In music theory, a trichord is a group of three different pitch classes found within a larger group (Friedmann 1990, 42). A trichord is a contiguous three-note set from a musical scale (Houlahan and Tacka 2008, 54) or a twelve-tone row.
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Alternate Russian definition
In late-19th to early 20th-century Russian musicology, the term trichord (трихорд) meant something more specific: a set of three pitches at least a tone apart within the range of a fourth or fifth. (for example, do-re-fa or do-fa-sol). Several of these pitch sets interlocking could form a larger set such as a pentatonic scale. It was first coined by theorist Pyotr Sokalsky in his 1888 book Русская народная музыка (Russian Folk Music) to explain the observed traits of the rural Russian folk music (especially from southern regions) that was just beginning to be recorded and published at this time. The term gained wide acceptance and usage, but as time went on it became less relevant to contemporary ethnomusicological findings; ethnomusicologist Kliment Kvitka opined in his 1928 article on Sokalsky's theories that it should also properly be used for pitch sets of three notes in the interval of a third, which had been found to be just as characteristic of Russian folk traditions (but which was unknown in Sokalsky's time). By mid-century, a group of Moscow-based ethnomusicologists (K. V. Kvitka, Ye. V. Gippius, A. V. Rudnyova, N. M. Bachinskaya, L. S. Mukharinskaya, among others) boycotted the use of the term altogether, yet it could still be seen in the mid-20th century due to its heavy use in the works of earlier theorists (Kastal'skii 1961, 9).
Etymology
The term is derived by analogy from the 20th-century use of the word "tetrachord". Unlike the tetrachord and hexachord, there is no traditional standard scale arrangement of three notes, nor is the trichord necessarily thought of as a harmonic entity (Rushton 2001)
Explanation
Just as a diatonic scale is conventionally said to be constructed of two disjunct tetrachords (CDEF+GABC=CDEFGABC), a pentatonic scale can be constructed of two disjunct trichords (ACD+EGA=ACDEGA; GAC+DEG=GACDEG).
Milton Babbitt's serial theory of combinatoriality makes much of the properties of three-note, four-note, and six-note segments of a twelve-tone row, which he calls, respectively, trichords, tetrachords, and hexachords, extending the traditional sense of the terms and retaining their implication of contiguity. He usually reserves the term "source set" for their unordered counterparts (especially hexachords), but does occasionally employ terms such as "source tetrachords" and "combinatorial trichords, tetrachords, and hexachords" instead (Babbitt 1955, 57–58, 60; Babbitt 1961, 76; Babbitt 2003, 59).