Diesis (scale theory): Difference between revisions

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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]].

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

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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 &lt; 2:1)}} scales, it is the diminished mosstep. In [[hard]] {{nowrap|(L:s &gt; 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 &lt; 2:1)}} scales, it is the diminished mosstep. In [[hard]] {{nowrap|(L:s &gt; 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;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]].
 * [[2048/2025]], the diaschisma, tuned pure in [[1/6-comma meantone]].