Diesis

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For the short film of the same name, see Diesis (Short Film).
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

First an octave, C to C, is played (2:1). Then three major thirds (5:4): C, E, G♯, B♯. The 2:1 octave C and the 125:64 B♯ are then compared. The difference, 128:125, is the diesis comma.
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[edit] See also

[edit] References

  1. ^ 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.