Ptolemismic clan: Difference between revisions

{{Technical data page}}

The '''ptolemismic clan''' of [[rank-3 temperament]]s [[tempering out|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 #Calliope|Didymus rank-3 family]]

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

* ''[[Sonic]]'' (+55/54) → [[Porcupine rank-3 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)]].

== Ptolemic ==

[[Subgroup]]: 2.3.5.11

[[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]]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 }}

[[Badness]] (Sintel): 0.187

See [[Marvel family #Apollo]].

See [[Keemic family #Keemic]].  

== Thrasher ==

See [[Archytas family #Ares]].  

[[Category:Temperament clans]]

[[Category:Ptolemismic clan| ]] <!-- main article -->

[[Category:Ptolemismic| ]] <!-- key article -->