Septischismic family: Difference between revisions

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The head of this family is septischismic (~~sometimes~~ ''garischismic''), which is generated by a [[3/2|perfect fifth]] and an independent generator for [[5/4]]. Two [[Pythagorean apotome]]s i.e. 14 fifths octave-reduced make a [[8/7|septimal major second (8/7)]]. Equivalently stated, the [[7/4|harmonic seventh (7/4)]] is found at the double-diminished octave (C–C𝄫), or the minor seventh minus a generic comma step which stands in for both the Pythagorean comma and the septimal comma.

The head of this family is septischismic (formerly ''garischismic''), which is generated by a [[3/2|perfect fifth]] and an independent generator for [[5/4]]. Two [[Pythagorean apotome]]s i.e. 14 fifths octave-reduced make a [[8/7|septimal major second (8/7)]]. Equivalently stated, the [[7/4|harmonic seventh (7/4)]] is found at the double-diminished octave (C–C𝄫), or the minor seventh minus a generic comma step which stands in for both the Pythagorean comma and the septimal comma.

Septischismic can be easily notated with [[chain-of-fifths notation]] with two additional sets of accidentals, one for the generic comma step, and the other for the generic aberschisma step which stands in for the [[schisma]] and the [[aberschisma]].

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Undecimal septischismic, a.k.a. cassaschismic, maps [[prime interval|prime]] [[11/1|11]] to +23 perfect fifths, so it is an [[expansion]] of the [[2.3.7.11 subgroup|2.3.7.11-subgroup]] version of [[gary]]. It is naturally a no-17 19-limit temperament, where the undevicesimal schisma of [[513/512]] is also added to the generic aberschisma step.

Septischismic has two reasonable extensions to add 17, which coalesce in the newt extension 270 & 311. Septinoellismic finds it a tad unintuitively as two aberschismas up and 4 commas down from a major second (^^4sM2) yet supported by 94edo, and septisperasmic finds it 4 aberschismas up from a minor second (4^m2), which can be deemed the more intuitive mapping, albeit it is not supported by any cassandra tuning except for 12edo, which notably has a very well tuned 17/16.

Septischismic has two reasonable extensions to add 29 and 31 into the system, that like before, coalesce in the newt extension 270 & 311 too. Septiplanar finds them in the chain of fifths, without need of third generators, thus they in the same plane to the rank-2 chain of fifths, mapped respectively to a major seventh – three commas (3sM7) and a perfect octave minus two commas (hP8). Because this extension is reached only through the septischismic chain of fifths, it is also available in [[gary]].

[[Subgroup]]: 2.3.5.7.11

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Comma list: 2080/2079, 4096/4095, 19712/19683

~~Mapping:~~ {{~~mapping~~| 1 0 0 25 -33 -13 | 0 1 0 -14 23 12 | 0 0 1 0 0 -1 }}

{{Mapping|legend=0| 1 0 0 25 -33 -13 | 0 1 0 -14 23 12 | 0 0 1 0 0 -1 }}

Optimal tunings:

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Badness (Sintel): 0.815

=== 2.3.5.7.11.13.19 subgroup ===

==== 2.3.5.7.11.13.19 subgroup ====

Subgroup: 2.3.5.7.11.13.19

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Badness (Sintel): 0.486

=== ~~Septinoellismic~~ ===

===== Septiplanar =====

Septischismic has two reasonable extensions to add 17, both of which coalesce in the structurally very similar temperament [[newt]]. Septinoellismic finds it a tad unintuitively as two aberschismas up and 4 commas down from a major second (^^4sM2) yet supported by 94edo, and septisperasmic finds it 4 aberschismas up from a minor second (4^m2), which can be deemed the more intuitive mapping, albeit it is not supported by any cassandra tuning except for 12edo which notably has a very well tuned 17/16.

