Archytas family: Difference between revisions

Ares: +link to ptolemismic clan
Rework intro; link to the rank-2 clan. Harmonic seventh ("otonal tetrad") ~ dominant seventh is a specific feature of the dominant temp, not this.
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The '''archytas family''' of temperaments [[tempering out|tempers out]] [[64/63]], and thereby identifies the [[otonal]] [[tetrad]] with the [[dominant seventh chord]], which is familiar from [[12edo]] and also a feature of [[22edo]] and [[27edo]].
The '''archytas family''' of [[rank-3 temperament|rank-3]] [[regular temperament|temperaments]] [[tempering out|tempers out]] [[64/63]]. The head of this family, archytas, tempers out 64/63 alone in the full 7-limit, so it has the same 2.3.7-[[subgroup]] structure as [[archy]] but giving [[prime harmonic|prime]] [[5/1|5]] an independent generator.
 
See [[Archytas clan]] for the rank-2 temperament without the last generator of archytas, and its various extensions.  


== Archytas ==
== Archytas ==