Diesis (scale theory) - Revision history

FloraC: Redirected page to Diesis#As a diatonic interval category

2026-06-10T06:45:22Z

Redirected page to Diesis#As a diatonic interval category

← Older revision		Revision as of 06:45, 10 June 2026
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	~~The '''diesis''' or '''enharmonic diesis''' is the diminished second or inverse diminished second, whichever is positive in size, in the~~ [[diatonic scale]]. An example of a diesis is the interval between C♯ and D♭. The diesis spans twelve [[perfect fifth]]s, and is observed in any tuning whose perfect fifth is not the same as [[12edo]]'s. Notes related by the diesis are said to be ''enharmonic'' to each other.		#redirect [[Diesis #As a diatonic interval category]]

	~~== Just intervals ==~~
	~~If the fifth represents the just~~ interval [[3/2]], the diesis or inverse diesis represents the [[Pythagorean comma]]. In [[meantone]], the diesis approximates a class of [[comma]]s separated by the syntonic comma ([[81/80]]), among which [[128/125]], the augmented comma, is notable for being tuned pure in [[quarter-comma meantone]]. Therefore ''diesis'' traditionally refers to the augmented comma by default. Other dieses according to this definition are
	* [[648/625]], the major diesis, tuned pure in [[1/3-comma meantone]].
	* [[2048/2025]], the diaschisma, tuned pure in [[1/6-comma meantone]].
	* [[32805/32768]], the schisma, tuned pure in 1/12-comma meantone.

	~~This is not to be confused with the [[diesis (interval region)\|related sense of the same term]], for which a number of other intervals are named despite not being reached through twelve fifths.~~

	~~== Generalization ==~~
	The diesis can be generalized to any [[mos scale]] as the '''mosdiesis''', defined as {{nowrap\| {{!}}L - 2s{{!}} }}, i.e. the difference between a large step and two small steps. In terms of [[stepspan]], it is usually the diminished mosstep or inverse diminished mosstep, whichever is positive. However, in ''n''L 1s scales, it is the double-diminished mosstep or inverse thereof since the small step itself is diminished. Except for ''n''L 1s scales, it is the diminished mosstep in [[soft]] {{nowrap\|(L:s < 2:1)}} scales and the inverse diminished mosstep in [[hard]] {{nowrap\|(L:s > 2:1)}} scales. It vanishes in basic {{nowrap\|(L:s {{=}} 2:1)}} scales.

	~~== See also ==~~
	* [[Diesis]] (disambiguation page)
	* [[Chroma]]

	~~[[Category:Terms]]~~
	~~[[Category:MOS scale~~]]

FloraC: Clarify

2026-04-10T16:44:38Z

Clarify

← Older revision		Revision as of 16:44, 10 April 2026
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	The '''diesis''' or '''enharmonic diesis''' is the diminished second or inverse diminished second, whichever is positive, in the [[diatonic scale]]. An example of a diesis is the interval between C♯ and D♭. The diesis spans twelve [[perfect fifth]]s, and is observed in any tuning whose perfect fifth is not the same as [[12edo]]'s. Notes related by the diesis are said to be ''enharmonic'' to each other.		The '''diesis''' or '''enharmonic diesis''' is the diminished second or inverse diminished second, whichever is positive in size, in the [[diatonic scale]]. An example of a diesis is the interval between C♯ and D♭. The diesis spans twelve [[perfect fifth]]s, and is observed in any tuning whose perfect fifth is not the same as [[12edo]]'s. Notes related by the diesis are said to be ''enharmonic'' to each other.

	== Just intervals ==		== Just intervals ==

FloraC: +section title. Note the relation to perfect fifths. Note possible confusion.

2025-04-28T17:34:30Z

+section title. Note the relation to perfect fifths. Note possible confusion.

