36edo: Difference between revisions

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=== Harmonics ===

In the 5-limit, 36edo offers no improvement over 12edo, since its nearest approximation to 5:4 is the overly-familiar 400-cent major third. However, it excels at the 7th harmonic and intervals involving 7. As a 3 and 7 tuning, or in other words as a tuning for the 2.3.7 [[just intonation subgroup]], 36edo's single degree of around 33 cents serves a double function as 49:48, the so-called [https://en.wikipedia.org/wiki/Septimal_diesis Slendro diesis] of around 36 cents, and as 64:63, the so-called [https://en.wikipedia.org/wiki/Septimal_comma septimal comma] of around 27 cents. Meanwhile, its second degree functions as 28:27, the so-called [https://en.wikipedia.org/wiki/Septimal_third-tone Septimal third-tone] (which = 49:48 x 64:63). The 2.3.7 subgroup can be extended to the [[k*N_subgroups|2*36 subgroup]] 2.3.25.7.55.13.17, and on this subgroup it tempers out the same commas as [[72edo]] does in the full [[17-limit]].

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 === Harmonics ===
 In the 5-limit, 36edo offers no improvement over 12edo, since its nearest approximation to 5:4 is the overly-familiar 400-cent major third. However, it excels at the 7th harmonic and intervals involving 7. As a 3 and 7 tuning, or in other words as a tuning for the 2.3.7 [[just intonation subgroup]], 36edo's single degree of around 33 cents serves a double function as 49:48, the so-called [https://en.wikipedia.org/wiki/Septimal_diesis Slendro diesis] of around 36 cents, and as 64:63, the so-called [https://en.wikipedia.org/wiki/Septimal_comma septimal comma] of around 27 cents. Meanwhile, its second degree functions as 28:27, the so-called [https://en.wikipedia.org/wiki/Septimal_third-tone Septimal third-tone] (which = 49:48 x 64:63). The 2.3.7 subgroup can be extended to the [[k*N_subgroups|2*36 subgroup]] 2.3.25.7.55.13.17, and on this subgroup it tempers out the same commas as [[72edo]] does in the full [[17-limit]].
 {{harmonics in equal|36|prec=2}}