24edo - Revision history

Vector at 14:39, 4 April 2026

2026-04-04T14:39:04Z

← Older revision		Revision as of 14:39, 4 April 2026
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	\|}		\|}
	Diatonic thirds are bolded.		Diatonic thirds are bolded.

			=== Derivation ===
			24edo is derived by doubling 12edo to allow for intervals of the 11- and 13-limit to be represented.

	==== Chords ====		==== Chords ====

Vector at 09:18, 27 March 2026

2026-03-27T09:18:23Z

← Older revision		Revision as of 09:18, 27 March 2026
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	==== JI approximation ====		==== JI approximation ====
	Although 24edo inherits its approximations of the 5-limit from 12edo, it doesn't allow one to stack more than one instance of 5/4 without excessive error accumulation. Furthermore, despite having a more accurate 7/4 than 12edo in terms of absolute error, the 7th harmonic suffers from the same problem, as well as worse problems.		Although 24edo inherits its approximations of the 5-limit from 12edo, it doesn't allow one to stack more than one instance of 5/4 without excessive error accumulation. Furthermore, despite having a more accurate 7/4 than 12edo in terms of absolute error, the 7th harmonic suffers from the same problem, as well as worse problems. 24edo is most usefully considered a 2.3.11.13.17.19 system.
	{{Harmonics in ED\|24\|31\|0}}		{{Harmonics in ED\|24\|31\|0}}
	{\| class="wikitable"		{\| class="wikitable"

Lumithesilly: we ignore my previous change im a lil dumb

2026-03-05T02:01:31Z

we ignore my previous change im a lil dumb

← Older revision		Revision as of 02:01, 5 March 2026
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	\|-		\|-
	!Steps		!Steps
	\|11		\|5
	\|'''12'''		\|'''6'''
	\|13		\|7
	\|'''14'''		\|'''8'''
	\|15		\|9
	\|}		\|}
	Diatonic thirds are bolded.		Diatonic thirds are bolded.

Lumithesilly: added steps to the thirds table

2026-03-05T02:00:59Z

added steps to the thirds table

← Older revision		Revision as of 02:00, 5 March 2026
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	\|'''24/19, 5/4'''		\|'''24/19, 5/4'''
	\|13/10		\|13/10
			\|-
			!Steps
			\|11
			\|'''12'''
			\|13
			\|'''14'''
			\|15
	\|}		\|}
	Diatonic thirds are bolded.		Diatonic thirds are bolded.

Inthar: /* Chords */

2026-02-23T04:58:30Z

Chords

← Older revision		Revision as of 04:58, 23 February 2026
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	Examples of friends in this system are a major third, a minor third, a neutral third, an inframinor third/ultramajor second, a paramajor fourth (~11/8), a paraminor fifth (~16/11) and, of course, the perfect fourth and perfect fifth. Examples of enemies are an ultraprime/inframinor second, and an infraoctave/ultramajor seventh. The most notable "frenemies"- that is, intervals that act as both "friends" and "enemies" at the same time- are a tritone, as well as a minor second, a major seventh, an ultramajor third/paraminor fourth (~13/10) and an inframinor sixth/paramajor fifth (~20/13). Crowding in this system is caused by intervals smaller than or equal to a major second relative to the unison or octave.		Examples of friends in this system are a major third, a minor third, a neutral third, an inframinor third/ultramajor second, a paramajor fourth (~11/8), a paraminor fifth (~16/11) and, of course, the perfect fourth and perfect fifth. Examples of enemies are an ultraprime/inframinor second, and an infraoctave/ultramajor seventh. The most notable "frenemies"- that is, intervals that act as both "friends" and "enemies" at the same time- are a tritone, as well as a minor second, a major seventh, an ultramajor third/paraminor fourth (~13/10) and an inframinor sixth/paramajor fifth (~20/13). Crowding in this system is caused by intervals smaller than or equal to a major second relative to the unison or octave.

			{{Navbox EDO}}
	{{Cat\|Edos}}		{{Cat\|Edos}}

Vector: made 24edo equivalences more obvious in the chord-building section

2026-02-08T20:55:24Z

made 24edo equivalences more obvious in the chord-building section

← Older revision		Revision as of 20:55, 8 February 2026
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	Because it contains 12edo and 8edo as subsets, 24edo has the capacity for all the same types of chords as those edos. As if that weren't enough, careful use of a set of rules known as the [[dinner party rules]] helps to add more viable chords to the list- every chord must be comprised of a chain of friends in which each note is a "friend" to every other note, no note can have an "enemy", and, there must not be any crowding except in tension chords.		Because it contains 12edo and 8edo as subsets, 24edo has the capacity for all the same types of chords as those edos. As if that weren't enough, careful use of a set of rules known as the [[dinner party rules]] helps to add more viable chords to the list- every chord must be comprised of a chain of friends in which each note is a "friend" to every other note, no note can have an "enemy", and, there must not be any crowding except in tension chords.

