In music a tuplet (also irrational rhythm or groupings, artificial division or groupings, abnormal divisions, irregular rhythm, gruppetto, extra-metric groupings, 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. The most common type is the "triplet".
The modern term 'tuplet' comes from a mistaken splitting of the suffixes of words like quintu(s)-(u)plet and sextu(s)-(u)plet, and from related mathematical terms such as "tuple", "-uplet" and "-plet", which are used to form terms denoting multiplets (Oxford English Dictionary, entries "multiplet", "-plet, comb. form", "-let, suffix", and "et, suffix1"). An alternative modern term, "irrational rhythm", was originally borrowed from Greek prosody where it referred to "a syllable having a metrical value not corresponding to its actual time-value, or ... a metrical foot containing such a syllable" (Oxford English Dictionary, entry "irrational"). The term would be incorrect if used in the mathematical sense (because the note-values are rational fractions) or in the more general sense of "unreasonable, utterly illogical, absurd".
Alternative terms found occasionally are "artificial division" (Jones 1974, 19), "abnormal divisions" (Donato 1963, 34), "irregular rhythm" (Read 1964, 181), and "irregular rhythmic groupings" (Kennedy 1994). The term "polyrhythm" (or "polymeter"), sometimes incorrectly used of "tuplets", actually refers to the simultaneous use of opposing time signatures. (Read 1964, 167)
Whereas normally two quarter notes (crotchets) are the same duration as a half note (minim), 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 (quavers) 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 2/3 their original duration. The triplet indication may also apply to notes of different values, for example a quarter note followed by one eighth note, in which case the quarter note may be regarded as two triplet eighths tied together (Gherkens 1921, 19).
Tuplet notation 
If the notes of the tuplet 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 (quintolet or pentuplet (Cunningham 2007, 111)) indicated with the numeral 5 means that five of the indicated note value total the duration normally occupied by four (or, as a division of a dotted note 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 3/8 or compound meters such as 6/8, 9/8, etc. time, a dotted quarter note). Some numbers are used inconsistently: for example septuplets (septolets or septimoles) usually indicate 7 notes in the duration of 4—or in compound meter 7 for 6—but may sometimes be used to mean 7 notes in the duration of 8 (Read 1964, 183–84). Thus, a septuplet lasting a whole note can be written with either quarter notes (7:4) or eighth notes (7:8). 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 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). This reflects the French usage of, for example, "six-pour-quatre" as an alternative name for the sextolet (Damour, Burnett, and Elwart 1838, 79; Hubbard 1924, 480).
There are disagreements about the sextuplet (pronounced with stress on the first syllable, according to Baker 1895, 177) or sestole or sestolet (Baker 1895, 177) or sextole (Baker 1895, 177) or sextolet (Baker 1895, 177; Cooper 1973, 32; Latham 2002; Shedlock 1876, 62, 68, 87, 93; Stainer and Barrett 1876, 395; Taylor 1879–89; Taylor 2001). This six-part division may be regarded either as a triplet with each note divided in half (2 + 2 + 2)—therefore with an accent on the first, third, and fifth notes—or else as an ordinary duple pattern with each note subdivided into triplets (3 + 3) and accented on both the first and fourth notes. Some authorities treat both groupings as equally valid forms (Damour, Burnett, and Elwart 1838, 80; Köhler 1858, 2:52–53; Latham 2002; Marx 1853, 114; Read 1964, 215), while others dispute this, holding the first type to be the "true" (or "real") sextuplet, and the second type to be properly a "double triplet", which should always be written and named as such (Kastner 1838, 94; Riemann 1884, 134–35; Taylor 1879–89, 3:478). Some go so far as to call the latter, when written with a numeral 6, a "false" sextuplet (Baker 1895, 177; Lobe 1881, 36; Shedlock 1876, 62). Still others, on the contrary, define the sextuplet precisely and solely as the double triplet (Stainer and Barrett 1876, 395; Sembos 2006, 86), and a few more, while accepting the distinction, contend that the true sextuplet has no internal subdivisions—only the first note of the group should be accented (Riemann 1884, 134; Taylor 1879–89, 3:478; Taylor 2001).
