Ptolemismic clan: Difference between revisions

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The '''ptolemismic clan''' of rank-3 temperaments tempers out the ptolemisma, [[100/99]]. But we can start with the rank-4 temperament.  
{{Technical data page}}
The '''ptolemismic clan''' of [[rank-3 temperament]]s [[tempering out|tempers out]] the ptolemisma, [[100/99]].  


Temperaments discussed elsewhere include:  
Strong extensions are apollo, keemic, 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-3 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-3 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 }}
: mapping generators: ~2, ~3, ~5


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


{{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]] (Sintel): 0.187
 
[[Badness]]: 0.0225 × 10<sup>-6</sup>
 
== No-7 ptolemismic ==
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
== Keemic ==
See [[Keemic family #Keemic]].  


{{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:Temperament clans]]
[[Category:Temperament clans]]
[[Category:Ptolemismic temperaments| ]] <!-- main article -->
[[Category:Ptolemismic clan| ]] <!-- main article -->
[[Category:Ptolemismic| ]] <!-- key article -->
[[Category:Rank 3]]
[[Category:Rank 3]]

Latest revision as of 08:36, 8 June 2026

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

The ptolemismic clan of rank-3 temperaments tempers out the ptolemisma, 100/99.

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

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

Ptolemic

Subgroup: 2.3.5.11

Comma list: 100/99

Subgroup-val mapping: [⟨1 0 0 2], ⟨0 1 0 -2], ⟨0 0 1 2]]

mapping generators: ~2, ~3, ~5

Optimal tunings:

  • WE: ~2 = 1199.2633 ¢, ~3/2 = 704.5205 ¢, ~5/4 = 383.8317 ¢
error map: ⟨-0.737 +1.829 -3.955 +4.358]
  • CWE: ~2 = 1200.0000 ¢, ~3/2 = 704.4751 ¢, ~5/4 = 383.0756 ¢
error map: ⟨0.000 +2.520 -3.238 +5.883]

Optimal ET sequence: 7, 12, 15, 19, 22, 34, 41, 56, 75e, 97, 131e

Badness (Sintel): 0.187

Apollo

See Marvel family #Apollo.

Keemic

See Keemic family #Keemic.

Thrasher

See Starling family #Thrasher.

Ares

Main article: Archytas and ares

See Archytas family #Ares.

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