Diesis

Diesis (128:125) demonstration

The octave C-C′, the three justly tuned major thirds C-E-G♯-B♯ and the descending diesis C′-B♯ are played (see example).

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In classical music from Western culture, a diesis (⫽ˈdaɪəsɪs⫽ DY-ə-siss or enharmonic diesis, plural dieses (⫽ˈdaɪəsiz⫽ DY-ə-seez),^[1] or "difference"; Greek: δίεσις "leak" or "escape"^[2][a] is either an accidental (see sharp), or a very small musical interval, usually defined as the difference between an octave (in the ratio 2:1) and three justly tuned major thirds (tuned in the ratio 5:4), 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 narrow of an octave, and the diesis describes the amount by which they are short. For instance, an octave (2:1) spans from C to C′, and three justly tuned major thirds (5:4) span from C to B♯ (namely, from C, to E, to G♯, to B♯). The difference between C-C′ (2:1) and C-B♯ (125:64) is the diesis (128:125). Notice that this coincides with the interval between B♯ and C', also called a diminished second.

As a comma, the above-mentioned 128:125 ratio is also known as the lesser diesis, enharmonic comma, or augmented comma.

Many acoustics texts use the term greater diesis^[2] or diminished comma for the difference between an octave and four justly tuned minor thirds (tuned in the ratio 6:5), which is equal to three syntonic commas minus a schisma, equal to 648:625 or about 62.57 cents (almost one 63.16 cent step-size in 19 equal temperament). Being larger, this diesis was termed the "greater" while the 128:125 diesis (41.06 cents) was termed the "lesser".^{[3][failed verification]}

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