Diatonic semitone - Revision history

Inthar: Changed redirect target from Diatonic#Minor second to Pythagorean tuning#Minor second

2025-12-30T21:18:40Z

Changed redirect target from Diatonic#Minor second to Pythagorean tuning#Minor second

← Older revision		Revision as of 21:18, 30 December 2025
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	#redirect [[~~Diatonic~~#Minor second]]		#redirect [[Pythagorean tuning#Minor second]]

Inthar: Redirected page to Diatonic#Minor second

2025-12-30T21:09:10Z

Redirected page to Diatonic#Minor second

← Older revision		Revision as of 21:09, 30 December 2025
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	{{Infobox interval\|256/243\|names=Chromatic semitone, augmented unison\|name=Chromatic semitone, augmented unison\|Name=Diatonic semitone, diatonic minor second}}The 3-limit '''diatonic semitone''', also called the '''diatonic minor second (m2)''' and represented by the ratio 256/243, is the smaller of the two seconds (1-step intervals) in the MOS diatonic scale. It is generated by stacking 5 fourths and octave-reducing. In [[Pythagorean tuning\|Pythagorean]] tuning, and thus purely-tuned [[just intonation]], it is approximately 90.2 cents in size, but as an interval in the abstract diatonic scale it may range between 0 and 171 cents, depending on the tuning.		#redirect [[Diatonic#Minor second]]

	It functions as the small step of the diatonic MOS, and along with the [[diatonic major second]] may be used to construct other diatonic intervals. For example, the [[diatonic minor third]] is a major second stacked with a minor second. The [[chromatic semitone]] is the difference between these two intervals. Note that the chromatic semitone itself is distinct from the diatonic semitone; they are separated by the [[12edo#~~Compton temperament\|Pythagorean comma]], which separates all~~ [[~~enharmonic]] intervals in Pythagorean tuning, and which, if tempered out, yields 12edo.~~

	~~As a harmonic interval, the diatonic semitone is usually considered a dissonance, due to its small size and complex ratio.~~

	~~== Scale info ==~~
	The diatonic scale contains two minor seconds. In the Ionian mode, minor seconds are found on the third and seventh scale degrees; the others have major seconds. The small number of minor seconds compared to major seconds ensures that thirds that include minor seconds (that is, minor thirds) are roughly evenly distributed with major thirds; in a scale with three small steps and four large steps, for example, six out of the seven thirds are minor.

	~~== Just intonation ==~~
	The diatonic semitone is a product of square superparticulars, denoted [[Interseptimal diesis\|S7]] * [[Archy\|S8]]<sup>2</sup>. When tempered out, it leads to blackwood temperament, which tunes the [[2.3.7 subgroup]] to [[Equipentatonic#~~5edo\|5edo~~]].

Vector: Created page with "{{Infobox interval|256/243|names=Chromatic semitone, augmented unison|name=Chromatic semitone, augmented unison|Name=Diatonic semitone, diatonic minor second}}The 3-limit '''diatonic semitone''', also called the '''diatonic minor second (m2)''' and represented by the ratio 256/243, is the smaller of the two seconds (1-step intervals) in the MOS diatonic scale. It is generated by stacking 5 fourths and octave-reducing. In Pythagorean tuning, and thu..."

2025-12-17T10:28:58Z

Created page with "{{Infobox interval|256/243|names=Chromatic semitone, augmented unison|name=Chromatic semitone, augmented unison|Name=Diatonic semitone, diatonic minor second}}The 3-limit '''diatonic semitone''', also called the '''diatonic minor second (m2)''' and represented by the ratio 256/243, is the smaller of the two seconds (1-step intervals) in the MOS diatonic scale. It is generated by stacking 5 fourths and octave-reducing. In Pythagorean tuning, and thu..."

New page

{{Infobox interval|256/243|names=Chromatic semitone, augmented unison|name=Chromatic semitone, augmented unison|Name=Diatonic semitone, diatonic minor second}}The 3-limit '''diatonic semitone''', also called the '''diatonic minor second (m2)''' and represented by the ratio 256/243, is the smaller of the two seconds (1-step intervals) in the MOS diatonic scale. It is generated by stacking 5 fourths and octave-reducing. In [[Pythagorean tuning|Pythagorean]] tuning, and thus purely-tuned [[just intonation]], it is approximately 90.2 cents in size, but as an interval in the abstract diatonic scale it may range between 0 and 171 cents, depending on the tuning.

It functions as the small step of the diatonic MOS, and along with the [[diatonic major second]] may be used to construct other diatonic intervals. For example, the [[diatonic minor third]] is a major second stacked with a minor second. The [[chromatic semitone]] is the difference between these two intervals. Note that the chromatic semitone itself is distinct from the diatonic semitone; they are separated by the [[12edo#Compton temperament|Pythagorean comma]], which separates all [[enharmonic]] intervals in Pythagorean tuning, and which, if tempered out, yields 12edo.

As a harmonic interval, the diatonic semitone is usually considered a dissonance, due to its small size and complex ratio.

== Scale info ==
The diatonic scale contains two minor seconds. In the Ionian mode, minor seconds are found on the third and seventh scale degrees; the others have major seconds. The small number of minor seconds compared to major seconds ensures that thirds that include minor seconds (that is, minor thirds) are roughly evenly distributed with major thirds; in a scale with three small steps and four large steps, for example, six out of the seven thirds are minor.

== Just intonation ==
The diatonic semitone is a product of square superparticulars, denoted [[Interseptimal diesis|S7]] * [[Archy|S8]]<sup>2</sup>. When tempered out, it leads to blackwood temperament, which tunes the [[2.3.7 subgroup]] to [[Equipentatonic#5edo|5edo]].