Abstract
Most current approaches to key-finding, either from symbolic data such as MIDI or from digital audio data, rely on pitch-class profiles. Our alternative approach is based on two ideas: first, that chord progressions, understood rather loosely as pairs of neighboring harmonic states demarcated by note onsets, are sufficient as windows for key-finding, at least in the chorale context; and second, that the encapsulated identity of a chord progression (modulo pitch-class transposition and revoicing) is sufficient – that is, that reduction of progressions to pitch-class distributions is not necessary for key-finding. The system has no access to explicit information about a chord progression other than its transpositional distribution in the training corpus, yet it is able to reach an almost stunning degree of subtlety in its harmonic analysis of chorales it’s never heard before. This suggests that reductionist approaches to tonality may be off the mark, or at least that pitch-class reductionism might not be necessary for a principled account of key.
Highlights
Most current approaches to key-finding, either from symbolic data such as MIDI or from digital audio data, rely on pitch-class profiles
Our alternative approach is based on two ideas: first, that chord progressions, understood rather loosely as pairs of neighboring harmonic states demarcated by note onsets, are sufficient as windows for key-finding, at least in the chorale context; and second, that the encapsulated identity of a chord progression is sufficient – that is, that reduction of progressions to pitch-class distributions is not necessary for key-finding
Most current approaches to key-finding, either from symbolic data such as MIDI or from digital audio data, use some form of the following procedure developed by Krumhansl and Schmuckler (Krumhansl 1990):
Summary
We define a chord progression as a pair of chords (each characterized as a collection of intervals above the bass) plus the ordered pitch-class interval between the two bass notes, measured in semitones. For each instance of a progression in the corpus, we determine the scale-degree identity of the first bass note relative to the chorale melody’s final pitch class (which is assumed to be the tonic); the table tallies the percentage of instances of each progression that occur on any given scale degree. In most of the remaining instances, the first bass note is a whole step above or below the tonic, which we would understand as scale degree 5 of a tonicized V (dominant) or III (relative major of a minor key). The ninth-ranked progression (n = 309), a variant of the V7 – I progression with the seventh chord in first inversion, has a much ‘flatter’ distribution than either of the other two, no doubt thanks to the frequent appearance of this progression in tonicizations and modulations instead of final cadences
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