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date: 24 May 2022

Film Music and Neo-Riemannian Theory

Abstract and Keywords

Triadic chromaticism is a feature of much dramatic film scoring, a repertoire that has previously received little in the way of sustained analytic attention from music theorists. Neo-Riemannian techniques, while limited in application in most previous studies to nineteenth-century music, are eminently suited to exploring this vast musical landscape. Using passages of characteristically “nonfunctional” tonal logic from scores by Hollywood’s leading composers, this article demonstrates the relevance of transformational parameters to the investigation of cinematic musical structure and expression. The interpretive usefulness of neo-Riemannian harmonic combinatoriality and its sensitivity to voice-leading is highlighted with intuitive but hermeneutically revealing analyses of music from John Williams, Bernard Herrmann, and Howard Shore. The interaction of diatonic functional and chromatic idioms is broached with examples from Alfred Newman, as is the notion of “tonal agnosticism,” which underlies much neo-Riemannian scholarship. Two larger analyses, of Alan Silvestri’s Back to the Future and Erich Wolfgang Korngold’s The Sea Hawk, illustrate the power and limitations of symmetry—too often an uncritically assumed desideratum for transformational approaches—for organizing film time. In light of these analyses, the wider prospects for future research in cinematic transformational analysis are considered.

Keywords: neo-Riemannian theory, film music, film music analysis, music analysis, transformation theory, chromaticism, Hollywood, film score, tonality, Herrmann, Williams, Silvestri, Korngold

Although assembled from diverse and often detachable theoretical components, there is one thing that has remained consistent in the development and application of neo-Riemannian theory (NRT): its target repertoire of nineteenth-century chromaticism.1 This specificity owes partially to the genesis of those theoretical components, many of which were formulated by German theorists of the mid-to-late 1800s such as Moritz Hauptmann, Arthur von Oettingen, and most of all Hugo Riemann. As Richard Cohn and other modern theorists have argued, these imported concerns include harmonic dualism,2 the combinatoriality of pitch relations,3 and variously configured Tonnetze.4 The urge to adapt German dualist theories with modern tools and priorities also stems from American theorists’ interest in Romantic-era music.5 The “Second Practice” of nineteenth-century harmony has been framed by neo-Riemannians as a corpus problematically resistant to leading theoretical paradigms for functional monotonality, but highly responsive to transformational approaches.6 These are taken to include any analytic practice that focuses on group-theoretically specified progression classes, idealized voice-leading patterns, or that adopts a dynamic view towards musical process such as cultivated by David Lewin in the 1980s and 1990s.7

Without a doubt some of the most perplexing and captivating music of the Romantic era is singularly compatible with transformational analytic techniques. Nevertheless, there is little in the toolkit that makes up NRT, or indeed the larger umbrella of transformation theory, which insists upon its sole application to works from the century of Schubert and Wagner. In fact, other repertoires may be better suited than this originally intended corpus. If nothing else, a great versatility comes from NRT’s combination of friendliness to nondiatonic materials and sensitivity to the expressive qualities of chromaticism. Despite almost three decades of disciplinary solidification, neo-Riemannian scholarship has not yet witnessed a concerted drive to serve other repertoires that use consonant triads (set-class (037)) in the ways the theory is eminently comfortable handling. Important exceptions in the realm of pop/rock,8 jazz,9 and twentieth-century concert idioms10 demonstrate a growing interest in widening NRT’s scope. Such extensions not only provide novel tools for under-inspected musical corpora but also enrich the theory as a whole and clarify its intellectual bases.11 And no repertoire is so primed to offer itself gladly to the mechanisms of triadic transformation theory as film music.

Film Music and Neo-Riemannian Theory

Example 1: Bernard Herrmann, “The Nautilus” mm. 1-8, from Mysterious Island.

Film Music and Neo-Riemannian Theory

Image 1: Discovery of the Nautilus, Mysterious Island.

In film music, tonal language and expressive requirements frequently collaborate to produce passages like that reproduced in Example 1.12 This excerpt from Bernard Herrmann’s score to Mysterious Island (1961, dir. Endfield) behaves in a more textbook “neo-Riemannian” fashion than many canonical NRT passages investigated by Romantic era–focused theorists. The music accompanies a dialogue-free scene in which the castaways on a fantastic island discover a submarine—soon revealed to be the property of Captain Nemo himself (Image 1). No diatonic prolongation of one (or several) key areas is present, nor does there seem to be a tonal teleology based on cadential goals or telegraphed thematic completion. The majority of triad-to-triad motions are chromatic, linking modally matched triads removed by thirds or semitones, governed by no predetermined scale. Herrmann’s voice-leading is nevertheless quite smooth, and the lexicon of triadic progressions is actually fairly limited. The organization into two-bar, three-chord units allows certain melodic motifs (such as permutations of the melodic intervallic pattern T1T3) to come to the fore. It is music that does have to it a sense of order, though the full nature of that order awaits discovery.

Despite the fact that Herrmann’s passage is clearly not a random assemblage of pitches, the tendency in film musicology with regard to passages such this—which are extremely common and characteristic of scores for “genre”—has been to fall back on analytical non-explanations. Abundant and audience-understood progressions are cause for the invoking of “nonfunctional” harmonies, “constant modulation,” “polytonality,” and “unrelated keys/chords.” The last is a particularly flagrant abdication of analytical rigor, as it supposes that the only way two harmonic objects could be meaningfully related is by a diatonic interval or process. A transformational approach can show that what seems erratic by diatonic logic may exhibit a perfectly sturdy logic by other relational parameters. Transformation theory is sensitive to matters of process and development. At the same time, it is less committed to static or a priori musical architectonics—the stuff that has come under heavy and sometimes deserved fire following the New Musicological regime, the same shift that opened the door for the current explosion of film musicological research. Neo-Riemannian theory’s bottom-up emphasis serves the perceptual realities of music for screen well, where salient musical features customarily occur close to the surface or shallow middle-ground, only very rarely relying on overarching tonal structures.13 The neo-Riemannian evaporation of classical tonal design expectations proves particularly liberating for the analysis of screen media.14

In this essay I provide an overview of this promising avenue for transformational research. Without question the flow of theoretical scholarship on film music analysis is steadily growing.15 With few exceptions, there is not yet a literature on neo-Riemannian analysis of film, however.16 For this reason, my efforts here are directed at outlining the ways in which neo-Riemannian tenets apply to the analysis of chromatic film music. Chromaticism based on the structure of the consonant triad (pan-triadicism, after Cohn 2012) is capable of serving a number of cinematic ends and has accordingly been well exploited by those involved in scoring films, from the earliest compilation scores to the latest summer blockbuster soundtracks. In the sections to follow, I consider four elements of NRT in relation to this repertoire: combinatoriality, parsimony, tonal agnosticism, and symmetry. While most of these investigations apply the tools and priorities of NRT and film musicology in a fairly conventional fashion, the two final analyses of this essay assume more heterodox perspectives. My investigation of the use of minor third sequences in Alan Silvestri’s score for Back to the Future jettisons the apparent foundational units of NRT analysis— its algebraic operators and directed networks— and instead uses a linear-reductive approach in considering harmonic cyclicality in film scoring. For my analysis of the meticulous hexatonicism of Korngold’s The Sea Hawk, the thing abjured is the need to immediately relate musical design back to drama. Formalistic analysis is an understandably taboo approach among film musicologists as it would seem to marginalize the very element—drama—that makes its subject distinctive. Yet if it is done conscientiously (and without making undue claims about composer intentionality or aesthetic value), analysis of film music-qua-pure music can be instructive on matters such as musical style and design, and its findings can be appreciated on their own or, often, related back to the film.

This narrative-neutral investigation of the Sea Hawk will be the exception however, and film music’s expressive purposes will in all other cases lie at the forefront of my analyses. Admittedly my attention does not primarily fall on the aesthetics or stylistic evolution of cinematic triadic chromaticism.17 But despite setting aside a full semiotics of pan-triadicism, one important lesson regarding tonal signification becomes clear from my analyses: musical meaning habitually arises from a deliberate play with the parameters singled out by transformation theory, those seemingly well suited to NRT analysis and those that slip outside its analytic comfort zone. Signification in chromatic film music are often the upshot of calculated maneuvers between binary categories such as parsimony/roughness, unary/complex, and tonal/atonal. That meaning in multimedia turns out to be dialectical in character should come as no surprise to theorists of film or music. But that it does so within the framework of this particular theoretical paradigm holds the promise of analytic mutual beneficiality: that investigating film music may provide insights back into the nature of transformation theory at large.

II. Combinatoriality

The transformational “alphabet” of any neo-Riemannian analysis consists of operators that alter triads in distinct and readily definable ways. Example 2 presents the inventory that will be employed in this study. For clarity’s sake, transformations are defined in terms of both inversion and pitch-displacements.18

Film Music and Neo-Riemannian Theory

Example 2: Transformation inventory.

