User:Xenllium/Xenllium's circulating scales: Difference between revisions

'''Xentwelve''' is a 12-tone circulating scale based on [[12edo|12 equal temperament]]. In summary, it is close to [[1/3-comma meantone]] in the natural keys and [[Pythagorean tuning]] in the remote keys. The generator is a perfect fifth, which comes in three sizes, with eight pure fifths (at C–G, C♯–G♯, E♭–B♭, E–B, F–C, F♯–C♯, B♭–F and B–F♯, frequency ratio [[3/2]]), three 1/3-comma meantone fifths (at D–A, G–D and A–E), and one narrow schismic fifth (at G♯–D♯ (A♭–E♭), frequency ratio [[16384/10935]]). It derives two major thirds exact [[5/4]] (at C–E and G–B) and one minor third exact [[6/5]] (at E–G), with a pure major triad (at C–E–G) and a pure minor triad (at E–G–B).

'''Xenthirtyone''' is a 31-tone circulating scale based on [[31edo|31 equal temperament]]. There are two circulating scales, named ''Xenthirtyone I'' and ''Xenthirtyone II'', generated by a major third, which comes in three sizes, with twenty-two pure major thirds, eight 1/4-Würschmidt-comma stretched major thirds, and one luna-comma stretched major third.