interval

in music and acoustics, the correlation of two tones according to pitch, that is, the frequency of sound vibration. The lower tone of an interval is known as its foundation, the upper its top. Tones employed in succession form a melodic interval; when used simultaneously, a harmonic interval. Each interval is determined by the volume, or quantitative, magnitude—that is, the number of steps it comprises—and the tonal, or qualitative, magnitude—that is, the number of whole tones or semitones it contains. Intervals formed within the limits of an octave are called simple intervals, and larger ones are called compound intervals. The names of intervals indicate the number of steps each embraces: the tonal size of the intervals determines whether they are minor, major, perfect, augmented, or diminished.

The simple intervals are perfect unison, minor second (a half tone), major second (one tone), minor third (1½ tones), major third (two tones), perfect fourth (2½ tones), augmented fourth (three tones), diminished fifth (three tones), perfect fifth (3½ tones), minor sixth (four tones), major sixth (4½tones), minor seventh (five tones), major seventh (5½tones), and perfect octave (six tones).

Compound intervals are created by adding a simple interval to the octave. They retain the characteristics of the analogous simple intervals; thus, there are ninths, tenths, elevenths, twelfths, thirteenths, fourteenths, and fifteenths (two octaves). Wider intervals are called a second above (or below) two octaves, a third above two octaves, and so on.

The enumerated intervals are known also as fundamental, or diatonic, intervals. Diatonic intervals can be increased or diminished by raising or lowering the foundation or top of the interval one chromatic semitone. If, simultaneously, both steps of an interval are subjected to alteration by a chromatic semitone in different directions, a double-augmented interval results; if one step is altered by one chromatic tone a double-diminished interval is produced. All intervals changed through alteration are called chromatic intervals. Intervals that differ in the quantity of steps they contain but are alike in tonal makeup (sound) are considered enharmonically equal—for example, F to G sharp (an augmented second) and F to A flat (a minor third).

All harmonic intervals are divided into consonant and dissonant intervals. The consonant intervals are the perfect unison and the octave (perfect consonance), the perfect fourth and the perfect fifth (very good consonance), and minor and major thirds and sixths (imperfect consonance). The dissonant intervals are minor and major seconds, the augmented fourth, the diminished fifth, and minor and major sevenths. The transference of the tones of an interval, during which the foundation becomes the upper tone of the interval and the top its lower tone, is called inversion; a new interval results. In inversion all perfect intervals remain perfect, minor intervals become major, major become minor, augmented become diminished, diminished become augmented, double augmented become double diminished, and double diminished become double augmented.