In musical set theory, an interval vector is an array of natural numbers which summarize the intervals present in a set of pitch classes. (That is, a set of pitches where octaves are disregarded.) Other names include: ic vector (or interval-class vector), PIC vector (or pitch-class interval vector) and APIC vector (or absolute pitch-class interval vector, which Michiel Schuijer states is more proper.)

While primarily an analytic tool, interval vectors can also be useful for composers, as they quickly show the sound qualities that are created by different collections of pitch class. That is, sets with high concentrations of conventionally dissonant intervals (i.e., seconds and sevenths) sound more dissonant, while sets with higher numbers of conventionally consonant intervals (i.e., thirds and sixths) sound more consonant. While the actual perception of consonance and dissonance involves many contextual factors, such as register, an interval vector can nevertheless be a helpful tool.

In twelve-tone equal temperament, an interval vector has six digits, with each digit representing the number of times an interval class appears in the set. Because interval classes are used, the interval vector for a given set remains the same, regardless of the set's permutation or vertical arrangement. The interval classes designated by each digit ascend from left to right. That is:

Interval class 0, representing unisons and octaves, is omitted.

In his 1960 book, The Harmonic Materials of Modern Music, Howard Hanson introduced a monomial method of notation for this concept, which he termed intervallic content: p^em^dn^c.s^bd^at^f for what would now be written ⟨abcdef⟩. The modern notation, introduced by Donald Martino in 1961, has considerable advantages^[specify] and is extendable to any equal division of the octave. Allen Forte in his 1973 work The Structure of Atonal Music notated the interval vector using square brackets, citing Martino; subsequent authors, e.g. John Rahn, use angled brackets.

A scale whose interval vector has six unique digits is said to have the deep scale property. The major scale and its modes have this property.

For a practical example, the interval vector for a C major triad (3-11B) in the root position, {C E G} (Play^ⓘ), is ⟨001110⟩. This means that the set has one major third or minor sixth (i.e. from C to E, or E to C), one minor third or major sixth (i.e. from E to G, or G to E), and one perfect fifth or perfect fourth (i.e. from C to G, or G to C). As the interval vector does not change with transposition or inversion, it belongs to the entire set class, meaning that ⟨001110⟩ is the vector of all major (and minor) triads. Some interval vectors correspond to more than one sets that cannot be transposed or inverted to produce the other. (These are called Z-related sets, explained below).

For a set of n pitch classes, the sum of all the numbers in the set's interval vector equals the binomial coefficient ${\displaystyle {\tbinom {n}{2}}={\tfrac {n(n-1)}{2}}}$, since the interval vector elements are computed comparing each pair of pitch classes from the set consisting of n elements. This corresponds also to the triangular number ${\displaystyle T_{n-1}}$.