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These temperament names are no longer in use, although older material may still reference them. If one must refer to these temperaments, it is recommended to do so with an ET join (e. g. "11-limit 12 & 85") or as a restriction of a different temperament (e. g. "no-7s cassandra")
These temperament names are no longer in use, although older material may still reference them. If one must refer to these temperaments, it is recommended to do so with an ET join (e. g. "11-limit 12 & 85") or as a restriction of a different temperament (e. g. "no-7s cassandra")
 
{| class="wikitable"
== Oviminor ==
|+
: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Oviminor (5-limit)]].''
!Deprecated name
 
!Subgroup
Oviminor was named by [[Eliora]] in 2022 after the facts that it takes 184 minor thirds of [[6/5]] to reach the interval class of [[4/3]], the Roman consul was Eggius in the year 184 AD, and the Latin word for egg is ovum, and with prefix ovi-. It sets a new record of complexity for a chain of nineteen 6/5's past [[egads]], though it is less accurate.
!EDO join
 
!Reason for deletion
[[Subgroup]]: 2.3.5.7
|-
 
|Oviminor
[[Comma list]]: 4375/4374, {{monzo| -100 53 48 -34 }}
|7-limit
 
|19 & 1600
{{Mapping|legend=1| 1 -134 -134 -401 | 0 184 185 548 }}
|More complex than egads (which shares the same generator) at lower accuracy
: mapping generators: ~2, ~5/3
|-
 
|Maqamschismic
[[Optimal tuning]]s:
|11 to 13-limit
* [[WE]]: ~2 = 1200.0193{{c}}, ~5/3 = 884.2638{{c}}
|41 & 53
: [[error map]]: {{val| +0.019 +0.010 -0.085 +0.032 }}
|Removes prime 7 from cassandra even though prime 11 has higher complexity and error
* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/3 = 884.2497{{c}}
|-
: error map: {{val| 0.000 -0.011 -0.120 +0.008 }}
|Quintapole
 
|7 to 11-limit
{{Optimal ET sequence|legend=1| 19, …, 1600, 1619, 4838, 6457c }}
|12 & 85
 
|Medium accuracy is not worth the high complexity; could lead to confusion with similarly named "quintupole"
[[Badness]] (Sintel): 14.7
|-
 
|Quintapole > Galeleic
== Maqamschismic (2.3.5.11) ==
|13 to 19-limit
Maqamschismic is equivalent to the no-7 [[cassandra]]. The 2.3.5.11.13 subgroup adds [[352/351]] to the comma list and tempers 11/9~39/32 together (and 16/13~27/22), providing a very simple framework for tuning [[maqam]]at (especially the Turkish version), as outlined by [[Ozan Yarman]]. 41edo and 53edo are simplest, but 94edo is more optimized. It is only slightly worse than the no-7 [[helenus]].
|12f & 85fg
 
|Medium accuracy is not worth the high complexity; not even supported by any patent vals
Subgroup: 2.3.5.11
|-
 
|Quintapole > Catagali
Comma list: 2200/2187, 4125/4096
|13 to 19-limit
 
|12f & 85g
Subgroup-val mapping: {{mapping| 1 0 15 -33 | 0 1 -8 23 }}
|Medium accuracy is not worth the high complexity; not even supported by any patent vals
 
|-
Optimal tunings:
|Quintapole > Quintain
* WE: ~2 = 1200.5458{{c}} ~3/2 = 702.4021{{c}}
|11 to 13-limit
* CWE: 2 = 1200.0000{{c}}, ~3/2 = 702.0906{{c}}
|12 & 85e
 
|Medium accuracy is not worth the high complexity
{{Optimal ET sequence|legend=0| 12e, …, 41, 53, 94, 147e, 241ce, 335ce }}
|-
 
|Bixby
Badness (Sintel): 1.34
|5-limit
 
|1 & 1c
=== 2.3.5.11.13 subgroup ===
|Too coarse even for detempering
Subgroup: 2.3.5.11.13
|-
 
|Archon
Comma list: 325/324, 352/351, 4125/4096
|5-limit
 
|1 & 1b
Subgroup-val mapping: {{mapping| 1 0 15 -33 -28 | 0 1 -8 23 20 }}
|Too coarse even for detempering
 
|-
Optimal tunings:
|Seesaw
* WE: ~2 = 1200.4565{{c}} ~3/2 = 702.3057{{c}}
|2.3.5(.11)
* CWE: 2 = 1200.0000{{c}}, ~3/2 = 702.0485{{c}}
|1b & 2
 
