11/8 - Revision history

FloraC: Text replacement - " {{Interval_Edo_Approximation | " to "{{Interval edo approximation|"

2025-11-03T13:01:48Z

Text replacement - " {{Interval_Edo_Approximation | " to "{{Interval edo approximation|"

← Older revision		Revision as of 13:01, 3 November 2025
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	== Approximations by EDOs ==		== Approximations by EDOs ==
	{{~~Interval_Edo_Approximation~~ \| 11/8}}		{{Interval edo approximation\|11/8}}
	<references group="note" />		<references group="note" />

Pailiaq at 07:23, 3 November 2025

2025-11-03T07:23:47Z

@@ Line 29: / Line 29: @@
 == Approximations by EDOs ==
+ {{Interval_Edo_Approximation | 11/8}}
 <references group="note" />

VectorGraphics at 03:33, 24 June 2025

2025-06-24T03:33:16Z

← Older revision		Revision as of 03:33, 24 June 2025
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	{{Wikipedia\|Major fourth and minor fifth}}		{{Wikipedia\|Major fourth and minor fifth}}

	In [[11-limit]] [[just intonation]], '''11/8''' is an '''undecimal [[superfourth]]''' of about 551.3{{cent}}. This interval is close (~3{{cent}}) to exactly between a [[4/3\|perfect fourth]] and [[729/512\|augmented fourth]], the latter of which is the ''augmented'' version of the [[Pythagorean tuning\|Pythagorean]] [[diatonic]] generator, therefore may be called the '''harmonic~~/undecimal~~ semiaugmented fourth'''.		In [[11-limit]] [[just intonation]], '''11/8''' is an '''undecimal [[superfourth\|semiaugmented fourth]]''' of about 551.3{{cent}}. This interval is close (~3{{cent}}) to exactly between a [[4/3\|perfect fourth]] and [[729/512\|augmented fourth]], the latter of which is the ''augmented'' version of the [[Pythagorean tuning\|Pythagorean]] [[diatonic]] generator, therefore may be called the '''harmonic semiaugmented fourth'''.

	This interval is the simplest superfourth in JI, and as it falls about halfway between [[12edo]]'s [[perfect fourth]] and [[tritone]], it is very xenharmonic. As an octave-reduced harmonic, it is a basis of consonance in 11-limit JI, alongside the lower odd numbers 9, 7, 5 and 3. It can be found in harmonic series chords such as 4:5:6:7:8:9:10:11:12, sitting somewhere between the stronger and more familiar consonances of 10 (prime 5) and 12 (prime 3).		This interval is the simplest superfourth in JI, and as it falls about halfway between [[12edo]]'s [[perfect fourth]] and [[tritone]], it is very xenharmonic. As an octave-reduced harmonic, it is a basis of consonance in 11-limit JI, alongside the lower odd numbers 9, 7, 5 and 3. It can be found in harmonic series chords such as 4:5:6:7:8:9:10:11:12, sitting somewhere between the stronger and more familiar consonances of 10 (prime 5) and 12 (prime 3).

Aura: added a comma

2025-05-09T01:09:02Z

added a comma

← Older revision		Revision as of 01:09, 9 May 2025
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	This interval is very well-represented in 24edo, making that system especially good for approximations of JI chords involving primes 3 and 11 such as 8:9:11:12. Not only that, but composers who have experience with 24edo may find it very useful not only as a fantastic addition to major chords, but also as an interesting chord root both for chord progressions within a key, and for modulations to key signatures that are not in the same chain of fifths. Furthermore, these same useful functions can carry over to higher EDOs with good 11-limit representation such as [[159edo]].		This interval is very well-represented in 24edo, making that system especially good for approximations of JI chords involving primes 3 and 11 such as 8:9:11:12. Not only that, but composers who have experience with 24edo may find it very useful not only as a fantastic addition to major chords, but also as an interesting chord root both for chord progressions within a key, and for modulations to key signatures that are not in the same chain of fifths. Furthermore, these same useful functions can carry over to higher EDOs with good 11-limit representation such as [[159edo]].

