Ptolemismic clan: Difference between revisions

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~~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]].

~~Temperaments discussed~~ elsewhere ~~include~~:

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

* ''[[Calliope]]''~~, {~~45/44, 81/80} → [[Didymus rank three family #Calliope|Didymus rank-3 family]]

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

* ''[[Jubilee]]''~~, {~~50/49, 99/98} → [[Jubilismic family #Jubilee|Jubilismic family]]

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

* ''[[Sonic]]''~~, {~~55/54~~, 100/99}~~ → [[Porcupine rank three family #Sonic|Porcupine rank-3 ~~family]]~~

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

* ''[[Thrasher]]'', {56/55, 100/99} → [[Starling family #Thrasher|Starling family]]

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

* [[Ares]], {64/63, 100/99} → [[Archytas family #Ares|Archytas family]]

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

* ''[[Apollo]]'', {100/99, 225/224} → [[Marvel family #Apollo|Marvel family]]

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

* ''[[Nakika]]''~~, {100/99,~~ 245/242} → [[Octagar family #Nakika|Octagar family]]

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

* ''[[Octarod]]''~~, {100/99,~~ 245/243} → [[Sensamagic family #Octarod|Sensamagic family]]

* ''[[~~Supermagic~~]]''~~, {100~~/~~99, 385/384}~~ → [[~~Keemic~~ family #~~Supermagic~~|~~Keemic~~ family]]

* ''[[~~Androboh]]'', {~~100/99~~, 1375/1372} → [[Gariboh family #Androboh|Gariboh family~~]]

== ~~Ptolemismic~~ ==

== Ptolemic ==

Subgroup: 2.3.5.7.11

[[Subgroup]]: 2.3.5.11

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

[[Comma list]]: 100/99

~~[[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 }}]~~

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

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

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

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

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

[[Badness]]: 0.0226 × 10-3

[[Badness]]: 0.~~0225~~ × 10-6

== ~~No-7 ptolemismic~~ ==

== Apollo ==

~~Subgroup: 2~~.~~3.5.11~~

See [[Marvel family #Apollo]].

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

== Supermagic ==

See [[Keemic family #Supermagic]].

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

== Thrasher ==

See [[Starling family #Thrasher]].

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

== Ares ==

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

See [[Archytas family #Ares]].

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

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

[[Category:Temperament clans]]

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

[[Category:Pages with mostly numerical content]]

[[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]].
-Temperaments discussed elsewhere include:
+Strong extensions are apollo, supermagic, thrasher, and ares, considered below. Discussed elsewhere are:
-* ''[[Calliope]]'', {45/44, 81/80} → [[Didymus rank three family #Calliope|Didymus rank-3 family]]
+* ''[[Calliope]]'' (+45/44 or 81/80) → [[Didymus rank three family #Calliope|Didymus rank-3 family]]
-* ''[[Jubilee]]'', {50/49, 99/98} → [[Jubilismic family #Jubilee|Jubilismic family]]
+* ''[[Jubilee]]'' (+50/49 or 99/98) → [[Jubilismic family #Jubilee|Jubilismic family]]
-* ''[[Sonic]]'', {55/54, 100/99} → [[Porcupine rank three family #Sonic|Porcupine rank-3 family]]
+* ''[[Sonic]]'' (+55/54) → [[Porcupine rank three family #Sonic|Porcupine rank-3 family]]
-* ''[[Thrasher]]'', {56/55, 100/99} → [[Starling family #Thrasher|Starling family]]
+* ''[[Nakika]]'' (+245/242) → [[Octagar family #Nakika|Octagar family]]
-* [[Ares]], {64/63, 100/99} → [[Archytas family #Ares|Archytas family]]
+* ''[[Octarod]]'' (+245/243) → [[Sensamagic family #Octarod|Sensamagic family]]
-* ''[[Apollo]]'', {100/99, 225/224} → [[Marvel family #Apollo|Marvel family]]
+* ''[[Androboh]]'' (+1375/1372) → [[Gariboh family #Androboh|Gariboh family]]
-* ''[[Nakika]]'', {100/99, 245/242} → [[Octagar family #Nakika|Octagar family]]
+For the rank-4 temperament, see [[Rank-4 temperament #Ptolemismic (100/99)]].
-* ''[[Octarod]]'', {100/99, 245/243} → [[Sensamagic family #Octarod|Sensamagic family]]
-* ''[[Supermagic]]'', {100/99, 385/384} → [[Keemic family #Supermagic|Keemic family]]
-* ''[[Androboh]]'', {100/99, 1375/1372} → [[Gariboh family #Androboh|Gariboh family]]
-== Ptolemismic ==
+== Ptolemic ==
-Subgroup: 2.3.5.7.11
+[[Subgroup]]: 2.3.5.11
-[[Comma list]]: [[100/99]]
+[[Comma list]]: 100/99
-[[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 }}]
+{{mapping|legend=2| 1 0 0 2 | 0 1 0 -2 | 0 0 1 2 }}
-[[POTE generator]]s: ~3/2 = 704.9532, ~5/4 = 384.0675, ~7/4 = 970.8803
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 704.9532, ~5/4 = 384.0675
-{{Val list|legend=1| 7d, 8d, 10e, 12, 15, 19, 22, 27e, 34d, 41, 90e, 131e }} <nowiki>*</nowiki>
+{{Optimal ET sequence|legend=1| 7, 12, 15, 19, 22, 34, 41, 56, 75e, 97, 131e }}
-<nowiki>*</nowiki> [[optimal patent val]]: [[104edo|104]]
+[[Badness]]: 0.0226 × 10<sup>-3</sup>
-[[Badness]]: 0.0225 × 10<sup>-6</sup>
-== No-7 ptolemismic ==
+== Apollo ==
-Subgroup: 2.3.5.11
+See [[Marvel family #Apollo]].
-[[Comma list]]: 100/99
+== Supermagic ==
+See [[Keemic family #Supermagic]].
-[[Sval]] [[mapping]]: [{{val| 1 0 0 2 }}, {{val| 0 1 0 -2 }}, {{val| 0 0 1 2 }}]
+== Thrasher ==
+See [[Starling family #Thrasher]].
-[[POTE generator]]s: ~3/2 = 704.9532, ~5/4 = 384.0675
+== Ares ==
+{{Main| Archytas and ares }}
-{{Val list|legend=1| 7, 12, 15, 19, 22, 34, 41, 56, 75e, 97, 131e }}
+See [[Archytas family #Ares]].
-[[Badness]]: 0.0226 × 10<sup>-3</sup>
-[[Category:Regular temperament theory]]
 [[Category:Temperament clans]]
-[[Category:Ptolemismic temperaments| ]] <!-- main article -->
+[[Category:Pages with mostly numerical content]]
+[[Category:Ptolemismic clan| ]] <!-- main article -->
+[[Category:Ptolemismic| ]] <!-- key article -->
 [[Category:Rank 3]]