DIESIS

:''This article is about the musical interval. For the use of ''diesis'' in typography, see Dagger (typography).''
A 'diesis' is a musical interval, usually meaning the difference between three justly tuned major thirds (tuned in the frequency ratio 5:4) and an octave (in the ratio 2:1), equal to 128:125 or about 41.06 cents. In 1/4 comma meantone the diesis retains its value of 128:125, and in other meantone tunings the defect from an octave, whatever it is, from three major thirds is the diminished second, sometimes also called a diesis. It is then the interval involved between pairs of notes which are enharmonic in equal temperament; for instance the interval between E and F♭, however large that is, is a diesis.
The word ''diesis'' has also been used to describe a large number of 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 around 90 cents. Other theorists have used it for various other intervals.
'See also:' ditonus.