5. The smallest interval used in music is called a semitone. [1] We may define a Semitone, as the distance between any one note, and the nearest note to it, above or below, on any instrument which has only twelve sounds in the octave. For example, on the piano, the nearest note to C is B on the one side (below), and C♯ on the other side (above). From B to C, and from C to C♯ are therefore both semitones. Similarly from F♯ to F♮, and from F♯ to G will be semitones; but from G to A will not be a semitone; for A is not the nearest note to G; G♯ (or A♭), comes between them.
6. If the semitones on each side of C be compared,
it will be seen that there is a difference between them. C and B are on two different places of the staff; one is on a line and the other on a space; but C and C♯ are both on the same place in the staff; but the latter note has an accidental before it. A semitone of which the two notes are on different degrees of the staff is called a diatonic semitone; the word "diatonic" means "through the tones, or degrees of the scale." A second meaning which is attached to the word will be explained later (§ 72). When the two notes of the semitone are on the same degree of the staff, and one of the two is altered by an accidental (e.g., C to C♯) the semitone is called chromatic, a word literally meaning "coloured." This use of the word will be further explained later.
7. As the word semitone means "half tone," it is evident that two semitones together will make a tone. Thus in the example given in § 6, as we find a semitone from B to C, and another semitone from C to C♯, the whole interval from B to C♯ is a tone. But as a tone is always composed of two notes on adjacent degrees of the staff, one being always on a line, and the other on the next space, above or below, it is necessary that of the two semitones one must be diatonic and one chromatic.[2] For if we take two diatonic semitones one above another,
the resulting interval will be from B to D♭; which is not a tone as the two notes are not on the next degrees of the scale to one another. And if we take two chromatic semitones,
it is equally clear that they will not make a tone; for now the resulting notes C♭ and C♯ are both on the same degree of the staff.
- ↑ In one sense this statement is not strictly accurate, as the "enharmonic diesis" (§ 52) is sometimes used in modulation. For ordinary purposes, however, the statement in the text is correct.
- ↑ The two semitones composing a tone are not of exactly the same size. It will be seen later (§ 50) that a diatonic semitone is larger than a chromatic; neither semitone is therefore exactly half the tone; but as the difference is of no practical importance in harmony, the student need not regard it. It is only mentioned here for the sake of accuracy.
