Most commonly, the beat is
represented in written music by the quarter-note, as in 2-4, 3-4, 4-4,
6-4 measure. 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. Compound measures are such as
contain more than two or three beats, and they must always be
multiplications, or groups, of a Simple measure; for whether so small
as to comprise only the fundamental groups of two or three beats (as in
2-4, 3-8, 3-4 measure), or so large as to embrace as many as twelve
beats or more (as in 4-4, 6-4, 6-8, 9-8, 12-8 measure), the measure
represents, practically, either the duple or triple species, Simple or
Compound. Thus, a measure of four beats, sometimes called (needlessly)
quadruple rhythm, is merely twice two beats; the species is actually
_duple_; the alternation of heavy and light pulses is regular; and
therefore the third beat is again an accent, as well as the first,
though _less heavy_. A measure of 6-8 is triple species, with accents
at beats one and four, precisely as if an additional vertical bar were
inserted after the third beat. In a word, then, the size of the
adopted measure is of no consequence, as long as it is retained
uniformly through the section to which it belongs; and there is no
_real_ difference between 2-4 and 4-4 measure, excepting in the number
of bars used.

A curious and rare exception to this rule of the compound measure
occurs when five o