~~Subgroup: 2.3.5.7.11.13.17.19~~

~~Comma list: 1225/1224, 1216/1215, 1540/1539, 1729/1728, 2080/2079~~

~~Subgroup-val mapping: {{mapping| 1 0 0 25 -33 -13 47 -6 | 0 1 0 -14 23 12 -30 5 | 0 0 1 0 0 -1 2 1 }}~~

~~Optimal tunings:~~

* WE: ~2 = 1199.970{{c}}, ~3/2 = 702.190{{c}}, ~5/4 = ~~386.177{{c}}~~

~~: error map: {{val|-0.030 +0.235 -0.137 -0.238 +0.044 -0.034 +0.286 -0.206}}~~

* CWE: ~2 = ~~1200.0000{{c}}, ~3/2~~ = ~~702.2307{{c}}, ~5/4~~ = ~~386.3245{{c}}~~

~~: error map: {{val|0.000 +0.282 -0.075 -0.150 +0.143 +0.083 +0.399 -0.088}}~~

~~{{Optimal ET sequence|legend=0|TBA}}~~

~~Badness (Sintel): 0.682~~

~~=== Septisperasmic ===~~

~~Subgroup: 2.3.5.7.11.13.17.19~~

~~Comma list: 1216/1215, 1540/1539, 1729/1728, 2080/2079, 2500/2499~~

~~Subgroup-val mapping: {{mapping| 1 0 0 25 -33 -13 -48 -6 | 0 1 0 -14 23 12 27 5 | 0 0 1 0 0 -1 4 1 }}~~

~~Optimal tunings:~~

* WE: ~2 = 1199.986{{c}}, ~3/2 = 702.206{{c}}, ~5/4 = 386.207{{c}}

~~: error map: {{val|-0.014 +0.251 -0.106 -0.056 -0.123 -0.084 +0.101 -0.193}}~~

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.228{{c}}, ~5/4 = 386.238{{c}}

~~: error map: {{val|0.000 +0.273 -0.075 -0.015 -0.078 -0.032 +0.148 -0.136}}~~

~~{{Optimal ET sequence|legend=0|TBA}}~~

~~Badness (Sintel): 1.096~~

~~=== Septiplanar ===~~

Septischismic has two reasonable extensions to add 29 and 31 into the system, that like before, coalesce in newt. Septiplanar finds them in the chain of fifths, without need of third generators, thus they in the same plane to the rank-2 chain of fifths, mapped respectively to a major seventh – three commas (3sM7) and a perfect octave minus two commas (hP8). Because this extension is reached only through the septischismic chain of fifths, it is also available in [[gary]].

Subgroup: 2.3.5.7.11.13.19.29

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Optimal tunings:

* WE: ~2 = 1199.~~948~~{{c}}, ~3/2 = 702.~~213~~{{c}}, ~5/4 = 386.~~379~~{{c}}

* WE: ~2 = 1199.9476{{c}}, ~3/2 = 702.2134{{c}}, ~5/4 = 386.3794{{c}}

: error map: {{val| -0.052 +0.206 -0.039 -0.389 +0.113 -0.190 -0.119 +0.603 }}

* CWE: ~2 = 1200.~~000~~{{c}}, ~3/2 = 702.~~244~~{{c}}, ~5/4 = 386.~~388~~{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.2440{{c}}, ~5/4 = 386.3884{{c}}

: error map: {{val| 0.000 +0.289 +0.075 -0.242 +0.293 +0.012 +0.095 +0.860 }}

Optimal ET sequence~~: TBA~~

{{Optimal ET sequence|legend=0| 41, 53j, 94, 176, 217, 270, 487, 581j, 1068j }}

Badness (Sintel): 0.758

===== 2.3.5.7.11.13.19.29.31 subgroup =====

====== 2.3.5.7.11.13.19.29.31 subgroup ======

Subgroup: 2.3.5.7.11.13.19.29.31

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Optimal tunings:

