Stephen JABLONSKY, Introducing tonality graphs: The chromatic circle of fifths

The paper shows how the working 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 of the First book of the Well-Tempered Clavier, the first movement of Mozart's Sonata in B flat major, KV 333, of Chopin's Prelude n. 9 in E major, of Debussy's Prélude à L'Après-midi d'un faune and of the second movement of Beethoven's fifth piano concerto.