384edo - Revision history

Eliora: +listen category

2026-06-10T17:22:33Z

+listen category

← Older revision		Revision as of 17:22, 10 June 2026
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	== External links ==		== External links ==
	* [http://tonalsoft.com/enc/number/5mu.aspx 5mu / pentamu] on [[Tonalsoft Encyclopedia]]		* [http://tonalsoft.com/enc/number/5mu.aspx 5mu / pentamu] on [[Tonalsoft Encyclopedia]]

			[[Category:Listen]]

Eliora: expand, add music, note significance of the temp as it reaches 11/7 and 13/8 quickly

2026-06-10T17:22:15Z

expand, add music, note significance of the temp as it reaches 11/7 and 13/8 quickly

← Older revision		Revision as of 17:22, 10 June 2026
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	== Theory ==		== Theory ==
	384edo is [[consistent]] in the [[7-odd-limit]]. The equal temperament [[tempering out\|tempers out]] the [[misty comma]] {{monzo\| 26 -12 -3 }}, and the 5-limit tritriple comma {{monzo\| 31 20 -27 }} in the 5-limit, and [[3136/3125]], [[5120/5103]], [[Landscape comma\|250047/250000]], and the [[mistisma]] 458752/455625 in the 7-limit.		384edo is [[consistent]] in the [[7-odd-limit]]. The equal temperament [[tempering out\|tempers out]] the [[misty comma]] {{monzo\| 26 -12 -3 }} and provides the [[optimal patent val]] for the 5-limit misty temperament. It also supports the 324 & 384 temperament which is an extension of misty that divides the octave into 12, reaches [[11/7]] and [[13/8]] within two steps, and is representable with a 36-note scale. It also tempers out the 5-limit tritriple comma {{monzo\| 31 20 -27 }} in the 5-limit, and [[3136/3125]], [[5120/5103]], [[Landscape comma\|250047/250000]], and the [[mistisma]] 458752/455625 in the 7-limit.

	=== As a tuning standard ===		=== As a tuning standard ===
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	** [[98304edo]] (13mu tuning)		** [[98304edo]] (13mu tuning)
	** [[196608edo]] (14mu tuning)		** [[196608edo]] (14mu tuning)

			== Scales ==
			* 19 13 19 13 19 13 19 13 19 13 19 13 19 13 19 13 19 13 19 13 19 13 19 13 - 324 & 384[24]
			* 13 13 5 13 13 5 13 13 5 13 13 5 ... (12 times) ... 13 13 5 13 13 5 13 13 5 - 324 & 384[36]
			== Music ==

			; [[Eliora]]

			* [https://www.youtube.com/watch?v=QR5SSfdAyLE ''Unmoveable''] (2026) - 324 & 384 temperament

	== External links ==		== External links ==
	* [http://tonalsoft.com/enc/number/5mu.aspx 5mu / pentamu] on [[Tonalsoft Encyclopedia]]		* [http://tonalsoft.com/enc/number/5mu.aspx 5mu / pentamu] on [[Tonalsoft Encyclopedia]]

ArrowHead294 at 23:08, 20 February 2025

2025-02-20T23:08:39Z

← Older revision		Revision as of 23:08, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|384~~}}		{{ED intro}}

	== Theory ==		== Theory ==

Fredg999: /* External links */ Misc. edits

2024-07-05T04:14:25Z

External links: Misc. edits

← Older revision		Revision as of 04:14, 5 July 2024
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	== External links ==		== External links ==
	* [http://tonalsoft.com/enc/number/5mu.aspx ~~Tonalsoft Encyclopedia \| ''~~5mu / pentamu'']		* [http://tonalsoft.com/enc/number/5mu.aspx 5mu / pentamu] on [[Tonalsoft Encyclopedia]]

FloraC: Rework (-windrose (16 gensteps isn't available in this edo)); +subsets and supersets

2023-11-07T08:32:00Z

Rework (-windrose (16 gensteps isn't available in this edo)); +subsets and supersets

← Older revision		Revision as of 08:32, 7 November 2023
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	== Theory ==		== Theory ==
	384edo is consistent in the 7-limit, tempering out the ~~misty comma~~ [[~~Misty~~ comma\|[26 -12 -~~3⟩]]~~, and the 5-limit tritriple comma [31 20 -~~27⟩~~ in the 5-limit, and [[3136/3125]], [[5120/5103]], [[Landscape comma\|250047/250000]], and the ~~mistisma~~ [[~~Mistismic temperaments\|~~458752/455625]] in the 7-limit.		384edo is [[consistent]] in the [[7-odd-limit]]. The equal temperament [[tempering out\|tempers out]] the [[misty comma]] {{monzo\| 26 -12 -3 }}, and the 5-limit tritriple comma {{monzo\| 31 20 -27 }} in the 5-limit, and [[3136/3125]], [[5120/5103]], [[Landscape comma\|250047/250000]], and the [[mistisma]] 458752/455625 in the 7-limit.

	=== ~~Relation to powers of two~~ ===		=== As a tuning standard ===
	~~Its adjacent~~ step is known as '''~~Pentamu~~''' (fifth MIDI-resolution unit, 5mu, 2<sup>5</sup> = 32 equal divisions of the [[12edo]] semitone).		A step of 384edo is known as a '''pentamu''' (fifth MIDI-resolution unit, 5mu, 2<sup>5</sup> = 32 equal divisions of the [[12edo]] semitone). The internal data structure of the 5mu 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 one other bit which is not used.

