Diesis (scale theory): Difference between revisions

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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

* [[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 ==

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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
 * [[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 ==