24edo - Revision history

Lucius Chiaraviglio: /* Brass */ Add Schilke B5 quartertone trumpet

2026-05-05T00:53:25Z

Brass: Add Schilke B5 quartertone trumpet

← Older revision		Revision as of 00:53, 5 May 2026
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	=== Brass ===		=== Brass ===
	Since the trombone is a free-pitched instrument, playing quartertones, or any other edo simply requires increased precision in moving the slide. If you want a brass instrument with fixed steps, [https://www.a-courtois.com/en/instruments/trompettes-2/t-o-m-a Courtois] and [https://www.vanlaartrumpets.nl/en/trumpets/quartertone Van Laar] both produce trumpets with an additional valve that enable you to easily play quartertones.		Since the trombone is a free-pitched instrument, playing quartertones, or any other edo simply requires increased precision in moving the slide. If you want a brass instrument with fixed steps, [https://www.a-courtois.com/en/instruments/trompettes-2/t-o-m-a Courtois] and [https://www.vanlaartrumpets.nl/en/trumpets/quartertone Van Laar] both produce trumpets with an additional valve that enable you to easily play quartertones. In addition, {{W\|Renold Schilke\|Schilke Music Products Incorporated}} built quartertone trumpets (model B5), as shown in All Things Brass And Technology's [https://www.youtube.com/watch?v=1ip0lOlQ2Xo&list=WL&index=257 ''Schilke B5 Quartertone Trumpet from 1971''] (2023).

	== Music ==		== Music ==

Yourmusic Productions: /* Instruments */ The Angine de Poitrine microtonal renaissance continues, add another sales link

2026-05-01T18:35:42Z

Instruments: The Angine de Poitrine microtonal renaissance continues, add another sales link

← Older revision		Revision as of 18:35, 1 May 2026
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	While these are playable, the extra frets can make playing chords and navigating the fretboard significantly more challenging for [[12edo]] chords and scales.		While these are playable, the extra frets can make playing chords and navigating the fretboard significantly more challenging for [[12edo]] chords and scales.

	More common is the "Sazocaster" tuning popularised by Australian band King Gizzard ~~and~~ the Lizard Wizard, which adds quarter tones between approximately half the regular frets. Multiple guitar makers, including [https://eastwoodguitars.com/products/sg2c-flying-banana-mt Eastwood] and [https://salamuzik.com/collections/guitar/products/professional-microtonal-electric-classical-guitar-with-equalizer-kg-5 Sala Muzik] have produced Sazocaster variations.		More common is the "Sazocaster" tuning popularised by Australian band [[King Gizzard & the Lizard Wizard]], which adds quarter tones between approximately half the regular frets. Multiple guitar makers, including [https://eastwoodguitars.com/products/sg2c-flying-banana-mt Eastwood] and [https://salamuzik.com/collections/guitar/products/professional-microtonal-electric-classical-guitar-with-equalizer-kg-5 Sala Muzik] have produced Sazocaster variations.

	[[File:Eastwood-guitars-phase-4-mt-2307179.jpg\|500px]]		[[File:Eastwood-guitars-phase-4-mt-2307179.jpg\|500px]]

	It is also possible to create a guitar that has quartertones on all the lower frets, then switches to regular 12edo at some point on the neck to keep the upper notes easily acessible, as demonstrated by the band [[Angine de Poitrine]]. Guitars using this layout are available at [https://www.microtonalguitar.org/product-page/angine-de-poitrine-style-fixed-microtonal-electric-guitar-ap24 microtonalguitar.org]		It is also possible to create a guitar that has quartertones on all the lower frets, then switches to regular 12edo at some point on the neck to keep the upper notes easily acessible, as demonstrated by the band [[Angine de Poitrine]]. Guitars using this layout are available at [https://www.microtonalguitar.org/product-page/angine-de-poitrine-style-fixed-microtonal-electric-guitar-ap24 microtonalguitar.org] and doubleneck guitar/basses are available from [https://eastwoodguitars.com/products/eastwood-microtonal-doubleneck-electric-guitar-bass Eastwood].

	=== Harp, Harpsichord, and Piano ===		=== Harp, Harpsichord, and Piano ===

Dave Keenan: /* Stein–Zimmermann accidentals */ Increase width of sesquiflat now that it is Zimmermann's, not Couper's.

2026-04-30T13:14:41Z

Stein–Zimmermann accidentals: Increase width of sesquiflat now that it is Zimmermann's, not Couper's.

