768edo - Revision history

Eliora: /* Theory */ it's actually an 11-limit OPV for bezique

2025-08-13T05:02:35Z

Theory: it's actually an 11-limit OPV for bezique

← Older revision		Revision as of 05:02, 13 August 2025
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	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.		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.

	It ~~is a strong tuning and a member of~~ the optimal ~~ET sequence~~ for the 32nd-octave [[bezique]] temperament.		It provides the 11-limit [[optimal patent val]] for the 32nd-octave [[bezique]] temperament.

	=== As a tuning standard ===		=== As a tuning standard ===

Eliora: /* Theory */ +fact it supports bezique

2025-08-08T01:02:04Z

Theory: +fact it supports bezique

← Older revision		Revision as of 01:02, 8 August 2025
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	== Theory ==		== 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 [[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.		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.

			It is a strong tuning and a member of the optimal ET sequence for the 32nd-octave [[bezique]] temperament.

	=== As a tuning standard ===		=== As a tuning standard ===

ArrowHead294 at 23:08, 20 February 2025

2025-02-20T23:08:52Z

← Older revision		Revision as of 23:08, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|768~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: /* Theory */ update

2025-01-13T13:40:32Z

Theory: update

← Older revision		Revision as of 13:40, 13 January 2025
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	== Theory ==		== 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 ===		=== 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 ===		=== Odd harmonics ===

Fredg999: /* External links */ Misc. edits

2024-07-05T04:17:54Z

External links: Misc. edits

← Older revision		Revision as of 04:17, 5 July 2024
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	== External links ==		== External links ==
	* [http://tonalsoft.com/enc/number/6mu.aspx ~~Tonalsoft Encyclopedia \| ''~~6mu / hexamu / 768-edo'']		* [http://tonalsoft.com/enc/number/6mu.aspx 6mu / hexamu / 768-edo] on [[Tonalsoft Encyclopedia]]

FloraC: /* Theory */ fix grammar

2023-11-07T08:25:02Z

Theory: fix grammar

← Older revision		Revision as of 08:25, 7 November 2023
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	=== As a tuning standard ===		=== 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		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 ===		=== Odd harmonics ===

FloraC: Rework

2023-11-07T07:51:58Z

Rework

@@ 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.
 == See also ==
@@ Line 19: / Line 30: @@
 ** [[98304edo]] (13mu tuning)
 ** [[196608edo]] (14mu tuning)

Royalmilktea: 768edo/6mu, infobox et, harmonics, commas, other mu temps.

2022-10-07T07:54:58Z

768edo/6mu, infobox et, harmonics, commas, other mu temps.

New page

{{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.

== See also ==

* [[Equal-step tuning|Equal multiplications]] of MIDI-resolution units
** [[24edo]] (1mu tuning)
** [[48edo]] (2mu tuning)
** [[96edo]] (3mu tuning)
** [[192edo]] (4mu tuning)
** [[384edo]] (5mu tuning)
** [[1536edo]] (7mu tuning)
** [[3072edo]] (8mu tuning)
** [[6144edo]] (9mu tuning)
** [[12288edo]] (10mu tuning)
** [[24576edo]] (11mu tuning)
** [[49152edo]] (12mu tuning)
** [[98304edo]] (13mu tuning)
** [[196608edo]] (14mu tuning)