All are “dualistic” in the sense that they act in equal and opposite ways on triads of opposing mode. For example, R transforms a major triad into a minor one rooted a m3 up, and transforms a minor triad into a major one a m3 down.19 The inventory is organized into two families. The first comprises the “canonical” neo-Riemannian operators (NROs), being P, L, and R. The second family includes two inversional cousins of the canonical group (S, N); these can be composed from combinations of P, L, and R, but occur with enough frequency and bear sufficient “absolute” sound in film music to occasionally warrant unary treatment.20

There exists some combination of Ls, Ps, and Rs that models any conceivable relation between the twenty-four major and minor triads.21 (In fact, L and R alone are sufficient). These atomic transformations assume the status of NRT’s absolute progressions. A harmonic motion that requires more than one NRO for its description will bear a compound transformation composed under the rules of algebraic associativity. From this potential for combinatorial description come two of the most useful properties of neo-Riemannian theory within the context of film musical analysis: the linkage of transformational complexity with aural distance, and the capacity to interpret one progression in terms of another.

The length and voice-leading work of a transformation—that is, how many constituent operators generate it and by how many semitones they shift—is useful in informally assessing distance and pitch-space pathways between triads without relying on a naive diatonic model.22 The more transformations included within a compound, the more complex it is. Two triads related by L are therefore “closer” than two related by LPL, and even closer than LPLPLPL (despite the fact that they produce exactly the same pair of chords). This distance metric can be used to capture intuitions regarding proximity vs. remoteness as well as familiarity vs. strangeness, both of which are important expressive parameters in film music.23

Film Music and Neo-Riemannian Theory

Image 2: Clark of the Arctic.

Film Music and Neo-Riemannian Theory

Example 3a: John Williams, arctic progression in cue “Fortress of Solitude,” from Superman.

Film Music and Neo-Riemannian Theory

Example 3b: Analysis of progression from “Fortress of Solitude.”

Example 3a reproduces an illustrative extract from John Williams’s 1978 score to Superman (dir. Richard Donner). This reduction is paired with Example 3b, a short diachronic network that demonstrates the way in which transformational length maps neatly onto perceived tonal distance. Like the example from Mysterious Island, this material accompanies a character as he explores a strange and wondrous landscape. In this case, it is Kansas farm boy Clark Kent making his way across a barren arctic plain (Image 2).24 The dozen chords involved in this progression are untethered to even the loosest sense of a governing tonic, but not every motion between them feels equally harmonically alien. The first four harmonies coincide with medium-distance shots of Kent. As if to match the relatively tight visual perspective in this portion of the scene, the transition from F to D and A minor is accomplished by relatively simple binary transformations, first a PR and then an RL. Both compounds retain triadic mode and involve only one intermediary chord, F major, increasing their sense of relatedness. As though to cement the background role of the implicit linking triad, Williams’s next chord is F itself, a tiny adjustment via the unary L of the previous A minor. F major matches a swell in orchestral volume and a newly awestruck look in Kent’s eyes.

The object of telegraphed wonder is revealed in the next shot and corresponding chord change—an impressive wide shot of the sprawling wilderness (depicted in Image 2) and a thickly scored C♯ minor. The PLP that accomplishes this cut is a particular ternary compound singled out by theorist Richard Cohn as historically associated with moments of musical uncanniness—the hexatonic pole, the most distant progression available between M3-related triads.25 The camera returns to Kent through the next four triadic steps through the progression, repeating the pattern of moderate⇨short⇨lengthy transformations as anticipation builds over what he will remove from his backpack (a magical crystal, it turns out). When the film’s perspective once again dilates to present the entire frozen landscape, another ternary transformation synchronizes with the cut. Williams lands now on G major, far-flung relative to its immediate predecessor G♯ minor as well as a parallel event within the scene’s cutting rhythm, C♯. In my analysis, a dotted nonlocal RPR transformation from those two emboldened chords captures this connection. And, to further associate the sight of that yawning landscape once again with the hexatonic pole relation, Williams launches G to D♯, albeit now with an intermediary of E minor that makes the transit even more extreme. Harmonically speaking, we are most assuredly not in Kansas anymore.

This musical paragraph from Superman demonstrates how the analysis of transformational complexity can reveal filmically significant patterns of aural proximity and remoteness. However, the number of operators involved in a transformation will only ever be part of the story of how a progression is heard.26 As important to analysis is the process of choosing a transformation in the first place, and—of particular relevance for the reading of a film score—the interrelationships between multiple transformations. This is the second boon of NRT’s combinatorial inclination: the ability to interpret one harmonic progression in terms of another. The decomposability of any tonal move into some concatenation of harmonic atoms allows the analyst to refer complex or novel sounding harmonic events back to simpler or accustomed motions and vice versa. This has great utility in tracking the shift of harmonic material across a cue or whole score as a function of an underlying model. For instance, if the motion C-maj⇨A♭-maj (PL) is motivic in a score, then a latter occurrence of, say, F♯-min⇨B♭-maj could be interpreted in terms of the original transformational motive, as PL∙P. In another situation, that same move may be heard as a variant of a different parent, say F♯-min⇨B-min (LR), in which case Fs-min⇨B♭-maj could garner a less intuitive but perfectly justifiable LRS description. Such interpretive underdetermination opens the avenue for a hermeneutics not unlike that commonly applied to traditional leitmotifs, and bears the same potential for charting gross or subtle shifts in dramatic representation across large spans of film time.27

Film Music and Neo-Riemannian Theory

Example 4a: Herrmann, “The Nautilus” analysis.

Analysis of “The Nautilus” from Herrmann’s Mysterious Island illustrates the interpretive upshots of neo-Riemannian combinatoriality. Example 4a assigns neo-Riemannian operators to the opening of the cue, with the coloristic but transformationally inessential vibraphone part reduced out. Note that some of the motions between triads are analyzed with more complex relations than are strictly necessary given our full inventory of NROs. The switch from B♭-min to E♭-maj in m. 2–3 could be interpreted as a ternary compound, PRL.28 Yet the analysis describes it through the considerably more elaborate (PL∙PR)∙PLP. Why the complexity?

Film Music and Neo-Riemannian Theory

Example 4b: Herrmann, germinal three chord fanfare found throughout Mysterious Island.

The rationale for this decision stems from the thematic derivation of the harmonies in “The Nautilus”: the cue, like many in Mysterious Island’s score, is based on a germinal motif heard in the opening credits, and twenty-nine (!) additional times prior to “The Nautilus.” The three-chord fanfare is shown in Example 4b, where it is analyzed as a succession of 3rd-relationship spawning RP and LP progressions, combined and reversed so as to return to the original B-min triad. By virtue of the sheer amount of repetition it undergoes, this fanfare cannot help but assume the status of a referential harmonic cell in Herrmann’s score, such that passages with similar but nonexact melodies, textures or progression types are all eventually heard in terms of it. The listener is accustomed to hearing minor triads at the end of three-chord units as progressing via PL∙PR back to the place where the units began. Since “The Nautilus” initiates an identical pattern in its first two measures, whatever pathway the third chord will take to the fourth will invariably be perceived through the lens of the expected first. Transformational analysis brings out this feature in a way no other analytic apparatus can. When E♭ major is heard in m. 4, it is through B minor that it must be referred. The analysis has the progression first “pass back through” B-min en route to E♭-maj, a step that garners PL∙PR, the normative transformation. The difference between expected and actual destination is represented by a further modification to E♭, through a PLP transformation. The result is a compound transformation that derives its intelligibility from the larger context of the score, rather than a rote application of the simplest combination of Ls, Ps, and Rs.

Film Music and Neo-Riemannian Theory

Example 4c: Transformational network for “The Nautilus.”

Analyses of this sort, which rely on a normative transformational frame against which variants and excursions are measured, are most elegantly represented through visual networks.29 Example 4c produces a network for the entire “Nautilus” cue that captures each sounding and possible progression in terms of that basic harmonic frame from the three-chord fanfare. The bolded right triangle consisting of B-,D-, and B♭-min triads is the transformational basis for the cue, while triads E♭-maj and D♯-min are shown attached as harmonic supplements off to the left side. Directed arrows indicate the path taken during the first eight measures, and dotted edges suggest implied but untaken pathways during this segment. A noteworthy aspect of the network is how it reveals that the triad D♯-min effectively creates a mirror-image sub-network to the normative 3-chord fanfare (composed from the same relations of PL, RP and PR∙LP). Such consistency of harmonic shapes and materials helps solidify the impression that E♭ is related primarily to B-min, rather than being an auxiliary chord to B♭ minor. But, more importantly, transformational regularity helps unify the tonal space Herrmann explores throughout the Mysterious Island score, maintaining its enigmatic tone even as it develops originary harmonic materials outside their initial, fairly static reference frame.

III. Voice-Leading

One rarely discussed dimension of film music is voice-leading. This is perhaps because unlike other parametric axes such as dissonance/consonance, tonal proximity/remoteness, and diatonic/chromatic, voice-leading does not suggest an obvious associative lane of interpretation. Neo-Riemannian methods can redress this neglect, directing us to refined but impactful ways in which the treatment of multiple musical lines can influence emotion and narrative. Common-tone retention and parsimony are prime among attributes to which NRT draws attention. L, P, and R are the only motions possible between two triads such that two common tones are preserved while a third is displaced; this leads to the potential of “voice-leading parsimony,” in which a sonority’s pitch classes are either held fast or moved by single tone. While the operators S, and N preserve only a single common pc, their parsimonious credentials are still vouched by the fact that acted-upon triads see their pitches move by only ic1. Like combinatorial complexity, the degree of smoothness achieved— either sounding literally or idealized between abstract Klangs—can provide another informal measure of distance and proximity where progressions seem no longer dictated by diatonic logic. This comes in particularly handy in analyzing the transitions between remote tonal stations; the simple presence of a common-tone connection can soften what may have otherwise been a bumpy path. Parsimony is an especially useful compositional tool if the individual harmonic waypoints themselves bear strikingly different colors. Smooth voice-leading enables them to be stitched together in such a way that their delicate connection may seem almost magical.