← Older revision		Revision as of 13:14, 30 April 2026
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	\| A "semiflat" or "half-flat" accidental, comprising a flat symbol mirrored horizontally so that the lobe is facing left.		\| A "semiflat" or "half-flat" accidental, comprising a flat symbol mirrored horizontally so that the lobe is facing left.
	\|-		\|-
	\| style="width: 40px;" \| [[File:HeQd3.svg\|~~36px~~\|center]]		\| style="width: 40px;" \| [[File:HeQd3.svg\|40px\|center]]
	\| A "flat and a half" or "sesquiflat" accidental, comprising a half-flat symbol and a regular flat symbol placed back to back.		\| A "flat and a half" or "sesquiflat" accidental, comprising a half-flat symbol and a regular flat symbol placed back to back.
	\|}		\|}
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	'''Pros:''' familiar, intuitive, and fairly easy to learn.		'''Pros:''' familiar, intuitive, and fairly easy to learn.

	'''Cons:''' can clutter a score easily (especially when used in microtonal key signatures), can get confusing when sight read at faster paces.		'''Cons:''' can clutter a score easily (especially when used in microtonal key signatures), can get confusing when sight read at faster paces.

	=== Persian quartertone accidentals ===		=== Persian quartertone accidentals ===

Yourmusic Productions: /* Instruments */ That didn't take long. Add sales link for AdP style partially quartertone fretted guitars.

2026-04-27T17:39:17Z

Instruments: That didn't take long. Add sales link for AdP style partially quartertone fretted guitars.

← Older revision		Revision as of 17:39, 27 April 2026
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	[[File:Eastwood-guitars-phase-4-mt-2307179.jpg\|500px]]		[[File:Eastwood-guitars-phase-4-mt-2307179.jpg\|500px]]

	It is also possible to create a guitar that has quartertones on all the lower frets, then switches to regular 12edo at some point on the neck to keep the upper notes easily acessible, as demonstrated by the band [[Angine de Poitrine]].		It is also possible to create a guitar that has quartertones on all the lower frets, then switches to regular 12edo at some point on the neck to keep the upper notes easily acessible, as demonstrated by the band [[Angine de Poitrine]]. Guitars using this layout are available at [https://www.microtonalguitar.org/product-page/angine-de-poitrine-style-fixed-microtonal-electric-guitar-ap24 microtonalguitar.org]

	=== Harp, Harpsichord, and Piano ===		=== Harp, Harpsichord, and Piano ===

Yourmusic Productions: /* Instruments */ replace dead links for guitar sales with currently active ones, add another method of partial 24edo that I suspect will soon be copied and spread more widely.

2026-04-03T08:26:02Z

Instruments: replace dead links for guitar sales with currently active ones, add another method of partial 24edo that I suspect will soon be copied and spread more widely.

← Older revision		Revision as of 08:26, 3 April 2026
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	Adam Hoey Xen ([https://www.youtube.com/@adamhoeyxen2199/videos on YouTube]) has used a "neutral thirds tuning" of F#-At-C#-Et-G#-Bt on a standard guitar to play in quartertones.		Adam Hoey Xen ([https://www.youtube.com/@adamhoeyxen2199/videos on YouTube]) has used a "neutral thirds tuning" of F#-At-C#-Et-G#-Bt on a standard guitar to play in quartertones.

	Guitars with 24 frets per octave are also an option ~~and some guitar makers~~, ~~such as Ron Sword's~~ [~~http~~://~~metatonalmusic~~.com ~~Metatonal Music~~]~~{{dead link}},~~ can ~~make~~ custom instruments and ~~perform re-fretting, with an example below~~:		Guitars with 24 frets per octave are also an option, although only [https://eastwoodguitars.com/products/hi-flier-edo-24-electric-microtonal-guitar Eastwood] offer this as a standard production model at the time of writing. Other luthiers you can commission custom microtonal instruments from, including 24edo ones, include [https://www.etsy.com/uk/listing/1154683769 JLJ instruments] and [https://meantoneguitar.com Meantone Guitar].

	[[File:24edo_guitar.jpg\|500px]]		[[File:24edo_guitar.jpg\|500px]]
Line 1,192:		Line 1,192:
	While these are playable, the extra frets can make playing chords and navigating the fretboard significantly more challenging for [[12edo]] chords and scales.		While these are playable, the extra frets can make playing chords and navigating the fretboard significantly more challenging for [[12edo]] chords and scales.