* WE: ~2 = 1199.~~930~~{{c}}, ~3/2 = 702.~~208~~{{c}}, ~5/4 = 386.~~406~~{{c}}

* WE: ~2 = 1199.9298{{c}}, ~3/2 = 702.2082{{c}}, ~5/4 = 386.4062{{c}}

: error map: {{val| -0.070 +0.183 -0.048 -0.513 +0.173 -0.225 -0.136 +0.353 +0.633 }}

* CWE: ~2 = 1200.000{{c}}, ~3/2 = 702.~~250~~{{c}}, ~5/4 = 386.~~420~~{{c}}

* CWE: ~2 = 1200.000{{c}}, ~3/2 = 702.2495{{c}}, ~5/4 = 386.4198{{c}}

: error map: {{val| 0.000 +0.295 +0.106 -0.319 +0.421 +0.047 +0.154 +0.688 +0.976 }}

Optimal ET sequence~~: TBA~~

{{Optimal ET sequence|legend=0| 41, 94, 135, 176, 217, 270, 311, 487, 581jk, 798k, 1068jk }}

Badness (Sintel): 0.793

=== Septifantasious ===

===== Septifantasious =====

Septifantasious tempers out [[1625/1624]] – the fantasia, and thus finds 29/16 as 3 aberschismas above 9/5 – that is to say, superminor seventh + 2 aberschismas (^^Sm7), and 31/16 one apotome higher as a hypermajor seventh + 2 aberschismas (^^HM7).

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Optimal tunings:

* WE: ~2 = 1199.~~983~~{{c}}, ~3/2 = 702.~~213~~{{c}}, ~5/4 = 386.~~172~~{{c}}

* WE: ~2 = 1199.9833{{c}}, ~3/2 = 702.2132{{c}}, ~5/4 = 386.1721{{c}}

: error map: {{val| -0.017 +0.242 -0.175 +0.005 -0.246 -0.091 -0.291 +0.495 }}

* CWE: ~2 = 1200.~~000~~{{c}}, ~3/2 = 702.~~233~~{{c}}, ~5/4 = 386.~~174~~{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.2228{{c}}, ~5/4 = 386.1741{{c}}

: error map: {{val| 0.000 +0.268 -0.140 +0.055 -0.193 -0.028 -0.225 +0.564 }}

Optimal ET sequence~~: TBA~~

{{Optimal ET sequence|legend=0| 41, 53, 94j, 217j, 258j, 270, 581j, 904, 945, 1215j }}

Badness (Sintel): 0.716

===== 2.3.5.7.11.13.19.29.31 subgroup =====

====== 2.3.5.7.11.13.19.29.31 subgroup ======

Subgroup: 2.3.5.7.11.13.19.29.31

Line 188:

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: error map: {{val| 0.000 +0.264 -0.192 +0.110 -0.284 -0.023 -0.297 +0.358 +0.431 }}

Optimal ET sequence~~: TBA~~

{{Optimal ET sequence|legend=0| 41, 53k, 94jk, 217jk, 229j, 270, 311, 581jk, 634, 904, 945, 1215jk }}

Badness (Sintel): 0.796

=== Septinoellismic ===

Subgroup: 2.3.5.7.11.13.17

Comma list: 1225/1224, 2080/2079, 2431/2430, 4096/4095

Subgroup-val mapping: {{mapping| 1 0 0 25 -33 -13 47 | 0 1 0 -14 23 12 -30 | 0 0 1 0 0 -1 2 }}

Optimal tunings:

* WE: ~2 = 1199.9654{{c}}, ~3/2 = 702.2159{{c}}, ~5/4 = 386.2053{{c}}

: error map: {{val| -0.035 +0.226 -0.178 -0.229 -0.006 -0.038 +0.252 }}

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.2359{{c}}, ~5/4 = 386.2080{{c}}