← Older revision		Revision as of 17:34, 28 April 2025
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	The '''diesis''' or '''enharmonic diesis''' is the diminished second or inverse diminished second, whichever is positive, in the [[diatonic scale]]. An example of a diesis is the interval between C♯ and D♭. The diesis is observed in any tuning whose [[perfect fifth]] is not the same as [[12edo]]'s. Notes related by the diesis are said to be ''enharmonic'' to each other.		The '''diesis''' or '''enharmonic diesis''' is the diminished second or inverse diminished second, whichever is positive, in the [[diatonic scale]]. An example of a diesis is the interval between C♯ and D♭. The diesis spans twelve [[perfect fifth]]s, and is observed in any tuning whose perfect fifth is not the same as [[12edo]]'s. Notes related by the diesis are said to be ''enharmonic'' to each other.

			== Just intervals ==
	If the fifth represents the just interval [[3/2]], the diesis or inverse diesis represents the [[Pythagorean comma]]. In [[meantone]], the diesis approximates a class of [[comma]]s separated by the syntonic comma ([[81/80]]), among which [[128/125]], the augmented comma, is notable for being tuned pure in [[quarter-comma meantone]]. Therefore ''diesis'' traditionally refers to the augmented comma by default. Other dieses according to this definition are		If the fifth represents the just interval [[3/2]], the diesis or inverse diesis represents the [[Pythagorean comma]]. In [[meantone]], the diesis approximates a class of [[comma]]s separated by the syntonic comma ([[81/80]]), among which [[128/125]], the augmented comma, is notable for being tuned pure in [[quarter-comma meantone]]. Therefore ''diesis'' traditionally refers to the augmented comma by default. Other dieses according to this definition are
	* [[648/625]], the major diesis, tuned pure in [[1/3-comma meantone]].		* [[648/625]], the major diesis, tuned pure in [[1/3-comma meantone]].
	* [[2048/2025]], the diaschisma, tuned pure in [[1/6-comma meantone]].		* [[2048/2025]], the diaschisma, tuned pure in [[1/6-comma meantone]].
	* [[32805/32768]], the schisma, tuned pure in 1/12-comma meantone.		* [[32805/32768]], the schisma, tuned pure in 1/12-comma meantone.

			This is not to be confused with the [[diesis (interval region)\|related sense of the same term]], for which a number of other intervals are named despite not being reached through twelve fifths.

	== Generalization ==		== Generalization ==

FloraC: Rework according to community feedback: introduce traditional diesis first and move mosdiesis to a section

2025-04-28T17:22:00Z

Rework according to community feedback: introduce traditional diesis first and move mosdiesis to a section

← Older revision		Revision as of 17:22, 28 April 2025
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	The '''diesis''' ~~(precisely, the~~ '''~~mosdiesis~~'''~~) of a [[MOS scale]]~~ is ~~the interval that is the difference between two generalized enharmonic notes, i.e.~~ the diminished ~~mosstep~~ or inverse diminished ~~mosstep~~, whichever is positive~~. In~~ [[~~soft~~]] ~~{{nowrap\|(L:s < 2:1)}} scales, it~~ is the ~~diminished mosstep~~. In [[~~hard~~]] ~~{{nowrap\|(L:s > 2:1)}} scales, it~~ is the ~~inverse diminished mosstep, since the diminished mosstep itself is negative. In basic {{nowrap\|(L:s {{=}} 2:1)}} scales, it~~ [[~~vanish~~]]es.		The '''diesis''' or '''enharmonic diesis''' is the diminished second or inverse diminished second, whichever is positive, in the [[diatonic scale]]. An example of a diesis is the interval between C♯ and D♭. The diesis is observed in any tuning whose [[perfect fifth]] is not the same as [[12edo]]'s. Notes related by the diesis are said to be ''enharmonic'' to each other.

