Ptolemismic clan: Difference between revisions

(15 intermediate revisions by 5 users not shown)

Line 1:

~~This~~ page ~~discusses some~~ rank-3 ~~temperaments~~ tempering out the ptolemisma, [[100/99]]~~. But we can start with the rank-4 temperament~~.

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

~~== Ptolemismic ==~~

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

~~Subgroup: 2.~~3.~~5.7.11~~

* ''[[Calliope]]'' (+45/44 or 81/80) → [[Didymus rank three 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]]

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

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

* ''[[Androboh]]'' (+1375/1372) → [[Gariboh family #Androboh|Gariboh family]]

For the rank-4 temperament, see [[Rank-4 temperament #Ptolemismic (100/99)]].

[[~~Comma list~~]]: ~~[[100/99]]~~

== Ptolemic ==

[[Subgroup]]: 2.3.5.11

[[~~Mapping~~]]: ~~[{{val| 1 0 0 0 2 }}, {{val| 0 1 0 0 -2 }}, {{val| 0 0 1 0 2 }}, {{val| 0 0 0 1 0 }}]~~

[[Comma list]]: 100/99

~~[[POTE generator]]s: ~3/~~2 ~~= 704.9532, ~5/4 = 384.0675, ~7/4 = 970.8803~~

~~{{Val list|legend~~=1~~| 7d~~, 8d, ~~10e, 12, 15, 19, 22, 27e, 34d, 41, 90e, 131e }} <nowiki>*<~~/~~nowiki>~~

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 704.9532, ~5/4 = 384.0675

~~<nowiki>*</nowiki> [[optimal patent val]]: [[104edo~~|~~104]]~~

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

[[Badness]]: 0.~~0225~~ × 10-6

[[Badness]]: 0.0226 × 10-3

~~== Ptolemy ==~~

~~Subgroup: 2.3.5.11~~

~~[[Comma list]]: 100/99~~

[[~~Sval~~]] ~~[[mapping]]: [{{val| 1 0 0 2 }}, {{val| 0 1 0 -2 }}, {{val| 0 0 1 2 }}]~~

== Apollo ==

See [[Marvel family #Apollo]].

[[~~POTE generator~~]]~~s: ~3/2 = 704.9532, ~5/4 = 384~~.~~0675~~

== Supermagic ==

See [[Keemic family #Supermagic]].

~~{{Val list|legend~~=~~1| 7, 12, 15, 19, 22, 34, 41, 56, 75e, 97, 131e }}~~

== Thrasher ==

See [[Starling family #Thrasher]].

[[~~Badness~~]]~~: 0~~.~~0226 × 10-3~~

== Ares ==

See [[Archytas family #Ares]].

[[Category:~~Regular temperament theory~~]]

[[Category:Temperament clans]]

[[Category:~~Temperament~~ clan]]

[[Category:Pages with mostly numerical content]]

[[Category:Ptolemismic ~~temperaments~~| ]]

[[Category:Ptolemismic clan| ]]

[[Category:Ptolemismic| ]]

[[Category:Rank 3]]

@@ Line 1: / Line 1: @@
-This page discusses some rank-3 temperaments tempering out the ptolemisma, [[100/99]]. But we can start with the rank-4 temperament.
+{{Technical data page}}
+The '''ptolemismic clan''' of [[Rank-3 temperament|rank-3]] [[regular temperament|temperament]]s [[tempering out|tempers out]] the ptolemisma, [[100/99]].
-== Ptolemismic ==
+Strong extensions are apollo, supermagic, thrasher, and ares, considered below. Discussed elsewhere are:
-Subgroup: 2.3.5.7.11
+* ''[[Calliope]]'' (+45/44 or 81/80) → [[Didymus rank three 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]]
+* ''[[Nakika]]'' (+245/242) → [[Octagar family #Nakika|Octagar family]]
+* ''[[Octarod]]'' (+245/243) → [[Sensamagic family #Octarod|Sensamagic family]]
+* ''[[Androboh]]'' (+1375/1372) → [[Gariboh family #Androboh|Gariboh family]]
+For the rank-4 temperament, see [[Rank-4 temperament #Ptolemismic (100/99)]].
-[[Comma list]]: [[100/99]]
+== Ptolemic ==
+[[Subgroup]]: 2.3.5.11
-[[Mapping]]: [{{val| 1 0 0 0 2 }}, {{val| 0 1 0 0 -2 }}, {{val| 0 0 1 0 2 }}, {{val| 0 0 0 1 0 }}]
+[[Comma list]]: 100/99
-[[POTE generator]]s: ~3/2 = 704.9532, ~5/4 = 384.0675, ~7/4 = 970.8803
+{{mapping|legend=2| 1 0 0 2 | 0 1 0 -2 | 0 0 1 2 }}
-{{Val list|legend=1| 7d, 8d, 10e, 12, 15, 19, 22, 27e, 34d, 41, 90e, 131e }} <nowiki>*</nowiki>
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 704.9532, ~5/4 = 384.0675
-<nowiki>*</nowiki> [[optimal patent val]]: [[104edo|104]]
+{{Optimal ET sequence|legend=1| 7, 12, 15, 19, 22, 34, 41, 56, 75e, 97, 131e }}
-[[Badness]]: 0.0225 × 10<sup>-6</sup>
+[[Badness]]: 0.0226 × 10<sup>-3</sup>
-== Ptolemy ==
-Subgroup: 2.3.5.11
-[[Comma list]]: 100/99
-[[Sval]] [[mapping]]: [{{val| 1 0 0 2 }}, {{val| 0 1 0 -2 }}, {{val| 0 0 1 2 }}]
+== Apollo ==
+See [[Marvel family #Apollo]].
-[[POTE generator]]s: ~3/2 = 704.9532, ~5/4 = 384.0675
+== Supermagic ==
+See [[Keemic family #Supermagic]].
-{{Val list|legend=1| 7, 12, 15, 19, 22, 34, 41, 56, 75e, 97, 131e }}
+== Thrasher ==
+See [[Starling family #Thrasher]].
-[[Badness]]: 0.0226 × 10<sup>-3</sup>
+== Ares ==
+{{Main| Archytas and ares }}
+See [[Archytas family #Ares]].
-[[Category:Regular temperament theory]]
+[[Category:Temperament clans]]
-[[Category:Temperament clan]]
+[[Category:Pages with mostly numerical content]]
-[[Category:Ptolemismic temperaments| ]] <!-- main article -->
+[[Category:Ptolemismic clan| ]] <!-- main article -->
+[[Category:Ptolemismic| ]] <!-- key article -->
 [[Category:Rank 3]]