INTERVAL

in music, the distance in pitch between one tone and another, whether sounded simultaneously (harmonic interval) or successively (melodic interval). Simple intervals encompass one octave or less. Compound intervals exceed the range of one octave and are heard as varieties of their simple counterparts: a tenth (octave plus a third, e.g., cce) is associated by the ear with a third (an interval encompassing three notes, e.g., ce). There are four perfect (P) intervals: prime, or unison (P1); octave (P8); fourth (P4); and fifth (P5), corresponding to the lowest in the harmonic overtone series. The other intervals (seconds, thirds, sixths, sevenths) have major (M) and minor (m) forms that differ in size by a half step (semitone). Both perfect and major intervals may be augmented (A), or enlarged by a half tonefor example, ce (M3) to ce (A3), or cg (P5) to cg (A5). Perfect and minor intervals may be diminished (d), or narrowed by a half tonefor example, eg (m3) to eg (d3), or fc (P5) to fc (d5). Enharmonic intervals are those that, in the system of equal temperament tuning, sound identical but are notated differentlyfor example, ce and cfaccording to the key in which the interval is written. Intervals are calculated in terms of ratios between the constituent frequenciesfor example, 2:1 for the octave, since the frequency of the higher pitch of an octave is twice that of the lower. For purposes of measurements of intervals outside the system of equal temperament, especially with reference to non-Western music, the octave is conveniently divided into 1,200 cents, with one semitone, or minor second, corresponding to 100 cents. So measured, the interval of a minor third, to cite but one instance, contains 300 cents in equal temperament, 294 in Pythagorean tuning, and 316 in just intonation.