Devadoot: Difference between revisions
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'''Devadoot''' is the name proposed by Mason Green for the non-octave-equivalent variant of [[Magic|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. | Devadoot is closely related to [[41edo|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 [[ | 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|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|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. | 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. | ||
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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. | 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 | Straight-fretted devadoot guitars would be a possibility; they would need to be tuned in [https://en.wikipedia.org/wiki/Major_thirds_tuning all-thirds] since the period is a major third. | ||
[[Category:41edo]] | |||
[[Category:magic]] | |||