Diesis: Difference between revisions

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== As a diatonic interval category ==

In the [[5L 2s|diatonic]] scale, the diesis, more specifically '''enharmonic diesis''', is ~~the distance between two [[enharmonic]] notes in~~ a ~~scale. In terms of diatonic degrees, it is the~~ diminished second or inverse diminished second, whichever is positive in size. 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.

In the [[5L 2s|diatonic]] scale, the diesis, more specifically '''enharmonic diesis''', is a diminished second or inverse diminished second, whichever is positive in size. 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 ===

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=== 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.

== Normal diesis ==

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 == As a diatonic interval category ==
-In the [[5L 2s|diatonic]] scale, the diesis, more specifically '''enharmonic diesis''', is the distance between two [[enharmonic]] notes in a scale. In terms of diatonic degrees, it is the diminished second or inverse diminished second, whichever is positive in size. 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.
+In the [[5L 2s|diatonic]] scale, the diesis, more specifically '''enharmonic diesis''', is a diminished second or inverse diminished second, whichever is positive in size. 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 ===
@@ Line 30: / Line 30: @@
 === 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.
 == Normal diesis ==