	More common is the "Sazocaster" tuning popularised by Australian band King Gizzard and the Lizard Wizard, which adds quarter tones between approximately half the regular frets. Multiple guitar makers, including [https://eastwoodguitars.com/products/hi-~~flyer~~-~~phase-iv~~-mt Eastwood] and [https://~~www~~.~~revelationguitars.co.uk~~/guitar/~~marrakesh~~-~~quarter~~-~~tone Revelation~~]~~{{dead link}},~~ have produced Sazocaster variations.		More common is the "Sazocaster" tuning popularised by Australian band King Gizzard and the Lizard Wizard, which adds quarter tones between approximately half the regular frets. Multiple guitar makers, including [https://eastwoodguitars.com/products/sg2c-flying-banana-mt Eastwood] and [https://salamuzik.com/collections/guitar/products/professional-microtonal-electric-classical-guitar-with-equalizer-kg-5 Sala Muzik] have produced Sazocaster variations.

	[[File:Eastwood-guitars-phase-4-mt-2307179.jpg\|500px]]		[[File:Eastwood-guitars-phase-4-mt-2307179.jpg\|500px]]

			It is also possible to create a guitar that has quartertones on all the lower frets, then switches to regular 12edo at some point on the neck to keep the upper notes easily acessible, as demonstrated by the band [[Angine de Poitrine]].

	=== Harp, Harpsichord, and Piano ===		=== Harp, Harpsichord, and Piano ===

Yourmusic Productions: unfortunately, some of the instrument selling links have recently died

2026-03-24T11:14:48Z

unfortunately, some of the instrument selling links have recently died

← Older revision		Revision as of 11:14, 24 March 2026
Line 1,186:		Line 1,186:
	Adam Hoey Xen ([https://www.youtube.com/@adamhoeyxen2199/videos on YouTube]) has used a "neutral thirds tuning" of F#-At-C#-Et-G#-Bt on a standard guitar to play in quartertones.		Adam Hoey Xen ([https://www.youtube.com/@adamhoeyxen2199/videos on YouTube]) has used a "neutral thirds tuning" of F#-At-C#-Et-G#-Bt on a standard guitar to play in quartertones.

	Guitars with 24 frets per octave are also an option and some guitar makers, such as Ron Sword's [http://metatonalmusic.com Metatonal Music], can make custom instruments and perform re-fretting, with an example below:		Guitars with 24 frets per octave are also an option and some guitar makers, such as Ron Sword's [http://metatonalmusic.com Metatonal Music]{{dead link}}, can make custom instruments and perform re-fretting, with an example below:

	[[File:24edo_guitar.jpg\|500px]]		[[File:24edo_guitar.jpg\|500px]]
Line 1,192:		Line 1,192:
	While these are playable, the extra frets can make playing chords and navigating the fretboard significantly more challenging for [[12edo]] chords and scales.		While these are playable, the extra frets can make playing chords and navigating the fretboard significantly more challenging for [[12edo]] chords and scales.

	More common is the "Sazocaster" tuning popularised by Australian band King Gizzard and the Lizard Wizard, which adds quarter tones between approximately half the regular frets. Multiple guitar makers, including [https://eastwoodguitars.com/products/hi-flyer-phase-iv-mt Eastwood] and [https://www.revelationguitars.co.uk/guitar/marrakesh-quarter-tone Revelation], have produced Sazocaster variations.		More common is the "Sazocaster" tuning popularised by Australian band King Gizzard and the Lizard Wizard, which adds quarter tones between approximately half the regular frets. Multiple guitar makers, including [https://eastwoodguitars.com/products/hi-flyer-phase-iv-mt Eastwood] and [https://www.revelationguitars.co.uk/guitar/marrakesh-quarter-tone Revelation]{{dead link}}, have produced Sazocaster variations.

