Whole tone - Revision history

Vector at 08:26, 28 April 2026

2026-04-28T08:26:35Z

← Older revision		Revision as of 08:26, 28 April 2026
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	== In just intonation ==		== In just intonation ==
	''TODO: complete section''		''TODO: complete section''

			=== 3-limit ===
			Overwhelmingly, "whole tone" in just intonation refers to 9/8. However, as a subcategory of second (specifically, major seconds), a couple more intervals meet the criteria.

			=== 5-limit ===
			The minor tone is 10/9. 10/9 and 9/8 stack to 5/4, and as previously mentioned in meantone temperament they are equated. An equal temperament that is distinctly consistent to the 9-odd-limit thus cannot support meantone.

			=== 7-limit ===

			==== 28/25 ====
			28/25 sits between 9/8 and 10/9 in size, and is the generator for the didacus temperament along with being the approximate size of a meantone-tempered whole tone.

			==== 8/7 ====
			8/7 is a very large major second, generally out of the bounds of whole tones but approximated as such in flat tunings of [[archy]] (7edo, 12edo, 17edo, and 22edo). It is the octave complement of the harmonic seventh, which is also the seventh harmonic (octave-reduced). It may be considered the "major tone".

			=== 11-limit ===

			==== 11/10 ====
			11/10, conversely, is on the flat side, but is equated with 10/9 in temperaments like porcupine and tetracot (widening the syntonic comma) and further with 9/8 (tempering it out entirely) in flattone.

			==== 25/22 ====
			25/22 is an 11-limit major second that functions as a sharp neogothic major second. It is the interval separating 11/10 and 5/4.

			=== Higher limit ===

			==== 17/15 ====
			17/15 however is perhaps the more proper neogothic major second, being the mediant of 8/7 and 9/8 much as 14/11 is the mediant of 9/7 and 5/4.

Inthar: /* As generators of temperaments */

2026-04-27T21:22:07Z

As generators of temperaments

← Older revision		Revision as of 21:22, 27 April 2026
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	== As generators of temperaments ==		== As generators of temperaments ==
	The most prominent whole-tone-generated temperament is [[~~didacus~~]], which is a no-threes subgroup temperament generated by a whole tone of about 194 cents that finds 5/4 at 2 steps and 7/4 at 5 steps; this is the most obvious temperament interpretation of the 12edo whole-tone scale. Didacus is a 6 cluster temperament.		The most prominent whole-tone-generated temperament is [[Didacus]], which is a no-threes subgroup temperament generated by a whole tone of about 194 cents that finds 5/4 at 2 steps and 7/4 at 5 steps; this is the most obvious temperament interpretation of the 12edo whole-tone scale. Didacus is a 6 cluster temperament.

	Another notable whole tone temperament is [[~~machine~~]], where a ~215c whole tone, interpreted as a very flat 8/7 or a sharp 9/8, stacks three times to 16/11. A more accurate but more complex interpretation is ''[[~~contraption~~]]'', which instead finds 7/4 at 10 steps as a 2.7.11 subgroup temperament. 11edo supports both temperaments, and in fact ~~contraption~~ is an 11-form temperament. In either case, the generator may be interpreted as 17/15 and 6 steps (octave-reduced) as a flat 17/16, so that they extend to 2.15.7.11.17.		Another notable whole tone temperament is [[Machine]], where a ~215c whole tone, interpreted as a very flat 8/7 or a sharp 9/8, stacks three times to 16/11. A more accurate but more complex interpretation is [[Contraption]], which instead finds 7/4 at 10 steps as a 2.7.11 subgroup temperament. 11edo supports both temperaments, and in fact Contraption is an 11-form temperament. In either case, the generator may be interpreted as 17/15 and 6 steps (octave-reduced) as a flat 17/16, so that they extend to 2.15.7.11.17.