|Too coarse even for detempering
{{Optimal ET sequence|legend=0| 12e, …, 41, 53, 94, 147e }}
|-
 
|Seesaw > Heavy windmill
Badness (Sintel): 0.862
|7 to 11-limit
 
|1bd & 2
== Quintapole ==
|Too coarse even for detempering
The ''quintapole'' temperament (12&amp;85) tempers out the marvel comma (225/224) and 7812500/7411887 (sepru-atritriyo). In the 11-limit, it tempers out the ptolemisma (100/99) as well as 85184/84035 (trilo-aquinru-agu). It is so named for the following reasons - it has the same commas as the [[Marvel family #Apollo|apollo temperament]], and its generator is a semitone five of which gives a flat fourth (~4/3, about 495 cents). [[User:Xenllium|Xenllium]] proposes the pronunciation of the word "quintapole" as /'kwɪntəpəʊl/ or /'kwɪntəpoʊl/, like as "quint-a-pole". ''Not to be confused with [[#Quintupole|quint<u>'''u'''</u>pole]] temperament (12&amp;121).''
|-
 
|Seesaw > Light windmill
Subgroup: 2.3.5.7
|7 to 11-limit
 
|1b & 2
[[Comma list]]: 225/224, 7812500/7411887
|Too coarse even for detempering
 
|-
[[Mapping]]: [{{val| 1 2 1 1 }}, {{val| 0 -5 16 22 }}]
|Sixseven
 
|2.3.7(.13)
[[Optimal tuning]]s:
|1 & 3
* [[WE]]: ~2 = 1198.959¢, ~21/20 = 98.908¢
|Too coarse even for detempering
* [[CWE]]: ~2 = 1200.000¢, ~21/20 = 98.968¢
|-
 
|Sixseven > Heaven
{{Optimal ET sequence|legend=1| 12, 73c, 85, 97d }}
|2.3.7.11(.13)
 
|1e & 3
[[Badness]] (Sintel): 4.872
|Too coarse even for detempering
 
|-
=== 11-limit ===
|Sept
Subgroup: 2.3.5.7.11
|7 to 13-limit
 
|7 & 14de
Comma list: 100/99, 225/224, 85184/84035
|No reason to leave prime 5 free in 7et rather than prime 7
 
|-
Mapping: [{{val| 1 2 1 1 0 }}, {{val| 0 -5 16 22 42 }}]
|Dog
 
|2.3.19
Optimal tunings:
|7 & 16
* WE: ~2 = 1198.982¢, ~21/20 = 98.870¢
|No reason to interpret the resultant scales as dog rather than mavila
* CWE: ~2 = 1200.000¢, ~21/20 = 98.931¢
|}
 
Optimal ET sequence: {{Optimal ET sequence| 12, 73ce, 85, 97d }}
 
Badness (Sintel): 3.450
 
==== Galileic ====
The name ''galileic'' comes from "{{w|Vincenzo Galilei}}", because this temperament is strongly related to [[Galilei's tuning]].
 
Subgroup: 2.3.5.7.11.13
 
Comma list: 100/99, 225/224, 275/273, 12168/12005
 
Mapping: [{{val| 1 2 1 1 0 -1 }}, {{val| 0 -5 16 22 42 57 }}]
 
Optimal tunings:
* WE: ~2 = 1198.912¢, ~21/20 = 98.902¢
* CWE: ~2 = 1200.000¢, ~21/20 = 98.970¢
 
Optimal ET sequence: {{Optimal ET sequence| 12f, 73ceff, 85f, 97d }}
 
Badness (Sintel): 3.231
 
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 100/99, 120/119, 225/224, 275/273, 2431/2401
 
Mapping: [{{val| 1 2 1 1 0 -1 5 }}, {{val| 0 -5 16 22 42 57 -11 }}]
 
Optimal tunings:
* WE: ~2 = 1198.798¢, ~18/17 = 98.903¢
* CWE: ~2 = 1200.000¢, ~18/17 = 98.986¢
 
Optimal ET sequence: {{Optimal ET sequence| 12f, 73ceffg, 85fg, 97dg }}
 
Badness (Sintel): 2.997
 
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 100/99, 120/119, 225/224, 247/245, 275/273, 361/357
 
Mapping: [{{val| 1 2 1 1 0 -1 5 4 }}, {{val| 0 -5 16 22 42 57 -11 3 }}]
 
