Collections

Beyond the diatonic modes, 20th-century composers organized pitch material around several non-diatonic pitch-class collections, each with a distinctive interval structure. The most important are the octatonic, whole-tone, hexatonic, and pentatonic collections.

The octatonic collection contains eight pitch classes arranged in a strictly alternating pattern of half steps and whole steps: H-W-H-W-H-W-H-W (or starting W-H). There are only three distinct octatonic collections (transpositions share pitch classes after three semitones), and each contains every interval class in balanced proportions. Composers such as Stravinsky, Bartók, and Messiaen exploited the collection's symmetry and its ability to suggest multiple tonal centers simultaneously. The whole-tone collection contains six pitch classes each a whole step apart: W-W-W-W-W-W. Only two distinct whole-tone collections exist (one on C, one on C♯). It contains no half steps or perfect fifths, giving it a floating, harmonically ambiguous character that Debussy used to great effect.

The hexatonic collection also contains six pitch classes, alternating minor thirds and half steps: H-m3-H-m3-H-m3. Four distinct hexatonic collections exist. Like the whole-tone collection it divides the octave symmetrically, making it useful for neo-Riemannian progressions among augmented triads and major/minor triads. The pentatonic collection — five pitch classes with no half steps — comes in two common forms: the major pentatonic (e.g., C-D-E-G-A) and the minor pentatonic (e.g., A-C-D-E-G). Its lack of semitones means no leading-tone tendencies, contributing to the open, modal sound found in folk music worldwide and in pop and jazz textures.