	~~The diesis or '''enharmonic diesis''' in the [[diatonic scale]] is the diminished second or inverse diminished second, whichever is positive, such as the interval between C♯ and D♭.~~ If the fifth represents the just interval [[3/2]], the diesis or inverse diesis represents the [[Pythagorean comma]]. In [[meantone]], it approximates a class of [[comma]]s separated by the syntonic comma ([[81/80]]), among which [[128/125]], the augmented comma, is notable for being tuned pure in [[quarter-comma meantone]]. Therefore ''diesis'' traditionally refers to the augmented comma by default. Other dieses according to this definition are		If the fifth represents the just interval [[3/2]], the diesis or inverse diesis represents the [[Pythagorean comma]]. In [[meantone]], the diesis approximates a class of [[comma]]s separated by the syntonic comma ([[81/80]]), among which [[128/125]], the augmented comma, is notable for being tuned pure in [[quarter-comma meantone]]. Therefore ''diesis'' traditionally refers to the augmented comma by default. Other dieses according to this definition are
	* [[648/625]], the major diesis, tuned pure in [[1/3-comma meantone]].		* [[648/625]], the major diesis, tuned pure in [[1/3-comma meantone]].
	* [[2048/2025]], the diaschisma, tuned pure in [[1/6-comma meantone]].		* [[2048/2025]], the diaschisma, tuned pure in [[1/6-comma meantone]].
	* [[32805/32768]], the schisma, tuned pure in 1/12-comma meantone.		* [[32805/32768]], the schisma, tuned pure in 1/12-comma meantone.

			== Generalization ==
			The diesis can be generalized to any [[mos scale]] as the '''mosdiesis''', defined as {{nowrap\| {{!}}L - 2s{{!}} }}, i.e. the difference between a large step and two small steps. In terms of [[stepspan]], it is usually the diminished mosstep or inverse diminished mosstep, whichever is positive. However, in ''n''L 1s scales, it is the double-diminished mosstep or inverse thereof since the small step itself is diminished. Except for ''n''L 1s scales, it is the diminished mosstep in [[soft]] {{nowrap\|(L:s < 2:1)}} scales and the inverse diminished mosstep in [[hard]] {{nowrap\|(L:s > 2:1)}} scales. It vanishes in basic {{nowrap\|(L:s {{=}} 2:1)}} scales.

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

Dummy index: /* See also */ +link

2024-12-07T13:55:01Z

ArrowHead294: Fix broken link

2024-11-25T14:47:15Z

Fix broken link

← Older revision		Revision as of 14:47, 25 November 2024
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	The '''diesis''' (precisely, the '''mosdiesis''') of a [[MOS scale]] is the interval that is the difference between two generalized enharmonic notes, i.e. the diminished mosstep or inverse diminished mosstep, whichever is positive. In [[soft]] {{nowrap\|(L:s < 2:1)}} scales, it is the diminished mosstep. In [[hard]] {{nowrap\|(L:s > 2:1)}} scales, it is the inverse diminished mosstep, since the diminished mosstep itself is negative. In basic {{nowrap\|(L:s {{=}} 2:1)}} scales, it [[vanish]]es.		The '''diesis''' (precisely, the '''mosdiesis''') of a [[MOS scale]] is the interval that is the difference between two generalized enharmonic notes, i.e. the diminished mosstep or inverse diminished mosstep, whichever is positive. In [[soft]] {{nowrap\|(L:s < 2:1)}} scales, it is the diminished mosstep. In [[hard]] {{nowrap\|(L:s > 2:1)}} scales, it is the inverse diminished mosstep, since the diminished mosstep itself is negative. In basic {{nowrap\|(L:s {{=}} 2:1)}} scales, it [[vanish]]es.

