# Tuplets in music

Anybody out there familiar with tuplets? I understand the concept behind them but I've been told that a duplet plays an opposite role from the other types of tuplets (fitting 2 smaller notes in the place of 3, instead of 2 notes in the place of one) why is this? And are there any other types of tuplets that follows this "opposite" pattern ?

There's some terminology confusion here. A tuplet is simply fitting some number of notes in the space of another amount of notes. You can always represent a tuplet as some kind of ratio.

A duplet is a specific kind of tuplet where 2 notes take up the space typical given to 3 and is represented as a 2:3 ratio. A triplet is a specific kind of tuplet where 3 notes take up the space typical given to 2 and is represented as a 3:2 ratio. As you can see the duplet and the triplet are highly related and have there ratios reversed showing they are complementary operations.

There are many(if not infinite) tuplets and if the ratio is reversed, the idea is the same. Here is a picture of a 5:4 tuplet (known as a quintuplet) and a 4:5 tuplet: As you can see when reversing the tuplet the results are much different.

• I've never seen anything like your second bar example. It looks very confusing to me or, at least, far from obvious. Do you know of any mainstream pieces where such a thing has been used? – JimM Mar 5 '17 at 10:07
• Where a tuplet group replaces a beat (or possibly two beats) a single number may be understandable. The 4:5 example above certainly needs the full ratio to be shown. – Laurence Payne Mar 5 '17 at 11:41

It's only opposite in that the length relationships are reversed. Instead of (for example) "three in the space of two" one has "two in the space of three." The underlying pulse is the same. For example, in 2/4 time with quarter note=120, the basic rate is 1 measure (2 quarter notes) per second. A quarter note triplet would have 3 quarter notes per second for the duration of the triplet notation (assuming three quarter notes per half note). The reverse of the previous procedure would be to write two notes (usually half notes) in the space of three (perhaps in a 3/4 measure.) Of course, one could write dotted quarters (or even use tied quarter-eighth and eighth-quarter patterns) to achieve the same note relations. I'd probably do the latter for two in the space of three, but other triplets (5 in the space of 4 or 2 or 1 or 4 in the space of 3 or the like) are often done with tuplets.

The main purpose of tuplets is to fit notes that cannot be represented by a power of two. Duplets are sort of an odd-man out here since they always can actually be written without resorting to tuplets in the power-of-2 based modern notation (mensural notation, in contrast, could have something like three semibreve notes per breve), so their main use is to picture the nature of a strong counterrhythm more vividly.

Apart from duplets, the usual convention is to put in more notes in a tuplet than usual, but not more than twice as many. However, this rule becomes shaky for septuplets: some composers prefer writing with a ratio of 7:8 rather than 7:4. When getting into such larger ratios, it is not unusual to indeed write "7:4" (a colonized fraction) as the tuplet indication rather than just "7". With more esoteric tuplets, this explicit notation becomes more common.