Dots and ties give you much freedom to write notes of varying lengths, but so far you must build your notes from halves of other notes. If you want to divide a note length into anything other
than halves or halves of halves - if you want to divide a beat into thirds or fifths, for example - you must write the number of the division over the notes. These unusual subdivisions are
called borrowed divisions because they sound as if they have been borrowed from a completely different meter. They can be difficult
to perform correctly and are avoided in music for beginners. The only one that is commonly used is triplets, which divide a note length into equal thirds.
Figure 1.62 Some Borrowed Divisions
Any common note length can be divided into an unusual number of equal-length notes and rests, for example by dividing a whole note into three instead of two "half" notes. The notes are
labeled with the appropriate number. If there might be any question as to which notes are involved in the borrowed division, a bracket is placed above them. Triplets are by far the most
common borrowed division.
Figure 1.63 Borrowed Duplets
In a compound meter (Section 1.2.4), which normally divides a beat into three, the borrowed division may divide the beat into two, as in a simple meter. You may also see duplets in swing
Notes in jazzy-sounding music that has a "swing" beat are often assumed to be triplet rhythms, even when they look like regular divisions; for example, two written eighth notes (or a dotted
quartersixteenth) might sound like a triplet quarter-eighth rhythm. In jazz and other popular music styles, a tempo (Section 1.2.8) notation that says swing
usually means that all rhythms should be played as triplets. Straight means to play the rhythms as written.
Note: Some jazz musicians prefer to think of a swing rhythm as more of a heavy accent on the second eighth, rather than as a triplet rhythm, particularly
when the tempo is fast. This distinction is not important for students of music theory, but jazz students will want to work hard on using both rhythm and articulation to produce a convincing
Figure 1.64 Swing Rhythms
Jazz or blues with a "swing" rhythm often assumes that all divisions are triplets. The swung triplets may be written as triplets, or they may simply be written as "straight" eighth notes
or dotted eighth-sixteenths. If rhythms are not written as triplets, the tempo marking usually includes an indication to "swing", or it may simply be implied by the style and genre of the