Macroharmony

There are slightly different definitions of macroharmony in the literature. In general, it may be said to determine pitch content within some duration of a musical composition.^[2] Dmitri Tymoczko defined it as "the total collection of notes used over small stretches of time".^[3] Neil Newton defined it as "the collection of pitches from which harmonies are sourced".^[4] Ciro Scotto wrote that it is "a large harmony that subsumes the individual chords", adding that he used it more specifically to denote pitch-class subsets.^[5] Julian Hook related it to the concept of a field of pitch classes, noting that the difference was one of terminology.^[2]

Scotto suggested the term to Tymoczko, who introduced and defined it in A Geometry of Music (2011).^[6] Tymoczko sought to discuss "music that is neither classically tonal nor completely atonal" (see chromaticism and nonchord tones).^[7] He observed that a macroharmony of between five and eight pitch classes, or a limited macroharmony, typically contributed to a sense of tonality.^[8] He included this feature, limited macroharmony, as one among five general (universal) features of "virtually all" music. The others were conjunct melodic motion, acoustic consonance, harmonic consistency, and pitch centricity. He considered their (non-)interaction, relative importance, and mutual reinforcement.^[9]

Of macroharmonies specifically, he asked:^[10]

• What is the number of pitch classes in a given macroharmony, if fewer than the total chromatic (aggregate)?
• What is the rate at which given macroharmonies change?^[a]
• What is the relationship (e.g., transpositional) between given macroharmonies?
• What are the intervallic qualities (consonance or dissonance) of a given macroharmony?

He proposed to show the rate at which pitch classes are used with "pitch-class circulation graphs" and the number and relative proportion of pitch classes on a large scale with "global macroharmonic profiles".^[10]