	Additional temperaments associated with whole tone generators include [[~~tetracot~~]] (which stacks a flat 10/9 four times to reach 3/2), and [[~~slendric~~]] (which stacks a just or slightly sharpened 8/7 three times to reach 3/2). The edges of the tetrachordal definition mentioned above represent [[~~porcupine~~]] (equalizing 9:10:11:12) and [[Equipentatonic#Semaphore\|~~semaphore~~]] (equalizing 6:7:8).		Additional temperaments associated with whole tone generators include [[Tetracot]] (which stacks a flat 10/9 four times to reach 3/2), and [[Slendric]] (which stacks a just or slightly sharpened 8/7 three times to reach 3/2). The edges of the tetrachordal definition mentioned above represent [[Porcupine]] (equalizing 9:10:11:12) and [[Equipentatonic#Semaphore\|Semaphore]] (equalizing 6:7:8).

	== In just intonation ==		== In just intonation ==
	''TODO: complete section''		''TODO: complete section''

Vector at 21:18, 27 April 2026

2026-04-27T21:18:19Z

← Older revision		Revision as of 21:18, 27 April 2026
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	Whole tones range roughly from 160 to 240 cents, and are preferably closer to 200 cents. Whole tones may be defined to be between ~165 and ~250 cents (1\3edP4 and 1\2edP4), based on the definition of a diatonic tetrachord.		Whole tones range roughly from 160 to 240 cents, and are preferably closer to 200 cents. Whole tones may be defined to be between ~165 and ~250 cents (1\3edP4 and 1\2edP4), based on the definition of a diatonic tetrachord.

	Sometimes, the term ''whole tone'' refers specifically to the interval 9/8 (the [[Pythagorean tuning\|Pythagorean]] major second), or to the intervals 9/8 and 10/9 together (the two sizes of whole tone in the [[Zarlino]] diatonic scale). These two sizes of whole tone are separated by a [[syntonic comma]], which is tempered out in [[meantone]] temperament. Therefore, meantone has a single whole tone in between 9/8 and 10/9 in size, hence the name. In 12edo, the whole tone divides the octave into six, and as a result whole-tone-generated scales are generally 6-form.		Sometimes, the term ''whole tone'' refers specifically to the interval 9/8 (the [[Pythagorean tuning\|Pythagorean]] major second), or to the intervals 9/8 and 10/9 together (the two sizes of whole tone in the [[Zarlino]] diatonic scale). These two sizes of whole tone are separated by a [[syntonic comma]], which is tempered out in [[meantone]] temperament. Therefore, meantone has a single whole tone in between 9/8 and 10/9 in size, hence the name. In 12edo, the whole tone divides the octave into six, and as a result whole-tone-generated scales are generally 6-form - thus, from a scale structure perspective, the whole tones of 22edo (218c) and 26edo (185c) may be used as upper and lower bounds.

	== Name ==		== Name ==

Hotcrystal0 at 19:32, 27 April 2026

2026-04-27T19:32:20Z

← Older revision		Revision as of 19:32, 27 April 2026
Line 3:		Line 3:
	Whole tones range roughly from 160 to 240 cents, and are preferably closer to 200 cents. Whole tones may be defined to be between ~165 and ~250 cents (1\3edP4 and 1\2edP4), based on the definition of a diatonic tetrachord.		Whole tones range roughly from 160 to 240 cents, and are preferably closer to 200 cents. Whole tones may be defined to be between ~165 and ~250 cents (1\3edP4 and 1\2edP4), based on the definition of a diatonic tetrachord.

	Sometimes, the term ''whole tone'' refers specifically to the interval 9/8 (the [[Pythagorean]] major second), or to the intervals 9/8 and 10/9 together (the two sizes of whole tone in the [[Zarlino]] diatonic scale). These two sizes of whole tone are separated by a [[syntonic comma]], which is tempered out in [[meantone]] temperament. Therefore, meantone has a single whole tone in between 9/8 and 10/9 in size, hence the name. In 12edo, the whole tone divides the octave into six, and as a result whole-tone-generated scales are generally 6-form.		Sometimes, the term ''whole tone'' refers specifically to the interval 9/8 (the [[Pythagorean tuning\|Pythagorean]] major second), or to the intervals 9/8 and 10/9 together (the two sizes of whole tone in the [[Zarlino]] diatonic scale). These two sizes of whole tone are separated by a [[syntonic comma]], which is tempered out in [[meantone]] temperament. Therefore, meantone has a single whole tone in between 9/8 and 10/9 in size, hence the name. In 12edo, the whole tone divides the octave into six, and as a result whole-tone-generated scales are generally 6-form.

