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== Maqamschismic (2.3.5.11) ==
== Maqamschismic (2.3.5.11) ==
Proposed by [[Eufalesio]] in 2026, 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]].
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]].


Subgroup: 2.3.5.11
Subgroup: 2.3.5.11
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Badness (Sintel): 3.302
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
[[Category:Temperament collections]]
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