Interval

Interval, in Music, is the difference of pitch between any two musical tones. Since pitch depends upon the vibration-frequencies, the relation between any two pitches is the numerical ratio between the two vibration-frequencies; and all pairs of tones within which the frequencies have the same ratios present equal intervals. The interval between any two tones, whether chosen or heard at random, is thus expressible as an arithmetical ratio; but musically it is only certain intervals which are recognised as being musical intervals, and what these are depends upon the Scale (q.v.) which is in use. Among the European nations and those of European descent the diatonic scale is employed; and this, when unmodified by Temperament (q.v.), presents the ratios given under Harmonics (q.v.). Within such a scale the various intervals that may be found are (C being taken to represent the keynote of the scale) minor second (= E—F or B—C') = 16/15; grave major second (= D—E or G—A) = 10/9; major second (= C—D, F—G, A—B) = 9/8; grave minor third (= D—F') = 32/27; minor third (= E—G, A—C', B—D') = 6/5; major third (= C—E, F—A, or G—B) = 5/4; perfect fourth (= C—F, D—G, E—A, G—C', or B—E') = 4/3; acute fourth (= A—D') = 27/20; acute augmented fourth (= F—B) = 45/32; grave diminished fifth (= B—F') = 64/45; grave fifth (= D—A) = 40/27; perfect fifth (= C—G, E—B, F—C', G—D', A—E') = 3/2; minor sixth (E—C', A—F', B—G') = 8/5; major sixth (= C—A, D—B, G—E') = 5/3; acute major sixth (= F—D') = 27/16; grave minor seventh (D—C', G—F', B—A') = 16/9; minor seventh (E—D', A—G') = 9/5; seventh (C—B, F—E') = 15/8; octave (C—C', D—D', &c.) = 2/1. By taking various notes of the diatonic scale as starting-points, and measuring known intervals from these, we arrive at intermediate notes of the scale, of which the following are examples, the vibration-ratios being given with reference to C:

The difference of pitch between C and C♯ or between D and D♭ is frequently called a semitone, and an interval increased or diminished by a semitone is said to be augmented or diminished. This applies especially to the interval of a fourth or a fifth, which with the octave are said to be perfect, because any augmentation or diminution mars their consonance. The major sixth or third may however be diminished to a 'minor' sixth or third without destroying the consonance; and the term 'minor' is also applied to the diminished second or seventh. The octave begins a new series, and thus the 'ninth' is the octave of the second, and so forth. For further discussion of the musical nomenclature, which is somewhat unsettled, see article 'Interval' in Grove's Dictionary of Music and Musicians; and for a numerical table of the various intermediate tones within the scale, see Daniell's Principles of Physics, 2d ed. pp. 390-91.