	The diesis or '''enharmonic diesis''' in the [[diatonic scale]] is the diminished second or inverse diminished second, whichever is positive, such as the interval between C♯ and D♭. If the fifth represents the just interval [[3/2]], the diesis or inverse diesis represents the [[Pythagorean comma]]. In [[meantone]], it approximates a class of [[comma]]s separated by the syntonic comma ([[81/80\|]), among which [[128/125]], the augmented comma, is notable for being tuned pure in [[quarter-comma meantone]]. Therefore ''diesis'' traditionally refers to the augmented comma by default. Other dieses according to this definition are		The diesis or '''enharmonic diesis''' in the [[diatonic scale]] is the diminished second or inverse diminished second, whichever is positive, such as the interval between C♯ and D♭. If the fifth represents the just interval [[3/2]], the diesis or inverse diesis represents the [[Pythagorean comma]]. In [[meantone]], it approximates a class of [[comma]]s separated by the syntonic comma ([[81/80]]), among which [[128/125]], the augmented comma, is notable for being tuned pure in [[quarter-comma meantone]]. Therefore ''diesis'' traditionally refers to the augmented comma by default. Other dieses according to this definition are
	* [[648/625]], the major diesis, tuned pure in [[1/3-comma meantone]].		* [[648/625]], the major diesis, tuned pure in [[1/3-comma meantone]].
	* [[2048/2025]], the diaschisma, tuned pure in [[1/6-comma meantone]].		* [[2048/2025]], the diaschisma, tuned pure in [[1/6-comma meantone]].

ArrowHead294 at 14:46, 25 November 2024

2024-11-25T14:46:59Z

← Older revision		Revision as of 14:46, 25 November 2024
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	The '''diesis''' (precisely the '''mosdiesis''') of a [[~~mos~~ scale]] is the interval that is the difference between two generalized enharmonic notes, i.e. the diminished mosstep or inverse diminished mosstep, whichever is positive. In [[soft]] {{nowrap\|(L:s < 2:1)}} scales, it is the diminished mosstep. In [[hard]] {{nowrap\|(L:s > 2:1)}} scales, it is the inverse diminished mosstep, since the diminished mosstep itself is negative. In basic {{nowrap\|(L:s {{=}} 2:1)}} scales, it [[vanish]]es.		The '''diesis''' (precisely, the '''mosdiesis''') of a [[MOS scale]] is the interval that is the difference between two generalized enharmonic notes, i.e. the diminished mosstep or inverse diminished mosstep, whichever is positive. In [[soft]] {{nowrap\|(L:s < 2:1)}} scales, it is the diminished mosstep. In [[hard]] {{nowrap\|(L:s > 2:1)}} scales, it is the inverse diminished mosstep, since the diminished mosstep itself is negative. In basic {{nowrap\|(L:s {{=}} 2:1)}} scales, it [[vanish]]es.

	The diesis or '''enharmonic diesis''' in the [[diatonic scale]] is the diminished second or inverse diminished second, whichever is positive~~. For example~~, the interval of C♯~~–~~D♭. If the fifth represents the just interval [[3/2]], the diesis or inverse diesis represents the [[Pythagorean comma]]. In [[meantone]], it approximates a class of [[comma]]s separated by the [[81/80\|~~syntonic comma]~~], among which [[128/125]], the augmented comma, is notable for being tuned pure in [[quarter-comma meantone]]. Therefore ''diesis'' traditionally refers to the augmented comma by default. Other dieses according to this definition are		The diesis or '''enharmonic diesis''' in the [[diatonic scale]] is the diminished second or inverse diminished second, whichever is positive, such as the interval between C♯ and D♭. If the fifth represents the just interval [[3/2]], the diesis or inverse diesis represents the [[Pythagorean comma]]. In [[meantone]], it approximates a class of [[comma]]s separated by the syntonic comma ([[81/80\|]), among which [[128/125]], the augmented comma, is notable for being tuned pure in [[quarter-comma meantone]]. Therefore ''diesis'' traditionally refers to the augmented comma by default. Other dieses according to this definition are
	* [[648/625]], the major diesis, tuned pure in [[1/3-comma meantone]].		* [[648/625]], the major diesis, tuned pure in [[1/3-comma meantone]].
	* [[2048/2025]], the diaschisma, tuned pure in [[1/6-comma meantone]].		* [[2048/2025]], the diaschisma, tuned pure in [[1/6-comma meantone]].