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). A duplet in compound time is more often written as 2:3 (a dotted quarter note split into two duplet eighth notes) than 2:1.5 (a dotted quarter note split into two duplet quarter notes), even though the former is inconsistent with a quadruplet also being written as 4:3 (a dotted quarter note split into two quadruplet eighth notes) (Anon. 1997–2000).
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.
Usage and purpose 
Traditional music notation favors duple divisions of a steady beat or time unit. A whole note (semibreve) divides into two half notes, a half note into two quarters, etc. and other notes are made by tying these together.
An irrational rhythm (by definition) is one that uses exact time points or durations that lie outside the scope of the duple system.
The n-tuplet notation shows the proportional increase or decrease of tempo needed for the bracketed notes, relative to the prevailing tempo. For example, a bracket labeled 5:4 (read five in the space of four) could group together durations (notes or rests) with a total of five sixteenth notes. A tempo 5/4 faster than usual then compresses these events into the space of four sixteenth notes.
The actual duration can be found by dividing the notated duration by the indicated tempo increase ((5/16)/(5/4) = 1/4, in this example).
Normally, the total duration of the bracketed notes is chosen to be exactly equal to the duration of one of the duple divisions. For the example of a 5:4 bracket, this is possible if the total bracketed duration has a 5 in its numerator, 5/16 in the example.
Sometimes though that requirement is dropped to create total durations not exactly expressible in the duple system. For example, one might have only three of the usual five sixteenth notes grouped by a bracket marked 3 of 5:4..
Tuplets may be counted, most often at extremely slow tempos, using the lowest common multiple (LCM) between the original and tuplet divisions. For example, with a 3-against-2 tuplet (triplets) the LCM is 6. Since 6/2=3 and 6/3=2 the quarter notes fall every three counts (overlined) and the triplets every two (underlined):
1 2 3 4 5 6
This is fairly easily brought up to tempo, and depending on the music may be counted in tempo, while 7-against-4, having an LCM of 28, may be counted at extremely slow tempos but must be played intuitively ("felt out") at tempo:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
- 1-2-3 / 1-2-3 / 1-2-3 / 1-2-3
The same principle can be applied to quintuplets, septuplets and so on.
See also 
|Look up tuplet in Wiktionary, the free dictionary.|
- Anon. 1997–2000. "Music Notation Questions Answered". Graphire Corporation, Graphire.com (Accessed 10 May 2013).
- Baker, Theodore (ed.). 1895. A Dictionary of Musical Terms. New York: G. Schirmer.
- Baker, Theodore, Nicolas Slonimsky, and Laura Dine Kuhn. 1995. Schirmer Pronouncing Pocket Manual of Musical Terms. New York: Schirmer Books. ISBN 0-8256-7223-6.
- Cooper, Paul. 1973. Perspectives in Music Theory: An Historical-Analytical Approach.. New York: Dodd, Mead. ISBN 0-396-06752-2.
- Cunningham, Michael G. 2007. Technique for Composers. Bloomington, Indiana: AuthorHouse. ISBN 1-4259-9618-3
- Damour, Antoine, Aimable Burnett, and Élie Elwart. 1838. Études élémentaires de la musique: depuis ses premières notions jusqu'à celles de la composition: divisées en trois parties: Connaissances préliminaires. Méthode de chant. Méthode d’harmonie. Paris: Bureau des Études élémentaires de la musique.
- Donato, Anthony. 1963. Preparing Music Manuscript. Englewood Cliffs, NJ: Prentice-Hall, Inc. Unaltered reprint, Westport, Conn.: Greenwood Press, 1977 ISBN 0-8371-9587-X.
