Archytas and ares

"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).

For technical data, see Archytas family #Archytas. See also: Archytas family #Ares.

Etymology

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.

Todo: add etymology Add name (person who coined the terms) and year (when they were coined). Review reasoning if possible.

Interval lattice

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  11-limit ares

Chords

Archytas enables the eponymous essentially tempered chords of archytas chords. Ares further enables ptolemismic and valinorsmic chords.

Scales

• Ares12