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

For the chain of guitar schools of the same name, see Diesis (guitar fraternity).

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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References

^ Mathieu, W.A. (1997). Harmonic Experience: Tonal Harmony from its Natural Origins to its Modern Expression, Inner Traditions International. pp.225-226. ISBN 0-89281-560-4.

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References