Comma

What it means

A comma is a very small interval difference that arises because different paths through the tonal system do not lead exactly to the same note.

Musical use

Two commas are especially important. The Pythagorean comma is the difference between twelve stacked pure fifths and seven octaves: the circle of fifths does not close but ends somewhat higher than it began. The syntonic comma is the difference between the major third that results from four pure fifths and the pure major third in the ratio 5:4; the former is noticeably wider than the latter.

From this excess it follows that no tuning system can have all intervals pure. Each distributes the difference differently: meantone tuning narrows the fifths to get many thirds pure, and accepts unusable remote keys in exchange. Well-tempered tunings distribute unequally, so that all keys stay playable and each retains a character of its own. Equal temperament distributes evenly over all twelve fifths: each is slightly too narrow, every major third noticeably too wide, but every key sounds alike in exchange.

For instruments with flexible intonation the comma remains a living quantity: a G♯ as a leading tone lies higher there than an A♭ as a lowered degree, although the piano plays both alike.

The Pythagorean comma arises between twelve pure fifths and seven octaves, the syntonic comma between four pure fifths and a pure major third plus two octaves.

Other names

Comma is the Latin and English form of the word. In the theory of temperament it stands for the small differences between purely calculated intervals, for instance the Pythagorean and the syntonic comma; in vocal notation, by contrast, a comma-shaped sign means a breath mark. Which meaning applies follows from the context.

Performance practice

When intonating, rely on beats instead of on displays: when a sonority is pure, it becomes calm. Take leading tones close to their goal and major thirds rather low. And do not be surprised if a passage deviates slightly from the piano — in an ensemble without a keyboard instrument, the purer solution is the right one.