	In more tonal music, 11/8 relative to the tonic ends up being used as the chord root for what amounts to a voicing variation of a 1/1-9/8-225/176-3/2 chord, which, is preceded by a variation on a 1/1-5/4-3/2-225/128 chord built on [[16/15]] relative to the tonic (basically, a type of [[Wikipedia: Neapolitan chord\|Neapolitan chord]]) and, followed up by a variation on the 1/1-5/4-3/2-16/9 dominant seventh chord (or potentially even a 1/1-5/4-3/2-16/9-16/15 dominant ninth chord) built on [[3/2]] relative to the tonic for a special type of half cadence. This is a dramatic musical gesture that [[User:Aura\|Aura]] has named the "simul half cadence".		In more tonal music, 11/8 relative to the tonic ends up being used as the chord root for what amounts to a voicing variation of a 1/1-9/8-225/176-3/2 chord, which, is preceded by a variation on a 1/1-5/4-3/2-225/128 chord built on [[16/15]] relative to the tonic (basically, a type of [[Wikipedia: Neapolitan chord\|Neapolitan chord]]), and, followed up by a variation on the 1/1-5/4-3/2-16/9 dominant seventh chord (or potentially even a 1/1-5/4-3/2-16/9-16/15 dominant ninth chord) built on [[3/2]] relative to the tonic for a special type of half cadence. This is a dramatic musical gesture that [[User:Aura\|Aura]] has named the "simul half cadence".

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

Aura at 18:05, 8 May 2025

2025-05-08T18:05:44Z

← Older revision		Revision as of 18:05, 8 May 2025
Line 26:		Line 26:
	This interval is very well-represented in 24edo, making that system especially good for approximations of JI chords involving primes 3 and 11 such as 8:9:11:12. Not only that, but composers who have experience with 24edo may find it very useful not only as a fantastic addition to major chords, but also as an interesting chord root both for chord progressions within a key, and for modulations to key signatures that are not in the same chain of fifths. Furthermore, these same useful functions can carry over to higher EDOs with good 11-limit representation such as [[159edo]].		This interval is very well-represented in 24edo, making that system especially good for approximations of JI chords involving primes 3 and 11 such as 8:9:11:12. Not only that, but composers who have experience with 24edo may find it very useful not only as a fantastic addition to major chords, but also as an interesting chord root both for chord progressions within a key, and for modulations to key signatures that are not in the same chain of fifths. Furthermore, these same useful functions can carry over to higher EDOs with good 11-limit representation such as [[159edo]].

	In more tonal music, 11/8 relative to the tonic ends up being used as the chord root for what amounts to a voicing variation of a 1/1-9/8-225/176-3/2 chord, which, is preceded by a variation on a 1/1-5/4-3/2-225/128 chord built on [[16/15]] relative to the tonic (a ~~variation on the~~ [[Wikipedia: Neapolitan chord\|Neapolitan chord]]) and, followed up by a variation on the 1/1-5/4-3/2-16/9 dominant seventh chord (or potentially even a 1/1-5/4-3/2-16/9-16/15 dominant ninth chord) built on [[3/2]] relative to the tonic for a special type of half cadence. This is a dramatic musical gesture that [[User:Aura\|Aura]] has named the "simul half cadence".		In more tonal music, 11/8 relative to the tonic ends up being used as the chord root for what amounts to a voicing variation of a 1/1-9/8-225/176-3/2 chord, which, is preceded by a variation on a 1/1-5/4-3/2-225/128 chord built on [[16/15]] relative to the tonic (basically, a type of [[Wikipedia: Neapolitan chord\|Neapolitan chord]]) and, followed up by a variation on the 1/1-5/4-3/2-16/9 dominant seventh chord (or potentially even a 1/1-5/4-3/2-16/9-16/15 dominant ninth chord) built on [[3/2]] relative to the tonic for a special type of half cadence. This is a dramatic musical gesture that [[User:Aura\|Aura]] has named the "simul half cadence".

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

Aura at 18:03, 8 May 2025

2025-05-08T18:03:25Z

← Older revision		Revision as of 18:03, 8 May 2025
Line 17:		Line 17:

