Suomeksi | In English

Tuplets

A note value, beat, or part of a beat can be divided into a number of irregular time values. For example, a crotchet can be divided into three, five, six, or seven parts. Moreover, a dotted crotchet can be divided into two, four, five, seven or another number of parts. The division names derive from the Latin numerals:

duplet (2)
triplet (3)
quadruplet (4)
quintuplet (5)
sextuplet (6)
septuplet (7)
octuplet (8)
nontuplet (9)
etc.

The word tuplet is common in American English.

The basic notation for tuplets is presented in the examples below. Subdivisions can be written with a number if the notes are beamed. With time values longer than the quaver, a tie or bracket can be used; the bracket is preferred as a tie can be mistaken for a legato slur.

The time values for tuplets are usually chosen to produce, when combined, a longer duration than the time value to be divided. Bars 4 and 5, however, show that it is possible to deviate from this rule. For example, Bartok and other 20th century composers wrote a duplet in quavers when the time signature was 3/8. They are more comprehensible to a musician than crotchets. Moreover, a 2/4 time signature uses quavers even though a crotchet may be divided into two or three.

 

Bar 4 shows that two quadruplets with an equal duration can be written in two different time values (a and b). The latter form is familiar from textbooks; the combined time values of the duplet exceed their actual duration. Composers have used both notations, and version a) is now more common. It is customary to also state the numerical ratio, where the latter number shows how many time values of the duplet are normally included in the part of the beat in question.

All examples of bar 5 apply the same time value. The bottom bar could use semiquavers or sixteenth notes; the symbol would then be 8:10 (or 4:5). The time value symbol after the note is common in modern art music, where duplets can include further irregular subdivisions.

Basic time values have the relationship 1:2:4:8:16 or semibreve, minim, crotchet (whole note, half note, quarter note), and so on. It is commonplace, however, that the durations have a relationship of 3:2 (triplet) or 2:3 (duplet). These tuplets can be written without numbers if the time signature allows.

The example below shows three time values on the top line and a corresponding set of two time values on the bottom line. Bars 1 and 2 show that a duplet has two fixed notations for the time values: the first notation is today more common; the second notation is used, for example, if a quadruplet is written in crotchets. The 6/8 time signature often uses dotted quavers instead of duplets.

The 3:2 relationship manifested in different time signatures:

Bar 4 shows a typical way of writing simple polymetre (or bimeter) in which a bar is divided into two and three parts of equal size. Bars 5 and 6 show tuplets (triplets) written on the top staves to correspond with the basic perfect time values indicated in the time signatures.

Successive time signatures 3/4 and 6/8 also illustrate the bimeter formed by the 3:2 relationship. You can experiment by playing the example below several times so that you hear three accents in the former and two accents in the latter.

The 1/16 figure below can help you to perceive a quadruplet; the bottom notes lie in line with the quadruplet notes. In popular music with African-American origins, a quadruplet is often written in successive dotted notes.

When a quadruplet extends past the barline, it is wise to use dotted time values:

In the example below, each bar has three time values on the top staves and four time values on the bottom staves. Like the duplet and triplet, the only time signatures to show the 4:3 relationship without the quadruplet or triplet symbol are the 6/8 and 12/8 time signatures.

The 4:3 relationship manifested in different time signatures:

This example shows that different notations can be used to describe musical events, producing a similar auditory experience. It also illustrates one of the specific challenges of traditional notation, the difficulty of describing polymeter in a readable and comprehensible manner. A crowd of tuplets produces unreadable rhythm; it would be more intelligible to express duration with a specific time signature.

Metric modulation

The term metric modulation is related to modern art music and Elliot Carter's compositions. The same phenomenon was, however, present in the change of time values/tactus in Renaissance music.

In metric modulation, the time value of the pulse changes and causes an abrupt change in the tempo. For example, if a triplet rhythm is perceived to consist of sets of two successive quavers and when this becomes the new beat unit, we have a metric modulation:

At the beginning, the tempo is 120 MM. In the second bar, we have six notes instead of four (a slow triplet written out). A new tempo derived from these triplet parts is 180 MM. The notation above the staff is common when the new tempo can easily be derived from the previous tempo. It is wise to give a new time signature, for example 6/8, if the alternative would be to continue writing as in bar 2. The new tempo in this context is actually 60 MM; in this time signature, a dotted crotchet is the typical beat unit.