Jazz Harmonic Analysis as Optimal Tonality Segmentation

When asked to improvise over the chord changes of a tune, jazz musicians, either by an intuitive or formal process, perform an analysis to obtain a harmonic road map that guides them through the possibilities of what notes and scales to play. The purpose of this harmonic analysis is to discover and understand underlying structures in the chord changes. A notation often used in jazz theory texts (e.g., Nettles and Graf 1997; Jaffe 2009) to represent this harmonic structure identifies a segmentation of the chord changes, the key center (or tonality) of each segment, and the harmonic function of each chord with respect to its key center and other chords. Performing such an analysis is a fundamental step if jazz improvisation is to be simulated by software. It is also an interesting and important problem to be considered on its own for the implementation of jazz compositional and teaching tools. This article presents a formulation of and an algorithm for the harmonic analysis of jazz chord sequences. Some familiarity with jazz harmony or traditional harmony is assumed. Here is an example of the intended kind of analysis. Consider the chord changes for Miles Davis’s Solar in Figure 1. These chord changes will be the input given to the harmonic analysis algorithm. The output of the algorithm is an annotated chord chart, as shown in Figure 2. Key centers are shown below the bars: The key center of bars 1 and 2 is C minor, that of bars 3–6 is F major, that of bars 7–9 is E major, and so on. Arrows and brackets represent dominant resolutions and related minor seventh chords (i.e., the related IIm7s), respectively (Nettles and Graf 1997). (These will be explained further in the section “Structural Analysis.”) Roman numeral chord symbols above the chords indicate their harmonic functions with respect to their key centers. For example, the Dm7 5 and G7 9 chords in bar 12 function as IIm7 5 and V7 chords, respectively, resolving to the root of the key