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The film composer James Horner died two years ago today. Horner was fond of cruising through what Frank Lehman in an article in Music Theory Spectrum (35/1) called "Horner Space," which is a directed cyclical arrangement of all twenty-four major triads: C-e-G-b-Bb-d-F-a-Ab-c-Eb-g-Gb-bb-Db-f-E-g#-B-d#-D-f#-A-c#--C... (Each triad is directed toward the one to its right.) This arrangement alternates major and minor triads, and groups the succession of triads into six quartets by the repeating root-motion pitch-class pattern of up M3 from a major triad to a minor triad, then up m3, then up M3, and finally down m2 to connect to the next quartet; each quartet can therefore be positioned in regsister a whole step below the previous. (A more general labeling using transformational labels -- like L, R, and S -- cannot define directed Horner space this precisely.)
A film composer's sequential path through this space typically does not use all the triads of each quartet; rather, only two or three in each quartet are used, and the remaining triads in the quartet are skipped over. If the chords in each quartet are numbered in order 1 through 4 (for example, 1 = C, 2 = e, 3 = G, 4 = b), then this quartet subset can therefore be succinctly represented with a series of numbers. For instance, 134 would represent a progression such as a-Ab-Eb-g-Gb-Db-f-E-B (4-1-3-4-1-3-4-1-3), which can be found a little ways into Horner's main title for A Beautiful Mind.
Horner and other film composers use different paths through this directed space in creating descending major-second sequences in recent movies: 12, 14, and 134 are the ones I hear the most often. A couple of years ago, I shared with the FMIG (Film and Multimedia Interest Group) community an example from classical music that moves through Horner space: the beginning of Variation VII of Reger's Variations on a Theme of Mozart, which uses a 12 (F-a-Eb-g). For this anniversary, I thought I would share another one: rehearsal 1 (and again at later points in the symphony) in the first movement of Prokofiev's Fourth Symphony, which uses a 14 (C-b-Bb-a-Ab-g).
Maybe I or someone else will find (or you already know of, and would share) a 134 in pre-Horner art music. In the meantime, requiescat in pace, James Horner.
-Scott Murphy, University of Kansas