Tuplet
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In music a tuplet (or irrational rhythm or, rarely, contrametric rhythm) is any consecutive group of notes whose note-values involve a fraction (other than a multiple of a power of 2). This is indicated by a number (or sometimes two), indicating the fraction involved. The notes involved are also often grouped with a bracket or (in older notation) a slur.
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[edit] Terminology
The modern term 'tuplet', predating but popularized by computer software, comes from the -tuplet suffix of names for individual tuplets: quintuplet, sextuplet, etc.[citation needed] Previously, there was no general term for these individual tuplets. The alternative modern term of 'irrational rhythm' is a misnomer as, in mathematical terminology, the note-values are rational (i.e. fractions), not irrational.
The term polyrhythm, sometimes incorrectly used to mean a tuplet, refers to the complex rhythm produced when non-tuplet rhythms are played against tuplets.
[edit] Explanation
The most common tuplet is the triplet (G. triole), shown at right.
Whereas normally two quarter notes are the same duration as a half note, three triplet quarter notes total that same duration, so the duration of a triplet quarter note is 2/3 the duration of a standard quarter note. Similarly, three triplet eighth notes are equal in duration to one quarter note. If several note values appear under the triplet bracket, they are all affected the same way, reduced to their original 2/3 duration.
[edit] Triplet notation
If the notes of the triplet are beamed together, the bracket (or slur) may be omitted and the number written next to the beam, as shown in the second illustration.
For other tuplets, the number indicates a ratio to the next lower power of two. So a quintuplet indicated with the numeral 5 means that five of the indicated note value total the duration normally occupied by four, equivalent to the second higher note value; for example, five quintuplet eighth notes total the same duration as a half note. Some numbers are used inconsistently: for example septuplets are sometimes used to mean 7 notes in the duration of 4, but other times to mean 7 notes in the duration of 8. To avoid ambiguity, composers sometimes write the ratio explicitly instead of just a single number, as shown in the third illustration; this is also done for more complex cases, e.g. 7:11.
In compound metre, even-numbered tuplets can indicate that a note value is changed in relation to the dotted version of the next higher note value. Thus, two duplet eighth notes (most often used in 6/8 meter) take the time normally totaled by three eighth notes, equal to a dotted quarter note. Four quadruplet eighth notes would also equal a dotted quarter note. The duplet eighth note is thus exactly the same duration as a dotted eighth note, but the duplet notation is more often used in compound meters.
[edit] Usage and purpose
Tuplets can produce rhythms such as the hemiola, or may be used as polyrhythms when played against the regular duration. They are extrametric rhythmic units.
[edit] See also
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