19edo: Difference between revisions
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[[38edo]], which doubles 19edo, provides an approximation of harmonic 11 that works well with the flat tendency of its 5-limit mapping. See [[undevigintone]]. [[57edo]] effectively corrects the harmonic 7 to just, although it is [[76edo]] that fits the best. See [[meanmag]]. | [[38edo]], which doubles 19edo, provides an approximation of harmonic 11 that works well with the flat tendency of its 5-limit mapping. See [[undevigintone]]. [[57edo]] effectively corrects the harmonic 7 to just, although it is [[76edo]] that fits the best. See [[meanmag]]. | ||
=== Miscellaneous properties === | |||
19edo has the flattest possible fifth of any edo that can possibly be diamond monotone in the 15-odd-limit. Using 11\19 as the fifth, the sharpest possible mapping of 5/4 where 10/9 is no greater than 9/8 is 4\19, and the sharpest possible 15/8 is 17\19. Here 16/15 is a quarter of 4/3 (the temperament doing this is [[negri]]), so 15/14, 14/13, and 13/12 must all be equated with 16/15 to 2\19 for them to be monotone in size. If the fifth were any flatter, 5/4 and 15/8 would have to be flatter, and 16/15 would have to be sharper, so diamond monotone in the 15-odd-limit becomes impossible. 19edo is, in fact, diamond monotone in the 15-odd-limit, and even the 17-odd-limit (see [[Monotonicity limits of small EDOs]]). The sharpest fifth where 15-odd-limit is possible is [[37edo#Miscellaneous properties|22\37]]. | |||
== Intervals == | == Intervals == | ||