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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.
| | #redirect [[Diesis #As a diatonic interval category]] |
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| 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
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| * [[648/625]], the major diesis, tuned pure in [[1/3-comma meantone]].
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| * [[2048/2025]], the diaschisma, tuned pure in [[1/6-comma meantone]].
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| * [[32805/32768]], the schisma, tuned pure in 1/12-comma meantone.
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| == Generalization ==
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| 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.
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| == See also ==
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| * [[Diesis]] (disambiguation page)
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| * [[Chroma]]
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| [[Category:Terms]]
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| [[Category:MOS scale]]
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