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
Rhythm (from Greek
Greek may refer to:
Greece
Anything of, from, or related to Greece, a country in Southern Europe:
*Greeks, an ethnic group.
*Greek language, a branch of the Indo-European language family.
**Proto-Greek language, the assumed ...
that involves dividing the
beat into a different number of equal
subdivisions from that usually permitted by the
time-signature
The time signature (also known as meter signature, metre signature, or measure signature) is a notational convention used in Western culture, Western musical notation to specify how many beat (music), beats (pulses) are contained in each measu ...
(e.g., triplets, duplets, etc.)" 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 of tuplet is the triplet.
Terminology
The modern term 'tuplet' comes from a
rebracketing
Rebracketing (also known as resegmentation or metanalysis) is a process in historical linguistics where a word originally derived from one set of morphemes is broken down or bracketed into a different set. For example, '' hamburger'', originally ...
of compound words like quintu(s)-(u)plet and sextu(s)-(u)plet, and from related mathematical terms such as "
tuple
In mathematics, a tuple is a finite ordered list (sequence) of elements. An -tuple is a sequence (or ordered list) of elements, where is a non-negative integer. There is only one 0-tuple, referred to as ''the empty tuple''. An -tuple is defi ...
", "-uplet" and "-plet", which are used to form terms denoting
multiplets (''Oxford English Dictionary'', entries "multiplet", "-plet, ''comb. form''", "-let, ''suffix''", and "-et, ''suffix''
1"). 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", "abnormal divisions", "irregular rhythm", and "irregular rhythmic groupings". The term "
polyrhythm
Polyrhythm is the simultaneous use of two or more rhythms that are not readily perceived as deriving from one another, or as simple manifestations of the same meter. The rhythmic layers may be the basis of an entire piece of music ( cross-rhyt ...
" (or "polymeter"), sometimes incorrectly used instead of "tuplets", actually refers to the simultaneous use of opposing time signatures.
Besides "triplet", the terms "duplet", "quadruplet", "quintuplet", "sextuplet", "septuplet", and "octuplet" are used frequently. The terms "nonuplet", "decuplet", "undecuplet", "dodecuplet", and "tredecuplet" had been suggested but up until 1925 had not caught on. By 1964 the terms "nonuplet" and "decuplet" were usual, while subdivisions by greater numbers were more commonly described as "group of eleven notes", "group of twelve notes", and so on.
Triplet
The most common tuplet is the triplet (German ''Triole'', French ''triolet'', Italian ''terzina'' or ''tripletta'', Spanish ''tresillo''). Whereas normally two
quarter notes (crotchets) are the same
duration as a
half note (minim), three (triplet) quarter notes have that same duration, so the duration of one of a triplet (three) quarter note is the
duration of a standard quarter note.
:
\new RhythmicStaff
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 their original duration.
:
\new RhythmicStaff
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.
:
\new RhythmicStaff
In some older scores, rhythms like this would be notated as a
dotted eighth note and a sixteenth note as a kind of shorthand presumably so that the beaming more clearly shows the beats.
Tuplet notation
Notation
Tuplets are typically notated either with a bracket or with a number above or below the
beam if the notes are beamed together. Sometimes, the tuplet is notated with a
ratio
In mathematics, a ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ...
(instead of just a number) — with the first number in the ratio indicating the number of notes in the tuplet and the second number indicating the number of normal notes they have the same duration as — or with a ratio and a note value.
:
Rhythm
Simple meter
For other tuplets, the number indicates a
ratio
In mathematics, a ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ...
to the next ''lower'' normal value in the prevailing meter (a
power of 2 in
simple meter). So a quintuplet (quintolet or pentuplet 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 or compound meters such as , , etc. time, a dotted quarter note).
:
\new RhythmicStaff
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. Thus, a septuplet lasting a whole note can be written with either quarter notes (7:4) or eighth notes (7:8).
:
\new RhythmicStaff
To avoid ambiguity, composers sometimes write the ratio explicitly instead of just a single number. 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. This reflects the French usage of, for example, "six-pour-quatre" as an alternative name for the ''sextolet''.
There are disagreements about the sextuplet (pronounced with stress on the first syllable, according to Baker—which is also called sestole, sestolet, sextole, or sextolet. 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. This is indicated by the beaming in the example below.
