In late-19th to early 20th-century Russian musicology, the term trichord ) 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.. The possible trichords on C would then be: 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 to explain the observed traits of the rural Russian folk music 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 ethnomusicologicalfindings; 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. By mid-century, a group of Moscow-based ethnomusicologists 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.
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 scalearrangement of three notes, nor is the trichord necessarily thought of as a harmonic entity. 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, but does occasionally employ terms such as "source tetrachords" and "combinatorial trichords, tetrachords, and hexachords" instead. Allen Forte occasionally makes informal use of the term trichord to mean what he usually calls "sets of three elements", and other theorists, 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 tertian or diatonic either.
Number of unique trichords
Typically, there are 12 tones in the western scale. Computing the number of unique trichords is a mathematical problem. A computer program can quickly iterate all the triads and remove the ones that are merely transpositions of others, leaving nineteen or, to within inversional equivalence, twelve. As an example, the following list contains all trichords that can be made including the note C, but includes 36 that are merely transpositions or transposed inversions of others:
While some of these chords are recognizable and ubiquitous, many others are unusual or rarely used. Although this list enumerates only trichords containing the note C, the number of all possible trichords inside a single octave is 220.