	== Terminology ==		== Terminology ==
	The naming pattern from [[11/9\|undecimal neutral third]] and [[12/11\|undecimal neutral second]] and their octave complements can be rigorously generalized and results in the somewhat unconventional '''harmonic/undecimal neutral fourth'''. This interval has also been termed the '''undecimal major fourth''' since the tempered version found in 24edo was dubbed the "major fourth" by [[Ivan Wyschnegradsky]], although this may be confusing in diatonic contexts.		The naming pattern from [[11/9\|undecimal neutral third]] and [[12/11\|undecimal neutral second]] and their octave complements can be rigorously generalized and results in the somewhat unconventional '''harmonic/undecimal neutral fourth'''. This interval has also been termed the '''undecimal major fourth''' since the tempered version found in [[24edo]] was dubbed the "major fourth" by [[Ivan Wyschnegradsky]], although this may be confusing in diatonic contexts.
	Because it is right between the diatonic fourth and tritone, it may also be called the '''(lesser) undecimal tritone'''.<ref>Kyle Gann (1998) [https://www.kylegann.com/Octave.html ''Anatomy of an Octave'']</ref>		Because it is right between the diatonic fourth and tritone, it may also be called the '''(lesser) undecimal tritone'''.<ref>Kyle Gann (1998) [https://www.kylegann.com/Octave.html ''Anatomy of an Octave'']</ref>
	More recently, [[Zhea Erose]] has suggested calling it something more simple: the '''harmonic fourth''' – under the idea that it is the simplest [[harmonic]] that is in the general (very) rough range of "fourths" when octave-reduced.		More recently, [[Zhea Erose]] has suggested calling it something more simple: the '''harmonic fourth''' – under the idea that it is the simplest [[harmonic]] that is in the general (very) rough range of "fourths" when octave-reduced.
Line 24:		Line 24:
	== Potential usage ==		== Potential usage ==

	This interval is very well-represented in [[24edo]], making that system especially good for approximations of JI chords involving primes 3 and 11 such as 8:9:11:12. Not only that, but composers who have experience with 24edo may find it very useful not only as a fantastic addition to major chords, but also as an interesting chord root both for chord progressions within a key, and for modulations to key signatures that are not in the same chain of fifths. Furthermore, these same useful functions can carry over to higher EDOs with good 11-limit representation such as [[159edo]].		This interval is very well-represented in 24edo, making that system especially good for approximations of JI chords involving primes 3 and 11 such as 8:9:11:12. Not only that, but composers who have experience with 24edo may find it very useful not only as a fantastic addition to major chords, but also as an interesting chord root both for chord progressions within a key, and for modulations to key signatures that are not in the same chain of fifths. Furthermore, these same useful functions can carry over to higher EDOs with good 11-limit representation such as [[159edo]].

	In more tonal music, 11/8 relative to the tonic ends up being used as the chord root for what amounts to a voicing variation of a 1/1-9/8-225/176-3/2 chord, which, is preceded by a variation on a 1/1-5/4-3/2-225/128 chord built on [[16/15]] relative to the tonic (a variation on the [[Wikipedia: Neapolitan chord\|Neapolitan chord]]) and, followed up by a variation on the 1/1-5/4-3/2-16/9 dominant seventh chord (or potentially even a 1/1-5/4-3/2-16/9-16/15 dominant ninth chord) built on [[3/2]] relative to the tonic for a special type of half cadence. This is a dramatic musical gesture that [[User:Aura\|Aura]] has named the "simul half cadence".		In more tonal music, 11/8 relative to the tonic ends up being used as the chord root for what amounts to a voicing variation of a 1/1-9/8-225/176-3/2 chord, which, is preceded by a variation on a 1/1-5/4-3/2-225/128 chord built on [[16/15]] relative to the tonic (a variation on the [[Wikipedia: Neapolitan chord\|Neapolitan chord]]) and, followed up by a variation on the 1/1-5/4-3/2-16/9 dominant seventh chord (or potentially even a 1/1-5/4-3/2-16/9-16/15 dominant ninth chord) built on [[3/2]] relative to the tonic for a special type of half cadence. This is a dramatic musical gesture that [[User:Aura\|Aura]] has named the "simul half cadence".

Aura at 17:58, 8 May 2025

2025-05-08T17:58:28Z

← Older revision		Revision as of 17:58, 8 May 2025
Line 15:		Line 15:

	This interval is the simplest superfourth in JI, and as it falls about halfway between [[12edo]]'s [[perfect fourth]] and [[tritone]], it is very xenharmonic. As an octave-reduced harmonic, it is a basis of consonance in 11-limit JI, alongside the lower odd numbers 9, 7, 5 and 3. It can be found in harmonic series chords such as 4:5:6:7:8:9:10:11:12, sitting somewhere between the stronger and more familiar consonances of 10 (prime 5) and 12 (prime 3).		This interval is the simplest superfourth in JI, and as it falls about halfway between [[12edo]]'s [[perfect fourth]] and [[tritone]], it is very xenharmonic. As an octave-reduced harmonic, it is a basis of consonance in 11-limit JI, alongside the lower odd numbers 9, 7, 5 and 3. It can be found in harmonic series chords such as 4:5:6:7:8:9:10:11:12, sitting somewhere between the stronger and more familiar consonances of 10 (prime 5) and 12 (prime 3).

