768edo: Difference between revisions

Line 3:

== 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.

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 [[bicommatic]] 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 ===

A step of 768edo is known as a '''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.

A step of 768edo is known as a '''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 ===

@@ Line 3: / Line 3: @@
 == 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.
+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 [[bicommatic]] 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 ===
-A step of 768edo is known as a '''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 &minus;) showing the direction of the pitch-bend up or down, and all six of the remaining bits used for the tuning data.
+A step of 768edo is known as a '''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 ===