In one of the few allusions to film music’s amenability to neo-Riemannian analysis in scholarly literature, theorist Guy Capuzzo enlists the cue “Aniron” from Howard Shore’s The Lord of the Rings: The Fellowship of the Ring (2002), using it as an example of parsimony across chromatic third relations (in an article primarily on pop music and NRT).30 Capuzzo isolates a passage that accompanies an ominous conversation between characters Aragorn and Arwen, shortly preceding a scene change that reveals the two are romantically involved (Image 3).31 Shore provides a brief chorale to accompany their dialogue, an elliptical discussion of Aragorn’s burden as secret heir to the throne. The music is analyzed in Example 5. The pervasive chromatic third relations that Capuzzo observes in this passage are very much tied up with Shore’s voice-leading procedures—they chiefly stem from harmonized neighbor motions involving alternation between root-position and inverted chords. During the vocal portion of the passage, starting at m. 11, the melodic line comes to rest on the common-tone A♭/G♯, while inner voices simultaneously alternate B and C (P) and E and E♭/D♯ (L). This PL compound is mirrored in the linkage of A and F minor by LP at the cue’s onset. The semitonal contrary motion is identical, there with L sending E to F and P sending A to A♭. However, the effect is subtly different due to the absence of common tones in the sustained wholetone pedal pitches, leaving the implication of linear continuity mostly to the melodic arpeggiations in the cello. Along with the comparatively non-parsimonious transition to C-maj in second inversion (a textbook instance of N) the overall trajectory is from greater contrast between chords to less.

Film Music and Neo-Riemannian Theory

Example 5: Howard Shore, analysis of preamble to “Aniron,” from Fellowship of the Ring.

Film Music and Neo-Riemannian Theory

Image 3: Aragorn and Arwen’s romantic tryst.

Shore uses the gradual shift in smoothness to achieve a tranquilizing effect, matching in harmonic content the move from the weighty realm of kingly responsibility into the private safe-haven of Aragorn and Arwen’s romance. The relaxation of voice-leading is reinforced by the overall harmonic exhalation, a kind of global SLIDE (S) from the dark A minor to the softly lit warmth of A♭/G♯ major—shown with the vertical transformation arrow between m. 1 and m. 7. This SLIDE is achieved not by direct motion, but by parsimonious recasting of E as LP-partner of A♭/G♯ (not, as one might expect in a functional setting, as an unrealized dominant of A minor). Perhaps the finest touch is how the LP bringing about the destination key occurs at the moment Arwen begins whispering to Aragorn in Elvish instead of speaking in English. It is a model usage of a major-mode major-mediant progression to suggest otherworldliness and enchantment.

Common tone–retaining operations such as realized in Shore’s Fellowship of the Ring score are esteemed highly by analysts in repertoires where harmonic shifts—and so it is argued, harmonic coherence—are accomplished with parsimonious voice-leading. That so much of Hollywood-style chromaticism hews closely to these conditions says as much about the general desire for linear clarity, or a tactile affinity for certain routines at keyboard/guitar, as it does the inherent structure of the LPRSN group. However, film composers have never felt beholden to principles of common practice voice-leading, such as prohibitions against parallel 8ves and 5ths or avoidance of jumpy bass lines. Considerable swathes of many scores from even the most “classically” trained composers may contain nothing but root position triads. Block-like shuffling of chords, transpositional shifts, and invariant chordal inversions are all common traits of film music, which together should steer us from any reflexive “smoothness = coherence” outlook. Rather, we ought to entertain surface roughness as a compositional choice to be integrated, not ignored or reduced away, within a transformational analysis.

Film Music and Neo-Riemannian Theory

Example 6: Herrmann, registral displacement maximizing disjunction in motif from Mysterious Island.

Thankfully, NRT need not deal solely with literal surface smoothness. It can handle implicit (or “abstract”) parsimony when physical voice-leading consists in something other than a series of clean scootches by little increments. Indeed, LPR compounds quickly generate triadic relations with no common tones. For such rough or “extravagant”32 relations, one has the option of casting them as compounds of LPR, or inventing a unary operation that captures their behavior if tonal context deems them “basic” or “directly intelligible.”33 Linear smoothness should be evaluated along a continuum that can convey dramatic or symbolic meaning. As witnessed in “Aniron,” tightly voice-led passages can map onto states of relaxation or effortlessness, while rough progressions (either complex compounds or bumpily led NROs) may project effort, tension, or intensification, particularly if triadic mode remains invariant. The effect need not be understated as it was during Aragorn’s nocturnal tryst. Take the motivic cell from Herrmann’s Mysterious Island analyzed in Example 6. The tritonal and hexatonic pole progressions are already complex by dint of their lengthy concatenation of NROs, but Herrmann magnifies the disjunction between each by placing chords in differing octaves (indicated with bracketed T-12 transformations). The play with register erases any trace of implicit semitonal voice-leading and evokes a feeling of inassimilable enormity and otherness.

Film Music and Neo-Riemannian Theory

Example 7: James Horner, passage from “You Don’t Dream in Cryo,” from Avatar.

Film Music and Neo-Riemannian Theory

Image 4: Massive strip mining revealed on Surface of Pandora.

An extended passage James Horner’s recent score to Avatar (2008, dir. James Cameron) demonstrates how pronounced motion along the spectrum of smooth⬄rough voice-leading can serve formal and expressive ends. Example 7 provides a heavily reduced transcription of a portion of the film’s first cue “You Don’t Dream in Cryo,” which occurs during an arrival sequence on the alien jungle planet of Pandora. This musical material scores Jake’s (Sam Worthington) preparations for landing, followed by panoramic tracking shot of the arrival, including reveals of the massive ecological devastation to Pandora already wrought by Jake’s military unit. The conclusion of the passage matches the dispatching of the unit onto the planet’s surface. A cursory glance at Horner’s music reveals it is about as far from idealized voice-leading smoothness as is possible without sounding successive chords in different octaves and voicings. Every triad is in root position, even those easily connectable by unary operators, and the first fifteen are all voice-led by brute transposition, with no attempt to convey contrapuntal independence among interior voices. So much for maximal smoothness!

Measures 1–7 of Example 7 accompany the sight of Jake suiting up prior to his disembarking on Pandora. This stretch contains both the roughest voice-leading and the most thoroughgoing triadic chromaticism, with each root relationship following the mostly third-driven melody in doggedly anti-functional fashion. Only the transformations R and RPL could conceivably occupy a diatonic space, and surrounded by so many chromatic progressions, they sound as tonally unanchored as anything else. Yet even within this thicket of parallel voice-leading, a neo-Riemannian methodology can reveal significant aspects of tonal design. Among the first things noticeable from the analysis is the near complete avoidance of transformational repetition. Even as the “melody” [pc 0-4-7-2-5, 1-4-8-2-5, E-2-6 …] adheres to a roughly predictable contour, the chords that decorate it do not. Just as very few triads are heard repeatedly, only one of the nine intertriadic moves are used on more than one occasion. This is RP, shifting minor triads up by m. 3, which by m. 7 lends a light octatonic feel to the overall progression. Harmonic density amidst linear bumpiness is an apt means of reinforcing the affect of the scene. The rigidity of triadic motion aligns with the feeling of imposed militarized order. But that order chafes against the inbuilt apprehension of the tonally ungrounded—and actively parsimony-resistant—progression. Small vacillations in the degree of transformational complexity contribute to the mood of suspense-despite-regimentation. The most parsimonious move, the S in m. 3, provides a momentary sigh within the larger musical sentence, but its calming effect is neutralized as it matches an ancillary character’s reference to the threat of death (a nice instance among many in modern film music of the SLIDE-relation associating with mortality or the uncanny).

The arrival at the next portion of this musical paragraph, mm. 7–9, continues this play with of parsimony and roughness for dramatic effect. A PL progression initiates the new section, just as it did in m. 1, and corresponds to the opening of a new vista: the reveal of staggering ecological devastation on the surface of Pandora. A shot of the denuded landscape is lingered upon, giving Horner a chance to arrest harmonic momentum with a twice-repeated E♭-min⇨D-maj⇨D-min oscillation (driven by SP). This creates another “smooth” respite that nevertheless highlights tonal polarization with its repetition of semitonal major/minor clashes. Measures 10–16 introduce a distinctly different texture and harmonic logic. Here a more active and teleologically driven melody focuses the tonal trajectory into diatonic territory (possibly even monotonal territory in B minor). Horner ushers the music first in another characteristic L oscillation, and then through a series of downwards diatonic thirds (L∙R∙L∙R∙LR) all the way to D. This final section, smoother by virtue of both transformational simplicity and a common-tone preserving melody, provides at last a sense of tonal groundedness, fittingly matching the spacecraft’s landing. The downward-chaining of diatonic thirds and the steadily arching melody also suits the increasing sentimentality of the scene, which ends with Jake reminiscing about how “one life ends, another begins.” As the ship’s crew disembarks on the planet for ethically questionable purposes, radical ambivalence is once again thrown in the mix with a long drawn out S-oscillation that concludes the paragraph.