: error map: {{val| 0.000 +0.281 -0.106 -0.129 +0.109 +0.096 +0.383 }}

{{Optimal ET sequence|legend=0| 53, 94, 176g, 217, 270, 311, 487, 581 }}

Badness (Sintel): 0.950

==== 19-limit ====

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 1216/1215, 1225/1224, 1540/1539, 1729/1728, 2080/2079

Subgroup-val mapping: {{mapping| 1 0 0 25 -33 -13 47 -6 | 0 1 0 -14 23 12 -30 5 | 0 0 1 0 0 -1 2 1 }}

Optimal tunings:

* WE: ~2 = 1199.9699{{c}}, ~3/2 = 702.2200{{c}}, ~5/4 = 386.2373{{c}}

: error map: {{val| -0.030 +0.235 -0.137 -0.238 +0.044 -0.034 +0.286 -0.206 }}

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.2374{{c}}, ~5/4 = 386.2384{{c}}

: error map: {{val| 0.000 +0.282 -0.075 -0.150 +0.143 +0.083 +0.399 -0.088 }}

{{Optimal ET sequence|legend=0| 53, 94, 176g, 217, 270, 311, 487, 581 }}

Badness (Sintel): 0.682

=== Septisperasmic ===

Subgroup: 2.3.5.7.11.13.17

Comma list: 2080/2079, 2500/2499, 4096/4095, 19712/19683

Subgroup-val mapping: {{mapping| 1 0 0 25 -33 -13 -48 | 0 1 0 -14 23 12 27 | 0 0 1 0 0 -1 4 }}

Optimal tunings:

* WE: ~2 = 1199.9797{{c}}, ~3/2 = 702.2164{{c}}, ~5/4 = 386.2286{{c}}

: error map: {{val| -0.020 +0.241 -0.126 -0.080 -0.136 -0.098 +0.068 }}

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.2281{{c}}, ~5/4 = 386.2332{{c}}

: error map: {{val| 0.000 +0.273 -0.081 -0.020 -0.071 -0.023 +0.137 }}

{{Optimal ET sequence|legend=0| 258, 270, 311, 581, 1485, 1796, 2066, 2647b }}

Badness (Sintel): 1.76

==== 19-limit ====

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 1216/1215, 1540/1539, 1729/1728, 2080/2079, 2500/2499

Subgroup-val mapping: {{mapping| 1 0 0 25 -33 -13 -48 -6 | 0 1 0 -14 23 12 27 5 | 0 0 1 0 0 -1 4 1 }}

Optimal tunings:

* WE: ~2 = 1199.9861{{c}}, ~3/2 = 702.2198{{c}}, ~5/4 = 386.2353{{c}}

: error map: {{val| -0.014 +0.251 -0.106 -0.056 -0.123 -0.084 +0.101 -0.193 }}

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.2278{{c}}, ~5/4 = 386.2383{{c}}

: error map: {{val| 0.000 +0.273 -0.075 -0.015 -0.078 -0.032 +0.148 -0.136 }}

{{Optimal ET sequence|legend=0| 258, 270, 311, 581, 1485, 1796, 2066 }}

Badness (Sintel): 1.10

== Androschismic ==

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Comma list: 2080/2079, 10648/10647, 43904/43875

~~Mapping:~~ {{~~mapping~~| 1 0 0 25 62 82 | 0 1 0 -14 -34 -43 | 0 0 1 0 -2 -3 }}

{{Mapping|legend=0| 1 0 0 25 62 82 | 0 1 0 -14 -34 -43 | 0 0 1 0 -2 -3 }}

Optimal tunings:

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Comma list: 1216/1215, 2080/2079, 3136/3135, 10648/10647

~~Mapping:~~ {{~~mapping~~| 1 0 0 25 62 82 -6 | 0 1 0 -14 -34 -43 5 | 0 0 1 0 -2 -3 1 }}

{{Mapping|legend=0| 1 0 0 25 62 82 -6 | 0 1 0 -14 -34 -43 5 | 0 0 1 0 -2 -3 1 }}

Optimal tunings:

