It is often useful to subdivide the beat into two or three parts. This can help us perform complicated rhythms. By feeling and counting the proper subdivision we can place notes with precision and confidence.
A triplet is three notes in the place of two. It is indicated by a 3 placed over the notes. Sometimes the bracket is omitted.

A duplet is indicated by a 2 and is two notes in the place of three. The examples at the left are two ways to notate the same rhythm, albeit with different time signatures. In 4/4 time, divide the quarter note into thirds to find the subdivision of the triplet. In 6/4 time, divide the quarter note in half.

Below is an excerpt from Beethoven. The time signature is Common Time. The 3's indicating the triplet eighth notes are only included in the first measure. Here the main theme enters on the fourth beat with stems up. Its rhythm is related to the duple subdivision of the beat. The dotted eighth note is equal to three sixteenths, plus the sixteenth-note makes a division of four. The red numbers reflect the least common denominator for the two subdivisions - 12.
Although it appears, visually, that the sixteenth note is about halfway between the last note of the triplet figure and the next measure, you can see that the two notes actually occur on successive twelfths of a beat!

The top example to the left (quadruplet) is 4 in the place of 3. All of the examples to the left would sound like four even notes, each 1/2-second long.

Any number of notes may be grouped together. Remember that the number tells how many notes TAKE THE PLACE OF ANOTHER NUMBER. Sometimes the other number takes some calculation.

Except for duplets (2 in place of 3), the number of notes to be replaced is USUALLY LESS than the number given.

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