IV. Tonal Agnosticism

Until the ending of this passage from the Avatar, a sense of stable key is totally absent. The constantly shifting harmonic focus precludes a robust sense of modulation, which requires a cadentially signaled or literally prolonged tonic in the first place. The lack of functional progressions also frustrates and ultimately obviates any definitive enharmonic spelling for chords; for example, the move in m. 3 could just as justifiably been spelled D-min⇨C♯-maj with no meaningful change to the analysis, nor the aural impression of the music. As actions on pitch classes rather than diatonically specified notes, the neo-Riemannian operators are strictly noncommittal with regard to enharmonic spelling. This strategic underdetermination frees the analyst from some of the most vexing problems inherent in analyzing chromatic music. By attending to abstract relations between triads (be they conceived as inversions, displacements, or smoothly accomplished transpositions), one is allowed to skirt issues of function, tonal weight, and prolongation that are so often the cause of analytic capsizing in the turbulent waters of triadic chromaticism. That is not to say that a tonic is necessarily absent in a passage described by NRT analysis; indeed, some of the excerpts already investigated here bear a trace of tonal hierarchy. Rather, such “tonal agnosticism” allows one to concentrate to other musical features which may be more pertinent to a film musical analysis, without having to claim every unusual progression is a cryptically altered diatonic motion or full-blown modulation. This agnostic attitude is at its most liberating when multiple chromatic transformations might otherwise demand answers to sticky questions of enharmonic identity, even when the music is telling us that diatonic scale degrees, or indeed, tonic orientation itself, are not strongly in operation. 34

The advantage of tonal agnosticism can be seen with the Mysterious Island fanfare already analyzed in Example 3a. Approaching the progression with the expectation that its constituents prolong one or more keys leads to being bogged down with unanswerable questions of Film Music and Neo-Riemannian Theory and so on. These tortured attempts to foist the structure of roman numeral space on a refractory progression leave us spinning in interpretive circles and tell us nothing about the actually pertinent qualities of the motif: that it is powered by two parsimonious third relations of differing size (m3 and M3) that together enable an P5-m6-P5 outer-voice pattern and a semitonal descent of both melody and fundamental bass.

While passages where functionality cedes analytic importance to transformational structure are common in film music (Examples 3 and 7 also behave mostly this manner), quite often we are confronted by stretches of underscore in which chromatic and diatonic logics interact in a meaning-generating way. Composers are quick to exploit the overlap of harmonic domains thanks to the potent ingredients of tonal associativity: the linkage of functional tonality, even in the most chromatic settings, with stability and normality and nondiatonic harmony with instability and difference. The push and pull of different modes of triadic organization can be observed in Alfred Newman’s music to Song of Bernadette (1943, dir. Henry King). Bernadette is a religious drama chronicling the visions of the Virgin Mary allegedly witnessed by a French teenager, Bernadette Soubirous, in the mid-nineteenth century. Newman employs the same deeply mannered late-Romantic language that was second nature to composers of Hollywood’s Golden Age, and the score reflects this aesthetic with its antique church-modal-meets-Mahler tonal rhetoric. It is a highly apt hybrid idiom, allowing Newman to suggest spiritual transcendence through means well described by neo-Riemannian analysis.

Film Music and Neo-Riemannian Theory

Example 8a: Alfred Newman, reveal of Virgin Mary, from Song of Bernadette.

Film Music and Neo-Riemannian Theory

Image 5: Virgin Mary’s F-major reveal.

Throughout The Song of Bernadette, Newman employs a clever strategy to evoke encounters of the human and divine: the alternation of modal and chromatic intervals between chords. “Modal” here is taken to include harmonic relationships available through the diatonic collection but not necessarily incorporating clear tonal function. In transformational terms, such moves are describable by a compounding of L and R but not P relations. Bernadette’s first vision of the Marian miracle, near a secluded grotto, is telegraphed with the passage reproduced in Example 8a below. The reveal of the figure of the Virgin (Image 5) synchronizes with a blazing B♭ major triad, the telic achievement of the music’s mounting volume and orchestral register. Indirect though it is, the overall progression is from F major to B♭ major. (Not pictured is a strong cadence into F-maj before the first measure.) The musical vision thus bears the residue of a customary dominant⇨tonic motion. Nonetheless, the succession is driven by a heaven-striving melodic line (C6 to B♭6) and the alternation of modal and chromatic moves—not any innate need to cadence. The seemingly atonal bass contributes to the impression of a forcible sundering of high and low, base(/bass) and empyrean. Despite its picturesque quality, however, the cello line can be treated as harmonically inessential, adorning more fundamental triadic pitches with piquant unresolved neighbors.

Film Music and Neo-Riemannian Theory

Example 8b: Analysis of reveal of Virgin Mary in Song of Bernadette.

The transformational analysis of Example 8b shows how the division of earthly and divine musical parameters plays out on a horizontal as well as vertical plane. With two PLs and a mighty tritonal RPRP, the first, third, and fifth chromatic transformations tug the tonal field away from any stable diatonic collection. Transformations 2 and 4, by contrast, gesture back toward diatonic firmament, even if the keys they specify are underdetermined. For this reason, any feasible roman numeral routines are left in scare quotes and are assigned more neutral “modal” Tn-type operations.

The progression that supports this revelation is transitional, preparing as it does the first major statement of Bernadette’s vision theme in B♭. Newman, however, goes on to circumvents the typical strategy of Classical-era scoring in which triadic chromaticism happens only during transitions and diatonic harmony and monotonality reign over thematic statements. Instead, Bernadette’s theme is itself intensely chromatic, and the cue loosens its grip on B♭ almost immediately after the key is captured, modulating widely for the remaining two minutes of the teenager’s holy visitation. When inspected in terms of overall progress from one key area to another, Newman’s cue shows a similar pattern to the surface-level alternation observed in the “Reveal” progression.

Film Music and Neo-Riemannian Theory

Example 8c: Tonal design of entire “first vision” cue.

Example 8c provides an overview of the entire tonal trajectory of the scene, from the tonally hazy material that precedes the reveal through the capture of B♭ and subsequent peregrinations, all the way to the conclusive E major. The mix of solid and broken lines reflects aspects of the cue’s tonal design. Dotted nodes, such as surround F♯ and C♯, entail weakly articulated tonal centers, and dotted arrows connect portions of the cue where the relevant transformation is not heard literally (that is, there is intervening material that separates tonics). As with the “reveal progression” of Example 8b, the principal chromatic motion is that of the mode-retaining major third progression. Similarly shared with 8b is the balanced admixture of chromatic and modal shifts, although here they are accomplished through medium-scale modulations rather than immediate chordal alterations. The only break in the pattern, the move from G♭ to G, is more of a synthesis of the two tonal strategies, a functionally explicable but nevertheless nondiatonic surprise cadence into G major. It is with touches like this, stratifying and synthesizing modal and chromatic impulses, that Newman is able so evocatively to paint a musical portrait of the humble teenager’s mystical ecstasy.

V. Symmetry

Film Music and Neo-Riemannian Theory

Example 9a: Hyper-Hexatonic system.

Film Music and Neo-Riemannian Theory

Example 9b: Hyper-Octatonic system.

Because the basic units of neo-Riemannian analysis are mode-flips and third relations, the symmetrical scale partitions that result from their iterations are accorded great theoretical emphasis. Symmetry has tremendous advantages for organizing disparate-seeming components of music, and it is an analytic aspiration, acknowledged or not, of almost any transformational network. The cycles most familiar to chromatic theory include the hexatonic (iterated LP/PL) and octatonic (RP/PR) systems, as well as Weitzmann regions (NR/RN) and the region that cycles through all six triads sharing a single pitch class (LPRLPR/PLRPLR/RLPRLP).35 Example 9 shows the layout of first two of these symmetrical spaces, using the conventionalized nomenclature for constituent cycles within the hyper hex- and octatonic universe (cardinal directions for the former, unique pitch class content for the latter). Segments of these cycles can be found in all eras and styles of film music. Though less common, complete cyclical rotations are notable elements of the scores from several composers like Miklós Rózsa and Jerry Goldsmith, who make heavy use of octatonic and hexatonic materials. Very often, cyclical completion is not so much the driving force of underscore as it is a by-product of the reinforcement and affective redoubling of single progression through repetition. When many of these progressions are linked, the result can have pronounced effects on the perceived temporal flow of a scene. With the right texture and pacing, harmonic symmetry can make cinematic time seem to stand still due to the uniformity of tonal procedures, or to speed up with the constant intensification that comes from iterated chromatic patterns.

