Olympic clan: Difference between revisions

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Temperaments discussed elsewhere are:

* ''[[Akea]]'' (+385/384) → [[Aberschismic family #Akea|Aberschismic family]]

* [[Cassaschismic]] (+19712/19683) → [[Septischismic family #Undecimal septischismic (cassaschismic)|Septischismic family]]

* ''[[Lif]]'' (+2401/2400) → [[Breed family #Lif|Breed family]]

* ''[[Baffin]]'' (+5632/5625) → [[Vishdelismic clan #Baffin|Vishdelismic clan]]

* ''[[Hera]]'' (+6144/6125) → [[Porwell family #Hera|Porwell family]]

* ''[[Orthoschismic]]'' (+540/539) → [[Schismic rank-3 family #Orthoschismic|Schismic rank-3 family]]

* [[Cassaschismic]] (+19712/19683) → [[Septischismic family #Undecimal septischismic (cassaschismic)|Septischismic family]]

Considered below are ~~[[#Orthoschismic|orthoschismic]],~~ [[#Pessoal|pessoal]], [[#Lux|lux]], and [[#Sophia|sophia]].

Considered below are [[#Pessoal|pessoal]], [[#Lux|lux]], and [[#Sophia|sophia]].

~~== Orthoschismic ==~~

~~Orthoschismic is related to [[schismic]], but with an additional generator for [[prime interval|prime]] [[7/1|7]], extended to the 11-limit in one of the most efficient ways possible.~~

Orthoschismic can be notated with [[chain-of-fifths notation]] with two additional set of accidentals, one for the generic comma step (one should choose whether this step represents the syntonic comma, which is more characteristic in schismic, or the septimal comma, which is more characteristic in [[olympic]]), and the other for the generic aberschisma step which stands in for the [[garischisma]] and the [[aberschisma]].

~~It was named by [[Flora Canou]] in 2023, using the Greek prefix [[wiktionary: ortho- #English|ortho-]] to signify the additional rank.~~

~~[[Subgroup]]: 2.3.5.7.11~~

~~[[Comma list]]: 540/539, 32805/32768~~

~~{{Mapping|legend=1| 1 0 15 0 17 | 0 1 -8 0 -5 | 0 0 0 1 -2 }}~~

~~[[Optimal tuning]]s:~~

* [[WE]]: ~2 = 1199.9335{{c}}, ~3/2 = 701.6817{{c}}, ~7/4 = 969.6199{{c}}

~~: [[error map]]: {{val| -0.067 -0.340 -0.233 +0.661 +0.502 }}~~

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.7248{{c}}, ~7/4 = 969.6728{{c}}

~~: error map: {{val| 0.000 -0.230 -0.112 +0.847 +0.713 }}~~

~~{{Optimal ET sequence|legend=1| 41, 53, 89, 94, 130, 183, 224, 354, 537, 578, 761d, 985d, 1115de }}~~

~~[[Badness]] (Sintel): 1.41~~

~~=== 13-limit ===~~

~~Subgroup: 2.3.5.7.11.13~~

~~Comma list: 540/539, 729/728, 4096/4095~~

~~Mapping: {{mapping| 1 0 15 0 17 -3 | 0 1 -8 0 -5 6 | 0 0 0 1 -2 -1 }}~~

~~Optimal tunings:~~

* WE: ~2 = 1199.9399{{c}}, ~3/2 = 701.6899{{c}}, ~7/4 = 969.6107{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.7264{{c}}, ~7/4 = 969.6672{{c}}

~~{{Optimal ET sequence|legend=0| 41, 53, 89, 94, 130, 183, 224, 354, 578, 985d }}~~

~~Badness (Sintel): 0.779~~

== Pessoal ==

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Comma list: 1716/1715, 2080/2079, 4096/4095

~~Mapping:~~ {{~~mapping~~| 2 0 1 10 14 13 | 0 1 0 -1 -3 -1 | 0 0 3 -1 2 -2 }}

{{Mapping|legend=0| 2 0 1 10 14 13 | 0 1 0 -1 -3 -1 | 0 0 3 -1 2 -2 }}

Optimal tunings:

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Comma list: 2080/2079, 3025/3024, 4096/4095

~~Mapping:~~ {{~~mapping~~| 1 0 -5 4 9 13 | 0 1 4 -1 -3 -5 | 0 0 5 2 -4 -7 }}

{{Mapping|legend=0| 1 0 -5 4 9 13 | 0 1 4 -1 -3 -5 | 0 0 5 2 -4 -7 }}

Optimal tunings:

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Comma list: 2080/2079, 4096/4095, 13720/13689

~~Mapping:~~ {{~~mapping~~| 1 0 2 3 11 7 | 0 1 0 0 -5 -2 | 0 0 5 -3 6 -2 }}

{{Mapping|legend=0| 1 0 2 3 11 7 | 0 1 0 0 -5 -2 | 0 0 5 -3 6 -2 }}

Optimal tunings:

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Comma list: 595/594, 833/832, 1156/1155, 4096/4095

~~Mapping:~~ {{~~mapping~~| 1 0 2 3 11 7 7 | 0 1 0 0 -5 -2 -2 | 0 0 5 -3 6 -2 4 }}

{{Mapping|legend=0| 1 0 2 3 11 7 7 | 0 1 0 0 -5 -2 -2 | 0 0 5 -3 6 -2 4 }}

Optimal tunings:

