Tuplets

Tap a steady beat and say "one-and, two-and": two syllables to each tap. Now, without changing the speed of your foot, say "tri-po-let, tri-po-let": three syllables to each tap. The beat has not moved; what changed is how it was divided. Simple meter divides the beat in two, and that third syllable does not fit any note value the meter normally uses. To write it, music has tuplets.

A group outside the normal division

A tuplet is a group of notes that does not follow the normal division of the measure or of its beats (Lacerda 1966, ch. XII). It is written with the same values the normal division uses, and a number over or under the group says how many notes it holds (Med 1996, ch. XXXII).

In two-four, each beat normally divides into two eighths. In the second measure, each beat holds three:

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The triplet

The most common tuplet is the triplet: three equal values in the place of two of the same kind (Med 1996, ch. XXXII). Three triplet eighths take the time of two eighths, so each lasts two thirds of a normal eighth (Blatter 2007, part 1, art. 4).

The same idea works on any value. Triplet quarters take the time of a half note:

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Triplet halves take the whole measure of four-four:

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And triplet sixteenths take the time of an eighth:

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How the group is marked

The number is set small, and some theorists want it in italics (Med 1996, ch. XXXII). When a beam already joins the group, the number is enough, as in the eighths above. When there is no beam, as in the triplet quarters and halves, a bracket shows where the group starts and ends. Lacerda allows a curved line instead, but prefers the bracket, because the curve can be mistaken for a slur (Lacerda 1966, ch. XII).

Some material brackets every group, beamed or not:

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The number sits on the side of the stems, next to the beam. When tuplets of the same value follow one another, not every group needs its number (Med 1996, ch. XXXII); here every group carries it.

Five, six, seven

Tuplets are named by the number of notes they hold (Lacerda 1966, ch. XII). After the triplet come the quintuplet, the sextuplet and the septuplet, commonly five, six or seven sixteenths in the time of four (Blatter 2007, part 1, art. 4):

Hear the passage♩ 84

Hear the passage♩ 84

A sextuplet can be heard in two ways, and its accents decide which: two groups of three, or three groups of two (Med 1996, ch. XXXII).

Hear the passage♩ 84

Hear the passage♩ 84

In groups of five or more, a very light secondary accent may be needed to make the group playable, and there is no rule for where it goes: it depends on the melody and on the performer (Lacerda 1966, ch. XII).

Which value a tuplet is written in depends on which normal division its count is closest to (Med 1996, ch. XXXII). Seven notes in a quarter are closer to eight thirty-seconds than to four sixteenths, so many composers write them as thirty-seconds (Blatter 2007, part 1, art. 4):

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Both septuplets sound the same. The second shows its ratio, 7:8, because the number alone would leave the reader doing arithmetic.

Fewer notes than the division: duplet and quadruplet

In compound meter the beat divides in three, and there the tuplet can go the other way. The duplet puts two notes in the time of three, and the quadruplet four in the time of three (Blatter 2007, part 1, art. 4):

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Med names the two directions. In an augmentative tuplet the number of notes grows, three in the place of two, five in the place of four, so the notes go faster than normal. In a diminutive one it shrinks, two in the place of three, and the notes go slower (Med 1996, ch. XXXII).

Unequal values and rests

A tuplet need not be made of equal values. It can mix longer and shorter notes, and include rests (Lacerda 1966, ch. XII). What matters is that the values add up to the group: a quarter and an eighth are the same three triplet eighths as three separate ones (Med 1996, ch. XXXII).

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A tuplet of equal values is called regular, and one of unequal values irregular (Med 1996, ch. XXXII). The values inside can also be subdivided, as long as they still add up (Blatter 2007, part 1, art. 4):

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The ratio

A number alone says how many notes there are, not in the time of how many. For the triplet everyone knows the answer; for rarer groups it is less clear. Since the middle of the twentieth century composers have written the ratio, the count and then the normal division: 3:2 is three in the time of two, 5:4 five in the time of four (Blatter 2007, part 1, art. 4). Contemporary scores use ratios such as 7:4, 7:5 and 11:10 (Med 1996, ch. XXXII).

The first example again, with the ratio on every group:

Hear the passage♩ 84

Names in other languages

Notes	English	French	German	Portuguese
2	duplet	duolet	Duole	duas-quiálteras
3	triplet	triolet	Triole	três-quiálteras, tercina
4	quadruplet	quartolet	Quartole	quatro-quiálteras
5	quintuplet	quintolet	Quintole	cinco-quiálteras
6	sextuplet	sextolet	Sextole	seis-quiálteras
7	septuplet	septolet	Septole	sete-quiálteras

The English, French and German names follow Med's list (Med 1996, ch. XXXII); the Portuguese ones follow Lacerda's rule of naming a group by its number of notes (Lacerda 1966, ch. XII). Lacerda notes that the Portuguese says "a tercina" or "três-quiálteras" for one group, never "três tercinas" (Lacerda 1966, ch. XII).

What comes next

A tuplet can also sound against a normal group in another voice, three against two, and Lacerda calls that simultaneity contra-ritmo (Lacerda 1966, ch. XII). That is where rhythm starts running in more than one layer at once: polyrhythm.