Octatonic Ladders in Back to the Future

The lure of octatonicism has held a special sway over film composers since the silent era. The cinematic ubiquity of octatonic materials (anything deriving from the set <0134679T>) owes much to the retention of Classical/Romantic associations surrounding the diminished seventh sonority, that reliable common practice capsule of maximized tertian dissonance and ambiguity. Used very much like an attention-grabbing “stinger” (to borrow film musicological terminology) in Mozart and Beethoven, the diminished seventh-as-shock-chord was already becoming a clichéd resource in the time of Schubert and Berlioz.36 Outworness had little effect in dissuading film composers from its employment, however. Composed-out diminished seventh chords are a predictable standby in music from the earliest scores and countless silent music anthologies with conventionalized musical topics—mysteriosos, hurries, fights, storms, struggles, and so on.37 While the tremolo dim sevenths of the proverbial damsel-tied-to-railway scene are far too imprinted by “old fashioned” and “corny” associations for today’s filmgoers, composers still make use of the underlying logic of stacked minor thirds and tritones to generate unbearable tension.

Alan Silvestri’s scores from the 1980s and 1990s contain some of the most thoroughgoing octatonicism in modern Hollywood. Soundtracks for films of as diverse genres as Predator, Who Framed Roger Rabbit, Death Becomes Her, and Contact are in places saturated with the collection. A distinctly Stravinskyian rhythmic and motivic sensibility betrays a probable inspiration for much of Silvestri’s octatonic music, though by the late 1990s the Russian influences are so thoroughly integrated into Silvestri’s own tuneful style that there is little point in drawing connections between, say, a tense cue such as Contact’s “Good To Go” and the Symphony in Three Movements.38 As we find in Stravinsky, Silvestri’s octatonic sonorities are often dissonant set classes rather than pure triads. This poses a problem for neo-Riemannian analysis, which is configured to deal with (037)s. Still, the central concerns of NRT—enharmonicism, voice-leading, symmetry and balance, harmonic space, and non-diatonic but tertian organization—remain operative, and thus offer a constructive investigative avenue into Silvestri’s oeuvre.

Minor third–derived sonorities and transformations infuse several cues from Silvestri’s most famous score, Back To The Future (1985, dir. Robert Zemeckis), most notably the lengthy action set piece “The Libyans” from the film’s first act. In the scene in question, the mad scientist Doc Brown (Christopher Lloyd) and his spirited protégé Marty McFly (Michael J. Fox) prepare for Brown’s inaugural visit to the future via his time machine–equipped DeLorean. The launch is interrupted when a van full of Libyans, incensed by Doc Brown’s theft of their plutonium, shoot and kill Brown and pursue McFly (Image 6). The hero escapes by accelerating the DeLorean to its maximum speed, triggering its time-travel mechanism and hurtling him into the past, just in the nick of time.

Film Music and Neo-Riemannian Theory

Example 10: Alan Silvestri, cell from “The Libyans” (Event d. to f.), from Back to the Future.

Film Music and Neo-Riemannian TheoryFilm Music and Neo-Riemannian Theory

Images 6a and b: The Libyans’ untimely arrival.

Silvestri’s music for the scene, almost five straight minutes, is as suffused with octatonicism as stock piano music for a train chase in 1915—although without ever outright stating a diminished seventh chord. Nor does Silvestri take the route accustomed from a composer such as Rózsa and employ direct RP/PR progressions to transit between m3-related chords. Instead, to continually ramp up musical urgency, he employs a more fundamentally transpositional, rather than smoothly displacemental, technique of harmonic transformation. Musical cells, such as the one reproduced in Example 10, contain equal parts melodic octatonicism (such as the T6-alternating ostinato bass), chordal superimposition (such as the overlaid and E and B♭ chords in m. 6) and incremental transposition up m. 3 (such as with the shift from C♯ to E to G). The seven measures of Example 10 accompany a moment of rapidly escalating tension, with the T3 from C♯ to E corresponding with the antagonists aiming their weapons at Doc Brown, and the parallel move up to G matching the realization that Brown’s pistol has no ammunition.

Film Music and Neo-Riemannian Theory

Example 11: Reduction of “The Libyans.”

The continual transference up the E-G-B♭-C♯ octatonic ladder is the tonal basis for Silvestri’s cue on several levels. Example 11 provides a reduction of the harmonic content for the entirety of “The Libyans,” along with indications of the shifts in dramatic action that occur at each carefully aligned synch point. Many of the reduced sonorities are not literal simultaneities but prominent horizontalized portions of the octatonic scale. Until event q., Silvestri’s pitch materials remain almost exclusively in the <1,2> octatonic collection. Also essentially invariant is the transpositional scheme. From events b. to j. and l. to o., the cue rotates around this collection more than three full times, spending almost 75 percent of its duration looping up this minor third cycle.

With this high degree of harmonic and motivic uniformity, any pattern-breaking progression becomes highly salient. Instances of interruption, resumption, and recasting of cyclical processes are critical devices for breathing dramatic variety into the repetitiousness of symmetry-driven sequences, and Silvestri recruits all three as the cue proceeds. The first major instance of interruption/resumption occurs precisely at the moment of tragic surprise of Doc Brown’s death (events j. through l.). This shocking twist forces a brief reversal of direction along the octatonic ladder, with a T9 dragging the B♭ bass back to its predecessor G. It is a rather literal “setback” in the otherwise ineluctable T3 climb toward the scene’s telos of arriving in the future.

The octatonic engine does not break down with Brown’s death but quickly resumes its revolutions as soon as Marty evades the assailants after event k. The cycle does change character dramatically at this stage, however. The second large formal segment of “The Libyans” (shown in the lower system of the reduction, starting with event q.) gradually breaks free of the established pattern once Marty’s heroics install a more optimistic, if still highly tense, tone to the scene. This is accomplished through a variety of tonal and thematic devices. First, Silvestri performs a hypermodulation to transfer the accustomed oct <1,2> collection to the fresh <0,2> (or F-A♭-B-D) system, switching ladders as it were and recasting the cue’s tonal “background” up a literal T1. Newly major-hued vertical harmony and more conventional functional progressions also begin to take effect at event r. The upwards T3’s return at event s., but with inverted major triads separated by whole-tone passing chords. These are clear indicators that the film’s heroic and lydian-inflected main theme is increasingly asserting itself over the cue’s erstwhile m. 3 intervallic obsessions.

The moment of cyclical completion arrives at event t., back to F major, heralded by a blazing but truncated statement of the main theme. This is a fitting harmonic telos by virtue of its synthesis of lydian, octatonic, and functional diatonic tonal components. The cycle is not quite done however, and one final upward twist greets the ultimate threat: a rocket launcher aimed at McFly. Even so, the sense of musical danger has greatly dissipated by this point. A newly strong sense of linear parsimony (indicated by the use of LRP compounds for the first time in the analysis) helps to support this first diegetic statement of the main theme. A♭ major is established at event v. and does not loosen its hold for the remainder of the cue, even projecting a shade of traditional diatonic prolongation between v. and z.. A last burst of octatonic panic at event y. matches the last-ditch threat that the escape vehicle will not successfully travel back in time in time, but an instantaneous success chord of A♭ at z. insures that all is well.

Hexatonic Gyrations in The Sea Hawk

Whereas the octatonic scale and associated progressions has held a lingering grip on film composers due to its connection with suspense, its sister collection, the hexatonic (<014589>) has retained Romantic connotations with magic, mystery, and the otherwordly.39 Chromatic major third progressions pepper scores from all sorts of genres and eras; the superhero, fantasy, and historical drama examples from Williams, Shore, and Newman already discussed derive much of their harmonic suggestiveness in PL and PLP. Just as the octatonic sound is linked with the crunchy diminished seventh, the distinctive quality of the augmented triad—that famously disorienting and ambivalent sonority—contributes much to hexatonicism’s fascination for film composers. Hexatonic progressions, cycles, and cycle segments abound where film composers seek to evoke the fantastic. When conjoined with certain stereotyped modulatory techniques, these types of progressions make up a considerable portion of what some intuitively might call the “film music sound.” Yet hex materials are not limited to moments of extremity or strangeness; in the hands of some composers, a PL may be all that is needed to lend extra verve to a swaggering swashbuckler leitmotif or sweep to a swooning love theme.

Film Music and Neo-Riemannian Theory

Example 12: Erich Wolfgang Korngold, assorted hexatonic materials from Sea Hawk action music.

Example 12a: Downward surface-level M3 cycle in “The Battle.”

Film Music and Neo-Riemannian Theory

Example 12b: Upwards phrase-level M3 cycle in “The Battle.”

Film Music and Neo-Riemannian Theory

Example 12c: Whole-tone surface-level melodic sequence and downward overall M3 progression in “The Duel.”

Film Music and Neo-Riemannian Theory

Example 12d: Downward surface-level M3 cycle in “The Duel.”

Film Music and Neo-Riemannian TheoryFilm Music and Neo-Riemannian Theory

Image 7: The Sea Hawk opening naval battle and final duel.

