In 1/4 comma meantone tuning, the diesis retains its value of 128:125. 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.
Some acoustics texts use the term Great Diesis for the difference between two 5:4 major thirds down and eight 3:2 fifths up, which is equal to two syntonic commas or about 43 cents. Being larger, this comma was termed "great" while the 128:125 comma was termed "lesser". But this "great diesis" is almost completely theoretical and almost never evoked in actual music, while the 128:125 "lesser diesis" is easily evoked and of great importance in Western harmony. Thus over time the term Great Diesis came to be frequently used for the 128:125 "lesser" comma. In short the terms are used in contradictory ways by various theorists and musicians.
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Last updated on Friday August 29, 2008 at 02:51:46 PDT (GMT -0700)
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