Optimal tunings:
* WE: ~2 = 1199.031¢, ~18/17 = 98.907¢
* CWE: ~2 = 1200.000¢, ~18/17 = 98.976¢
 
Optimal ET sequence: {{Optimal ET sequence| 12f, 73ceffg, 85fg, 97dg }}
 
Badness (Sintel): 2.765
 
==== Catagali ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 100/99, 225/224, 847/845, 1040/1029
 
Mapping: [{{val| 1 2 1 1 0 0 }}, {{val| 0 -5 16 22 42 45 }}]
 
Optimal tunings:
* WE: ~2 = 1199.021¢, ~21/20 = 98.801¢
* CWE: ~2 = 1200.000¢, ~21/20 = 98.860¢
 
Optimal ET sequence: {{Optimal ET sequence| 12f, 73ce, 85 }}
 
Badness (Sintel): 3.065
 
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 100/99, 120/119, 225/224, 442/441, 847/845
 
Mapping: [{{val| 1 2 1 1 0 0 5 }}, {{val| 0 -5 16 22 42 45 -11 }}]
 
Optimal tunings:
* WE: ~2 = 1198.792¢, ~18/17 = 98.805¢
* CWE: ~2 = 1200.000¢, ~18/17 = 98.887¢
 
Optimal ET sequence: {{Optimal ET sequence| 12f, 73ceg, 85g }}
 
Badness (Sintel): 2.951
 
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 100/99, 120/119, 209/208, 225/224, 361/357, 442/441
 
Mapping: [{{val| 1 2 1 1 0 0 5 4 }}, {{val| 0 -5 16 22 42 45 -11 3 }}]
 
Optimal tunings:
* WE: ~2 = 1199.037¢, ~18/17 = 98.808¢
* CWE: ~2 = 1200.000¢, ~18/17 = 98.875¢
 
Optimal ET sequence: {{Optimal ET sequence| 12f, 73ceg, 85g }}
 
Badness (Sintel): 2.720
 
=== Quintain ===
Subgroup: 2.3.5.7.11
 
Comma list: 225/224, 245/242, 5000/4851
 
Mapping: [{{val| 1 2 1 1 1 }}, {{val| 0 -5 16 22 30 }}]
 
Optimal tunings:
* WE: ~2 = 1198.804¢, ~21/20 = 98.718¢
* CWE: ~2 = 1200.000¢, ~21/20 = 98.784¢
 
Optimal ET sequence: {{Optimal ET sequence| 12, 61c, 73c, 85e }}
 
Badness (Sintel): 3.730
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 225/224, 245/242, 275/273, 1040/1029
 
Mapping: [{{val| 1 2 1 1 1 0 }}, {{val| 0 -5 16 22 30 45 }}]
 
Optimal tunings:
* WE: ~2 = 1198.830¢, ~21/20 = 98.700¢
* CWE: ~2 = 1200.000¢, ~21/20 = 98.768¢
 
Optimal ET sequence: {{Optimal ET sequence| 12f, 61cf, 73c, 85e }}
 
Badness (Sintel): 3.302
 
== Bixby ==
{{Main| Bixby }}
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: [[4/3]]
 
{{Mapping|legend=1| 1 2 0 | 0 0 1 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1020.058{{c}}, ~5/4 = 674.394{{c}}
: [[error map]]: {{val| -179.942 +138.161 -71.803 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~5/4 = 629.521{{c}}
: error map: {{val| 0.000 +498.045 +243.208 }}
 
{{Optimal ET sequence|legend=1| 1c, 2b, 3bbcc }}
 
[[Badness]] (Sintel): 0.424
 
== Archon ==
{{Main| Archon }}
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: [[5/4]]
 
{{Mapping|legend=1| 1 0 2 | 0 1 0 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1268.274{{c}}, ~3/2 = 612.921{{c}}
: [[error map]]: {{val| +68.274 -20.760 -249.765 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 614.055{{c}}
: error map: {{val| 0.000 -87.900 -386.314 }}
 
{{Optimal ET sequence|legend=1| 2c }}
 
[[Badness]] (Sintel): 0.474
 
== Seesaw ==
{{Main| Seesaw }}
Seesaw tempers out the [[6/5|classic minor third (6/5)]], equating the [[5/1|fifth]] and [[6/1|sixth harmonic]]s. It was named by [[User:Xenllium|Xenllium]] in 2026.
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 6/5
 
{{Mapping|legend=1| 1 0 1 | 0 1 1 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1155.569{{c}}, ~3/2 = 643.349{{c}}
: [[error map]]: {{val| -44.431 -103.037 +168.173 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 627.511{{c}}
: error map: {{val| 0.000 -74.444 +241.197 }}
 
{{Optimal ET sequence|legend=1| 2 }}
 
[[Badness]] (Sintel): 0.367
 
=== 2.3.5.11 subgroup ===
This temperament is extended to the 2.3.5.11 subgroup naturally, tempering out both [[11/10]] and [[12/11]], undecimal neutral seconds.
 