	[[File:Eastwood-guitars-phase-4-mt-2307179.jpg\|500px]]		[[File:Eastwood-guitars-phase-4-mt-2307179.jpg\|500px]]

FloraC: Name for 4096/4095

2026-03-03T11:00:48Z

Name for 4096/4095

← Older revision		Revision as of 11:00, 3 March 2026
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	\| 0.42		\| 0.42
	\| Sathurugu		\| Sathurugu
	\| ~~Schismina~~		\| Minisma
	\|-		\|-
	\| 17		\| 17

Lucius Chiaraviglio: /* Theory */ Fix wording

2026-01-26T19:56:29Z

Theory: Fix wording

← Older revision		Revision as of 19:56, 26 January 2026
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	Aside from harmony, it also preserves the melodic resources of 12edo, containing minor and major seconds and thirds. However, it adds several new intervals, including neutral seconds and thirds, so new melodies can be written in 24edo that aren't possible in 12edo. This also means 24edo contains new scales, most notably the "neutral diatonic" [[3L 4s]] [[MOS]] with step pattern LssLsLs, where ''L'' is a major second and ''s'' is a neutral second. These scales also contain chords unfamiliar to 12edo, such as the [[neutral tetrad]].		Aside from harmony, it also preserves the melodic resources of 12edo, containing minor and major seconds and thirds. However, it adds several new intervals, including neutral seconds and thirds, so new melodies can be written in 24edo that aren't possible in 12edo. This also means 24edo contains new scales, most notably the "neutral diatonic" [[3L 4s]] [[MOS]] with step pattern LssLsLs, where ''L'' is a major second and ''s'' is a neutral second. These scales also contain chords unfamiliar to 12edo, such as the [[neutral tetrad]].

	While the 7th harmonic is poorly tuned, the intervals 24edo has do serve as reasonable substitutes to 7-limit intervals melodically, though it equates [[7/6]] with [[8/7]] due to vanishing of [[49/48]], leading to [[semaphore]]. Nonetheless, scales of semaphore are quite interesting, especially the 9-note [[5L 4s]] MOS. A supermajor chord is available as [0 9 14], and a subminor chord as [0 5 14]; ~~though~~, they~~'re~~ better described as ultramajor and inframinor, being interpreted much more accurately as [[10:13:15]] and [[26:30:39\|1/(10:13:15)]] respectively, the corresponding temperament being [[barbados]], the 2.3.13/5 temperament tempering out 676/675. These chords are relatively simple and may serve as alternatives to the regular [[4:5:6]] and [[10:12:15\|1/(4:5:6)]] triads as bases for harmony; see [[Extraclassical tonality]].		While the 7th harmonic is poorly tuned, the intervals 24edo has do serve as reasonable substitutes to 7-limit intervals melodically, though it equates [[7/6]] with [[8/7]] due to vanishing of [[49/48]], leading to [[semaphore]]. Nonetheless, scales of semaphore are quite interesting, especially the 9-note [[5L 4s]] MOS. A supermajor chord is available as [0 9 14], and a subminor chord as [0 5 14]; however, they are better described as ultramajor and inframinor, being interpreted much more accurately as [[10:13:15]] and [[26:30:39\|1/(10:13:15)]] respectively, the corresponding temperament being [[barbados]], the 2.3.13/5 temperament tempering out 676/675. These chords are relatively simple and may serve as alternatives to the regular [[4:5:6]] and [[10:12:15\|1/(4:5:6)]] triads as bases for harmony; see [[Extraclassical tonality]].

	A notable superset of 24edo is [[72edo]], which has good approximations up to the [[19-limit]], and especially the [[11-limit]]. The tunings supplied by [[72edo]] cannot be used for all low-limit just intervals, but they can be used on the 17-limit [[kN subgroups\|324 subgroup]] 2.3.125.35.11.325.17.19, making some of the excellent approximations of 72 available in 24edo. Chords based on this subgroup afford considerable scope for harmony, including in particular intervals and chords using only 2, 3, 11, 17, and 19. One will find that 24edo is consistent in the no-7s 19-odd-limit, though the 2.3.11.17.19 [[subgroup]] is where it is the most accurate.		A notable superset of 24edo is [[72edo]], which has good approximations up to the [[19-limit]], and especially the [[11-limit]]. The tunings supplied by [[72edo]] cannot be used for all low-limit just intervals, but they can be used on the 17-limit [[kN subgroups\|324 subgroup]] 2.3.125.35.11.325.17.19, making some of the excellent approximations of 72 available in 24edo. Chords based on this subgroup afford considerable scope for harmony, including in particular intervals and chords using only 2, 3, 11, 17, and 19. One will find that 24edo is consistent in the no-7s 19-odd-limit, though the 2.3.11.17.19 [[subgroup]] is where it is the most accurate.

