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 [[magic]] that uses a flattened [[5/4|major third]] as a [[period]], five of which make a tritave ([[3/1]]), and a generator which can equivalently be designated as an [[octave]], a [[3/2|perfect fifth]], or a large quarter tone (i.e., an octave minus three periods). The name was proposed by [[Mason Green]].

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.

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|~~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]]).

Compared to the more common 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]], 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 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|Magic[22] 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 mos scales, most of which are improper. The smallest proper mos scales 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.

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 [[integer limit|''n''-integer-limit]] [[chord of nature]] (rather than just [[odd limit]]s). The Graham complexity of the complete 10-integer-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-integer-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 does not handle 12-integer-limit harmonies as well.

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

~~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~~]]

[[Category:Magic]]

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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 [[magic]] that uses a flattened [[5/4|major third]] as a [[period]], five of which make a tritave ([[3/1]]), and a generator which can equivalently be designated as an [[octave]], a [[3/2|perfect fifth]], or a large quarter tone (i.e., an octave minus three periods). The name was proposed by [[Mason Green]].
-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.
+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|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]]).
+Compared to the more common 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]], 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 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|Magic[22] 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 mos scales, most of which are improper. The smallest proper mos scales 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.
+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 [[integer limit|''n''-integer-limit]] [[chord of nature]] (rather than just [[odd limit]]s). The Graham complexity of the complete 10-integer-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-integer-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 does not handle 12-integer-limit harmonies as well.
+Straight-fretted devadoot guitars would be a possibility; they would need to be tuned in {{w|Major thirds tuning|all-thirds}} since the period is a major third.
-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]]
+[[Category:Magic]]