	It is very well-represented in [[24edo]], making that system especially good for approximations of JI chords involving primes 3 and 11 such as 8:9:11:12. Not only that, but composers who have experience with 24edo may find it very useful not only as a fantastic addition to major chords, but also as an interesting chord root both for chord progressions within a key, and for modulations to key signatures that are not in the same chain of fifths. Furthermore, these same useful functions can carry over to higher EDOs with good 11-limit representation such as [[159edo]].

	== Terminology ==		== Terminology ==
Line 25:		Line 23:

	== Potential usage ==		== Potential usage ==

			This interval is very well-represented in [[24edo]], making that system especially good for approximations of JI chords involving primes 3 and 11 such as 8:9:11:12. Not only that, but composers who have experience with 24edo may find it very useful not only as a fantastic addition to major chords, but also as an interesting chord root both for chord progressions within a key, and for modulations to key signatures that are not in the same chain of fifths. Furthermore, these same useful functions can carry over to higher EDOs with good 11-limit representation such as [[159edo]].

	In more tonal music, 11/8 relative to the tonic ends up being used as the chord root for what amounts to a voicing variation of a 1/1-9/8-225/176-3/2 chord, which, is preceded by a variation on a 1/1-5/4-3/2-225/128 chord built on [[16/15]] relative to the tonic (a variation on the [[Wikipedia: Neapolitan chord\|Neapolitan chord]]) and, followed up by a variation on the 1/1-5/4-3/2-16/9 dominant seventh chord (or potentially even a 1/1-5/4-3/2-16/9-16/15 dominant ninth chord) built on [[3/2]] relative to the tonic for a special type of half cadence. This is a dramatic musical gesture that [[User:Aura\|Aura]] has named the "simul half cadence".		In more tonal music, 11/8 relative to the tonic ends up being used as the chord root for what amounts to a voicing variation of a 1/1-9/8-225/176-3/2 chord, which, is preceded by a variation on a 1/1-5/4-3/2-225/128 chord built on [[16/15]] relative to the tonic (a variation on the [[Wikipedia: Neapolitan chord\|Neapolitan chord]]) and, followed up by a variation on the 1/1-5/4-3/2-16/9 dominant seventh chord (or potentially even a 1/1-5/4-3/2-16/9-16/15 dominant ninth chord) built on [[3/2]] relative to the tonic for a special type of half cadence. This is a dramatic musical gesture that [[User:Aura\|Aura]] has named the "simul half cadence".

Aura: Decided to move the usage example to its own subsection, other examples of its usage by other composers are welcome in this section

2025-05-08T17:56:39Z

Decided to move the usage example to its own subsection, other examples of its usage by other composers are welcome in this section

← Older revision		Revision as of 17:56, 8 May 2025
Line 16:		Line 16:
	This interval is the simplest superfourth in JI, and as it falls about halfway between [[12edo]]'s [[perfect fourth]] and [[tritone]], it is very xenharmonic. As an octave-reduced harmonic, it is a basis of consonance in 11-limit JI, alongside the lower odd numbers 9, 7, 5 and 3. It can be found in harmonic series chords such as 4:5:6:7:8:9:10:11:12, sitting somewhere between the stronger and more familiar consonances of 10 (prime 5) and 12 (prime 3).		This interval is the simplest superfourth in JI, and as it falls about halfway between [[12edo]]'s [[perfect fourth]] and [[tritone]], it is very xenharmonic. As an octave-reduced harmonic, it is a basis of consonance in 11-limit JI, alongside the lower odd numbers 9, 7, 5 and 3. It can be found in harmonic series chords such as 4:5:6:7:8:9:10:11:12, sitting somewhere between the stronger and more familiar consonances of 10 (prime 5) and 12 (prime 3).