Subgroup: 2.3.5.11
 
Comma list: 6/5, 11/10
 
Mapping: {{mapping| 1 0 1 2 | 0 1 1 1 }}
 
Optimal tunings:
* WE: ~2 = 1156.418{{c}}, ~3/2 = 643.202{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 627.023{{c}}
 
{{Optimal ET sequence|legend=0| 2 }}
 
Badness (Sintel): 0.499
 
=== Heavy windmill ===
Heavy windmill tempers out [[9/7]] and [[15/14]] in the 7-limit.
 
Subgroup: 2.3.5.7
 
Comma list: 6/5, 9/7
 
Mapping: {{mapping| 1 0 1 0 | 0 1 1 2 }}
 
Optimal tunings:
* WE: ~2 = 1161.600{{c}}, ~3/2 = 571.169{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 559.563{{c}}
 
{{Optimal ET sequence|legend=0| 2 }}
 
Badness (Sintel): 0.676
 
==== 11-limit ====
Subgroup: 2.3.5.7.11
 
Comma list: 6/5, 9/7, 11/10
 
Mapping: {{mapping| 1 0 1 0 2 | 0 1 1 2 1 }}
 
Optimal tunings:
* WE: ~2 = 1166.584{{c}}, ~3/2 = 568.073{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 558.941{{c}}
 
{{Optimal ET sequence|legend=0| 2 }}
 
Badness (Sintel): 0.774
 
=== Light windmill ===
Light windmill tempers out [[8/7]] and [[21/20]] in the 7-limit.
 
Subgroup: 2.3.5.7
 
Comma list: 6/5, 8/7
 
Mapping: {{mapping| 1 0 1 3 | 0 1 1 0 }}
 
Optimal tunings:
* WE: ~2 = 1134.018{{c}}, ~3/2 = 670.285{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 667.893{{c}}
 
{{Optimal ET sequence|legend=0| 2 }}
 
Badness (Sintel): 0.629
 
==== 11-limit ====
Subgroup: 2.3.5.7.11
 
Comma list: 6/5, 8/7, 11/10
 
Mapping: {{mapping| 1 0 1 3 2 | 0 1 1 0 1 }}
 
Optimal tunings:
* WE: ~2 = 1136.109{{c}}, ~3/2 = 672.403{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 668.374{{c}}
 
{{Optimal ET sequence|legend=0| 2 }}
 
Badness (Sintel): 0.681
 
== Sixseven ==
Sixseven tempers out the [[7/6|septimal minor third (7/6)]], equating the [[6/1|sixth]] and [[7/1|seventh harmonic]]s. It was named by [[User:Xenllium|Xenllium]] in 2026.
 
[[Subgroup]]: 2.3.7
 
[[Comma list]]: 7/6
 
{{Mapping|legend=1| 1 0 1 | 0 1 1 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1218.135{{c}}, ~3/2 = 734.187{{c}}
: [[error map]]: {{val| +18.135 +50.367 -198.368 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 738.927{{c}}
: error map: {{val| 0.000 +36.972 -229.899 }}
 
{{Optimal ET sequence|legend=1| 1, 2d, 3, 5dd }}
 
[[Badness]] (Sintel): 0.329
 
=== 2.3.7.13 subgroup ===
This temperament is extended to the 2.3.7.13 subgroup naturally, tempering out both [[13/12]] and [[14/13]], tridecimal neutral seconds.
 
Subgroup: 2.3.7.13
 
Comma list: 7/6, 13/12
 
Mapping: {{mapping| 1 0 1 2 | 0 1 1 1 }}
 
Optimal tunings:
* WE: ~2 = 1220.937{{c}}, ~3/2 = 734.003{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 739.780{{c}}
 
{{Optimal ET sequence|legend=0| 1, 2d, 3, 5ddf }}
 
Badness (Sintel): 0.422
 
=== Heaven ===
Heaven tempers out [[11/9]] and [[22/21]] in the 2.3.7.11 subgroup.
 
