Ptolemismic clan: Difference between revisions
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m Text replacement - "Category:Temperament clans" to "Category:Temperament clans Category:Pages with mostly numerical content" |
m Text replacement - "rank-3 temperament" to "rank-3 temperament" |
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{{Technical data page}} | {{Technical data page}} | ||
The '''ptolemismic clan''' of [[ | The '''ptolemismic clan''' of [[rank-3 temperament]]s [[tempering out|tempers out]] the ptolemisma, [[100/99]]. | ||
Strong extensions are apollo, | Strong extensions are apollo, keemic, thrasher, and ares, considered below. Discussed elsewhere are: | ||
* ''[[Calliope]]'' (+45/44 or 81/80) → [[Didymus rank | * ''[[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]] | * ''[[Jubilee]]'' (+50/49 or 99/98) → [[Jubilismic family #Jubilee|Jubilismic family]] | ||
* ''[[Sonic]]'' (+55/54) → [[Porcupine rank | * ''[[Sonic]]'' (+55/54) → [[Porcupine rank-3 family #Sonic|Porcupine rank-3 family]] | ||
* ''[[Nakika]]'' (+245/242) → [[Octagar family #Nakika|Octagar family]] | * ''[[Nakika]]'' (+245/242) → [[Octagar family #Nakika|Octagar family]] | ||
* ''[[Octarod]]'' (+245/243) → [[Sensamagic family #Octarod|Sensamagic family]] | * ''[[Octarod]]'' (+245/243) → [[Sensamagic family #Octarod|Sensamagic family]] | ||
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[[Comma list]]: 100/99 | [[Comma list]]: 100/99 | ||
{{ | {{Mapping|legend=2| 1 0 0 2 | 0 1 0 -2 | 0 0 1 2 }} | ||
: mapping generators: ~2, ~3, ~5 | |||
[[Optimal tuning]] | [[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 }} | {{Optimal ET sequence|legend=1| 7, 12, 15, 19, 22, 34, 41, 56, 75e, 97, 131e }} | ||
[[Badness]]: 0. | [[Badness]] (Sintel): 0.187 | ||
== Apollo == | == Apollo == | ||
See [[Marvel family #Apollo]]. | See [[Marvel family #Apollo]]. | ||
== | == Keemic == | ||
See [[Keemic family # | See [[Keemic family #Keemic]]. | ||
== Thrasher == | == Thrasher == | ||
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[[Category:Temperament clans]] | [[Category:Temperament clans]] | ||
[[Category:Ptolemismic clan| ]] <!-- main article --> | [[Category:Ptolemismic clan| ]] <!-- main article --> | ||
[[Category:Ptolemismic| ]] <!-- key 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:
- 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
- Nakika (+245/242) → Octagar family
- Octarod (+245/243) → Sensamagic family
- Androboh (+1375/1372) → Gariboh family
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
- 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
Keemic
Thrasher
See Starling family #Thrasher.