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→Subgroup extensions: restore the intermediate 2.3.5.11-subgroup extension. Normalize mappings. Unify precision and various cleanup.
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== Subgroup extensions ==
== Subgroup extensions ==
=== 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]].


=== Tridecaschismic (2.3.5.13) ===
Subgroup: 2.3.5.11
Proposed by [[Eufalesio]] in 2026, tridecaschismic adds the [[325/324|marveltwin comma]] to the comma list, benefitting from a fifth that is just, or practically indistinguishable from just, like in 53edo. It is has among the lowest badness of schismic extensions. It is also equivalent to  the 2.3.5.13 [[restriction]] of 13-limit [[cassandra]].


Subgroup: 2.3.5.13
Comma list: 2200/2187, 4125/4096


Comma list: 32805/32768, 325/324
Subgroup-val mapping: {{mapping| 1 0 15 -33 | 0 1 -8 23 }}
 
: Mapping: [⟨1 1 7 -8], ⟨0 1 -8 20]]


Optimal tunings:
Optimal tunings:
* WE: ~2 = 1200.5458{{c}} ~3/2 = 702.4021{{c}}
* CWE: 2 = 1200.0000{{c}}, ~3/2 = 702.0906{{c}}


* WE: ~2 = 1200.333 ¢ ~3/2 = 702.109 ¢
{{Optimal ET sequence|legend=0| 12e, …, 41, 53, 94, 147e, 241ce, 335ce }}
* CWE: 2 = 1200 ¢, ~3/2 = 701.919 ¢
 
{{Optimal ET sequence|legend=0| 12, …, 41, 53, 65f, 94, 118f, 147, 200}}
 
Badness (Sintel): 0.582


==== Maqamschismic (2.3.5.11.13 subgroup) ====
Badness (Sintel): 1.34
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 [[Middle-Eastern music#Level 2|''maqamāt'']], specially Turkish ''maqāmāt'', as outlined by [[Ozan Yarman|Ozar Yarman]]. It is equivalent to the no-7 [[cassandra]]. 41edo and 53edo are simplest, but 94edo is more optimized. It is only slightly worse than the no-7 [[Schismatic family#13-limit 3|helenus]].


==== 2.3.5.11.13 subgroup ====
Subgroup: 2.3.5.11.13
Subgroup: 2.3.5.11.13


Comma list: 325/324, 352/351, 4125/4096
Comma list: 325/324, 352/351, 4125/4096


Mapping: {{mapping| 1 1 7 -10 -8 | 0 1 -8 23 20 }}
Subgroup-val mapping: {{mapping| 1 0 15 -33 -28 | 0 1 -8 23 20 }}


Optimal tunings:
Optimal tunings:
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Badness (Sintel): 0.862
Badness (Sintel): 0.862
=== Tridecaschismic (2.3.5.13) ===
Proposed by [[Eufalesio]] in 2026, tridecaschismic adds the [[325/324|marveltwin comma]] to the comma list, benefitting from a fifth that is just, or practically indistinguishable from just, like in 53edo. It is has among the lowest badness of schismic extensions. It is also equivalent to the 2.3.5.13 [[restriction]] of 13-limit [[cassandra]].
Subgroup: 2.3.5.13
Comma list: 325/324, 32805/32768
Subgroup-val mapping: {{mapping| 1 0 15 -28 | 0 1 -8 20 }}
Optimal tunings:
* WE: ~2 = 1200.3326{{c}} ~3/2 = 702.1092{{c}}
* CWE: 2 = 1200.0000{{c}}, ~3/2 = 701.9189{{c}}
{{Optimal ET sequence|legend=0| 12, …, 41, 53, 412cf, 465cf, …, 783ccff, 836ccfff }}
Badness (Sintel): 0.582
==== 2.3.5.13.19 subgroup ====
Subgroup: 2.3.5.13
Comma list: 325/324, 361/360, 513/512
Subgroup-val mapping: {{mapping| 1 0 15 -28 9 | 0 1 -8 20 -3 }}
Optimal tunings:
* WE: ~2 = 1200.4236{{c}}, ~3/2 = 702.1510{{c}}
* CWE: 2 = 1200.0000{{c}}, ~3/2 = 701.9064{{c}}
{{Optimal ET sequence|legend=0| 12, …, 41, 53 }}
Badness (Sintel): 0.354


=== Photia (2.3.5.17) ===
=== Photia (2.3.5.17) ===
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: ''See also: [[No-elevens subgroup temperaments #Garibaldia]] and [[No-elevens subgroup temperaments #Pontia|#Pontia]]''
: ''See also: [[No-elevens subgroup temperaments #Garibaldia]] and [[No-elevens subgroup temperaments #Pontia|#Pontia]]''


Nestoria is notable for having one of the lowest-badness subgroup extensions of schismic. Note that despite prime [[19/1|19]] being optimized by a flatter fifth, the fifth in optimal tunings of nestoria is generally not flatter than the fifth in optimal schismic due to its optimization considering intervals like [[19/10]] and [[19/15]]. Much like tridecaschismic, 
Nestoria is notable for having one of the lowest-badness subgroup extensions of schismic. Note that despite prime [[19/1|19]] being optimized by a flatter fifth, the fifth in optimal tunings of nestoria is generally not flatter than the fifth in optimal schismic due to its optimization considering intervals like [[19/10]] and [[19/15]].  


[[Subgroup]]: 2.3.5.19
[[Subgroup]]: 2.3.5.19
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[[Badness]] (Sintel): 0.126
[[Badness]] (Sintel): 0.126
==== 2.3.5.13.19 subgroup ====
Subgroup: 2.3.5.13
Comma list: 1216/1215, 325/234, 513/512
: Mapping: [⟨1 1 7 -8], ⟨0 1 -8 20]]
Optimal tunings:
* WE: ~2 = 1200.424 ¢ ~3/2 = 702.151 ¢
* CWE: 2 = 1200 ¢, ~3/2 = 701.906¢
{{Optimal ET sequence|legend=0| 12, …, 41, 53, 94, 147, 200h}}
Badness (Sintel): 0.354


=== Taylor (2.3.5.13) ===
=== Taylor (2.3.5.13) ===
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