Diesis (scale theory): Difference between revisions

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 ~~the negative~~ 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 ~~negative~~ 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.

~~In meantone tunings (including [[12edo]]), the~~ diesis or ''enharmonic diesis'' in the [[diatonic scale]] is the diminished second or ~~the negative~~ diminished second, whichever is positive. For example, the interval of C♯ – D♭.

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

* [[648/625]], the major diesis, tuned pure in [[1/3-comma meantone]].

If the fifth ~~approximates~~ the just interval [[3/2]], ~~then~~ the diesis or ~~the negative~~ diesis ~~approximates~~ the [[Pythagorean comma]]. In [[meantone]], the ~~diesis also approximates~~ [[128/125]], the augmented comma, ~~which traditionally goes by the name of~~ ''diesis''.

* [[2048/2025]], the diaschisma, tuned pure in [[1/6-comma meantone]].

* [[32805/32768]], the schisma, tuned pure in 1/12-comma meantone.

== See also ==

@@ 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 the negative 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 negative 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.
-In meantone tunings (including [[12edo]]), the diesis or ''enharmonic diesis'' in the [[diatonic scale]] is the diminished second or the negative diminished second, whichever is positive. For example, the interval of C♯&#x200A;&ndash;&#x200A;D♭.
+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♯&#x200A;&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 are
+* [[648/625]], the major diesis, tuned pure in [[1/3-comma meantone]].
-If the fifth approximates the just interval [[3/2]], then the diesis or the negative diesis approximates the [[Pythagorean comma]]. In [[meantone]], the diesis also approximates [[128/125]], the augmented comma, which traditionally goes by the name of ''diesis''.
+* [[2048/2025]], the diaschisma, tuned pure in [[1/6-comma meantone]].
+* [[32805/32768]], the schisma, tuned pure in 1/12-comma meantone.
 == See also ==