- Gehrkens, Karl W. 1921. Music Notation and Terminology. New York and Chicago: The A. S. Barnes Company.
- Hubbard, William Lines. 1924. Musical Dictionary, revised and enlarged edition. Toledo: Squire Cooley Co. Reprinted as The American History and Encyclopedia of Music. Whitefish, Montana: Kessinger Publishing, 2005. ISBN 1-4179-0200-0.
- Humphries, Carl. 2002. The Piano Handbook. San Francisco, CA: Backbeat Books; London: Hi Marketing. ISBN 0-87930-727-7.
- Jones, George Thaddeus. 1974. Music Theory: The Fundamental Concepts of Tonal Music Including Notation, Terminology, and Harmony. New York, Hagerstown, San Francisco, London: Barnes & Noble Books. ISBN 0-06-460137-4.
- Lobe, Johann Christian. 1881. Catechism of Music, new and improved edition, edited and revised from the 20th German edition by John Henry Cornell, translated by Fanny Raymond Ritter. New York: G. Schirmer. (First edition of English translation by Fanny Raymond Ritter. New York: J. Schuberth 1867.)
- Kennedy, Michael. 1994. "Irregular Rhythmic Groupings. (Duplets, Triplets, Quadruplets)". Oxford Dictionary of Music, second edition, associate editor, Joyce Bourne. Oxford and New York: Oxford University Press. ISBN 0-19-869162-9.
- Köhler, Louis. 1858. Systematische Lehrmethode für Clavierspiel und Musik: Theoretisch und praktisch, 2 vols.. Leipzig: Breitkopf und Härtel.
- Latham, Alison (ed.). 2002. "Sextuplet [sextolet]". The Oxford Companion to Music. Oxford and New York: Oxford University Press. ISBN 0-19-866212-2.
- Marx, Adolf Bernhard. 1853. Universal School of Music, translated from the fifth edition of the original German by August Heinrich Wehrhan. London.
- Peckman, Jon. 2007. Picture Yourself Drumming: Step-by-Step Instruction for Drum Kit Setup, Reading Music, Learning from the Pros, and More. Boston, MA: Thomson Course Technology. ISBN 1-59863-330-9
- Read, Gardner. 1964. Music Notation: A Manual of Modern Practice. Boston: Alleyn and Bacon, Inc. Second edition, Boston: Alleyn and Bacon, Inc., 1969., reprinted as A Crescendo Book, New York: Taplinger Pub. Co., 1979. ISBN 0-8008-5459-4 (cloth), ISBN 0-8008-5453-5 (pbk).
- Riemann, Hugo. 1884. Musikalische Dynamik und Agogik: Lehrbuch der musikalischen Phrasirung auf Grund einer Revision der Lehre von der musikalischen Metrik und Rhythmik. Hamburg: D. Rahter; St. Petersburg: A. Büttner; Leipzig: Fr. Kistnet.
- Schonbrun, Marc. 2007. The Everything Music Theory Book: A Complete Guide to Taking Your Understanding of Music to the Next Level. The Everything Series. Avon, Mass.: Adams Media. ISBN 1-59337-652-9.
- Sembos, Evangelos C. 2006. Principles of Music Theory: A Practical Guide, second edition. Morrisville, NC: Lulu Press, Inc. ISBN 1-4303-0955-5.
- Shedlock, Emma L. 1876. A Trip to Music-Land: An Allegorical and Pictorial Exposition of the Elements of Music. London, Glasgow, and Edinburgh: Blackie & Son.
- Stainer, John, and William Alexander Barrett. 1876. A Dictionary of Musical Terms. London: Novello, Ewer and Co.
- Taylor, Franklin. 1879–89. "Sextolet". A Dictionary of Music and Musicians (A.D. 1450–1883) by Eminent Writers, English and Foreign, 4 vols, edited by Sir George Grove, 3:478. London: Macmillan and Co.
- Taylor, Franklin. 2001. "Sextolet, Sextuplet." The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan Publishers.