# Trichord

In music theory, a trichord (/trkɔːrd/) 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.

Webern's Concerto Op. 24, tone row (Whittall 2008, 97), composed of four trichords: P RI R I.

In musical set theory there are twelve trichords given inversional equivalency, and, without inversonal equivalency, nineteen trichords. These are numbered 1-12, with symmetrical trichords being unlettered and with uninverted and inverted nonsymmetrical trichords lettered A or B, respectively. They are often listed in prime form, but may exist in different voicings; different inversions at different transpositions. For example, the major chord, 3-11B (prime form: [0,4,7]), is an inversion of the minor chord, 3-11A (prime form: [0,3,7]). 3-5A and B are the Viennese trichord (prime forms: [0,1,6] and [0,5,6]).

## Historical Russian definition

In late-19th to early 20th-century Russian musicology, the term trichord (трихорд (/trixоrd/)) meant something more specific: a set of three pitches, each at least a tone apart but all within the range of a fourth or fifth. (for example, do-re-fa, or do-fa-sol). The possible trichords on C would then be:

Note Number Intervals
C D F 0 2 5 2, 3 (M2, m3)
C D G 0 2 7 2, 5 (M2, P4)
C D/E F 0 3 5 3, 2 (m3, M2)
C E G 0 3 7 3, 4 (m3, M3)
C E F/G 0 4 6 4, 2 (M3, M2)
C E G 0 4 7 4, 3 (M3, m3)
C F G 0 5 7 5, 2 (P4, M2)

Several of these pitch sets interlocking could form a larger set such as a pentatonic scale (such as C-D-F-G-B-C'). 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).

## References to term 'trichord'

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).

Allen Forte occasionally makes informal use of the term trichord (Forte 1973, 124 and 126) to mean what he usually calls "sets of three elements" (Forte 1973, 3, 23, 27, and 47), and other theorists (notably including Howard Hanson 1960, and Carlton Gamer 1967, 37, 46, 50–52), mean by the term triad a three-note pitch collection which is not necessarily a contiguous segment of a scale or a tone row and not necessarily (in twentieth-century music) tertian or diatonic either.

## References

• Babbitt, Milton (1955). "Some Aspects of Twelve-Tone Composition". The Score and I. M. A. Magazine, no. 12 (June): 53–61.
• Babbitt, Milton (1961). "Set Structure as a Compositional Determinant". Journal of Music Theory 5, no. 1 (Spring): 72–94.
• Babbitt, Milton (2003). "Twelve-Tone Invariants as Compositional Determinants (1960)". In The Collected Essays of Milton Babbitt, edited by Stephen Peles, Stephen Dembski, Andrew Mead, and Joseph Straus, 55–69. Princeton: Princeton University Press.
• Forte, Allen (1973). The Structure of Atonal Music. New Haven and London: Yale University Press. ISBN 0-300-01610-7 (cloth) ISBN 0-300-02120-8 (pbk).
• Friedmann, Michael L. (1990). Ear Training for Twentieth-Century Music. ISBN 978-0-300-04537-6.
• Gamer, Carleton (1967). "Some Combinational Resources of Equal-Tempered Systems". Journal of Music Theory 11, no. 1 (Spring): 32-59.
• Hanson, Howard (1960). Harmonic Materials of Modern Music: Resources of the Tempered Scale. New York: Appleton-Century-Crofts.
• Houlahan, Mícheál, and Philip Tacka (2008). Kodály Today: A Cognitive Approach to Elementary Music Education. Oxford and New York: Oxford University Press. ISBN 978-0-19-531409-0.
• Kastal'skii, Aleksandr Dmitrievich (1961). Особенности народно-русской музыкальной системы [Properties of the Russian Folk Music System], edited by T. V. Popova. Moscow: Gosudarstvennoe muzykal'noe izdatel’stvo. (Reprint of a 1923 original.)
• Rushton, Julian (2001). "Trichord". The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan Publishers.
• Whittall, Arnold (2008). The Cambridge Introduction to Serialism. New York: Cambridge University Press. ISBN 978-0-521-68200-8 (pbk).
• Gilbert, Steven E. (1970). "The Trichord: An Analytic Outlook for Twentieth-Century Music". Ph.D. diss. New Haven: Yale University.