Harmonic Analysis in David Cope's Experiments in Musical Intelligence
Harmonic functions are analyzed in David Cope's Experiments in Musical Intelligence (hereafter, EMI) with the conviction that, similarly to natural languages, musical grammars depend on syntax rather then semantics. In language, nouns can function as subjects or objects depending on their context. In tonal music, for example, a dominant chord may be syntactically a statement when articulated in the beginning of a phrase, or a consequent when sounding at a cadential moment.
Cope developed in 1985 (Cope 1987) the SPEAC system, the first musical implementation of an augmented transition network (ATN), a finite-state automaton with recursive succession rules between sub-phrases allowing for logical syntax substitutions.
|Outline of David Cope's algorithms in Experiments in Musical Intelligence|
David Cope SPEAC
SPEAC is an acronym for a functional analytical system based on five identifiers, where S stands for statement (declaration of material or ideas, in most cases preceding or following any other SPEAC function), P for preparation (typically occurring prior to statements and antecedents), E for extension (primarily following statements but also any other SPEAC function), A for antecedent (normally preceding consequents), and C for consequent (must be preceded by antecedents either directly or indirectly when including intervening extensions). Succession rules for each of SPEAC abstractions have imposed limitations where a statement can be followed by either P, E or A, a preparation by S, A, or C, an extension by S, P, A, or C, an antecedent by E, C, and a conclusion by S, P, E, A. Any of SPEAC abstractions are assigned to a grouping of notes depending on levels of tension between intervals, metrical placement, and agogic emphasis, measured both in the preceding and following groups. At the intervallic level, tension measurements depart from basic acoustical concepts. Tension is evaluated based on lower-occurring and lower-rooted intervals, and upper-occurring and upper-rooted intervals, respectively indicating least and most tension. Given one harmonic series per pitch class (typically considering only the first sixteen partials), an interval’s acoustic fundamental is determined by identifying the harmonic series where the given interval appears positioned closer to the fundamental. The next step is to define the interval’s root by locating the member of the interval closest to a fundamental’s multiple. In this fashion, minor seconds are ranked with the highest tension (occurring highest in the series (16/15) with upper root), and perfect fifths with the lowest tension (lower placement in the series (3/2) and lower root).
The data resulting from this preliminary analytical stage is converted to an intuitive scale of numerical values. The converting procedure reduces all intervals to the octave space, where numerical values are distributed symmetrically around the augmented fourth, with the exception of the perfect fifth which, just as unisons and octaves, produces the lowest tension levels.
The following stages in SPEAC analysis cover metric placement and agogic. The further away an interval is positioned to the right of the barline, the higher the level of tension produced independently measured at the beat and off-beat levels. Agogic analysis looks at note duration, where larger values translate to lower tension measurements. The combined action between SPEAC analysis and pattern matching (explained ahead) allows the proper cataloguing of musical components and the construction of appropriate lexicons according to syntactical functions thus ensuring logical recombinancy.