FloraC: "Enharmonic" is also used here in a generalized sense

2024-11-25T12:24:01Z

"Enharmonic" is also used here in a generalized sense

← Older revision		Revision as of 12:24, 25 November 2024
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	The '''diesis''' (precisely the '''mosdiesis''') of a [[mos scale]] is the interval that is the difference between two enharmonic notes, i.e. the diminished mosstep or inverse diminished mosstep, whichever is positive. In [[soft]] {{nowrap\|(L:s < 2:1)}} scales, it is the diminished mosstep. In [[hard]] {{nowrap\|(L:s > 2:1)}} scales, it is the inverse diminished mosstep, since the diminished mosstep itself is negative. In basic {{nowrap\|(L:s {{=}} 2:1)}} scales, it [[vanish]]es.		The '''diesis''' (precisely the '''mosdiesis''') of a [[mos scale]] is the interval that is the difference between two generalized enharmonic notes, i.e. the diminished mosstep or inverse diminished mosstep, whichever is positive. In [[soft]] {{nowrap\|(L:s < 2:1)}} scales, it is the diminished mosstep. In [[hard]] {{nowrap\|(L:s > 2:1)}} scales, it is the inverse diminished mosstep, since the diminished mosstep itself is negative. In basic {{nowrap\|(L:s {{=}} 2:1)}} scales, it [[vanish]]es.

	The diesis or '''enharmonic diesis''' in the [[diatonic scale]] is the diminished second or inverse diminished second, whichever is positive. For example, the interval of C♯–D♭. If the fifth represents the just interval [[3/2]], the diesis or inverse diesis represents the [[Pythagorean comma]]. In [[meantone]], it approximates a class of [[comma]]s separated by the [[81/80\|syntonic comma]], among which [[128/125]], the augmented comma, is notable for being tuned pure in [[quarter-comma meantone]]. Therefore ''diesis'' traditionally refers to the augmented comma by default. Other dieses according to this definition are		The diesis or '''enharmonic diesis''' in the [[diatonic scale]] is the diminished second or inverse diminished second, whichever is positive. For example, the interval of C♯–D♭. If the fifth represents the just interval [[3/2]], the diesis or inverse diesis represents the [[Pythagorean comma]]. In [[meantone]], it approximates a class of [[comma]]s separated by the [[81/80\|syntonic comma]], among which [[128/125]], the augmented comma, is notable for being tuned pure in [[quarter-comma meantone]]. Therefore ''diesis'' traditionally refers to the augmented comma by default. Other dieses according to this definition are

ArrowHead294 at 01:22, 24 November 2024

2024-11-24T01:22:57Z

← Older revision		Revision as of 01:22, 24 November 2024
Line 1:		Line 1:
	The '''diesis''' (precisely the '''mosdiesis''') of a [[mos scale]] is the interval that is the difference between two enharmonic notes, i.e. the diminished mosstep or inverse diminished mosstep, whichever is positive. In [[soft]] (L:s < 2:1) scales, it is the diminished mosstep. In [[hard]] (L:s > 2:1) scales, it is the inverse diminished mosstep, since the diminished mosstep itself is negative. In basic (L:s = 2:1) scales, it [[vanish]]es.		The '''diesis''' (precisely the '''mosdiesis''') of a [[mos scale]] is the interval that is the difference between two enharmonic notes, i.e. the diminished mosstep or inverse diminished mosstep, whichever is positive. In [[soft]] {{nowrap\|(L:s < 2:1)}} scales, it is the diminished mosstep. In [[hard]] {{nowrap\|(L:s > 2:1)}} scales, it is the inverse diminished mosstep, since the diminished mosstep itself is negative. In basic {{nowrap\|(L:s {{=}} 2:1)}} scales, it [[vanish]]es.