One of the most impressive instances of hexatonic magic in film music is Erich Wolfgang Korngold score to The Sea Hawk (1940, dir. Michael Curtiz), a rip-roaring nautical adventure starring Errol Flynn as the English privateer Geoffrey Thorpe. Throughout the soundtrack, hexatonic organization steers the musical fore- and shallow middle-ground. This can be observed especially in his music for action scenes, in which brief M3 cycles govern the musical surface while stepwise intensificatory modulations and interjections of heroic diatonic themes direct the cue’s overall tonal course. Example 12 presents a small gallery of short extracts from two fight sequences, the first the film’s opening naval battle and the second the climactic duel (Images 7). A variation on The Sea Hawk’s main “Romance theme,” (explored in depth further on), Example 12a spirals down the G-E♭-B augmented triad (of the Western system). Ex 12b sends a more extended thematic idea up the D-F♯-B♭ (southern) circle of major thirds, connecting tonics indirectly through a deft chromatic modulation. The measure-long sequence of Example 12c, from the final combat scene, accomplishes an overall shift down one major third, from E to C, during its course. Rather than pure hexatonicism, the overriding tonal force is its constantly ascending whole-tone scales, products of melodic M2 + M2 trichords racing above a restless tritonal sequence below. Example 12d, perhaps the most straightforwardly (048)-spawned motif in the score, simply races down the (northern) C-A♭-E chord, though the bass line, working in contrary motion, provides a non-augmented (but still firmly hexatonic) supporting edifice. Collectively, these motifs supply tonal disorientation and turbulence for their scenes of swashbuckling excitement. Each dashes from one barely established tonal center to another, resting on one chordal footing only for as long as it takes to make the swing over to a new one.

Film Music and Neo-Riemannian Theory

Example 13: Korngold, Sea Hawk romance theme.

Given the pugnacious provenance of these motifs, it may come as a surprise that the ultimate source for hexatonic materials in The Sea Hawk’s score is a sweeping lyrical melody heard in the main title cue, reproduced in Example 13. The broad rounded binary/small ternary form, scored with soaring strings and luscious homophonic accompaniment, stands in affective contrast to both the fight music motives above and to the heroically brash A theme that precedes it in the titles. This “Romance Theme” offers a prime instance of the contrastingly melodious second-theme paradigm de rigueur for main title cues in Classical Hollywood.40 Swooning lyricism does not equate with diatonicism here, however: the musical idea is hexatonic from top to bottom, with the western hexatonic system (E♭-G–B) guiding almost every move on the fore-, middle- and background levels.

The theme’s ostensible tonic is the B major that initiates each of its two phrases, yet its upper major mediant, E♭, encloses it at both ends. Measures 1–3 of Example 13, the transitional tail end of the heroic A theme, showcase a prolongation of E♭ by a brisk major third cycle through G and B major. E♭ also serves as the modulatory goal for the theme’s second half, and following its capture in m. 15, is solidified with an restatement of the title’s heroic fanfare in that key. The entire segment of the main title has something of an LP∙PL(E♭) background. Closer to the surface, the independent keys Korngold traverses within each phrase also fall entirely within the western hexatonic compass. Even the dominant thirteenth chords that facilitate the sequencing at the end of the second phrase serve as much as first-inversion hexatonic mediants as root-position dominants, and they support a melody made up of the pitches of the <37E> augmented triad. Although a handful of surface level harmonies behave diatonically, they serve to tonicize G, B, or E♭, leading to an overall impression of unadulterated hexatonic magic.

Film Music and Neo-Riemannian Theory

Example 14a: Analysis of m. 4–8.

Film Music and Neo-Riemannian Theory

Example 14b: Analysis of mm. 8–11.

Examples 14a through 14c convert these observations into transformation networks, all of which use the six-sided outline of the western hexatonic system as their scaffolding. As in previous networks, implied but indirect connections are conveyed through dotted arrows. New to these diagrams is the addition of small triadic nodes that house chords not strictly within the governing space of the network; these account for the occasional dominants and predominants that secure various pegs along the hexatonic cycle but do not draw their pitches from it. For clarity’s sake, functioning dominants are housed “inside” the hexagon and predominants outside of it. With measures 4–8, charted in Ex 14a, it is evident that the first pass through this network is a complete B⇨G⇨E♭…. A dotted arrow summarizes the trajectory of measures 3–5, which on their surface rely on the insertion temporary non-hex chords to stretch out the span between E♭ and B major. The second phrase is a varied repetition of the first that sees the extra-hexatonic F-minor triad landing on B minor rather than G minor; this shift signals realignment of the rotation through the western hex system from clockwise to counterclockwise. Otherwise, B minor behaves much as G did in the previous pass, acting as a functioning predominant en-route to a hasty cadential affirmation of G major.

Film Music and Neo-Riemannian Theory

Example 14c: Analysis of mm. 12–18.

As Example 14c shows, the longer consequent phrase for the theme (mm. 12–18), makes good on this reversal of direction, depositing the listener first in B and then in E♭ once again, both of which are prepared similarly to G by their own personal dominants (which are effectively hexatonic slash-chords). In fact, Korngold’s systematized visitation of these three dominant chordal roots creates its own implicit internal major third cycle, a circuitous hopscotch from D to F♯ to B♭, which suggests an enclosed, hierarchically lower eastern hex system. With a little additional diatonic meandering around E, Korngold wraps up his theme and prepares for the resumption of the A theme.

Film Music and Neo-Riemannian Theory

Example 15: “Background” analysis of entire Sea Hawk romance theme.

To synthesize the rotations that each segment takes through hexatonic space, Example 15 offers an overall analysis of the romance theme. Visits to non-B/E♭/G-major pegs are elided to provide the clearest picture of how the hexatonic way stations form the basis of the theme’s symmetrical gyrations. All told, there are six successive full or partial (including dotted arcs) rotations through the western hexatonic system, represented by the six concentric loops that encircle B, E♭, and G. Loop size corresponds purely with chronology. Motions within the theme (everything from mm. 4–18) are demarcated by their occurrence within the blue hexagon, a matter of pure graphical convenience to segregate it from the pre-theme third progressions that get the ball rolling in mm. 1–3.

What is remarkable about the tightly coiled hexatonicism evinced by this background level network is not its total referability to a single symmetrical space per se. Passages of comparably thorough hexatonicism are widespread in the Romantic repertoire and have already been well-dissected by neo-Riemannian analysts. What distinguishes Korngold’s Sea Hawk theme and many other works in the larger Hollywood harmonic practice is the fashion in which pan-triadic chromaticism is accommodated seamlessly into a formally straightforward—and singable—melodic structure. The transformational corkscrews here are not tonal special effects as they so often are in Romantic musical rhetoric—the familiar Lisztian modulations, Schubertian transitions, Brucknerian sequences, or Wagnerian continuous stretches of developmental prose. Rather, they are essential and smoothly assimilated components of the very fabric of a lyrical theme, replacing diatonic logic on all but the most superficial levels. Even though the example comes from an extra-narratival overture rather than diegetic underscore, its incorporation of neo-Riemannian transformations is emblematic of Hollywood chromaticism in general. Absent common-practice regulative musical syntaxes such as monotonality or long-range prolongation, chromaticism in film music frequently finds a way to penetrate many levels of musical structure. Best of all for filmgoers, this is done without losing any of the associative “oomph” that attracts so many dramatically minded composers to symmetrical progressions in the first place.

VI. Prospects

I have argued here that the range of applications of transformational thinking and neo-Riemannian tools to film music analysis is promisingly wide. The prospects for further research uniting NRT and film musicology are bright—for several reasons brighter than previous attempts to bring the traditional concerns of music theory to cinema soundtracks. Unlike the scattered attempts to incorporate Schenkerian thought to film score analysis during the 1970s through 1990s, the present moment seems poised to witness healthy expansion and development in “film music theory.”41 In particular, neo-Riemannian theory is sufficiently novel to be a source of excitement to many theorists, but, with the publication of several dedicated monographs/anthologies and routine conference panels, it has matured out of its stage of scholarly growing pains. Elements of NRT are widely taught and understood, in some locations even at the undergraduate level. Something similar is true of film musicology, which is now firmly established and enjoying remarkable growth, albeit with still little in the way of contributions from music theorists. That so much of the most characteristic music of the silver screen conforms smoothly to the analytic desiderata of transformation theory makes the union of these two disciplines a natural and encouraging development.

Much remains to be done before something like “transformational film music theory” can be trumpeted. Although I have outlined some of the ways in which the technical machinery of NRT can contribute to our understanding of film musical structure (and vice versa), the value of transformational thinking goes far beyond the recognition of combinatoriality, parsimony, enharmonicism, or symmetry in film music. Among the largely unexplored avenues that theorists and film musicologists can most productively investigate:

  1. 1. Stylistic evolution. Film music practice is no more a unified idiom than nineteenth century Romanticism. Indeed, because of variety of dramatic purposes/genres and national subcultures, it contains within it a far greater eclecticism in its styles and methods than practically any arbitrary span of previous music history. An important contribution neo-Riemannian methods can offer, then, is the tracking of differences across practices, both in place and time. Where one progression falls out of favor and another takes its place, when certain linear routines become a norm rather than a special effect—these are stylistic questions that transformational theory is primed to answer.

  2. 2. Aesthetics: The remarkable longevity of the fantastic associations of chromaticism should be plainly evident in the examples on display in this chapter. Less obvious is why triadic transformations should hold the affective sway they do in film musical practices. Rather than falling back on analytical bad habits, such as lumping all mediant progressions together as “coloristic” or “bizarre,” transformational methods can arrive at fine-tuned distinctions in quality and usage of harmonic routines. Such work as Cohn’s semiotics of the hexatonic pole, Bribitzer-Stull’s on the Tarnhelm progression, Murphy’s work on many of the remaining progression classes, points to one way in which an aesthetic of film harmony may benefit from transformational tools. Other ways, suggested by the hermeneutic orientation of this chapter, may involve investigating the relationship of voice-leading or symmetry to larger units of musical discourse than the atoms of absolute progressions.

