Diesis

In classical music from Western culture, a diesis (/ˈdaɪəsɪs/ DY-ə-siss or enharmonic diesis, plural dieses (/ˈdaɪəsiz/ DY-ə-seez),[1] or "difference"; Greek: δίεσις "leak" or "escape"[2][a] is either an accidental (see sharp), or a very small musical interval, usually defined as the difference between an octave (in the ratio 2:1) and three justly tuned major thirds (tuned in the ratio 5:4), equal to 128:125 or about 41.06 cents.

[3][failed verification] In any tuning system, the deviation of an octave from three major thirds, however large that is, is typically referred to as a diminished second.

In quarter-comma meantone, since major thirds are justly tuned, the width of the diminished second coincides with the above-mentioned value of 128:125.

The word diesis has also been used to describe several distinct intervals, of varying sizes, but typically around 50 cents.

Philolaus used it to describe the interval now usually called a limma, that of a justly tuned perfect fourth (4:3) minus two whole tones (9:8), equal to 256:243 or about 90.22 cents.