BEATS.—The beats are the units in our System of Measurement,—as it were, the inches upon our yardstick of time; they are the particles of time that we mark when we "count," or that the conductor marks with the "beats" of his baton. Broadly speaking, the ordinary beat (in moderate tempo) is about equivalent to a second of time; to less or more than this, of course, in rapid or slow tempo. 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 or seven beats are grouped together. This involves a mingling of the duple and triple species, and, consequently, an irregular disposition of the accents; for instance, 5-4 measure is either 3+2 or 2+3 beats, with corresponding accentuation:

[Illustration: Beat accentuation]

RHYTHM.—This word signifies arrangement,—a principle applied, in music, to the distribution or arrangement of the tones according to their various time-values. The system of measurement (or metric system) furnishes tone material with all the details of division, proportion and comparison; but this, alone, is not rhythm. The metric system affords the basis for rational and definable rhythm, but "rhythm" itself does not enter into the proposition until differentiated factors are associated and opposed to each other.

[Illustration: Example 3. Rhythm.]

The first measure of this hymn is, by itself, merely an exponent of the metric principle, for it consists of three uniform quarter-notes. The second measure, however, is a rhythmic one, because, by dotting the first of the three beats, three different time-values are obtained (dotted quarter, eighth, and quarter). Further, by association and comparison with each other, both measures assume a collective rhythmic significance.

The rhythmic disposition of the tones is to a certain extent optional with the composer, but by no means wholly so; the rules of rhythm are probably the most definite and obvious of all the rules of music writing. They do not concern the analytical student intimately, but at least the general distinction between regular and irregular rhythm should be understood:—We have seen that the natural accent (the "heavy" pulse) is invariably represented by the first beat of a rhythmic group; and that one or two lighter pulses intervene before the next accent appears. Further, it is self-evident that the rhythmic weight of a tone is proportionate to its length, or time-value; longer tones produce heavier, and shorter tones lighter, impressions. The deduction from these two facts is, then, that the rhythmic arrangement is regular when the comparatively longer tones occupy the accented beats, or the accented fractions of the beats; and irregular when shorter tones occupy the accents, or when longer tones are shifted to any comparatively lighter pulse of the measure or group.

The rhythm of the second measure in Ex. 3 is regular, because the longest tone stands at the beginning of the measure, thus confirming (and, in fact, creating) the accent. The rhythm in Ex. 1 is also regular, throughout, the light eighth-notes occupying the light third beat, and the heavy dotted-quarter the heavy pulse (in the third measure). Ex. 2 is strikingly definite in rhythm, because the time-values are so greatly diversified; and the arrangement is regular.

On the other hand, the following is an example of irregular rhythm:

[Illustration: Example 4. Fragment of Beethoven.]

The longer (heavier) tones are placed in the middle of the measure, between the beats; the tie at the end of measure 3 places the heavy note at the end, instead of the beginning, of the measure, and cancels the accent of the fourth measure. These irregular forms of rhythm are called syncopation. See also Ex. 6, second Phrase.

MELODY.—Any succession of single tones is a melody. If we strike the keys of the piano with two or more fingers of each hand simultaneously, we produce a body of tones, which—if they are so chosen that they blend harmoniously—is called a Chord; and a series of such chords is an illustration of what is known as Harmony. If, however, we play with one finger only, we produce a melody. The human voice, the flute, horn,—all instruments capable of emitting but one tone at a time,—produce melody.

Melody constitutes, then, a line of tones. If, as we have said, Time is the canvas upon which the musical images are thrown, Melodies are the lines which trace the design or form of these images. This indicates the extreme importance of the melodic idea in music form. Without such "tone-lines" the effect would be similar to that of daubs or masses of color without a drawing, without the evidence of contour and shape.

A good melody, that is, a melody that appeals to the intelligent music lover as tuneful, pleasing, and intelligible, is one in which, first of all, each successive tone and each successive group of tones stands in a rational harmonic relation to the one before it, and even,