	~~In addition,~~ in ~~light of~~ 384 ~~being a multiple of~~ 32, ~~384bc val supports [[windrose]] temperament in the 7-limit~~.		=== Prime harmonics ===
			{{Harmonics in equal\|384\|intervals=prime}}

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

	~~=== Prime harmonics ===~~
	~~{{harmonics in equal\|384\|prec=3\|start=2\|intervals=prime}}~~
	== See also ==		== See also ==

	* [[Equal-step tuning\|Equal multiplications]] of MIDI-resolution units		* [[Equal-step tuning\|Equal multiplications]] of MIDI-resolution units
	** [[24edo]] (1mu tuning)		** [[24edo]] (1mu tuning)
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	** [[98304edo]] (13mu tuning)		** [[98304edo]] (13mu tuning)
	** [[196608edo]] (14mu tuning)		** [[196608edo]] (14mu tuning)

			== External links ==
			* [http://tonalsoft.com/enc/number/5mu.aspx Tonalsoft Encyclopedia \| ''5mu / pentamu'']

Eliora at 21:27, 22 December 2022

2022-12-22T21:27:54Z

← Older revision		Revision as of 21:27, 22 December 2022
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	=== Relation to powers of two ===		=== Relation to powers of two ===
	Its adjacent step is known as '''Pentamu''' (fifth MIDI-resolution unit, 5mu, 2<sup>5</sup> = 32 equal divisions of the [[12edo]] semitone). In addition, in light of 384 being a multiple of 32, 384bc val supports [[windrose]] temperament in the 7-limit.		Its adjacent step is known as '''Pentamu''' (fifth MIDI-resolution unit, 5mu, 2<sup>5</sup> = 32 equal divisions of the [[12edo]] semitone).

			In addition, in light of 384 being a multiple of 32, 384bc val supports [[windrose]] temperament in the 7-limit.

	=== Prime harmonics ===		=== Prime harmonics ===

Eliora: cleanup and a new fact

2022-12-22T21:24:26Z

cleanup and a new fact

← Older revision		Revision as of 21:24, 22 December 2022
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	{{Infobox ET}}		{{Infobox ET}}
	The '''384 equal divisions of the octave''' ('''384edo'''), or '''384(-tone) equal temperament''' ('''384tet''', '''384et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 384 [[equal]] parts of 3.125 [[Cent\|cents]] each. Its adjacent step is known as '''Pentamu''' (fifth MIDI-resolution unit, 5mu, 2<sup>5</sup> = 32 equal divisions of the [[12edo]] semitone).		{{EDO intro\|384}}
	{{~~harmonics in equal~~\|384~~\|prec~~=~~3\|start~~=~~2\|intervals~~=~~prime}}~~
			== Theory ==
	384edo is consistent in the 7-limit, tempering out the misty comma [[Misty comma\|[26 -12 -3⟩]], and the 5-limit tritriple comma [31 20 -27⟩ in the 5-limit, and [[3136/3125]], [[5120/5103]], [[Landscape comma\|250047/250000]], and the mistisma [[Mistismic temperaments\|458752/455625]] in the 7-limit.		384edo is consistent in the 7-limit, tempering out the misty comma [[Misty comma\|[26 -12 -3⟩]], and the 5-limit tritriple comma [31 20 -27⟩ in the 5-limit, and [[3136/3125]], [[5120/5103]], [[Landscape comma\|250047/250000]], and the mistisma [[Mistismic temperaments\|458752/455625]] in the 7-limit.

			=== Relation to powers of two ===
			Its adjacent step is known as '''Pentamu''' (fifth MIDI-resolution unit, 5mu, 2<sup>5</sup> = 32 equal divisions of the [[12edo]] semitone). In addition, in light of 384 being a multiple of 32, 384bc val supports [[windrose]] temperament in the 7-limit.

			=== Prime harmonics ===
			{{harmonics in equal\|384\|prec=3\|start=2\|intervals=prime}}
	== See also ==		== See also ==

Royalmilktea: 384edo/5mu page, infobox et, harmonics, and other mu temps. added

2022-10-07T07:37:55Z

384edo/5mu page, infobox et, harmonics, and other mu temps. added

New page

{{Infobox ET}}
The '''384 equal divisions of the octave''' ('''384edo'''), or '''384(-tone) equal temperament''' ('''384tet''', '''384et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 384 [[equal]] parts of 3.125 [[Cent|cents]] each. Its adjacent step is known as '''Pentamu''' (fifth MIDI-resolution unit, 5mu, 2<sup>5</sup> = 32 equal divisions of the [[12edo]] semitone).
{{harmonics in equal|384|prec=3|start=2|intervals=prime}}
384edo is consistent in the 7-limit, tempering out the misty comma [[Misty comma|[26 -12 -3⟩]], and the 5-limit tritriple comma [31 20 -27⟩ in the 5-limit, and [[3136/3125]], [[5120/5103]], [[Landscape comma|250047/250000]], and the mistisma [[Mistismic temperaments|458752/455625]] 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)
** [[768edo]] (6mu 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)