Devadoot

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Devadoot is the name proposed by Mason Green for the non-octave-equivalent variant of magic temperament that has a period of a flattened major third, five of which make a tritave (3:1), and a generator which can equivalently be designated as an octave, a perfect fifth, or a large quarter tone (i. e., an octave minus three periods).

Devadoot is closely related to 41edo, which has near-just (slightly sharp) tritaves. If the tritaves of 41edo are compressed to be just, then the octaves will be slightly flat (by less than half a cent). However the difference between these tunings is so small as to be practically negligible.

Compared to the standard version of magic, devadoot switches the roles of the generator and period. As such it may be thought of as the magic counterpart of angel temperament, and is named accordingly (Devadoot is the Hindi word for "messenger from God/the gods"; i. e., an angel). The use of a Hindi name is because this scale generates a MOS which is closely related to magic[22]. Whereas angel temperament is well-suited to Western common practice music, magic[22] and therefore also devadoot may prove useful for Indian music (see also magic22 as srutis).

There are 13 steps in a period (i. e., a major third), and the generator is 2 steps. This generates a large number of different MOSes, most of which are improper. The smallest proper MOSes are those with 1, 2, 6, and 7 notes per period. The last two are by far the most interesting, and they are closely related to magic[19] and magic[22] respectively. While they are not octave-repeating, they do have relatively long chains of octaves (five or six of them, respectively) which makes the non-octave-repeating quality less obvious than it otherwise would be.

The devadoot[7] scale derived from 41edo has step pattern 2 2 2 2 2 2 1 (per period). Since octaves are no longer exactly equivalent, we must evaluate the Graham complexity of the entire N-integer-limit chord of nature (rather than just odd limits). The Graham complexity of the complete 10-limit otonality is 4; this means that devadoot[7] allows for 3 each (up to period equivalency) of the basic "major-like" (otonal) and "minor-like" (utonal) 10-limit chords. Since there are slightly more than three periods in an octave, this actually means that there are around 9 such chords per octave, which allows considerable freedom of modulation. Much like angel, it handles the 10-integer-limit amazingly but doesn't handle 12-integer-limit harmonies as well.

Straight-fretted devadoot guitars would be a possibility; they would need to be tuned in all-thirds since the period is a major third.