ArrowHead294 at 16:13, 26 January 2026

2026-01-26T16:13:09Z

← Older revision		Revision as of 16:13, 26 January 2026
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	24edo/24-TET, also known as the quarter-tone system, is the double of [[12edo\|12edo/12-TET]], so it contains all of the notes of 12edo. It adds to 12edo another circle of it spaced a quarter tone apart, which contains unfamiliar intervals not found in 12edo, such as neutral seconds and thirds. Since it contains 12edo, it is very desirable for microtonalists who want new intervals while still having access to familiar ones.		24edo/24-TET, also known as the quarter-tone system, is the double of [[12edo\|12edo/12-TET]], so it contains all of the notes of 12edo. It adds to 12edo another circle of it spaced a quarter tone apart, which contains unfamiliar intervals not found in 12edo, such as neutral seconds and thirds. Since it contains 12edo, it is very desirable for microtonalists who want new intervals while still having access to familiar ones.

	The [[5-limit]] approximations in 24edo are the same as those in 12edo, tempering out [[81/80]], [[128/125]], [[648/625]], and [[531441/524288]], so 24edo offers nothing new as far as approximating the 5-limit is concerned. However, it maps the [[7/1\|7th harmonic]] differently from 12edo, with [[7/4]] mapped to 950 ~~[[cents]]~~ rather than 1000 ~~cents~~ in 12edo, being 18.8 ~~cents~~ flat of just rather than 31.2 ~~cents~~ sharp in 12edo. Most intervals of 7 are still approximated quite poorly for its size, though chords like [[6:7:9]] are nonetheless closer to just than in 12edo. Still, if one wishes to approximate intervals of 7 while still having access to the notes of 12edo, it is best to use finer divisions like [[36edo]], [[48edo]], [[72edo]], or [[84edo]].		The [[5-limit]] approximations in 24edo are the same as those in 12edo, tempering out [[81/80]], [[128/125]], [[648/625]], and [[531441/524288]], so 24edo offers nothing new as far as approximating the 5-limit is concerned. However, it maps the [[7/1\|7th harmonic]] differently from 12edo, with [[7/4]] mapped to 950{{c}} rather than 1000{{c}} in 12edo, being 18.8{{c}} flat of just rather than 31.2{{c}} sharp in 12edo. Most intervals of 7 are still approximated quite poorly for its size, though chords like [[6:7:9]] are nonetheless closer to just than in 12edo. Still, if one wishes to approximate intervals of 7 while still having access to the notes of 12edo, it is best to use finer divisions like [[36edo]], [[48edo]], [[72edo]], or [[84edo]].

	However, 24edo approximates the [[11/1\|11th harmonic]] very accurately at 550 ~~cents~~, only 1.3 ~~cents~~ flat of just. Most intervals of 11, such as [[11/8]], [[11/6]], [[11/10]], and [[11/9]], are approximated accurately as well. It is thus usable as an [[2.3.11 subgroup\|2.3.11-]] or [[2.3.5.11 subgroup\|2.3.5.11-]][[subgroup]] system, notably tempering out [[121/120]], splitting [[6/5]] into two neutral seconds of [[11/10]][[~]][[12/11]], and [[243/242]], splitting [[3/2]] into two 11/9 neutral thirds. It also has a decent approximation of the [[13/1\|13th harmonic]] at 850 ~~cents~~, being 9.5 ~~cents~~ sharp of just. Intervals of 13 are thus represented decently, with [[13/10]], [[15/13]], and their [[octave complement]]s being especially close to just due to the cancellation of the sharpness of harmonics 5 and 13. It is thus a good tuning for the 2.3.5.11.13 and 2.3.11.13/5 subgroups, tempering out [[144/143]] in the former, so that [[11/9]] and [[16/13]] are equated, and [[676/675]] in both subgroups, so two 15/13's add up to [[4/3]]. Finally, 24edo shares its tunings of harmonics [[17/1\|17]] and [[19/1\|19]] with 12edo, meaning that 7 and to an extent 5 are the only low primes 24edo tunes particularly poorly. Nonetheless, it is not the best system for approximating JI if one wishes to use prime 7, with other equal temperaments like [[22edo]], [[27edo]], and especially [[31edo]] being more accurate.		However, 24edo approximates the [[11/1\|11th harmonic]] very accurately at 550{{c}}, only 1.3{{c}} flat of just. Most intervals of 11, such as [[11/8]], [[11/6]], [[11/10]], and [[11/9]], are approximated accurately as well. It is thus usable as an [[2.3.11 subgroup\|2.3.11-]] or [[2.3.5.11 subgroup\|2.3.5.11-]][[subgroup]] system, notably tempering out [[121/120]], splitting [[6/5]] into two neutral seconds of {{nowrap\|[[11/10]][[~]][[12/11]]}}, and [[243/242]], splitting [[3/2]] into two 11/9 neutral thirds. It also has a decent approximation of the [[13/1\|13th harmonic]] at 850{{c}}, being 9.5{{c}} sharp of just. Intervals of 13 are thus represented decently, with [[13/10]], [[15/13]], and their [[octave complement]]s being especially close to just due to the cancellation of the sharpness of harmonics 5 and 13. It is thus a good tuning for the 2.3.5.11.13 and 2.3.11.13/5 subgroups, tempering out [[144/143]] in the former, so that [[11/9]] and [[16/13]] are equated, and [[676/675]] in both subgroups, so two 15/13's add up to [[4/3]]. Finally, 24edo shares its tunings of harmonics [[17/1\|17]] and [[19/1\|19]] with 12edo, meaning that 7 and to an extent 5 are the only low primes 24edo tunes particularly poorly. Nonetheless, it is not the best system for approximating JI if one wishes to use prime 7, with other equal temperaments like [[22edo]], [[27edo]], and especially [[31edo]] being more accurate.