@@ Line 5: / Line 5: @@
 {{Main| Septischismic }}
-The head of this family is septischismic (sometimes ''garischismic''), which is generated by a [[3/2|perfect fifth]] and an independent generator for [[5/4]]. Two [[Pythagorean apotome]]s i.e. 14 fifths octave-reduced make a [[8/7|septimal major second (8/7)]]. Equivalently stated, the [[7/4|harmonic seventh (7/4)]] is found at the double-diminished octave (C–C𝄫), or the minor seventh minus a generic comma step which stands in for both the Pythagorean comma and the septimal comma.
+The head of this family is septischismic (formerly ''garischismic''), which is generated by a [[3/2|perfect fifth]] and an independent generator for [[5/4]]. Two [[Pythagorean apotome]]s i.e. 14 fifths octave-reduced make a [[8/7|septimal major second (8/7)]]. Equivalently stated, the [[7/4|harmonic seventh (7/4)]] is found at the double-diminished octave (C–C𝄫), or the minor seventh minus a generic comma step which stands in for both the Pythagorean comma and the septimal comma.
 Septischismic can be easily notated with [[chain-of-fifths notation]] with two additional sets of accidentals, one for the generic comma step, and the other for the generic aberschisma step which stands in for the [[schisma]] and the [[aberschisma]].
@@ Line 33: / Line 33: @@
 Undecimal septischismic, a.k.a. cassaschismic, maps [[prime interval|prime]] [[11/1|11]] to +23 perfect fifths, so it is an [[expansion]] of the [[2.3.7.11 subgroup|2.3.7.11-subgroup]] version of [[gary]]. It is naturally a no-17 19-limit temperament, where the undevicesimal schisma of [[513/512]] is also added to the generic aberschisma step.
+Septischismic has two reasonable extensions to add 17, which coalesce in the newt extension 270 & 311. Septinoellismic finds it a tad unintuitively as two aberschismas up and 4 commas down from a major second (^^4sM2) yet supported by 94edo, and septisperasmic finds it 4 aberschismas up from a minor second (4^m2), which can be deemed the more intuitive mapping, albeit it is not supported by any cassandra tuning except for 12edo, which notably has a very well tuned 17/16.
+Septischismic has two reasonable extensions to add 29 and 31 into the system, that like before, coalesce in the newt extension 270 & 311 too. Septiplanar finds them in the chain of fifths, without need of third generators, thus they in the same plane to the rank-2 chain of fifths, mapped respectively to a major seventh – three commas (3sM7) and a perfect octave minus two commas (hP8). Because this extension is reached only through the septischismic chain of fifths, it is also available in [[gary]].
 [[Subgroup]]: 2.3.5.7.11
@@ Line 55: / Line 59: @@
 Comma list: 2080/2079, 4096/4095, 19712/19683
-Mapping: {{mapping| 1 0 0 25 -33 -13 | 0 1 0 -14 23 12 | 0 0 1 0 0 -1 }}
