768edo: Difference between revisions

Line 1:

{{Infobox ET}}The '''768 equal divisions of the octave''' ('''768edo'''), or '''768(-tone) equal temperament''' ('''768tet''', '''768et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 768 [[equal]] parts of 1.5625 [[Cent|cents]] each. Its adjacent step is known as '''Hexamu''' (sixth MIDI-resolution unit, 6mu, 2<sup>6</sup> = 64 equal divisions of the [[12edo]] semitone).

{{~~harmonics in equal~~|768~~|prec~~=~~3|start~~=~~2|intervals~~=~~prime}}~~

768edo is consistent in the 7-limit, tempering out the [[mutt comma]] [-44 -3 ~~21⟩~~ and the 5-limit [[commatic]] comma [-37 38 -~~10⟩~~ in the 5-limit, and [[Horwell comma|65625/65536]], [[250047/250000]], [[Mitonismic temperaments|5250987/5242880]], [-12 -5 11 -2⟩, [7 18 -2 -~~11⟩~~, and [-36 8 4 5⟩ in the 7-limit.

== Theory ==

768edo is [[consistent]] in the [[7-odd-limit]]. The equal temperament [[tempering out|tempers out]] the [[mutt comma]] {{monzo| -44 -3 21 }} and the 5-limit [[commatic]] comma {{monzo| -37 38 -10 }} in the 5-limit, and [[Horwell comma|65625/65536]], [[250047/250000]], [[Mitonismic temperaments|5250987/5242880]], {{monzo| -12 -5 11 -2 }}, {{monzo| 7 18 -2 -11 }}, and {{monzo| -36 8 4 5 }} in the 7-limit.

=== As a tuning standard ===

Its adjacent step is known as '''hexamu''' (sixth MIDI-resolution unit, 6mu, 2<sup>6</sup> = 64 equal divisions of the [[12edo]] semitone). The internal data structure of the 6mu requires one byte, with the first two bits reserved as flags, one to indicate the byte's status as data, and one to indicate the sign (+ or -) showing the direction of the pitch-bend up or down, and all six of the remaining bits used for the tuning data

=== Odd harmonics ===

=== Subsets and supersets ===

Since 768 factors into {{factorization|768}}, 768edo has subset edos {{EDOs| 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, and 384 }}.

== See also ==

Line 19:

Line 30:

** [[98304edo]] (13mu tuning)

** [[196608edo]] (14mu tuning)

== External links ==

* [http://tonalsoft.com/enc/number/6mu.aspx Tonalsoft Encyclopedia | ''6mu / hexamu / 768-edo'']

@@ Line 1: / Line 1: @@
-{{Infobox ET}}The '''768 equal divisions of the octave''' ('''768edo'''), or '''768(-tone) equal temperament''' ('''768tet''', '''768et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 768 [[equal]] parts of 1.5625 [[Cent|cents]] each. Its adjacent step is known as '''Hexamu''' (sixth MIDI-resolution unit, 6mu, 2<sup>6</sup> = 64 equal divisions of the [[12edo]] semitone).
+{{Infobox ET}}
-{{harmonics in equal|768|prec=3|start=2|intervals=prime}}
+{{EDO intro|768}}
-edo is consistent in the 7-limit, tempering out the [[mutt comma]] [-44 -3 21⟩ and the 5-limit [[commatic]] comma [-37 38 -10⟩ in the 5-limit, and [[Horwell comma|65625/65536]], [[250047/250000]], [[Mitonismic temperaments|5250987/5242880]], [-12 -5 11 -2⟩, [7 18 -2 -11⟩, and [-36 8 4 5⟩ in the 7-limit.
+== Theory ==
+edo is [[consistent]] in the [[7-odd-limit]]. The equal temperament [[tempering out|tempers out]] the [[mutt comma]] {{monzo| -44 -3 21 }} and the 5-limit [[commatic]] comma {{monzo| -37 38 -10 }} in the 5-limit, and [[Horwell comma|65625/65536]], [[250047/250000]], [[Mitonismic temperaments|5250987/5242880]], {{monzo| -12 -5 11 -2 }}, {{monzo| 7 18 -2 -11 }}, and {{monzo| -36 8 4 5 }} in the 7-limit.
+=== As a tuning standard ===
+Its adjacent step is known as '''hexamu''' (sixth MIDI-resolution unit, 6mu, 2<sup>6</sup> = 64 equal divisions of the [[12edo]] semitone). The internal data structure of the 6mu requires one byte, with the first two bits reserved as flags, one to indicate the byte's status as data, and one to indicate the sign (+ or -) showing the direction of the pitch-bend up or down, and all six of the remaining bits used for the tuning data
+=== Odd harmonics ===
+{{Harmonics in equal|768|intervals=prime}}
+=== Subsets and supersets ===
+Since 768 factors into {{factorization|768}}, 768edo has subset edos {{EDOs| 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, and 384 }}.
 == See also ==
@@ Line 19: / Line 30: @@
 ** [[98304edo]] (13mu tuning)
 ** [[196608edo]] (14mu tuning)
+== External links ==
+* [http://tonalsoft.com/enc/number/6mu.aspx Tonalsoft Encyclopedia | ''6mu / hexamu / 768-edo'']