	Aside from harmony, it also preserves the melodic resources of 12edo, containing minor and major seconds and thirds. However, it adds several new intervals, including neutral seconds and thirds, so new melodies can be written in 24edo that aren't possible in 12edo. This also means 24edo contains new scales, most notably the ~~neutralized~~ diatonic [[3L 4s]] [[MOS]] with step pattern LssLsLs, where L is a major second and s is a neutral second. These scales also contain chords unfamiliar to 12edo, such as the [[neutral tetrad]].		Aside from harmony, it also preserves the melodic resources of 12edo, containing minor and major seconds and thirds. However, it adds several new intervals, including neutral seconds and thirds, so new melodies can be written in 24edo that aren't possible in 12edo. This also means 24edo contains new scales, most notably the "neutral diatonic" [[3L 4s]] [[MOS]] with step pattern LssLsLs, where ''L'' is a major second and ''s'' is a neutral second. These scales also contain chords unfamiliar to 12edo, such as the [[neutral tetrad]].

	While the 7th harmonic is poorly tuned, the intervals 24edo has do serve as reasonable substitutes to 7-limit intervals melodically, though it equates [[7/6]] with [[8/7]] due to vanishing of [[49/48]], leading to [[semaphore]]. Nonetheless, scales of semaphore are quite interesting, especially the 9-note [[5L 4s]] MOS. A supermajor chord is available as [0 9 14], and a subminor chord as [0 5 14], ~~though~~ they're better described as ultramajor and inframinor, being interpreted much more accurately as [[10:13:15]] and [[26:30:39\|1/(10:13:15)]] respectively, the corresponding temperament being [[barbados]], the 2.3.13/5 temperament tempering out 676/675. These chords are relatively simple and may serve as alternatives to the regular [[4:5:6]] and [[10:12:15\|1/(4:5:6)]] triads as bases for harmony; see [[Extraclassical tonality]].		While the 7th harmonic is poorly tuned, the intervals 24edo has do serve as reasonable substitutes to 7-limit intervals melodically, though it equates [[7/6]] with [[8/7]] due to vanishing of [[49/48]], leading to [[semaphore]]. Nonetheless, scales of semaphore are quite interesting, especially the 9-note [[5L 4s]] MOS. A supermajor chord is available as [0 9 14], and a subminor chord as [0 5 14]; though, they're better described as ultramajor and inframinor, being interpreted much more accurately as [[10:13:15]] and [[26:30:39\|1/(10:13:15)]] respectively, the corresponding temperament being [[barbados]], the 2.3.13/5 temperament tempering out 676/675. These chords are relatively simple and may serve as alternatives to the regular [[4:5:6]] and [[10:12:15\|1/(4:5:6)]] triads as bases for harmony; see [[Extraclassical tonality]].