  3. 3. Non-triadic Harmony: Neo-Riemannian operators constrain one’s focus to motions between consonant triads. But film music draws on a much richer vocabulary of sonorities than simple major and minor chords. Though the NROs offer less help there, specialized operations for 7th chords (developed independently by several theorists) as well as generic transformational tools, such as GISes and Tn/In networks, offer an auspicious way into the music of composers with complex harmonic languages, including the neglected figures of Leonard Rosenman, Jerry Fielding, David Shire, and John Corigliano.

  4. 4. Nonc-chromatic Harmony: If a transformational theory can be applied to non-triadic harmony, it can also be reconfigured to handle functional diatonic music—which makes up the vast majority of non-genre film scoring—with equal facility. Diatonic function was built into Lewin’s vision of transformational analysis from the beginning, and recent work from Steven Rings indicates that tonality, viewed through a transformational lens, can yield surprisingly deep (and, useful for film music, hermeneutically rich) insights.

  5. 5. Score Analysis: The passages analyzed by neo-Riemannian theory tend to be restricted in scope, demonstrating interesting features at the level of the progression rather than larger scale formal units. While there are good reasons for this, mindful application of transformational thinking to broader spans of musical content can provide a way to track patterns of change and evolution in the grosser components of a film score (whole cues, or even soundtracks) while sidestepping fraught grounds of searching for something like “a movie’s home key.”

  6. 6. Repertoires: Hollywood genre film proffered the bulk of the examples investigated in this chapter. However, generic domain—underanalyzed by theorists as it is—makes up but one of the promising repertoires that these methods could benefit. Alternative corpuses are an obvious place to start, including the huge worlds of independent and international film. Television, a sister repertoire to film but one with sometimes importantly different practices, is another. Video game music comprises another area with emerging analytical literature that could profit from transformational approaches. Particularly because of their distinct modes of listening and temporality, electronic games may generate insights into musical transformation unavailable to the linear structure shared by film and concert musics.

As music theory continues to healthily shed its preoccupation with western art musics in favor of a more ecumenical purview, it is hoped that these sites for further investigation (and many more in the vast universe of music for screen) will garner full treatments warranted by their scope and relevance to contemporary listeners. Once momentum gathers for analyzing film music, the prospect of delving into such a rewarding repertoire, so close to home for many, should promise transformations of film musicology and theory undreamt of even a decade ago. Film music will then finally no longer resemble an untouched “mysterious island” of a repertoire.


I would like to thank Alex Rehding, Christopher Hasty, and especially Scott Murphy for their generous feedback and advice at various stages of this research.


(1) Richard Cohn’s article, “An Introduction to Neo-Riemannian Theory: A Survey and Historical Perspective,” Journal of Music Theory 42.2 (1998), presents the domain of this theoretical system—both in terms of repertoire and conceptual apparatus—as squarely located in the nineteenth century.

(2) A concise account of the origins of dualist thinking can be found in Henry Klumpenhouwer’s “Dualist Tonal Space and Transformation in Nineteenth-Century Thought,” in The Cambridge History of Western Music Theory, ed. Thomas Christensen (Cambridge, UK: Cambridge University Press, 2002). For an introduction to and reevaluation of harmonic dualism in Riemann specifically, see Alexander Rehding, Hugo Riemann and the Birth of Modern Musical Thought (Cambridge, UK: Cambridge University Press, 2003). Contemporary defenses, critiques, and analytic applications of this highly contentious theoretical attitude can be found, respectively, in Klumpenhouwer “Harmonic Dualism as Historical and Structural Imperative”; Dmitri Tymoczko “Dualism and the Beholder’s Eye: Inversional Symmetry in Chromatic Tonal Music”; and Rehding “Dualistic Forms”, all in The Oxford Handbook to Neo-Riemannian Music Theories, ed. Alexander Rehding and Edward Gollin (Oxford, UK: Oxford University Press, 2011).

(3) See Edward Gollin, “From Matrix to Map: Tonbestimmung, the Tonnetz, and Riemann’s Combinatorial Conception of the Interval,” in Oxford Handbook to Neo-Riemannian Music Theories (OHTNRMT). Gollin locates the origins of Riemann’s symbolic and combinatorial (and, for neo-Riemannians, protoalgebraic) representation of tone relations in the work of Moritz Drobisch. Nora Engebretsen discusses Riemann’s versatile taxonomy of root-relations and their relation to current transformational attitudes in “Neo-Riemannian Perspectives on the Harmonieschritte” in OHTNRMT. The “UTT” system devised by Julian Hook in “Uniform Triadic Transformations,” Journal of Music Theory 46.1–2 (2002) presents the culmination of the Riemannian abstraction of harmonic progressions to algebraic functions.

(4) Background on tone networks and applications to modern transformational theories can be found in Kevin Mooney, “The ‘Table of Relations’ and Music Psychology in Hugo Riemann’s Harmonic Theory” (Ph.D. diss., New York, Columbia University, 1996) and Gollin, “Representations of Space and Conceptions of Distance in Transformational Theories” (Ph.D. diss., Cambridge, MA, Harvard University, 2000).

(5) The centrality of the romantic repertoire to NRT is clear in the objects of some of its most notable analyses. These include Cohn, “As Wonderful as Star Clusters: Instruments for Gazing at Tonality in Schubert,” Nineteenth-Century Music 22.3 (1999); David Lewin, “Some Notes on Analyzing Wagner: The Ring and Parsifal,” 19th-Century Music 16.1 (1992); and all the case studies in David Kopp’s Chromatic Transformations in Nineteenth-Century Music (Cambridge, UK: Cambridge University Press, 2002).

(6) The idea that non-monotonality and pervasive chromaticism in the nineteenth century constitutes a genuinely distinct tonal mode of composition (and hearing) from common practice tonality is explored in the essays of William Kinderman and Harald Krebs’ The Second Practice of Nineteenth Century Tonality (Lincoln: University of Nebraska Press, 1996). This notion is further treated by Tymoczko, “Dualism and the Beholder’s Eye” and Cohn, Audacious Euphony: Chromaticism and the Triad’s Second Nature (Oxford, UK: Oxford University Press, 2012).

(7) The Lewinian attitude towards music as a product of active changes rather than discrete objects is one of the most significant and enduring legacies of modern music theory; its foundational text is Lewin, Generalized Musical Intervals and Transformations (New York: Oxford University Press, 2007). Steven Rings’s work carries on this tradition strongly, nicely outlining it in Tonality and Transformation (Oxford, UK: Oxford University Press, 2011). The transformational stance is provided intellectual background in Klumpenhouwer, “In Order to Stay Asleep as Observers: The Nature and Origins of Anti-Cartesian in Lewin’s GMIT,” Music Theory Spectrum 28.2 (2006), and problematized in Harrison, “Three Short Essays on Neo-Riemannian Theory,” in OHTNRMT, 2011.

(8) See Guy Capuzzo, “Neo-Riemannian Theory and the Analysis of Pop-Rock Music,” Music Theory Spectrum 26.2 (2004).

(9) See Maristella Feustle, “Neo-Riemannian Theory and Post-Bop Jazz: Applications of an Extended Analytical Framework for Seventh Chords,” (PhD diss., Bowling Green University, 2005); Capuzzo, “Pat Martino and the ‘Nature of the Guitar’: An Intersection of Neo-Riemannian Theory and Jazz Theory,” Music Theory Online 12.1 (2006); John Bishop, “A Permutational Triadic Approach to Jazz Harmony and the Chord/Scale Relationship,” (Ph.D. diss., Baton Rouge, Louisiana State University, 2012); and Sara Briginshaw, “A Neo-Riemannian Approach to Jazz Analysis,” Nota Bene: The Canadian Undergraduate Journal of Research 5.1 (2012).

(10) See Harrison, “Three Essays,” and Timothy Johnson, John Adams’s Nixon in China (Farnham, UK: Ashgate, 2011).

(11) There is also good reason to expand NRT’s musical scope: it magnifies its pedagogical value for students more familiar with Radiohead than Reger. See, for example Nora Engebretsen and Per Broman’s article “Transformational Theory in the Undergraduate Curriculum: A Case for Teaching the Neo-Riemannian Approach,” Journal of Music Theory Pedagogy 21 (2007).

(12) All musical examples in this article are solely the product of the author’s own transcription from film DVDs and soundtrack albums.

(13) One theorist who has contemplated the possibility of film-spanning tonal design is Ronald Rodman. See Rodman, “Tonal Closure and Design in The Wizard of Oz,” Indiana Theory Review (1998); and “Tonal Design and the Aesthetic of Pastiche in Herbert Stothart’s Maytime” in Music and Cinema, ed. James Buhler et al. (Hanover, NH: Wesleyan University Press, 2000).