:
\new RhythmicStaff
Some authorities treat both groupings as equally valid forms, 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. Some go so far as to call the latter, when written with a numeral 6, a "false" sextuplet. Still others, on the contrary, define the sextuplet precisely and solely as the double triplet, 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.)
Compound meter
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 note
180px, Figure 1. An eighth note with stem extending up, an eighth note with stem extending down, and an eighth rest.
180px, Figure 2. Four eighth notes beamed together.
An eighth note ( American) or a quaver ( British) is a musical note pl ...
s (most often used in
meter) take the time normally totaled by three eighth notes, equal to a dotted quarter note. Four quadruplet (or quartole) 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.
:
\new RhythmicStaff
A duplet in compound time is more often written as 2:3 (a dotted quarter note split into two duplet eighth notes) than 2: (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 four quadruplet eighth notes).
Nested tuplets
On occasion, tuplets are used "inside" tuplets. These are referred to as ''nested tuplets''.
:
\new RhythmicStaff
Counting
Tuplets can produce rhythms such as the
hemiola or may be used as
polyrhythm
Polyrhythm is the simultaneous use of two or more rhythms that are not readily perceived as deriving from one another, or as simple manifestations of the same meter. The rhythmic layers may be the basis of an entire piece of music ( cross-rhyt ...
s when played against the regular duration. They are
extrametric rhythmic units. The example below shows sextuplets in quintuplet time.
:
<< \relative c' \\ \relative c'
>>
Tuplets may be
counted, most often at extremely slow tempos, using the
least common multiple (LCM) between the original and tuplet divisions. For example, with a 3-against-2 tuplet (triplets) the LCM is 6. Since and the quarter notes fall every three counts (overlined) and the triplets every two (underlined):
:
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:
:
To play a
half-note
''Half Note'' is a live album by saxophonist Clifford Jordan which was recorded in 1974 and first released on the SteepleChase label in 1985. (minim) triplet accurately in a
bar
Bar or BAR may refer to:
Food and drink
* Bar (establishment), selling alcoholic beverages
* Candy bar
* Chocolate bar
Science and technology
* Bar (river morphology), a deposit of sediment
* Bar (tropical cyclone), a layer of cloud
* Bar (un ...
of , count eighth-note triplets and tie them together in groups of four
:
<< \relative c' \\ \relative c'
>>
With a stress on each target note, one would count: 1 – 2 – 3 1 – 2 – 3 1 – 2 – 3 1 – 2 – 3 1
The same principle can be applied to quintuplets, septuplets, and so on.
Quadruplet figure in drumming
According to Jon Peckman, in
drumming, "quadruplet" refers to one group of three sixteenth-note triplets "with an extra
on-tuplet eighthnote added on to the end", thus filling one beat in time, with four notes of equal value. Shown below is a quadruplet with each note on a different drum in a
kit
Kit may refer to:
Places
*Kitt, Indiana, US, formerly Kit
* Kit, Iran, a village in Mazandaran Province
* Kit Hill, Cornwall, England
People
* Kit (given name), a list of people and fictional characters
* Kit (surname)
Animals
* Young animals:
...
used as a
fill.
:
\new Staff <<
\new voice \relative c'
\new voice \relative c''
>>
See also
*
Composite rhythm
*
Cross-beat
*
Duple and quadruple metre
*
Metre (hymn)
*
Metre (poetry)
In poetry, metre ( Commonwealth spelling) or meter ( American spelling; see spelling differences) is the basic rhythmic structure of a verse or lines in verse. Many traditional verse forms prescribe a specific verse metre, or a certain set ...
*
Metric modulation
*
List of musical works in unusual time signatures
*
Schaffel
*
Sextuple metre
*
Triple metre
Triple metre (or Am. triple meter, also known as triple time) is a musical metre characterized by a ''primary'' division of 3 beats to the bar, usually indicated by 3 ( simple) or 9 ( compound) in the upper figure of the time signature, with , , ...
References
Sources
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Further reading
*
Baker, Theodore,
Nicolas Slonimsky, and Laura Dine Kuhn. 1995. ''Schirmer Pronouncing Pocket Manual of Musical Terms''. New York: Schirmer Books. .
External links
*
{{DEFAULTSORT:Irrational Rhythm
Note values
de:Notenwert#Triole