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Section 4.5 Tuplets

Tuplet is a generic term that describes a grouping of notes that would not normally occur within a beat.
A quarter note naturally divides into two eighth notes or four sixteenth notes. A triplet is a grouping of three eighth notes that occurs within the span of the quarter note. A quintuplet would be a grouping of five sixteenth notes to occur within the span of one quarter note. It is not uncommon to see quintuplets, sextuplets, and septuplets.
An example with triplets, quintuplets, and sextuplets
If you write a piece of music that naturally has a triplet division to the beat, you should use \(\begin{smallmatrix}6\\8\end{smallmatrix}\), \(\begin{smallmatrix}9\\8\end{smallmatrix}\) or \(\begin{smallmatrix}12\\8\end{smallmatrix}\) depending on the number of beats in each measure.
Figure 4.5.1. Two measures that sound the same
In compound meter, a duplet is a grouping of two eighth notes to occur within the span of a dotted quarter note and a quadruplet is a grouping of four eighth notes to occur with the span of a dotted quarter note.
An example with duplets and quadruplets in compound meter, 6/8