	It is very well-represented in [[24edo]], making that system especially good for approximations of JI chords involving primes 3 and 11 such as 8:9:11:12. Not only that, but composers who have experience with 24edo may find it very useful not only as a fantastic addition to major chords, but also as an interesting chord root both for chord progressions within a key, and for modulations to key signatures that are not in the same chain of fifths. Furthermore, these same useful functions can carry over to higher EDOs with good 11-limit representation such as [[159edo]]. For example, in more tonal music, 11/8 relative to the tonic ends up being used as the chord root for what amounts to a voicing variation of a 1/1-9/8-225/176-3/2 chord, which, is preceded by a variation on a 1/1-5/4-3/2-225/128 chord built on [[16/15]] relative to the tonic (a variation on the [[Wikipedia: Neapolitan chord\|Neapolitan chord]]) and, followed up by a variation on the 1/1-5/4-3/2-16/9 dominant seventh chord (or potentially even a 1/1-5/4-3/2-16/9-16/15 dominant ninth chord) built on [[3/2]] relative to the tonic for a special type of half cadence. This is a dramatic musical gesture that [[User:Aura\|Aura]] has named the "simul half cadence".		It is very well-represented in [[24edo]], making that system especially good for approximations of JI chords involving primes 3 and 11 such as 8:9:11:12. Not only that, but composers who have experience with 24edo may find it very useful not only as a fantastic addition to major chords, but also as an interesting chord root both for chord progressions within a key, and for modulations to key signatures that are not in the same chain of fifths. Furthermore, these same useful functions can carry over to higher EDOs with good 11-limit representation such as [[159edo]].

	== Terminology ==		== Terminology ==
Line 23:		Line 23:
	More recently, [[Zhea Erose]] has suggested calling it something more simple: the '''harmonic fourth''' – under the idea that it is the simplest [[harmonic]] that is in the general (very) rough range of "fourths" when octave-reduced.		More recently, [[Zhea Erose]] has suggested calling it something more simple: the '''harmonic fourth''' – under the idea that it is the simplest [[harmonic]] that is in the general (very) rough range of "fourths" when octave-reduced.
	Furthermore, as stacks of this interval form a core axis of [[Alpharabian tuning]], it has also been dubbed the '''Axirabian paramajor fourth''' or more simply the '''just paramajor fourth'''.		Furthermore, as stacks of this interval form a core axis of [[Alpharabian tuning]], it has also been dubbed the '''Axirabian paramajor fourth''' or more simply the '''just paramajor fourth'''.

			== Potential usage ==

			In more tonal music, 11/8 relative to the tonic ends up being used as the chord root for what amounts to a voicing variation of a 1/1-9/8-225/176-3/2 chord, which, is preceded by a variation on a 1/1-5/4-3/2-225/128 chord built on [[16/15]] relative to the tonic (a variation on the [[Wikipedia: Neapolitan chord\|Neapolitan chord]]) and, followed up by a variation on the 1/1-5/4-3/2-16/9 dominant seventh chord (or potentially even a 1/1-5/4-3/2-16/9-16/15 dominant ninth chord) built on [[3/2]] relative to the tonic for a special type of half cadence. This is a dramatic musical gesture that [[User:Aura\|Aura]] has named the "simul half cadence".

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

Aura: Added an example of how 11/8 might be used as a chord root in more tonal compositions

2025-05-08T17:54:25Z

Added an example of how 11/8 might be used as a chord root in more tonal compositions

← Older revision		Revision as of 17:54, 8 May 2025
Line 16:		Line 16:
	This interval is the simplest superfourth in JI, and as it falls about halfway between [[12edo]]'s [[perfect fourth]] and [[tritone]], it is very xenharmonic. As an octave-reduced harmonic, it is a basis of consonance in 11-limit JI, alongside the lower odd numbers 9, 7, 5 and 3. It can be found in harmonic series chords such as 4:5:6:7:8:9:10:11:12, sitting somewhere between the stronger and more familiar consonances of 10 (prime 5) and 12 (prime 3).		This interval is the simplest superfourth in JI, and as it falls about halfway between [[12edo]]'s [[perfect fourth]] and [[tritone]], it is very xenharmonic. As an octave-reduced harmonic, it is a basis of consonance in 11-limit JI, alongside the lower odd numbers 9, 7, 5 and 3. It can be found in harmonic series chords such as 4:5:6:7:8:9:10:11:12, sitting somewhere between the stronger and more familiar consonances of 10 (prime 5) and 12 (prime 3).

