Schisma
The smallest interval considered in tuning theory, a twelfth of the syntonic comma.
What it means
The schisma is one of the smallest intervals that plays any role at all in tuning theory: the tiny difference between the syntonic comma and the Pythagorean comma. It amounts to only a little over two cents and is thus practically imperceptible to the human ear as a pitch difference.
Numerically, the schisma arises when twelve pure fifths are stacked and the result is compared with eight pure octaves plus one pure major third — the extremely small remainder left over is the schisma.
Musical use
In practice, the schisma serves mainly as a calculating quantity in tuning theory, explaining why certain enharmonically equated pitches — such as B-sharp and C — do not match exactly in just intonation but only up to this tiny leftover interval. Certain historical tuning systems, so-called schismatic temperaments, deliberately exploit this small difference to allow for nearly pure fifths and thirds.
Because the schisma is so small, it is never consciously heard in ordinary music-making and remains a theoretical quantity for music theorists and tuning researchers.
The schisma should be distinguished from the syntonic comma and the Pythagorean comma, the two considerably larger commas whose difference produces it in the first place, and from the diesis, another small but likewise larger remainder used in tuning theory.