Trichord

A trichord is a set of three distinct pitches. In music theory, the term most often refers to unordered sets of three pitch classes, analyzed for their intervallic content and relationship to other sets. Unlike a chord, a trichord does not necessarily imply harmonic function or a specific vertical arrangement.

The analysis of trichords, along with other pitch-class sets, is a fundamental aspect of post-tonal music theory, particularly in the works of composers who explored atonality and serialism. Trichords are categorized by their prime form, which is the most compact representation of the set under transposition and inversion. The prime form is conventionally listed within square brackets, such as [012] or [016].

The study of trichords involves identifying their intervallic content using interval vectors. An interval vector summarizes the number of occurrences of each interval class (IC1 through IC6) within the set. This allows for comparison between different trichords and provides insight into their sonic properties. For example, a trichord containing a minor second, major second, and minor third (like C-C#-D#) would have a different intervallic profile than one containing a major third and tritone (like C-E-F#).

Trichords can be used to generate musical material, create motivic connections, and establish harmonic areas within a composition. The relationships between different trichords can be explored through set theory operations such as transposition (Tn), inversion (In), and multiplication (Mn). These operations allow for the transformation of one trichord into another, creating variations and developing musical ideas.