453{{c}}


[[POTE tuning|POTE generator]]: ~81/56 = 634.026
{{Optimal ET sequence|legend=0| 87, 94, 181 }}


{{Val list|legend=1| 17c, 36c, 53, 229dd, 282dd }}
Badness (Sintel): 1.19


[[Badness]]: 0.100127
=== 23-limit ===
Subgroup: 2.3.5.7.11.13.17.19.23


== 11-limit ==
Comma list: 300/299, 325/324, 352/351, 375/374, 385/384, 400/399, 484/483
Comma list: 99/98, 121/120, 5120/5103


Mapping: [&lt;1 0 -13 -3 -5|, &lt;0 3 29 11 16|]
Mapping: {{mapping| 1 -1 -4 12 -2 6 -12 -15 -13 | 0 9 22 -32 19 -8 56 67 61 }}


POTE generator: ~63/44 = 634.027
Optimal tunings:  
* WE: ~2 = 1200.0163{{c}}, ~11/9 = 344.7461{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 344.7416{{c}}


Vals: {{Val list| 17c, 36ce, 53, 70, 123de }}
{{Optimal ET sequence|legend=0| 87, 94, 181 }}


Badness: 0.056134
Badness (Sintel): 1.17


== 13-limit ==
== Quanic ==
Comma list: 99/98, 121/120, 169/168, 352/351
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.


Mapping: [&lt;1 0 -13 -3 -5 0|, &lt;0 3 29 11 16 7|]
[[Subgroup]]: 2.3.5.7


POTE generator: ~13/9 = 634.012
[[Comma list]]: 5120/5103, 5832000/5764801


Vals: {{Val list| 17c, 36ce, 53, 70, 123de }}
{{Mapping|legend=1| 1 1 -4 0 | 0 5 54 24 }}
: mapping generators: ~2, ~160/147


Badness: 0.032102
[[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 }}


= Ketchup =
{{Optimal ET sequence|legend=1| 94, 111, 205 }}
[[Comma list]]: 5120/5103, 1071875/1062882
 
[[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"