	A notable superset of 24edo is [[72edo]], which has good approximations up to the [[19-limit]], and especially the [[11-limit]]. The tunings supplied by [[72edo]] cannot be used for all low-limit just intervals, but they can be used on the 17-limit [[kN subgroups\|324 subgroup]] 2.3.125.35.11.325.17.19, making some of the excellent approximations of 72 available in 24edo. Chords based on this subgroup afford considerable scope for harmony, including in particular intervals and chords using only 2, 3, 11, 17, and 19. One will find that 24edo is consistent in the no-7s 19-odd-limit, though the 2.3.11.17.19 [[subgroup]] is where it is the most accurate.		A notable superset of 24edo is [[72edo]], which has good approximations up to the [[19-limit]], and especially the [[11-limit]]. The tunings supplied by [[72edo]] cannot be used for all low-limit just intervals, but they can be used on the 17-limit [[kN subgroups\|324 subgroup]] 2.3.125.35.11.325.17.19, making some of the excellent approximations of 72 available in 24edo. Chords based on this subgroup afford considerable scope for harmony, including in particular intervals and chords using only 2, 3, 11, 17, and 19. One will find that 24edo is consistent in the no-7s 19-odd-limit, though the 2.3.11.17.19 [[subgroup]] is where it is the most accurate.
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	=== Miscellaneous properties ===		=== Miscellaneous properties ===
	Its step, at 50 ~~cents~~, is notable for being generally seen as one of the most dissonant intervals possible (in fact, typical harmonic entropy models show a peak around this point). Intervals less than 40 ~~cents~~ tend to be perceived as being closer to a unison, and thus, more consonant as a result, while intervals larger than approximately 60 ~~cents~~ are often perceived as having less "tension", and thus are also considered to be more consonant.		Its step, at 50{{c}}, is notable for being generally seen as one of the most dissonant intervals possible (in fact, typical harmonic entropy models show a peak around this point). Intervals less than 40{{c}} tend to be perceived as being closer to a unison, and thus, more consonant as a result, while intervals larger than approximately 60{{c}} are often perceived as having less "tension", and thus are also considered to be more consonant.

	== Intervals ==		== Intervals ==
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	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
	\| ~~width~~="40px" \| [[File:Koron_sign.svg\|39px\|center]]		\| style="width: 40px;" \| [[File:Koron_sign.svg\|39px\|center]]
	\| '''Koron''' = quarter-tone flat		\| '''Koron''' = quarter-tone flat
	\|-		\|-
	\| ~~width~~="40px" \| [[File:Sori_sign.svg\|39px\|center]]		\| style="width: 40px;" \| [[File:Sori_sign.svg\|39px\|center]]
	\| '''Sori''' = quarter-tone sharp		\| '''Sori''' = quarter-tone sharp
	\|}		\|}
Line 410:		Line 410:

	'''Cons:''' not as familiar as traditional notation, and thus not immediately accessible to many traditional musicians who are just starting out with microtonality.		'''Cons:''' not as familiar as traditional notation, and thus not immediately accessible to many traditional musicians who are just starting out with microtonality.


	We also have, from the appendix to [[The Sagittal Songbook]] by [[Jacob Barton\|Jacob A. Barton]], a diagram of how to notate 24edo in the Revo flavor of Sagittal:		We also have, from the appendix to [[The Sagittal Songbook]] by [[Jacob Barton\|Jacob A. Barton]], a diagram of how to notate 24edo in the Revo flavor of Sagittal:
Line 1,030:		Line 1,029:

	Important MOSes include:		Important MOSes include:
	* Semaphore ~~4L1s~~ 55455 (generator: 5\24)		* Semaphore 4L 1s 55455 (generator: 5\24)
	* Semaphore ~~5L4s~~ 414141414 (generator: 5\24)		* Semaphore 5L 4s 414141414 (generator: 5\24)
	* Mohajira ~~3L4s~~ 3434343 (generator: 7\24)		* Mohajira 3L 4s 3434343 (generator: 7\24)
	* Mohajira ~~7L3s~~ 3313313313 (generator: 7\24)		* Mohajira 7L 3s 3313313313 (generator: 7\24)

	== Octave stretch or compression ==		== Octave stretch or compression ==

Lucius Chiaraviglio: /* Intervals */ sed -E "s#([0-9]+)/([0-9]+)#\\[\\[\\1/\\2\\]\\]#g" 24EDOintervals.txt > 24EDOintervals.new.txt

2026-01-20T11:06:10Z

Intervals: sed -E "s#([0-9]+)/([0-9]+)#\\[\\[\\1/\\2\\]\\]#g" 24EDOintervals.txt > 24EDOintervals.new.txt

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