8. A Scale is a succession of notes arranged according to some regular plan. Many different kinds of scales have been used at various times and in different parts of the world; in modern European music only two are employed, which are called the diatonic and the chromatic scale.
9. The word "diatonic" has been already explained in § 6 as meaning "through the degrees." A diatonic scale is a succession of notes in which there is one note, neither more nor less, on each degree of the staff—that is to say, on each line and space. The way in which the scales are constructed will be explained later (see Chapter III.); at present we simply give the forms of them. There are two varieties of the diatonic scale, known as major (or greater) and minor (or less) scale from the nature of the interval between the first and third notes of the scale.
MAJOR SCALE.
MINOR SCALE.
Other forms of the minor scale frequently to be met with will be explained later. It will be seen that each of these scales contains only seven different notes. This is because the eighth note, or octave (Latin, "octavus" = eighth), is a repetition of the first note at a different pitch; and from this note the series recommences.
10.—The scientific reason why octaves resemble each other so much more closely than two notes at any other interval is that the upper of two notes at a distance of an octave from one another is the first "upper-partial" tone (§ 36) of the lower, and that all its harmonics are also harmonics of the lower note; therefore, the "compound tone" (Chapter II., § 40) of the higher note contains no new sound, which is not also in the compound tone of the lower note. The higher note is merely the reinforcement of certain upper-partials of the lower note; but this is not the case with two notes at any other interval than the octave, or, of course, the double octave, &c.
11. A chromatic scale is a scale consisting entirely of semitones, and it is called chromatic because some of its notes require accidentals (flats or sharps) before them (§ 6).
As will be explained later, the chromatic scale is frequently written in a different way from that here given; but, however written, it equally consists of semitones.
