Archytas and ares: Difference between revisions
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{{Redirect|Archytas|the ancient Greek Pythagorean|Wikipedia: Archytas}} | {{Redirect|Archytas|the ancient Greek Pythagorean|Wikipedia: Archytas}} | ||
'''Archytas''' is the [[rank-3]] [[regular temperament|temperament]] [[tempering out]] [[64/63]], with the same 2.3.7- | '''Archytas''' is the [[rank-3]] [[regular temperament|temperament]] [[tempering out]] [[64/63]], with the same [[2.3.7 subgroup|2.3.7-subgroup]] structure as [[archy]] but giving [[prime harmonic|prime]] [[5/1|5]] an independent generator. It has an obvious extension to the [[11-limit]] tempering out [[100/99]] and [[176/175]], called '''ares''', as 64/63 = (100/99)⋅(176/175). | ||
These temperaments are named after the ancient Greek mathematician {{w|Archytas}} and the Greek god {{w|Ares}} respectively, the latter being most likely related to the fact that Archytas was Greek, in addition to the pattern of naming rank-3 temperaments after deities. | These temperaments are named after the ancient Greek mathematician {{w|Archytas}} and the Greek god {{w|Ares}} respectively, the latter being most likely related to the fact that Archytas was Greek, in addition to the pattern of naming rank-3 temperaments after deities. | ||
Latest revision as of 09:05, 3 October 2026
| Archytas; ares |
64/63, 100/99 (11-limit)
11-odd-limit: 13.6 ¢
11-odd-limit: ? notes
- "Archytas" redirects here. For the ancient Greek Pythagorean, see Wikipedia: Archytas.
Archytas is the rank-3 temperament tempering out 64/63, with the same 2.3.7-subgroup structure as archy but giving prime 5 an independent generator. It has an obvious extension to the 11-limit tempering out 100/99 and 176/175, called ares, as 64/63 = (100/99)⋅(176/175).
These temperaments are named after the ancient Greek mathematician Archytas and the Greek god Ares respectively, the latter being most likely related to the fact that Archytas was Greek, in addition to the pattern of naming rank-3 temperaments after deities.
See Archytas family #Archytas and #Ares for technical data.
Interval lattice
-
11-limit ares
Chords and harmony
Archytas enables the eponymous essentially tempered chords of archytas chords. Ares further enables ptolemismic, valinorsmic, and ares chords.