Ptolemismic clan: Difference between revisions
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Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
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The '''ptolemismic clan''' of rank-3 | The '''ptolemismic clan''' of [[Rank-3 temperament|rank-3]] [[temperament]]s [[Tempering out|tempers out]] the ptolemisma, [[100/99]]. | ||
Temperaments discussed elsewhere include: | Temperaments discussed elsewhere include: | ||
* ''[[Calliope]]'' | * ''[[Calliope]]'' (+45/44 or 81/80) → [[Didymus rank three family #Calliope|Didymus rank-3 family]] | ||
* ''[[Jubilee]]'' | * ''[[Jubilee]]'' (+50/49 or 99/98) → [[Jubilismic family #Jubilee|Jubilismic family]] | ||
* ''[[Sonic]]'' | * ''[[Sonic]]'' (+55/54) → [[Porcupine rank three family #Sonic|Porcupine rank-3 family]] | ||
* ''[[Thrasher]]'' | * ''[[Thrasher]]'' (+56/55) → [[Starling family #Thrasher|Starling family]] | ||
* [[Ares]] | * [[Ares]] (+64/63) → [[Archytas family #Ares|Archytas family]] | ||
* ''[[Apollo]]'' | * ''[[Apollo]]'' (+225/224) → [[Marvel family #Apollo|Marvel family]] | ||
* ''[[Nakika]]'' | * ''[[Nakika]]'' (+245/242) → [[Octagar family #Nakika|Octagar family]] | ||
* ''[[Octarod]]'' | * ''[[Octarod]]'' (+245/243) → [[Sensamagic family #Octarod|Sensamagic family]] | ||
* ''[[Supermagic]]'' | * ''[[Supermagic]]'' (+385/384) → [[Keemic family #Supermagic|Keemic family]] | ||
* ''[[Androboh]]'' | * ''[[Androboh]]'' (+1375/1372) → [[Gariboh family #Androboh|Gariboh family]] | ||
For the rank-4 temperament, see [[Rank-4 temperament #Ptolemismic (100/99)]]. | |||
[[ | |||
== No-7 ptolemismic == | == No-7 ptolemismic == | ||
Subgroup: 2.3.5.11 | [[Subgroup]]: 2.3.5.11 | ||
[[Comma list]]: 100/99 | [[Comma list]]: 100/99 | ||
{{mapping|legend=2| 1 0 0 2 | 0 1 0 -2 | 0 0 1 2 }} | |||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 704.9532, ~5/4 = 384.0675 | ||
{{Optimal ET sequence|legend=1| 7, 12, 15, 19, 22, 34, 41, 56, 75e, 97, 131e }} | {{Optimal ET sequence|legend=1| 7, 12, 15, 19, 22, 34, 41, 56, 75e, 97, 131e }} | ||
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[[Category:Temperament clans]] | [[Category:Temperament clans]] | ||
[[Category:Ptolemismic | [[Category:Ptolemismic clan| ]] <!-- main article --> | ||
[[Category:Ptolemismic| ]] <!-- key article --> | |||
[[Category:Rank 3]] | [[Category:Rank 3]] | ||
Revision as of 05:50, 18 September 2023
The ptolemismic clan of rank-3 temperaments tempers out the ptolemisma, 100/99.
Temperaments discussed elsewhere include:
- Calliope (+45/44 or 81/80) → Didymus rank-3 family
- Jubilee (+50/49 or 99/98) → Jubilismic family
- Sonic (+55/54) → Porcupine rank-3 family
- Thrasher (+56/55) → Starling family
- Ares (+64/63) → Archytas family
- Apollo (+225/224) → Marvel family
- Nakika (+245/242) → Octagar family
- Octarod (+245/243) → Sensamagic family
- Supermagic (+385/384) → Keemic family
- Androboh (+1375/1372) → Gariboh family
For the rank-4 temperament, see Rank-4 temperament #Ptolemismic (100/99).
No-7 ptolemismic
Subgroup: 2.3.5.11
Comma list: 100/99
Sval mapping: [⟨1 0 0 2], ⟨0 1 0 -2], ⟨0 0 1 2]]
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.9532, ~5/4 = 384.0675
Optimal ET sequence: 7, 12, 15, 19, 22, 34, 41, 56, 75e, 97, 131e
Badness: 0.0226 × 10-3