+{{Mapping|legend=0| 1 0 0 25 -33 -13 | 0 1 0 -14 23 12 | 0 0 1 0 0 -1 }}
 Optimal tunings:
@@ Line 67: / Line 71: @@
 Badness (Sintel): 0.815
-=== 2.3.5.7.11.13.19 subgroup ===
+==== 2.3.5.7.11.13.19 subgroup ====
 Subgroup: 2.3.5.7.11.13.19
@@ Line 84: / Line 88: @@
 Badness (Sintel): 0.486
-=== Septinoellismic ===
+===== Septiplanar =====
-Septischismic has two reasonable extensions to add 17, both of which coalesce in the structurally very similar temperament [[newt]]. Septinoellismic finds it a tad unintuitively as two aberschismas up and 4 commas down from a major second (^^4sM2) yet supported by 94edo, and septisperasmic finds it 4 aberschismas up from a minor second (4^m2), which can be deemed the more intuitive mapping, albeit it is not supported by any cassandra tuning except for 12edo which notably has a very well tuned 17/16.
-Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 1225/1224, 1216/1215, 1540/1539, 1729/1728, 2080/2079
-Subgroup-val mapping: {{mapping| 1 0 0 25 -33 -13 47 -6 | 0 1 0 -14 23 12 -30 5 | 0 0 1 0 0 -1 2 1 }}
-Optimal tunings:
-* WE: ~2 = 1199.970{{c}}, ~3/2 = 702.190{{c}}, ~5/4 = 386.177{{c}}
-: error map: {{val|-0.030 +0.235 -0.137 -0.238 +0.044 -0.034 +0.286 -0.206}}
-* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.2307{{c}}, ~5/4 = 386.3245{{c}}
-: error map: {{val|0.000 +0.282 -0.075 -0.150 +0.143 +0.083 +0.399 -0.088}}
-{{Optimal ET sequence|legend=0|TBA}}
-Badness (Sintel): 0.682
-=== Septisperasmic ===
-Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 1216/1215, 1540/1539, 1729/1728, 2080/2079, 2500/2499
-Subgroup-val mapping: {{mapping| 1 0 0 25 -33 -13 -48 -6 | 0 1 0 -14 23 12 27 5 | 0 0 1 0 0 -1 4 1 }}
-Optimal tunings:
-* WE: ~2 = 1199.986{{c}}, ~3/2 = 702.206{{c}}, ~5/4 = 386.207{{c}}
-: error map: {{val|-0.014 +0.251 -0.106 -0.056 -0.123 -0.084 +0.101 -0.193}}
-* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.228{{c}}, ~5/4 = 386.238{{c}}
-: error map: {{val|0.000 +0.273 -0.075 -0.015 -0.078 -0.032 +0.148 -0.136}}
-{{Optimal ET sequence|legend=0|TBA}}
-Badness (Sintel): 1.096
-=== Septiplanar ===
-Septischismic has two reasonable extensions to add 29 and 31 into the system, that like before, coalesce in newt. Septiplanar finds them in the chain of fifths, without need of third generators, thus they in the same plane to the rank-2 chain of fifths, mapped respectively to a major seventh – three commas (3sM7) and a perfect octave minus two commas (hP8). Because this extension is reached only through the septischismic chain of fifths, it is also available in [[gary]].
 Subgroup: 2.3.5.7.11.13.19.29
@@ Line 130: / Line 96: @@
 Optimal tunings:
-* WE: ~2 = 1199.948{{c}}, ~3/2 = 702.213{{c}}, ~5/4 = 386.379{{c}}
+* WE: ~2 = 1199.9476{{c}}, ~3/2 = 702.2134{{c}}, ~5/4 = 386.3794{{c}}
