Diesis
Diesis is a term from the Greek for very small distances between notes, smaller than a semitone. In tuning theory the minor diesis means the remainder by which three pure major thirds stacked on one another fall short of the octave. It measures about 41 cents.
- Pure major third
- ratio 5:4, about 386 cents
- Three major thirds
- about 1159 cents
- Octave
- 1200 cents
- Minor diesis
- difference, about 41 cents (128:125)
- In Italian
- diesis = sharp sign
Three thirds, no octave
If you stack three pure major thirds you have the ratio 5/4 · 5/4 · 5/4 = 125/64. The octave would be 128/64. The chain of thirds therefore stays below the octave by 128:125. Expressed in cents that is about 41. This is the minor diesis.
Three major thirds from C: C – E – G♯ – B♯
In pure tuning the B♯ (marked) would be about 41 cents lower than the C above. On the piano the difference disappears: B♯ and C are the same key, equal temperament distributes the remainder over all thirds.
For comparison: the octave C – C
The octave 2:1 is pure. The diesis is the gap between the B♯ of the chain of thirds and this C.
In the glossary: Pythagorean comma · Perfect intervals · Enharmonic equivalence
| Calculation | Cents |
|---|---|
| One pure major third (5:4) | 386.3 |
| Three pure major thirds | 1158.9 |
| Octave (2:1) | 1200 |
| Difference = minor diesis | 41.1 |
What it says about tuning
In tuning theory the diesis explains why pure intervals cannot be chained together at will without contradictions arising: the pure third and the pure octave cannot both be kept exactly in every key. Equal temperament solves this problem by distributing such remainders evenly over the twelve semitones and so letting every third deviate from the pure third by a small amount.
Distinctions
The diesis is not the same as the commas of tuning theory. All are small remainders, but they differ in origin and size. The Pythagorean comma (about 23.5 cents) arises from the chain of twelve pure fifths, the syntonic comma (about 21.5 cents) from the difference between the Pythagorean and the pure major third. The minor diesis arises from the chain of three pure major thirds.
In present-day Italian diesis simply denotes the sharp sign. Both meanings go back to the same word stem but mean different things.
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Related terms
Pythagorean commaPerfect intervalsEnharmonic equivalenceCommaThird
Editor: Maik Krohm · reviewed on 3 October 2026
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