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, 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 | 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]]. | ||
Revision as of 14:47, 25 November 2024
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 (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 vanishes.
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 commas 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.
See also
- Diesis (disambiguation page)