	It is very well-represented in 24edo, making that system especially good for approximations of JI chords involving primes 3 and 11 such as 8:9:11:12. Not only that, but composers who have experience with 24edo may find it very useful not only as a fantastic addition to major chords, but also as an interesting root ~~motion~~ both for chord progressions within a key and for modulations to key signatures that are not in the same chain of fifths. Furthermore, these same useful functions can carry over to higher EDOs with good 11-limit representation such as [[159edo]].		It is very well-represented in [[24edo]], making that system especially good for approximations of JI chords involving primes 3 and 11 such as 8:9:11:12. Not only that, but composers who have experience with 24edo may find it very useful not only as a fantastic addition to major chords, but also as an interesting chord root both for chord progressions within a key, and for modulations to key signatures that are not in the same chain of fifths. Furthermore, these same useful functions can carry over to higher EDOs with good 11-limit representation such as [[159edo]]. For example, in more tonal music, 11/8 relative to the tonic ends up being used as the chord root for what amounts to a voicing variation of a 1/1-9/8-225/176-3/2 chord, which, is preceded by a variation on a 1/1-5/4-3/2-225/128 chord built on [[16/15]] relative to the tonic (a variation on the [[Wikipedia: Neapolitan chord\|Neapolitan chord]]) and, followed up by a variation on the 1/1-5/4-3/2-16/9 dominant seventh chord (or potentially even a 1/1-5/4-3/2-16/9-16/15 dominant ninth chord) built on [[3/2]] relative to the tonic for a special type of half cadence. This is a dramatic musical gesture that [[User:Aura\|Aura]] has named the "simul half cadence".

	== Terminology ==		== Terminology ==
	The naming pattern from [[11/9\|undecimal neutral third]] and [[12/11\|undecimal neutral second]] and their octave complements can be rigorously generalized and results in the somewhat unconventional '''harmonic/undecimal neutral fourth'''. This interval has also been termed the '''undecimal major fourth''' since the tempered version found in [[24edo]] was dubbed the "major fourth" by [[Ivan Wyschnegradsky]], although this may be confusing in diatonic contexts.		The naming pattern from [[11/9\|undecimal neutral third]] and [[12/11\|undecimal neutral second]] and their octave complements can be rigorously generalized and results in the somewhat unconventional '''harmonic/undecimal neutral fourth'''. This interval has also been termed the '''undecimal major fourth''' since the tempered version found in 24edo was dubbed the "major fourth" by [[Ivan Wyschnegradsky]], although this may be confusing in diatonic contexts.
	Because it is right between the diatonic fourth and tritone, it may also be called the '''(lesser) undecimal tritone'''.<ref>Kyle Gann (1998) [https://www.kylegann.com/Octave.html ''Anatomy of an Octave'']</ref>		Because it is right between the diatonic fourth and tritone, it may also be called the '''(lesser) undecimal tritone'''.<ref>Kyle Gann (1998) [https://www.kylegann.com/Octave.html ''Anatomy of an Octave'']</ref>
	More recently, [[Zhea Erose]] has suggested calling it something more simple: the '''harmonic fourth''' – under the idea that it is the simplest [[harmonic]] that is in the general (very) rough range of "fourths" when octave-reduced.		More recently, [[Zhea Erose]] has suggested calling it something more simple: the '''harmonic fourth''' – under the idea that it is the simplest [[harmonic]] that is in the general (very) rough range of "fourths" when octave-reduced.

Sintel: /* Terminology */ .

2025-05-01T21:09:30Z

Terminology: .

← Older revision		Revision as of 21:09, 1 May 2025
Line 22:		Line 22:
	Because it is right between the diatonic fourth and tritone, it may also be called the '''(lesser) undecimal tritone'''.<ref>Kyle Gann (1998) [https://www.kylegann.com/Octave.html ''Anatomy of an Octave'']</ref>		Because it is right between the diatonic fourth and tritone, it may also be called the '''(lesser) undecimal tritone'''.<ref>Kyle Gann (1998) [https://www.kylegann.com/Octave.html ''Anatomy of an Octave'']</ref>
	More recently, [[Zhea Erose]] has suggested calling it something more simple: the '''harmonic fourth''' – under the idea that it is the simplest [[harmonic]] that is in the general (very) rough range of "fourths" when octave-reduced.		More recently, [[Zhea Erose]] has suggested calling it something more simple: the '''harmonic fourth''' – under the idea that it is the simplest [[harmonic]] that is in the general (very) rough range of "fourths" when octave-reduced.
	Furthermore, as stacks of this interval form a core axis of [[Alpharabian tuning]], it has also been dubbed the '''Axirabian paramajor fourth''' or more simply the '''just paramajor fourth'''..		Furthermore, as stacks of this interval form a core axis of [[Alpharabian tuning]], it has also been dubbed the '''Axirabian paramajor fourth''' or more simply the '''just paramajor fourth'''.

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