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In music a tuplet (also irrational rhythm, artificial division, abnormal divisions, irregular rhythm, or, rarely, contrametric rhythm) is "any rhythm that involves dividing the beat into a different number of equal subdivisions from that usually permitted by the time-signature (e.g. triplets, duplets, etc.)" (Humphries 2002, 266). 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.
[edit] TerminologyThe modern term 'tuplet' comes from a mistaken reading of the -plet, -let, or -et suffixes of words like tri-plet, quadru-plet, quintu-plet, sextu-plet, etc., and from the mathematical terms "tuple", "-uplet", and "-plet", which are used with prefixed numerals to form terms denoting multiplets having the specified number of members (Oxford English Dictionary, entries "multiplet", "-plet, comb. form", "-let, suffix", and "et, suffix1"). The alternative modern term of 'irrational rhythm' would be a misnomer if it were used either in the mathematical sense (because the note-values are rational fractions), or in the more general sense of "unreasonable, utterly illogical, absurd". However, this musical term was originally borrowed from Greek prosody, where it meant "a syllable having a metrical value not corresponding to its actual time-value, or of a metrical foot containing such a syllable" (Oxford English Dictionary, entry "irrational"). Other alternative terms found occasionally are "artificial division" (Jones 1974, 19), "abnormal divisions" (Donato 1963, 34), and "irregular rhythm" (Read 1964, 181). The term "polyrhythm" (or "polymeter"), sometimes incorrectly used to mean a tuplet, refers to the complex rhythm produced by the simultaneous use of opposing time signatures (Read 1964, 167). [edit] ExplanationThe most common tuplet is the triplet (Ger. triole, Fr. triolet, It. tripletta), shown at right.  Tuplet: a standard triplet; a triplet denoted without a bracket; a tuplet denoted as a ratio 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 notationIf 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 normal value in the prevailing meter. So a quintuplet indicated with the numeral 5 means that five of the indicated note value total the duration normally occupied by four (or, in compound time, three), equivalent to the second higher note value; for example, five quintuplet eighth notes total the same duration as a half note (or, in compound time, a dotted quarter 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 (Read 1964, 184). 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 cases like 7:11, where the validity of this practice is established by the complexity of the figure. A French alternative is to write pour ("for") or de ("of") in place of the colon, or above the bracketed "irregular" number (Read 1964, 219–21).  In compound meter, 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 far more common in compound meters (Jones 1974, 20). In drumming, "quadruplet" refers to one group of three sixteenth-note triplets "with an extra [non-tuplet eighth] note added on to the end", thus filling one beat in 4/4 time (Peckman 2007, 127–28), with four notes of unequal value. [edit] Usage and purposeTuplets can produce rhythms such as the hemiola, or may be used as polyrhythms when played against the regular duration. They are extrametric rhythmic units. Traditional music notation privileges duple divisions of a steady beat or prevailing time unit. A whole note divides into two half notes, a half note into two quarters, etc. Up to any given tolerance, by tying together sufficiently many notes, purely duple notation can express any time point or duration. An irrational rhythm occurs when a musical score indicates an exact time point or duration that lies outside the scope of the duple system. Rather than specifying the new tempo by means of a metronome marking, the prevailing notation indicates the proportional increase or decrease relative to the prevailing tempo. For example, a bracket labeled 5:4 (read five in the space of four) might group together durations (occurring as a sequence of notes and rests) that total to the equivalent of, say, five sixteenth notes. A tempo 5/4 faster than usual then compresses these events into the space of four sixteenth notes. While, in principle, one can increase the pace of any sequence of rhythmic events by 20%, the completion of an irrational rhythm will usually return the count to the duple system. For this to occur with a 5:4 bracket, the total bracketed duration must have a 5 in its numerator, 5/16 in the example. Note that one obtains the actual duration of the bracketed events by dividing two fractions, the notated duration and the indicated tempo increase, (5/16)/(5/4) = 1/4, in this example. Another variant involves a tempo increase that does not return to the original duple rhythm framework. For example, one might have merely three sixteenth notes grouped by a bracket marked 3 of 5:4. [edit] Practical considerationsTo play a half-note (minim) triplet accurately in a bar of 4/4, count eighth-note triplets and tie them together in groups of four. With a stress on each target note, one would count:
The same principle can be applied to quintuplets, septuplets and so on. [edit] See also
[edit] References
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