384edo: Difference between revisions

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

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.

=== Prime harmonics ===

{{~~harmonics~~ in equal|384|~~prec~~=3|~~start=~~2~~|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 }}.

== See also ==

* [[Equal-step tuning|Equal multiplications]] of MIDI-resolution units

** [[24edo]] (1mu tuning)

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

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

== External links ==

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

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 {{Infobox ET}}
-{{EDO intro|384}}
+{{ED intro}}
 == Theory ==
-edo 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.
+edo 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). In addition, in light of 384 being a multiple of 32, 384bc val supports [[windrose]] temperament in the 7-limit.
+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 &minus;) showing the direction of the pitch-bend up or down, and one other bit which is not used.
 === Prime harmonics ===
-{{harmonics in equal|384|prec=3|start=2|intervals=prime}}
+{{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 }}.
 == See also ==
 * [[Equal-step tuning|Equal multiplications]] of MIDI-resolution units
 ** [[24edo]] (1mu tuning)
@@ Line 26: / Line 29: @@
 ** [[98304edo]] (13mu tuning)
 ** [[196608edo]] (14mu tuning)
+== External links ==
+* [http://tonalsoft.com/enc/number/5mu.aspx 5mu / pentamu] on [[Tonalsoft Encyclopedia]]