But the composer is at liberty to adopt any value he pleases (8th, 16th, half-note) as beat.

In the first study in Clementi's "Gradus ad Parnassum," the time-signature is 3-1, the whole note as beat; in the 8th Sung Without Words it is 6-16, the sixteenth note as beat; in the last pianoforte sonata of Beethoven (op.

111), last movement, the time-signatures are 9-16, 6-16, and 12-32, the latter being, probably, the smallest beat ever chosen.
MEASURES .-- A measure is a group of beats.

The beats are added together, in measures, to obtain a larger unit of time, because larger divisions are more convenient for longer periods; just as we prefer to indicate the dimensions of a house, or farm, in feet or rods, rather than in inches.
Measures differ considerably in extent in various compositions, inasmuch as the number of beats enclosed between the vertical bars may be, and is, determined quite arbitrarily.

What is known as a Simple measure contains either the two beats (heavy-light) of the fundamental duple group, or the three beats (heavy-light-light) of the triple group, shown in the preceding chapter.