Generative theory of tonal music

A generative theory of tonal music (GTTM) is a theory of music conceived by American composer and music theorist Fred Lerdahl and American linguist Ray Jackendoff and presented in the 1983 book of the same title. It constitutes a "formal description of the musical intuitions of a listener who is experienced in a musical idiom" with the aim of illuminating the unique human capacity for musical understanding.

The collaboration between Lerdahl and Jackendoff was inspired by Leonard Bernstein's 1973 Charles Eliot Norton Lectures at Harvard University, wherein he called for researchers to uncover a musical grammar that could explain the human musical mind in a scientific manner comparable to Noam Chomsky's revolutionary transformational or generative grammar.

Unlike the major methodologies of music analysis that preceded it, GTTM construes the mental procedures under which the listener constructs an unconscious understanding of music, and uses these tools to illuminate the structure of individual compositions. The theory has been influential, spurring further work by its authors and other researchers in the fields of music theory, music cognition and cognitive musicology.

GTTM focuses on four hierarchical systems that shape our musical intuitions. Each of these systems is expressed in a strict hierarchical structure where dominant regions contain smaller subordinate elements and equal elements exist contiguously within a particular and explicit hierarchical level. In GTTM any level can be small-scale or large-scale depending on the size of its elements.

GTTM considers grouping analysis to be the most basic component of musical understanding. It expresses a hierarchical segmentation of the piece into motives, phrases, periods and still larger sections.

Metrical structure expresses the intuition that the events of a piece are related to a regular alternation of strong and weak beats at a number of hierarchical levels. It is a crucial basis for all the structures and reductions of GTTM.

Time-span reductions (TSRs) are based on information gleaned from metrical and grouping structures. They establish tree structure-style hierarchical organizations uniting time-spans at all temporal levels of a work. The TSR analysis begins at the smallest levels, where metrical structure marks off the music into beats of equal length (or more precisely into attack points separated by uniform time-spans) and moves through all larger levels where grouping structure divides the music into motives, phrases, periods, theme groups and still greater divisions. It further specifies a “head” (or most structurally important event) for each time-span at all hierarchical levels of the analysis. A completed TSR analysis is often called a Time-Span tree.

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