	Examples of friends in this system are a major third, a minor third, a neutral third, an inframinor third~~, an~~ ultramajor second, a paramajor fourth (~11/8), a paraminor fifth (~16/11) and, of course, the perfect fourth and perfect fifth. Examples of enemies are an ultraprime~~, an~~ inframinor second, an infraoctave~~, and an~~ ultramajor seventh. The most notable "frenemies"- that is, intervals that act as both "friends" and "enemies" at the same time- are a tritone, as well as a minor second, a major seventh, an ultramajor third~~, an inframinor sixth, a~~ paraminor fourth (~13/10) and a paramajor fifth (~20/13). Crowding in this system is caused by intervals smaller than or equal to a major second relative to the unison or octave.		Examples of friends in this system are a major third, a minor third, a neutral third, an inframinor third/ultramajor second, a paramajor fourth (~11/8), a paraminor fifth (~16/11) and, of course, the perfect fourth and perfect fifth. Examples of enemies are an ultraprime/inframinor second, and an infraoctave/ultramajor seventh. The most notable "frenemies"- that is, intervals that act as both "friends" and "enemies" at the same time- are a tritone, as well as a minor second, a major seventh, an ultramajor third/paraminor fourth (~13/10) and an inframinor sixth/paramajor fifth (~20/13). Crowding in this system is caused by intervals smaller than or equal to a major second relative to the unison or octave.

	{{Cat\|Edos}}		{{Cat\|Edos}}

Vector at 20:53, 8 February 2026

2026-02-08T20:53:13Z

← Older revision		Revision as of 20:53, 8 February 2026
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			[[File:24edo.png\|thumb\|11- and 13-limit intervals often fall about halfway in between 12edo intervals.]]
	'''24edo''', or 24 equal divisions of the octave, is the equal tuning featuring steps of (1200/24) = 50 cents, 24 of which stack to the perfect octave [[2/1]]. It is arguably one of the most common entry points into microtonality due to containing the familiar pitches of [[12edo]].		'''24edo''', or 24 equal divisions of the octave, is the equal tuning featuring steps of (1200/24) = 50 cents, 24 of which stack to the perfect octave [[2/1]]. It is arguably one of the most common entry points into microtonality due to containing the familiar pitches of [[12edo]].

Inthar: /* Chords */

2026-01-25T17:06:57Z

Chords

← Older revision		Revision as of 17:06, 25 January 2026
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	Examples of friends in this system are a major third, a minor third, a neutral third, an inframinor third, an ultramajor second, a paramajor fourth (~11/8), a paraminor fifth (~16/11) and, of course, the perfect fourth and perfect fifth. Examples of enemies are an ultraprime, an inframinor second, an infraoctave, and an ultramajor seventh. The most notable "frenemies"- that is, intervals that act as both "friends" and "enemies" at the same time- are a tritone, as well as a minor second, a major seventh, an ultramajor third, an inframinor sixth, a paraminor fourth (~13/10) and a paramajor fifth (~20/13). Crowding in this system is caused by intervals smaller than or equal to a major second relative to the unison or octave.		Examples of friends in this system are a major third, a minor third, a neutral third, an inframinor third, an ultramajor second, a paramajor fourth (~11/8), a paraminor fifth (~16/11) and, of course, the perfect fourth and perfect fifth. Examples of enemies are an ultraprime, an inframinor second, an infraoctave, and an ultramajor seventh. The most notable "frenemies"- that is, intervals that act as both "friends" and "enemies" at the same time- are a tritone, as well as a minor second, a major seventh, an ultramajor third, an inframinor sixth, a paraminor fourth (~13/10) and a paramajor fifth (~20/13). Crowding in this system is caused by intervals smaller than or equal to a major second relative to the unison or octave.

			{{Cat\|Edos}}

Aura: Figured I'd add one more interval...

2026-01-10T20:25:15Z

Figured I'd add one more interval...

← Older revision		Revision as of 20:25, 10 January 2026
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	!Just interpretation		!Just interpretation
	\|15/13		\|15/13
	\|'''19/16'''		\|'''19/16, 6/5'''
	\|11/9		\|11/9
	\|'''24/19, 5/4'''		\|'''24/19, 5/4'''

Hkm: /* Theory */

2026-01-10T19:09:03Z

Theory

← Older revision		Revision as of 19:09, 10 January 2026
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	\|'''19/16'''		\|'''19/16'''
	\|11/9		\|11/9
	\|'''24/19'''		\|'''24/19, 5/4'''
	\|13/10		\|13/10
	\|}		\|}