Another example of a classical composer moving through "Horner space"

Scott Murphy

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

Frank Lehman

Ah, one of my favorite tonal spaces!

I actually briefly mention the Prokofiev in a footnote (fn27) in the MTS article, and go into a bit more detail on it and a few other examples in my dissertation (pp. 214-223), though that Reger example is news to me! Since then, I've kept my ear out for other instances of the space, though it is far from common in either film or classical music. One close-ish example, not so far from the Prokofiev in structure, is the Benedictus from Schnittke's Requiem, which dribbles down from E-D#-d-C#-c#-C-c-B before breaking the pattern with a move to a-minor. I vaguely recall some other Schnittke progressions that do similar things, but will have to search my notes to be more specific.

And there's also Rachmaninoff's wonderful and underrated First Symphony, which is all over Horner Space -- and the wellspring of many an additional Hornerism too ! 

Frank Lehman

One more --

If you count musical theater, one other example that Horner *definitely* was aware of is "One Hand, One Heart" from West Side Story, which features a pretty famous 134 pattern in Scott's nomenclature (Gb: I-iii-bVII...).

Horner didn't just help himself to this progression over and over in his filmography, he also lifted the song's final cadence for his (admittedly quite beautiful) theme to For the Greater Glory, in addition to the 134 cell. 

Every score of his is a harmonic scavenger hunt!