Subgroup: 2.3.7.11
 
Comma list: 7/6, 11/9
 
Mapping: {{mapping| 1 0 1 0 | 0 1 1 2 }}
 
Optimal tunings:
* WE: ~2 = 1210.810{{c}}, ~3/2 = 783.079{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 785.173{{c}}
 
{{Optimal ET sequence|legend=0| 1e, 2de, 3 }}
 
Badness (Sintel): 0.577
 
==== 2.3.7.11.13 subgroup ====
Subgroup: 2.3.7.11.13
 
Comma list: 7/6, 11/9, 13/12
 
Mapping: {{mapping| 1 0 1 0 2 | 0 1 1 2 1 }}
 
Optimal tunings:
* WE: ~2 = 1210.595{{c}}, ~3/2 = 783.176{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 784.989{{c}}
 
{{Optimal ET sequence|legend=0| 1e, 2de, 3 }}
 
Badness (Sintel): 0.627
 
== Sept ==
{{See also|Whitewood family}}Sept preserves the 2.3.7-subgroup of mapping of 7edo, and harmonic 5 is mapped to an independent generator. As harmonic 5 is way more accurately approximated than 7 by 7edo, this temperament provides little improvement to 7edo's 7-limit tuning, so in what way this temperament is useful remains unexplained. It would make much more sense to, for example, preserve the 5-limit structure of 7edo and give prime 7 an independent generator instead, which is exactly what [[jamesbond]] does.
 
This temperament used to be known as ''mujannab''.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 54/49, 64/63
 
{{Mapping|7 11 0 20|0 0 1 0|legend=1}}
 
[[Optimal tuning|Optimal tunings]]:
 
* [[WE]]: ~9/8 = 170.823{{c}}, ~5/4 = 393.792{{c}} (~15/14 = 52.145{{c}})
 
: [[error map]]: {{val|-4.236 -22.898 -0.994 +47.642}}
 
* [[CWE]]: ~9/8 = 171.429{{c}}, ~5/4 = 392.719{{c}} (~15/14 = 49.862{{c}})
 
: error map: {{val|0.000 -16.241 +6.406 +59.746}}
 
{{Optimal ET sequence|7, 14d|legend=1}}
 
[[Badness]] (Sintel): 2.68
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 45/44, 54/49, 64/63
 
Mapping: {{mapping|7 11 0 20 8|0 0 1 0 1}}
 
Optimal tunings:
 
* WE: ~11/10 = 170.817{{c}}, ~5/4 = 393.252{{c}} (~33/32 = 51.619{{c}})
* CWE: ~11/10 = 171.429{{c}}, ~5/4 = 391.840{{c}} (~33/32 = 48.983{{c}})
 
{{Optimal ET sequence|7, 14de|legend=0}}
 
Badness (Sintel): 2.02
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 27/26, 45/44, 52/49, 64/63
 
Mapping: {{mapping|7 11 0 20 8 26|0 0 1 0 1 0}}
 
Optimal tunings:
 
* WE: ~11/10 = 170.795{{c}}, ~5/4 = 393.611{{c}} (~33/32 = 52.021{{c}})
* CWE: ~11/10 = 171.429{{c}}, ~5/4 = 392.725{{c}} (~33/32 = 49.868{{c}})
 
{{Optimal ET sequence|7, 14de|legend=0}}
 
Badness (Sintel): 1.77
[[Category:Temperament collections]]
[[Category:Temperament collections]]
==Dog==
Dog is based by 2L 5s or 7L 2s scale that makes 81/76 vanish, so 19/16 is a major third. It can be viewed as a 2.3.19-subgroup analogue of mavila.
Subgroup: 2.3.19
Comma list: 81/76
Subgroup-val mapping: [⟨1 0 -2], ⟨0 1 4]]
mapping generators: ~2, ~3
Optimal tunings:
WE: ~2 = 1203.3813 ¢, ~3/2 = 680.5089 ¢
error map: ⟨+3.381 -18.065 +31.285]
CWE: ~2 = 1200.0000 ¢, ~3/2 = 680.5856 ¢
error map: ⟨0.000 -21.369 +24.8295]
Optimal ET sequence: 2, 5h, 7, 16, 23
Badness (Sintel): 0.491
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