	The diesis or '''enharmonic diesis''' in the [[diatonic scale]] is the diminished second or inverse diminished second, whichever is positive. For example, the interval of C♯~~ ~~&ndash~~;&#x200A~~;D♭. If the fifth represents the just interval [[3/2]], the diesis or inverse diesis represents the [[Pythagorean comma]]. In [[meantone]], it approximates a class of [[comma]]s separated by the [[81/80\|syntonic comma]], among which [[128/125]], the augmented comma, is notable for being tuned pure in [[quarter-comma meantone]]. Therefore ''diesis'' traditionally refers to the augmented comma by default. Other dieses according to this definition are		The diesis or '''enharmonic diesis''' in the [[diatonic scale]] is the diminished second or inverse diminished second, whichever is positive. For example, the interval of C♯–D♭. If the fifth represents the just interval [[3/2]], the diesis or inverse diesis represents the [[Pythagorean comma]]. In [[meantone]], it approximates a class of [[comma]]s separated by the [[81/80\|syntonic comma]], among which [[128/125]], the augmented comma, is notable for being tuned pure in [[quarter-comma meantone]]. Therefore ''diesis'' traditionally refers to the augmented comma by default. Other dieses according to this definition are
	* [[648/625]], the major diesis, tuned pure in [[1/3-comma meantone]].		* [[648/625]], the major diesis, tuned pure in [[1/3-comma meantone]].
	* [[2048/2025]], the diaschisma, tuned pure in [[1/6-comma meantone]].		* [[2048/2025]], the diaschisma, tuned pure in [[1/6-comma meantone]].

Godtone at 15:51, 7 September 2024

2024-09-07T15:51:41Z

← Older revision		Revision as of 15:51, 7 September 2024
Line 1:		Line 1:
	The '''diesis''' (precisely the '''mosdiesis''') of a [[mos scale]] is the interval that is the difference between two enharmonic notes, i.e. the diminished mosstep or inverse diminished mosstep, whichever is positive. In [[soft]] (L:s < 2:1) scales, it is the diminished mosstep. In [[hard]] (L:s > 2:1) scales, it is the inverse diminished mosstep, since the diminished mosstep itself is negative. In basic (L:s = 2:1) scales, it [[vanish]]es.		The '''diesis''' (precisely the '''mosdiesis''') of a [[mos scale]] is the interval that is the difference between two enharmonic notes, i.e. the diminished mosstep or inverse diminished mosstep, whichever is positive. In [[soft]] (L:s < 2:1) scales, it is the diminished mosstep. In [[hard]] (L:s > 2:1) scales, it is the inverse diminished mosstep, since the diminished mosstep itself is negative. In basic (L:s = 2:1) scales, it [[vanish]]es.

	The diesis or '''enharmonic diesis''' in the [[diatonic scale]] is the diminished second or inverse diminished second, whichever is positive. For example, the interval of C♯ – D♭. If the fifth represents the just interval [[3/2]], the diesis or inverse diesis represents the [[Pythagorean comma]]. In [[meantone]], it approximates a class of [[comma]]s separated by the [[81/80\|syntonic comma]], among which [[128/125]], the augmented comma, is notable for being tuned pure in [[quarter-comma meantone]]. Therefore ''diesis'' traditionally refers to the augmented comma by default. Other dieses are		The diesis or '''enharmonic diesis''' in the [[diatonic scale]] is the diminished second or inverse diminished second, whichever is positive. For example, the interval of C♯ – D♭. If the fifth represents the just interval [[3/2]], the diesis or inverse diesis represents the [[Pythagorean comma]]. In [[meantone]], it approximates a class of [[comma]]s separated by the [[81/80\|syntonic comma]], among which [[128/125]], the augmented comma, is notable for being tuned pure in [[quarter-comma meantone]]. Therefore ''diesis'' traditionally refers to the augmented comma by default. Other dieses according to this definition are
	* [[648/625]], the major diesis, tuned pure in [[1/3-comma meantone]].		* [[648/625]], the major diesis, tuned pure in [[1/3-comma meantone]].
	* [[2048/2025]], the diaschisma, tuned pure in [[1/6-comma meantone]].		* [[2048/2025]], the diaschisma, tuned pure in [[1/6-comma meantone]].

← Older revision		Revision as of 13:55, 7 December 2024
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	== See also ==		== See also ==
	* [[Diesis]] (disambiguation page)		* [[Diesis]] (disambiguation page)
			* [[Chroma]]

	[[Category:Terms]]		[[Category:Terms]]
	[[Category:MOS scale]]		[[Category:MOS scale]]