Diesis
- This article is about the musical interval. For the use of diesis in typography, see Dagger (typography).
A diesis is a comma type of 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 12-tone equal temperament, on a piano for example, three major thirds in a row equal an octave, but three justly-tuned major thirds fall quite a bit flat of an octave, and the diesis describes the amount by which they are flat.
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.[1]
Diesis (128:125) demonstration
See also
References
- Mathieu, W.A. (1997). Harmonic Experience: Tonal Harmony from its Natural Origins to its Modern Expression. Inner Traditions International, 225-226. ISBN 0-89281-560-4.
Source: adapted by the editor from Wikipedia, the free encyclopedia; from the article "Diesis". Image Credit.