 : error map: {{val| -0.052 +0.206 -0.039 -0.389 +0.113 -0.190 -0.119 +0.603 }}
-* CWE: ~2 = 1200.000{{c}}, ~3/2 = 702.244{{c}}, ~5/4 = 386.388{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.2440{{c}}, ~5/4 = 386.3884{{c}}
 : error map: {{val| 0.000 +0.289 +0.075 -0.242 +0.293 +0.012 +0.095 +0.860 }}
-Optimal ET sequence: TBA
+{{Optimal ET sequence|legend=0| 41, 53j, 94, 176, 217, 270, 487, 581j, 1068j }}
 Badness (Sintel): 0.758
-===== 2.3.5.7.11.13.19.29.31 subgroup =====
+====== 2.3.5.7.11.13.19.29.31 subgroup ======
 Subgroup: 2.3.5.7.11.13.19.29.31
@@ Line 147: / Line 113: @@
 Optimal tunings:
-* WE: ~2 = 1199.930{{c}}, ~3/2 = 702.208{{c}}, ~5/4 = 386.406{{c}}
+* WE: ~2 = 1199.9298{{c}}, ~3/2 = 702.2082{{c}}, ~5/4 = 386.4062{{c}}
 : error map: {{val| -0.070 +0.183 -0.048 -0.513 +0.173 -0.225 -0.136 +0.353 +0.633 }}
-* CWE: ~2 = 1200.000{{c}}, ~3/2 = 702.250{{c}}, ~5/4 = 386.420{{c}}
+* CWE: ~2 = 1200.000{{c}}, ~3/2 = 702.2495{{c}}, ~5/4 = 386.4198{{c}}
 : error map: {{val| 0.000 +0.295 +0.106 -0.319 +0.421 +0.047 +0.154 +0.688 +0.976 }}
-Optimal ET sequence: TBA
+{{Optimal ET sequence|legend=0| 41, 94, 135, 176, 217, 270, 311, 487, 581jk, 798k, 1068jk }}
 Badness (Sintel): 0.793
-=== Septifantasious ===
+===== Septifantasious =====
 Septifantasious tempers out [[1625/1624]] – the fantasia, and thus finds 29/16 as 3 aberschismas above 9/5 – that is to say, superminor seventh + 2 aberschismas (^^Sm7), and 31/16 one apotome higher as a hypermajor seventh + 2 aberschismas (^^HM7).
@@ Line 166: / Line 132: @@
 Optimal tunings:
-* WE: ~2 = 1199.983{{c}}, ~3/2 = 702.213{{c}}, ~5/4 = 386.172{{c}}
+* WE: ~2 = 1199.9833{{c}}, ~3/2 = 702.2132{{c}}, ~5/4 = 386.1721{{c}}
 : error map: {{val| -0.017 +0.242 -0.175 +0.005 -0.246 -0.091 -0.291 +0.495 }}
-* CWE: ~2 = 1200.000{{c}}, ~3/2 = 702.233{{c}}, ~5/4 = 386.174{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.2228{{c}}, ~5/4 = 386.1741{{c}}
 : error map: {{val| 0.000 +0.268 -0.140 +0.055 -0.193 -0.028 -0.225 +0.564 }}
-Optimal ET sequence: TBA
+{{Optimal ET sequence|legend=0| 41, 53, 94j, 217j, 258j, 270, 581j, 904, 945, 1215j }}
 Badness (Sintel): 0.716
-===== 2.3.5.7.11.13.19.29.31 subgroup =====
+====== 2.3.5.7.11.13.19.29.31 subgroup ======
 Subgroup: 2.3.5.7.11.13.19.29.31
@@ Line 188: / Line 154: @@
 : error map: {{val| 0.000 +0.264 -0.192 +0.110 -0.284 -0.023 -0.297 +0.358 +0.431 }}
-Optimal ET sequence: TBA
+{{Optimal ET sequence|legend=0| 41, 53k, 94jk, 217jk, 229j, 270, 311, 581jk, 634, 904, 945, 1215jk }}
 Badness (Sintel): 0.796
+=== Septinoellismic ===
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 1225/1224, 2080/2079, 2431/2430, 4096/4095
+Subgroup-val mapping: {{mapping| 1 0 0 25 -33 -13 47 | 0 1 0 -14 23 12 -30 | 0 0 1 0 0 -1 2 }}
+Optimal tunings:
+* WE: ~2 = 1199.9654{{c}}, ~3/2 = 702.2159{{c}}, ~5/4 = 386.2053{{c}}