(14) David Neumeyer considers the standard categories of large-scale tonal structure in light of the logistical demands of film composition. He concludes that projecting tonal norms from concert music onto soundtracks is a questionable enterprise, one that should be entertained only in exceptional cases and with an eye to music’s associational, rather than abstract and teleological, qualities. See Neumeyer, “Tonal Design and Narrative in Film Music: Herrmann’s A Portrait of Hitch and The Trouble with Harry,” Indiana Theory Review (2001). For a perspective on classical cadential categories in film music, see Lehman, “Hollywood Cadences: Music and the Structure of Cinematic Expectation,” Music Theory Online 19.4 (2013).

(15) For a description of the state of music theory in film musicology, see Lehman, “Music Theory Through the Lens of Film,” Journal of Film Music 5.1-2 (2013). A pandisciplinary survey that includes reference to extant theory research in film studies can be found in Robyn Stillwell, “Film Music Literature Review,” Journal of Film Music 1.1 (2002).

(16) What exists of a literature on transformational film music analysis is largely the product of one theorist, Scott Murphy. Murphy’s primary line of research has been the application of the Kurthian concept of “absolute progression” to film musical syntax. Representative publications of his in this area include “The Major Tritone Progression in Recent Hollywood Science Fiction Films” (Music Theory Online 12.2, 2006); “The Tritone Within: Interpreting Harmony in Elliot Goldenthat’s Score for Final Fantasy: The Spirits Within” in The Music of Fantasy Cinema, ed. Janet K. Halfyard (Sheffield: Equinox Publishing Ltd, 2012); “Transformational Theory and the Analysis of Film Music” in The Oxford Handbook of Film Music Studies, ed. David Neumeyer (Oxford, UK: Oxford University Press, 2013); and “Scoring Loss in Recent Popular Film and Television,” Music Theory Spectrum (forthcoming). The author’s own work on neo-Riemannian analysis of film music can be found in Lehman, “Transformational Analysis and the Representation of Genius in Film Music,” Music Theory Spectrum 35.1 (2013); “Reading Tonality Through Film: Transformational Hermeneutics and the Music of Hollywood,” (Ph.D. diss., Cambridge, MA, Harvard University, 2012); and “Frame-Scapes: Exploring Boundaries in Goldsmith’s Star Trek,” Paper presented at New York Music and Moving Image Conference (May 2011).

(17) Some forays into the aesthetics of film chromaticism include Royal Brown, Undertones and Overtones: Reading Film Music (Berkeley: University of California Press, 1994); Janet Halfyard, “Music Afoot: Supernatural Horror-comedies and the Diabolus in Musica” in Music in The Horror Film, ed. Neil Lerner (New York: Routledge, 2009); and Ilario Meandri, “Dal Meraviglioso all’Antimusica su alcuni cliché del fantastico nel mainstream musicale hollywoodiano” in Suono/Immagine/Genere, ed. Ilario Meandri and Andrea Valle (Turin: Kaplan, 2011).

(18) These are the only five operators that involve two or fewer semitonal displacements. This accounts for the nonadmission of Cohn’s H(expole, e.g., C-maj⬄A♭-min) and my own M(odalverwandt, e.g., C-maj⬄G-min), both of which have a voice-leading work value of 3.

(19) One could also incorporate nondualistic transformations into such an inventory. These may be simple transpositions (Tn-type operations) or Lewinian diatonic-functional transformations (such as DOM or MED). While such extended libraries of available moves may have their uses in studies where functional tonicity is an important parameter, I focus on more purely chromatic passages (hence the more homogenous dualistic family).

(20) S, the so-called “SLIDE” relation, has the peculiar role of altering chord quality while retaining the triadic third. This quality opens the door for a variety of interesting usages and associations in film music, such as representation of dream-space in Hans Zimmer’s Inception or undeath in James Newton Howard’s The Sixth Sense.

(21) The properties of generalized L, P, and R operators are explored in Cohn, “Neo-Riemannian Operations, Parsimonious trichords, and Their “Tonnetz” Representations,” Journal of Music Theory 41.1 (1997); and Robert Morris, “Voice Leading Spaces,” Music Theory Spectrum 20.2 (1998).

(22) These two metrics do not always yield comparable distances. For example, the transformation S has a unary word length but voice-leading work of two. Cohn (2012, 6–8) explores this important misalignment.

(23) See Gollin 2000 for an exhaustive exploration of the linkage of transformational “word length” and aural complexity.

(24) Manifest similarities in orchestration and tonal vocabulary point toward an inspiration from Vaughan Williams’s score to the 1948 film Scott of the Antarctic (and its resultant adaptation in his Sinfonia Antartica). Vaughan Williams’s score is a feast of triadic chromaticism that also inspired Jerry Goldsmith, John Williams’s compositional peer, on several occasions.

(25) Besides its rich archaeology of a single progression, Cohn’s article, “Uncanny Resemblances: Tonal Signification in the Freudian Age,” Journal of the American Musicological Society 57.2 (2004), is of significance for bringing semiotic and cultural perspectives into what had previously been the fairly meaning-averse landscape of transformation theory.

(26) The “Fortress” passage itself behaves this way at times. Melodic and linear forces stitch together the chords between D♯ minor and G major more closely than the book-end transformations, overriding some of the “complexity” of the interior RLRP transformation. Of course, dynamics and especially orchestration play a role of equal importance in establishing norms of distance and perspective in landscape music such as this, and a more thorough analysis would certainly take their contributions into account.

(27) In his analysis of James Newton Howard’s Treasure Planet, Scott Murphy (2006) treats the score’s emblematic progression, T6, in this way, as a leitharmonie that can be transformationally varied without changing its ultimate referand.

(28) In a different setting, it could be labeled more simply still, with a transformation that exchanges P5 related chords such as C-maj⬄G-min (a transformation I have elsewhere called M, the “Modalverwandt,” inverting a triad about its dualistic “fifth”).

(29) The default space for network analysis among many neo-Riemannians has been the symmetrical lattice known as the equal-tempered Tonnetz. While I rely on less predetermined grids in this chapter, the Tonnetz can be a powerful tool. For a film musical application, see Jamie Lynn Webster, “The Music of Harry Potter: Continuity and Change in the First Five Films,” Ph.D. diss., Eugene, University of Oregon, 2009.

(30) Capuzzo 2004, 196–197.

(31) Capuzzo notes that the “passage is shot through with chromatic third relations and p parsimony [literally sounded retention of common tones], a few octave doublings and register shifts notwithstanding.” His reduction, which segregates the progression into three registral streams, shows a taut semitonal continuity from sonority to sonority, especially in the upper voices. Capuzzo’s analysis highlight the way in which chromatic mediants are spawned from the treatment of individual voices; in this specific cue, the preponderance of M3-related chords may be the result of the passage’s motivic derivation from the “Rivendell” theme, which is comprised of little more than to LP related chords, each of which is internally ornamented by a ^5-^♭6-^5 pattern (the essence of L).

(32) See Robert C. Cook, “Parsimony and Extravagance,” Journal of Music Theory 48.1 (2005).

(33) This is the tack taken by Kopp (2000, 166–169) in devising chromatic mediant progressions that rely on no intervening chords to garner their intelligibility. For example, Kopp’s M relation links triads that may only share one common tone together (ex C-maj to A♭-maj).

(34) Another upshot of this enharmonically liberated landscape is the ability to deal with root progressions that hew to symmetrical partitions of the octave (the hex- and octatonic cycles, namely) with far greater ease than diatonic theories of chromaticism are able to, something that is explored in Section Vthis chapter.

(35) Cohn presents something approaching a unified theory of triadic chromaticism using these various cyclic transformations in Audacious Euphony (2012).

(36) Richard Taruskin’s article, “Chernomor to Kashchei: Harmonic Sorcery; Or, Stravinsky’s Angle,” Journal of the American Musicological Society 38.1 (1985), stands as the definitive study of the stylistic and associative aspects of the octatonic scale in the nineteenth century, which he ascribes mostly to the music and theories of Russian nationalist composers, of which (early) Stravinsky was a member.

(37) Diminished sevenths pepper what is considered by many musicologists to be the original film score, Saint-Säens’s L’Assassinat de duc de Guise of 1908. By the time of Hans Erdmann’s Nosferatu in 1922, the device’s de rigueur status, particularly for horror genre films, was truly solidified.

(38) See Halfyard 2009, 34–35, for more on the Silvestri/Stravinsky connection.

(39) Discussion and a number of archetypically fantastic examples can be found in Cohn, “Maximally Smooth Cycles, Hexatonic Systems, and the Analysis of Late-Romantic Triadic Progressions,” Music Analysis 15.1 (1996), and, regarding one particular hexatonic progression, Matthew Bribitzer-Stull, “From Nibelheim to Hollywood: The Associativity of Harmonic Progression,” Paper presented at the annual meeting of the Society for Music Theory, Baltimore (2007).

(40) The label romantic theme is adopted from Royal S. Brown, who calls it a “floating theme … that attaches itself to various characters and situations” (Brown 1994, 98).

(41) Besides important work from Rodman (1998 and 2010) and especially Neumeyer (1998), some Schenkerian and pseudo-Schenkerian endeavors include Alfred Cochran, “Style, Structure, and Tonal Organization in the Early Film Scores of Aaron Copland” (Ph.D. diss., Washington, DC: Catholic University of America, 1986), and George Burt, The Art of Film Music (Boston: Northeastern University Press, 1994).