Diesis (scale theory)

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)
• Chroma