+: error map: {{val| -0.035 +0.226 -0.178 -0.229 -0.006 -0.038 +0.252 }}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.2359{{c}}, ~5/4 = 386.2080{{c}}
+: error map: {{val| 0.000 +0.281 -0.106 -0.129 +0.109 +0.096 +0.383 }}
+{{Optimal ET sequence|legend=0| 53, 94, 176g, 217, 270, 311, 487, 581 }}
+Badness (Sintel): 0.950
+==== 19-limit ====
+Subgroup: 2.3.5.7.11.13.17.19
+Comma list: 1216/1215, 1225/1224, 1540/1539, 1729/1728, 2080/2079
+Subgroup-val mapping: {{mapping| 1 0 0 25 -33 -13 47 -6 | 0 1 0 -14 23 12 -30 5 | 0 0 1 0 0 -1 2 1 }}
+Optimal tunings:
+* WE: ~2 = 1199.9699{{c}}, ~3/2 = 702.2200{{c}}, ~5/4 = 386.2373{{c}}
+: error map: {{val| -0.030 +0.235 -0.137 -0.238 +0.044 -0.034 +0.286 -0.206 }}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.2374{{c}}, ~5/4 = 386.2384{{c}}
+: error map: {{val| 0.000 +0.282 -0.075 -0.150 +0.143 +0.083 +0.399 -0.088 }}
+{{Optimal ET sequence|legend=0| 53, 94, 176g, 217, 270, 311, 487, 581 }}
+Badness (Sintel): 0.682
+=== Septisperasmic ===
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 2080/2079, 2500/2499, 4096/4095, 19712/19683
+Subgroup-val mapping: {{mapping| 1 0 0 25 -33 -13 -48 | 0 1 0 -14 23 12 27 | 0 0 1 0 0 -1 4 }}
+Optimal tunings:
+* WE: ~2 = 1199.9797{{c}}, ~3/2 = 702.2164{{c}}, ~5/4 = 386.2286{{c}}
+: error map: {{val| -0.020 +0.241 -0.126 -0.080 -0.136 -0.098 +0.068 }}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.2281{{c}}, ~5/4 = 386.2332{{c}}
+: error map: {{val| 0.000 +0.273 -0.081 -0.020 -0.071 -0.023 +0.137 }}
+{{Optimal ET sequence|legend=0| 258, 270, 311, 581, 1485, 1796, 2066, 2647b }}
+Badness (Sintel): 1.76
+==== 19-limit ====
+Subgroup: 2.3.5.7.11.13.17.19
+Comma list: 1216/1215, 1540/1539, 1729/1728, 2080/2079, 2500/2499
+Subgroup-val mapping: {{mapping| 1 0 0 25 -33 -13 -48 -6 | 0 1 0 -14 23 12 27 5 | 0 0 1 0 0 -1 4 1 }}
+Optimal tunings:
+* WE: ~2 = 1199.9861{{c}}, ~3/2 = 702.2198{{c}}, ~5/4 = 386.2353{{c}}
+: error map: {{val| -0.014 +0.251 -0.106 -0.056 -0.123 -0.084 +0.101 -0.193 }}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.2278{{c}}, ~5/4 = 386.2383{{c}}
+: error map: {{val| 0.000 +0.273 -0.075 -0.015 -0.078 -0.032 +0.148 -0.136 }}
+{{Optimal ET sequence|legend=0| 258, 270, 311, 581, 1485, 1796, 2066 }}
+Badness (Sintel): 1.10
 == Androschismic ==
@@ Line 214: / Line 248: @@
 Comma list: 2080/2079, 10648/10647, 43904/43875
-Mapping: {{mapping| 1 0 0 25 62 82 | 0 1 0 -14 -34 -43 | 0 0 1 0 -2 -3 }}
+{{Mapping|legend=0| 1 0 0 25 62 82 | 0 1 0 -14 -34 -43 | 0 0 1 0 -2 -3 }}
 Optimal tunings:
@@ Line 229: / Line 263: @@
 Comma list: 1216/1215, 2080/2079, 3136/3135, 10648/10647
-Mapping: {{mapping| 1 0 0 25 62 82 -6 | 0 1 0 -14 -34 -43 5 | 0 0 1 0 -2 -3 1 }}
+{{Mapping|legend=0| 1 0 0 25 62 82 -6 | 0 1 0 -14 -34 -43 5 | 0 0 1 0 -2 -3 1 }}
 Optimal tunings: