Diesis (scale theory): Difference between revisions

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In scale ~~theory~~, the '''diesis''' is the ~~difference between two enharmonic notes in~~ a scale, i.e. the diminished ~~second~~ (~~a minor second~~ diminished ~~by a~~ [[~~chroma~~]]).

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 ==

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]]

[[Category:MOS scale]]

@@ Line 1: / Line 1: @@
-In scale theory, the '''diesis''' is the difference between two enharmonic notes in a scale, i.e. the diminished second (a minor second diminished by a [[chroma]]).
+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 ==
+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]]
+[[Category:MOS scale]]