@@ Line 27: / Line 27: @@
 Temperaments discussed elsewhere are:
 * ''[[Akea]]'' (+385/384) → [[Aberschismic family #Akea|Aberschismic family]]
-* [[Cassaschismic]] (+19712/19683) → [[Septischismic family #Undecimal septischismic (cassaschismic)|Septischismic family]]
 * ''[[Lif]]'' (+2401/2400) → [[Breed family #Lif|Breed family]]
 * ''[[Baffin]]'' (+5632/5625) → [[Vishdelismic clan #Baffin|Vishdelismic clan]]
 * ''[[Hera]]'' (+6144/6125) → [[Porwell family #Hera|Porwell family]]
+* ''[[Orthoschismic]]'' (+540/539) → [[Schismic rank-3 family #Orthoschismic|Schismic rank-3 family]]
+* [[Cassaschismic]] (+19712/19683) → [[Septischismic family #Undecimal septischismic (cassaschismic)|Septischismic family]]
-Considered below are [[#Orthoschismic|orthoschismic]], [[#Pessoal|pessoal]], [[#Lux|lux]], and [[#Sophia|sophia]].
+Considered below are [[#Pessoal|pessoal]], [[#Lux|lux]], and [[#Sophia|sophia]].
-== Orthoschismic ==
-Orthoschismic is related to [[schismic]], but with an additional generator for [[prime interval|prime]] [[7/1|7]], extended to the 11-limit in one of the most efficient ways possible.
-Orthoschismic can be notated with [[chain-of-fifths notation]] with two additional set of accidentals, one for the generic comma step (one should choose whether this step represents the syntonic comma, which is more characteristic in schismic, or the septimal comma, which is more characteristic in [[olympic]]), and the other for the generic aberschisma step which stands in for the [[garischisma]] and the [[aberschisma]].
-It was named by [[Flora Canou]] in 2023, using the Greek prefix [[wiktionary: ortho- #English|ortho-]] to signify the additional rank.
-[[Subgroup]]: 2.3.5.7.11
-[[Comma list]]: 540/539, 32805/32768
-{{Mapping|legend=1| 1 0 15 0 17 | 0 1 -8 0 -5 | 0 0 0 1 -2 }}
-[[Optimal tuning]]s:
-* [[WE]]: ~2 = 1199.9335{{c}}, ~3/2 = 701.6817{{c}}, ~7/4 = 969.6199{{c}}
-: [[error map]]: {{val| -0.067 -0.340 -0.233 +0.661 +0.502 }}
-* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.7248{{c}}, ~7/4 = 969.6728{{c}}
-: error map: {{val| 0.000 -0.230 -0.112 +0.847 +0.713 }}
-{{Optimal ET sequence|legend=1| 41, 53, 89, 94, 130, 183, 224, 354, 537, 578, 761d, 985d, 1115de }}
-[[Badness]] (Sintel): 1.41
-=== 13-limit ===
-Subgroup: 2.3.5.7.11.13
-Comma list: 540/539, 729/728, 4096/4095
-Mapping: {{mapping| 1 0 15 0 17 -3 | 0 1 -8 0 -5 6 | 0 0 0 1 -2 -1 }}
-Optimal tunings:
-* WE: ~2 = 1199.9399{{c}}, ~3/2 = 701.6899{{c}}, ~7/4 = 969.6107{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.7264{{c}}, ~7/4 = 969.6672{{c}}
-{{Optimal ET sequence|legend=0| 41, 53, 89, 94, 130, 183, 224, 354, 578, 985d }}
-Badness (Sintel): 0.779
 == Pessoal ==
@@ Line 99: / Line 62: @@
 Comma list: 1716/1715, 2080/2079, 4096/4095
-Mapping: {{mapping| 2 0 1 10 14 13 | 0 1 0 -1 -3 -1 | 0 0 3 -1 2 -2 }}
+{{Mapping|legend=0| 2 0 1 10 14 13 | 0 1 0 -1 -3 -1 | 0 0 3 -1 2 -2 }}
 Optimal tunings:
@@ Line 136: / Line 99: @@
 Comma list: 2080/2079, 3025/3024, 4096/4095
-Mapping: {{mapping| 1 0 -5 4 9 13 | 0 1 4 -1 -3 -5 | 0 0 5 2 -4 -7 }}
+{{Mapping|legend=0| 1 0 -5 4 9 13 | 0 1 4 -1 -3 -5 | 0 0 5 2 -4 -7 }}
 Optimal tunings:
@@ Line 171: / Line 134: @@
 Comma list: 2080/2079, 4096/4095, 13720/13689
-Mapping: {{mapping| 1 0 2 3 11 7 | 0 1 0 0 -5 -2 | 0 0 5 -3 6 -2 }}
+{{Mapping|legend=0| 1 0 2 3 11 7 | 0 1 0 0 -5 -2 | 0 0 5 -3 6 -2 }}
 Optimal tunings:
@@ Line 186: / Line 149: @@
 Comma list: 595/594, 833/832, 1156/1155, 4096/4095
-Mapping: {{mapping| 1 0 2 3 11 7 7 | 0 1 0 0 -5 -2 -2 | 0 0 5 -3 6 -2 4 }}
+{{Mapping|legend=0| 1 0 2 3 11 7 7 | 0 1 0 0 -5 -2 -2 | 0 0 5 -3 6 -2 4 }}
 Optimal tunings: