Introducing tonality graphs: The chromatic circle of fifths

Abstract

The paper shows how the workings of harmonic progressions can be graphed on a
time/tonal space continuum, the tonality graph (TG). It provides an effective means
of showing the extent to which a piece is either diatonic or chromatic, of demonstrating
modulation and tonicization; it forms an efficient indicator of the speed of the
harmonic rhythm as well as of its regularity or syncopation and facilitates an appreciation
of chord frequency. The utilisation of the TG is illustrated through analyses
of passages from J.-S. Bach’s Prelude in C major from the First book of the Well-
Tempered Clavier, the first movement of Mozart’s Sonata in B flat major, KV 333,
Chopin’s Prelude n. 9 in E major, Debussy’s Prélude à L’Après-midi d’un faune and
the second movement of Beethoven’s fifth piano concerto.