Modulation Mining—Computer-Aided Exploration of Functional Chord Forms

Abstract

The different labelling systems defined by the functional theories of harmony have been developed from about 1870 to 1950, without the help of computers. The complexity of harmonic labels spans from pure triads over added characteristic dissonances, over alterations of the fifth, up to non-chord notes like suspensions. Computer-based evaluation of functional label expressions shows that thereby their cardinality increases up to several thousands. For this, we present the basic theory, a concrete program implemented in Prolog, and some empirical results. The software is capable of analysing historic published analyses by inductively collecting all appearing labels, as well as theories as such, where the set of labels is given deductively, by regular expressions. A major application is the mining for possible modulation chords, i.e. different functional labels which result in (enharmonically) the same pitch classes. That this strategy had actually been applied by composers manually is explained by significant examples from the Romantic period.