Ptolemismic clan: Difference between revisions

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The '''ptolemismic clan''' of [[~~Rank-3 temperament|~~rank-3~~]] [[regular temperament|~~temperament]]s [[tempering out|tempers out]] the ptolemisma, [[100/99]].

The '''ptolemismic clan''' of [[rank-3 temperament]]s [[tempering out|tempers out]] the ptolemisma, [[100/99]].

Strong extensions are apollo, ~~supermagic~~, thrasher, and ares, considered below. Discussed elsewhere are:

Strong extensions are apollo, keemic, thrasher, and ares, considered below. Discussed elsewhere are:

* ''[[Calliope]]'' (+45/44 or 81/80) → [[Didymus rank ~~three~~ family #Calliope|Didymus rank-3 family]]

* ''[[Calliope]]'' (+45/44 or 81/80) → [[Didymus rank-3 family #Calliope|Didymus rank-3 family]]

* ''[[Jubilee]]'' (+50/49 or 99/98) → [[Jubilismic family #Jubilee|Jubilismic family]]

* ''[[Sonic]]'' (+55/54) → [[Porcupine rank ~~three~~ family #Sonic|Porcupine rank-3 family]]

* ''[[Sonic]]'' (+55/54) → [[Porcupine rank-3 family #Sonic|Porcupine rank-3 family]]

* ''[[Nakika]]'' (+245/242) → [[Octagar family #Nakika|Octagar family]]

* ''[[Octarod]]'' (+245/243) → [[Sensamagic family #Octarod|Sensamagic family]]

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[[Comma list]]: 100/99

: mapping generators: ~2, ~3, ~5

[[Optimal tuning]] ([[~~POTE~~]]): ~2 = 1\1, ~3/2 = 704.~~9532~~, ~5/4 = ~~384~~.~~0675~~

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1199.2633{{c}}, ~3/2 = 704.5205{{c}}, ~5/4 = 383.8317{{c}}

: [[error map]]: {{val| -0.737 +1.829 -3.955 +4.358 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 704.4751{{c}}, ~5/4 = 383.0756{{c}}

: error map: {{val| 0.000 +2.520 -3.238 +5.883 }}

{{Optimal ET sequence|legend=1| 7, 12, 15, 19, 22, 34, 41, 56, 75e, 97, 131e }}

[[Badness]]: 0.~~0226 × 10<sup>-3</sup>~~

[[Badness]] (Sintel): 0.187

== Apollo ==

See [[Marvel family #Apollo]].

== ~~Supermagic~~ ==

== Keemic ==

See [[Keemic family #~~Supermagic~~]].

See [[Keemic family #Keemic]].

== Thrasher ==

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== Ares ==

See [[Archytas family #Ares]].

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-The '''ptolemismic clan''' of [[Rank-3 temperament|rank-3]] [[regular temperament|temperament]]s [[tempering out|tempers out]] the ptolemisma, [[100/99]].
+{{Technical data page}}
+The '''ptolemismic clan''' of [[rank-3 temperament]]s [[tempering out|tempers out]] the ptolemisma, [[100/99]].
-Strong extensions are apollo, supermagic, thrasher, and ares, considered below. Discussed elsewhere are:
+Strong extensions are apollo, keemic, thrasher, and ares, considered below. Discussed elsewhere are:
-* ''[[Calliope]]'' (+45/44 or 81/80) → [[Didymus rank three family #Calliope|Didymus rank-3 family]]
+* ''[[Calliope]]'' (+45/44 or 81/80) → [[Didymus rank-3 family #Calliope|Didymus rank-3 family]]
 * ''[[Jubilee]]'' (+50/49 or 99/98) → [[Jubilismic family #Jubilee|Jubilismic family]]
-* ''[[Sonic]]'' (+55/54) → [[Porcupine rank three family #Sonic|Porcupine rank-3 family]]
+* ''[[Sonic]]'' (+55/54) → [[Porcupine rank-3 family #Sonic|Porcupine rank-3 family]]
 * ''[[Nakika]]'' (+245/242) → [[Octagar family #Nakika|Octagar family]]
 * ''[[Octarod]]'' (+245/243) → [[Sensamagic family #Octarod|Sensamagic family]]
@@ Line 15: / Line 16: @@
 [[Comma list]]: 100/99
-{{mapping|legend=2| 1 0 0 2 | 0 1 0 -2 | 0 0 1 2 }}
+{{Mapping|legend=2| 1 0 0 2 | 0 1 0 -2 | 0 0 1 2 }}
+: mapping generators: ~2, ~3, ~5
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 704.9532, ~5/4 = 384.0675
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.2633{{c}}, ~3/2 = 704.5205{{c}}, ~5/4 = 383.8317{{c}}
+: [[error map]]: {{val| -0.737 +1.829 -3.955 +4.358 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 704.4751{{c}}, ~5/4 = 383.0756{{c}}
+: error map: {{val| 0.000 +2.520 -3.238 +5.883 }}
 {{Optimal ET sequence|legend=1| 7, 12, 15, 19, 22, 34, 41, 56, 75e, 97, 131e }}
-[[Badness]]: 0.0226 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.187
 == Apollo ==
 See [[Marvel family #Apollo]].
-== Supermagic ==
+== Keemic ==
-See [[Keemic family #Supermagic]].
+See [[Keemic family #Keemic]].
 == Thrasher ==
@@ Line 33: / Line 39: @@
 == Ares ==
-{{Main| Ares }}
+{{Main| Archytas and ares }}
 See [[Archytas family #Ares]].