	== Name ==		== Name ==

Vector: Created page with "A whole tone is an interval that is the size of a major second that functions as the large step of a diatonic scale. Whole tones range roughly from 160 to 240 cents, and are preferably closer to 200 cents. Whole tones may be defined to be between ~165 and ~250 cents (1\3edP4 and 1\2edP4), based on the definition of a diatonic tetrachord. Sometimes, the term ''whole tone'' refers specifically to the interval 9/8 (the Pythagorean major second), or to the inte..."

2026-03-27T09:07:24Z

Created page with "A whole tone is an interval that is the size of a major second that functions as the large step of a diatonic scale. Whole tones range roughly from 160 to 240 cents, and are preferably closer to 200 cents. Whole tones may be defined to be between ~165 and ~250 cents (1\3edP4 and 1\2edP4), based on the definition of a diatonic tetrachord. Sometimes, the term ''whole tone'' refers specifically to the interval 9/8 (the Pythagorean major second), or to the inte..."

New page

A whole tone is an interval that is the size of a [[major second]] that functions as the large step of a [[diatonic]] scale.

Whole tones range roughly from 160 to 240 cents, and are preferably closer to 200 cents. Whole tones may be defined to be between ~165 and ~250 cents (1\3edP4 and 1\2edP4), based on the definition of a diatonic tetrachord.

Sometimes, the term ''whole tone'' refers specifically to the interval 9/8 (the [[Pythagorean]] major second), or to the intervals 9/8 and 10/9 together (the two sizes of whole tone in the [[Zarlino]] diatonic scale). These two sizes of whole tone are separated by a [[syntonic comma]], which is tempered out in [[meantone]] temperament. Therefore, meantone has a single whole tone in between 9/8 and 10/9 in size, hence the name. In 12edo, the whole tone divides the octave into six, and as a result whole-tone-generated scales are generally 6-form.

== Name ==
''Whole tone'' comes from diatonic scale theory, which comprises the diatonic scale of five whole tones and two semitones; the step ratio of diatonic is either exactly or roughly 2:1 in most historical tunings, thus a semitone is roughly half of a whole tone. This is not to be confused with the sense of ''tone'' to refer to a note.

== Qualities ==
While the whole tone is itself a quality of second (the major second), the various commatic inflections are considered by some theorists to represent subqualities of whole tone; 9/8 is the "major tone" and 10/9 the "minor tone".

== As generators of temperaments ==
The most prominent whole-tone-generated temperament is [[didacus]], which is a no-threes subgroup temperament generated by a whole tone of about 194 cents that finds 5/4 at 2 steps and 7/4 at 5 steps; this is the most obvious temperament interpretation of the 12edo whole-tone scale. Didacus is a 6 cluster temperament.

Another notable whole tone temperament is [[machine]], where a ~215c whole tone, interpreted as a very flat 8/7 or a sharp 9/8, stacks three times to 16/11. A more accurate but more complex interpretation is ''[[contraption]]'', which instead finds 7/4 at 10 steps as a 2.7.11 subgroup temperament. 11edo supports both temperaments, and in fact contraption is an 11-form temperament. In either case, the generator may be interpreted as 17/15 and 6 steps (octave-reduced) as a flat 17/16, so that they extend to 2.15.7.11.17.

Additional temperaments associated with whole tone generators include [[tetracot]] (which stacks a flat 10/9 four times to reach 3/2), and [[slendric]] (which stacks a just or slightly sharpened 8/7 three times to reach 3/2). The edges of the tetrachordal definition mentioned above represent [[porcupine]] (equalizing 9:10:11:12) and [[Equipentatonic#Semaphore|semaphore]] (equalizing 6:7:8).

== In just intonation ==
''TODO: complete section''