Some Useful Terms and Techniques
Pitch  a note with a specific octave position, e.g. "the Aflat below middle C", "Dnatural^{4}", etc. In tonal music, spelling counts; there is an enormous functional difference found in tonal music between Bflat and Asharp. In much twentieth century music, by contrast, the spelling of a pitch is a matter of convenience; functional differences between enharmonically equivalent pitches such as those found in tonal music may be lacking completely.
Pitch Class (p.c.)  The identity of a note without regard for its octave position or spelling. All Bflats in all octaves are members of the same pitch class; Asharp and Bflat are members of the same pitch class.
Pitch Interval (ip)  The distance between two pitches. In much twentieth century music, the distinction between dissonance and consonance (i.e. between intervals that suggest repose and intervals that suggest tension) is absent: in analyzing 20th c. music, therefore, intervals are often measured in semitones: a major third may not be functionally equivalent to a diminished fourth in tonal music, but they both can be expressed as ip4, i.e. as a pitch interval of four semitones. (ip +4 denotes an ascending ip4, ip &endash;4 a descending ip4.)
Interval Class (i.c.)  The distance between two pitch classes. The identity, or size, of an interval expressed as a number of semitones without regard to (1) spelling, (2) octave compounding, or (3) inversion; the minor third Cnatural^{4} Eflat^{4, }the major sixth Eflat^{4}  Cnatural^{5}, and the minor tenth Cnatural^{4}  Eflat^{5} are all members of the same interval class (see chart).














Pitch Collection  any group of pitches. If we remove octave duplicates we get a
Pitch Class Collection (or Pitch Class Set)  a group of pitch classes, considered without regard to their order or to duplication of content. The p.c. membership of a scale or mode may be termed a collection, as can any other combination of pitch classes.
A p.c. set can have any number of members from 1 to 12. A collection containing six members is called a hexachord, one with five members a pentachord, one with four members a tetrachord, one with three members a trichord, and a collection or p.c. set with two members a dyad. (Sets larger than a hexachord are sometimes referred to as heptachords, octachords, nonachords, etc., but just as often will be termed "7p.c. sets", "8p.c. sets", etc.)
Aggregate  a collection of all twelve pitch classes; a 12p.c. set.
Integer Notation  a "spellingneutral" way of identifying the twelve pitch classes. By convention, Cnatural is used as the point of origin for the chromatic aggregate; this in no way implies any special status for that (or any other) p.c. All spellings of Cnatural (e.g. Bsharp, Dflatflat) are assigned integer 0, all spellings of Csharp (e.g. Dflat) integer 1, all spellings of Dnatural (e.g. Eflatflat) integer 2, etc. up to integer 11 (Bnatural or Cflat).


























Interval vector  An inventory of the interval classes present in a p.c. set is called its interval vector. By convention, the interval vector is a sixdigit number enclosed in [square brackets]. A set’s interval vector is reckoned by starting with the first p.c. of the set and finding the interval class of which the interval between it and each other p.c. is a part, moving to the next p.c. of the set and computing the number of half steps between it and each remaining p.c. in the set, and repeating the procedure until you reach the set’s last p.c.
Example: The pentachord C, D, F, G, A.
(1) The interval class between C and D is 2; between C and F is 5, between C and G is also 5; between C and A is 3. (See tally below.)












(2) The i.c. between D and F is 3 (5  2 = 3); between D and G is 5; between D and A is 5 (9  2 = 7, which is a member of i.c. 5). (See tally below.)












(3) The i.c. between F and G is 2; between F and A is 4. (See tally below.)












(4) The i.c. between G and A is 2. (See tally below.)












The interval vector of the set, which may be expressed in integer notation as (0, 2, 5, 7, 9), is [034140], because the set contains
no intervals of i.c. 1,
3 intervals of i.c. 2,
2 of i.c. 3,
1 of i.c. 4,
4 of i.c. 5,
and none of i.c. 6.
What is the interval vector of: the whole tone scale? the major scale? a dominant seventh chord? a fully diminished seventh chord?