36edo: Difference between revisions

36edo's patent val, like 12, tempers out 81/80, 128/125, and 648/625 in the 5-limit. It departs from 12 in the 7-limit, tempering out 686/675 and 1029/1000, and as a no-fives temperament, 1029/1024 and 118098/117649. The no-fives temperament tempering out 1029/1024, [[slendric]], is well supported by 36edo, its generator of ~8/7 represented by 7 steps of 36edo. In the 11-limit, the patent val tempers out 56/55, 245/242, and 540/539, and is the [[optimal patent val]] for the rank four temperament tempering out 56/55, as well as the rank-3 temperament [[melpomene]] tempering out 81/80 and 56/55. In the 13-limit, it tempers out 78/77 and 91/90, in the 17-limit 51/50, and in the 19-limit 76/75 and 96/95.

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=== Colored notes ===

One way of notating 36edo (at least for people who aren't colorblind) is to use colors. For example, {{colored note|blue|A}} is 33{{frac|3}}{{c}} below {{colored note|A}} and {{colored note|red|A}} is 33{{frac|3}} cents above {{colored note|A}}. Or, the colors could be written out (red A, blue C♯, etc.) or abbreviated as rA, bC♯, etc. This use of red and blue is consistent with [[Kite's_color_notation|color notation]] (ru and zo).

=== Ups and downs notation ===

Alternatively, one can use sharps and flats with arrows, borrowed from extended [[Helmholtz–Ellis notation]]:

 

If the arrows are taken to have their own layer of enharmonic spellings, then in some cases notes may be best denoted using double arrows.

This notation uses the same sagittal sequence as [[43edo#Sagittal notation|43-EDO]], is a subset of the notation for [[72edo#Sagittal notation|72-EDO]], and is a superset of the notations for EDOs [[18edo#Sagittal notation|18]], [[12edo#Sagittal notation|12]], and [[6edo#Sagittal notation|6]].

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<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct