4/3 - Revision history

FloraC: /* Temperaments */ - duplicate from 3/2. Bixby not worth the space

2026-01-27T11:09:45Z

Temperaments: - duplicate from 3/2. Bixby not worth the space

← Older revision		Revision as of 11:09, 27 January 2026
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	== Temperaments ==		== Temperaments ==
	4/3 can be used as a generator for ~~many~~ temperaments, such as [[meantone]], [[superpyth]], and [[schismic]]. ~~Meantone sharpens 4/3 to around 500–505{{C}} and map four of them to [[8/5]] plus an octave, while superpyth flattens 4/3 to around 489–491{{C}} and map two of them to~~ [[~~7/4]]. Schismic leaves 4/3 close to just, and slightly sharp in optimal tunings, so eight 4/~~3~~'s stack to [[5~~/~~4]] plus three octaves.~~		4/3 can be used as an alternative generator for temperaments generated by an octave and a fifth of 3/2, such as [[meantone]], [[superpyth]], and [[schismic]]. See [[3/2 #In regular temperament theory]] for details.

	~~If 4/3 is taken as a comma to be [[Tempering out\|tempered out]], it leads to [[bixby]] temperament, the simplest [[circular~~ temperament]]~~. This temperament is very inaccurate and is only supported by [[1edo]]~~.

	== See also ==		== See also ==

Overthink: /* Temperaments */ add paragraph on 4/3-generated temperaments and de-emphasize bixby

2026-01-27T05:07:29Z

Temperaments: add paragraph on 4/3-generated temperaments and de-emphasize bixby

← Older revision		Revision as of 05:07, 27 January 2026
Line 80:		Line 80:

	== Temperaments ==		== Temperaments ==
	If 4/3 is taken as a comma to be [[Tempering out\|tempered out]], it leads to [[bixby]] temperament, the simplest [[circular temperament]].		4/3 can be used as a generator for many temperaments, such as [[meantone]], [[superpyth]], and [[schismic]]. Meantone sharpens 4/3 to around 500–505{{C}} and map four of them to [[8/5]] plus an octave, while superpyth flattens 4/3 to around 489–491{{C}} and map two of them to [[7/4]]. Schismic leaves 4/3 close to just, and slightly sharp in optimal tunings, so eight 4/3's stack to [[5/4]] plus three octaves.

			If 4/3 is taken as a comma to be [[Tempering out\|tempered out]], it leads to [[bixby]] temperament, the simplest [[circular temperament]]. This temperament is very inaccurate and is only supported by [[1edo]].

	== See also ==		== See also ==

FloraC: Undo revision 211123 by M1k1 H2tsun2 (talk)

2025-09-27T11:47:27Z

Undo revision 211123 by M1k1 H2tsun2 (talk)

← Older revision		Revision as of 11:47, 27 September 2025
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	}}		}}
	{{Infobox Interval		{{Infobox Interval
	\| Name = ~~threerish pure fourth,~~ just perfect fourth		\| Name = just perfect fourth
	\| Color name = w4, wa 4th		\| Color name = w4, wa 4th
	\| Sound = jid_4_3_pluck_adu_dr220.mp3		\| Sound = jid_4_3_pluck_adu_dr220.mp3

M1k1 H2tsun2: add it in the first, rather than the other place.

2025-09-27T10:37:40Z

add it in the first, rather than the other place.

← Older revision		Revision as of 10:37, 27 September 2025
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	}}		}}
	{{Infobox Interval		{{Infobox Interval
	\| Name = just perfect fourth		\| Name = threerish pure fourth, just perfect fourth
	\| Color name = w4, wa 4th		\| Color name = w4, wa 4th
	\| Sound = jid_4_3_pluck_adu_dr220.mp3		\| Sound = jid_4_3_pluck_adu_dr220.mp3

VectorGraphics at 06:44, 25 January 2025

2025-01-25T06:44:54Z

← Older revision		Revision as of 06:44, 25 January 2025
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	\|}		\|}
	<references/>		<references/>

			== Temperaments ==
			If 4/3 is taken as a comma to be [[Tempering out\|tempered out]], it leads to [[bixby]] temperament, the simplest [[circular temperament]].

	== See also ==		== See also ==

Aura at 06:07, 25 December 2024

2024-12-25T06:07:27Z

← Older revision		Revision as of 06:07, 25 December 2024
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	Much like 3/2, 4/3 is valuable as a framework for constructing [[chord]]s. However, while 3/2 provides the framework for [[5-limit]] triads involving intervals like 5/4 and [[6/5]], 4/3 provides a possible framework for [[7-limit]] triads involving intervals like [[7/6]] and [[8/7]], though such triads are [[Condissonance\|ambisonances]] (that is, they're both consonant and dissonant at the same time) at best.		Much like 3/2, 4/3 is valuable as a framework for constructing [[chord]]s. However, while 3/2 provides the framework for [[5-limit]] triads involving intervals like 5/4 and [[6/5]], 4/3 provides a possible framework for [[7-limit]] triads involving intervals like [[7/6]] and [[8/7]], though such triads are [[Condissonance\|ambisonances]] (that is, they're both consonant and dissonant at the same time) at best.

	Because up to two instances of 4/3 can fit within the span of an [[octave]], it is very easy to create xenharmonic chords using 4/3 as a framework. Regardless, the usage of 4/3 as a framework for chords is intimately connected with the use of [[tritave]]s in the same capacity- at least in [[Octave #Octave equivalence\|octave-equivalent]] systems- due to the same pitch classes being involved in both 6:7:8 and 4:7:12 where 7 is kept as the same note, thus rendering the two chords as different voicings of the same underlying unit.		Because up to two instances of 4/3 can fit within the span of an [[octave]], it is very easy to create xenharmonic chords using 4/3 as a framework. Regardless, the usage of 4/3 as a framework for chords is intimately connected with the use of [[tritave]]s in the same capacity- at least in [[Octave #Octave equivalence\|octave-equivalent]] systems- due to the same pitch classes being involved in both 6:7:8 and 4:7:12 where 7 is kept as the same note, thus rendering the two chords as different voicings of the same underlying harmonic unit.

	== Approximations by EDOs ==		== Approximations by EDOs ==

Aura at 06:06, 25 December 2024

2024-12-25T06:06:29Z

← Older revision		Revision as of 06:06, 25 December 2024
Line 24:		Line 24:
	Much like 3/2, 4/3 is valuable as a framework for constructing [[chord]]s. However, while 3/2 provides the framework for [[5-limit]] triads involving intervals like 5/4 and [[6/5]], 4/3 provides a possible framework for [[7-limit]] triads involving intervals like [[7/6]] and [[8/7]], though such triads are [[Condissonance\|ambisonances]] (that is, they're both consonant and dissonant at the same time) at best.		Much like 3/2, 4/3 is valuable as a framework for constructing [[chord]]s. However, while 3/2 provides the framework for [[5-limit]] triads involving intervals like 5/4 and [[6/5]], 4/3 provides a possible framework for [[7-limit]] triads involving intervals like [[7/6]] and [[8/7]], though such triads are [[Condissonance\|ambisonances]] (that is, they're both consonant and dissonant at the same time) at best.

	Because up to two instances of 4/3 can fit within the span of an [[octave]], it is very easy to create xenharmonic chords using 4/3 as a framework. Regardless, the usage of 4/3 as a framework for chords is intimately connected with the use of [[tritave]]s in the same capacity- at least in [[Octave #Octave equivalence\|octave-equivalent]] systems- due to the same pitch classes being involved in both 6:7:8 and 4:7:12 where 7 is kept as the same note, thus rendering the two chords as different voicings of the same underlying ~~chord~~.		Because up to two instances of 4/3 can fit within the span of an [[octave]], it is very easy to create xenharmonic chords using 4/3 as a framework. Regardless, the usage of 4/3 as a framework for chords is intimately connected with the use of [[tritave]]s in the same capacity- at least in [[Octave #Octave equivalence\|octave-equivalent]] systems- due to the same pitch classes being involved in both 6:7:8 and 4:7:12 where 7 is kept as the same note, thus rendering the two chords as different voicings of the same underlying unit.

	== Approximations by EDOs ==		== Approximations by EDOs ==

Aura at 06:01, 25 December 2024

2024-12-25T06:01:55Z

← Older revision		Revision as of 06:01, 25 December 2024
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	Much like 3/2, 4/3 is valuable as a framework for constructing [[chord]]s. However, while 3/2 provides the framework for [[5-limit]] triads involving intervals like 5/4 and [[6/5]], 4/3 provides a possible framework for [[7-limit]] triads involving intervals like [[7/6]] and [[8/7]], though such triads are [[Condissonance\|ambisonances]] (that is, they're both consonant and dissonant at the same time) at best.		Much like 3/2, 4/3 is valuable as a framework for constructing [[chord]]s. However, while 3/2 provides the framework for [[5-limit]] triads involving intervals like 5/4 and [[6/5]], 4/3 provides a possible framework for [[7-limit]] triads involving intervals like [[7/6]] and [[8/7]], though such triads are [[Condissonance\|ambisonances]] (that is, they're both consonant and dissonant at the same time) at best.

	Because up to two instances of 4/3 can fit within the span of an [[octave]], it is very easy to create xenharmonic chords using 4/3 as a framework. Regardless, the usage of 4/3 as a framework for chords is intimately connected with the use of [[tritave]]s in the same capacity- at least in [[Octave #Octave equivalence\|octave-equivalent]] systems due to the same pitch classes being involved in both 6:7:8 and 4:7:12 where 7 is kept as the same note.		Because up to two instances of 4/3 can fit within the span of an [[octave]], it is very easy to create xenharmonic chords using 4/3 as a framework. Regardless, the usage of 4/3 as a framework for chords is intimately connected with the use of [[tritave]]s in the same capacity- at least in [[Octave #Octave equivalence\|octave-equivalent]] systems- due to the same pitch classes being involved in both 6:7:8 and 4:7:12 where 7 is kept as the same note, thus rendering the two chords as different voicings of the same underlying chord.

	== Approximations by EDOs ==		== Approximations by EDOs ==

Aura at 06:00, 25 December 2024

2024-12-25T06:00:32Z

← Older revision		Revision as of 06:00, 25 December 2024
Line 24:		Line 24:
	Much like 3/2, 4/3 is valuable as a framework for constructing [[chord]]s. However, while 3/2 provides the framework for [[5-limit]] triads involving intervals like 5/4 and [[6/5]], 4/3 provides a possible framework for [[7-limit]] triads involving intervals like [[7/6]] and [[8/7]], though such triads are [[Condissonance\|ambisonances]] (that is, they're both consonant and dissonant at the same time) at best.		Much like 3/2, 4/3 is valuable as a framework for constructing [[chord]]s. However, while 3/2 provides the framework for [[5-limit]] triads involving intervals like 5/4 and [[6/5]], 4/3 provides a possible framework for [[7-limit]] triads involving intervals like [[7/6]] and [[8/7]], though such triads are [[Condissonance\|ambisonances]] (that is, they're both consonant and dissonant at the same time) at best.

	Because up to two instances of 4/3 can fit within the span of an [[octave]], it is very easy to create xenharmonic chords using 4/3 as a framework. Regardless, the usage of 4/3 as a framework for chords is intimately connected with the use of [[tritave]]s in the same capacity- at least in [[Octave #Octave equivalence\|octave-equivalent]] systems due to the same pitch classes being involved in 6:7:8 and 4:7:12 ~~when the~~ 7 is kept as the same note.		Because up to two instances of 4/3 can fit within the span of an [[octave]], it is very easy to create xenharmonic chords using 4/3 as a framework. Regardless, the usage of 4/3 as a framework for chords is intimately connected with the use of [[tritave]]s in the same capacity- at least in [[Octave #Octave equivalence\|octave-equivalent]] systems due to the same pitch classes being involved in both 6:7:8 and 4:7:12 where 7 is kept as the same note.

	== Approximations by EDOs ==		== Approximations by EDOs ==

Aura at 05:59, 25 December 2024

2024-12-25T05:59:56Z

← Older revision		Revision as of 05:59, 25 December 2024
Line 24:		Line 24:
	Much like 3/2, 4/3 is valuable as a framework for constructing [[chord]]s. However, while 3/2 provides the framework for [[5-limit]] triads involving intervals like 5/4 and [[6/5]], 4/3 provides a possible framework for [[7-limit]] triads involving intervals like [[7/6]] and [[8/7]], though such triads are [[Condissonance\|ambisonances]] (that is, they're both consonant and dissonant at the same time) at best.		Much like 3/2, 4/3 is valuable as a framework for constructing [[chord]]s. However, while 3/2 provides the framework for [[5-limit]] triads involving intervals like 5/4 and [[6/5]], 4/3 provides a possible framework for [[7-limit]] triads involving intervals like [[7/6]] and [[8/7]], though such triads are [[Condissonance\|ambisonances]] (that is, they're both consonant and dissonant at the same time) at best.

	Because up to two instances of 4/3 can fit within the span of an [[octave]], it is very easy to create xenharmonic chords using 4/3 as a framework~~, though because [[16/9]] clashes with the octave through crowding{{citation needed}}, these types of chords are dissonances~~.		Because up to two instances of 4/3 can fit within the span of an [[octave]], it is very easy to create xenharmonic chords using 4/3 as a framework. Regardless, the usage of 4/3 as a framework for chords is intimately connected with the use of [[tritave]]s in the same capacity- at least in [[Octave #Octave equivalence\|octave-equivalent]] systems due to the same pitch classes being involved in 6:7:8 and 4:7:12 when the 7 is kept as the same note.

	Regardless, the usage of 4/3 as a framework for chords is intimately connected with the use of [[tritave]]s in the same capacity- at least in [[Octave #Octave equivalence\|octave-equivalent]] systems.~~{{clarify\|please explain why this is in a bit more detail}}~~

	== Approximations by EDOs ==		== Approximations by EDOs ==