Musical Transfiguration

Musical Transfi Transfiguration guration TRANSFORMATIONAL ASPECTS OF THE COMPOSITIONAL STYLE OF JOHN WILLIAMS IN THE ANTA GONIST’S GONIST’S CUES OF THE EARLY THE EARLY HARRY POTTER FILMS

by Matthew Nace [250547326] | MUSIC-9520B-001: Transformational Theory | April 13, 2016 for Dr. Catherine Nolan, Don Wright Faculty of Music, University of Western Ontario

Musical Transfiguration

Musical Transfiguration I.

INTRODUCTION

Perhaps no composer of the last fifty years has been so instrumental in defining the recognisable “Hollywood Sound” as Sound” as John Williams. From Star Wars, through Indiana Jones and E.T., to Jurassic Park, he has scored scored many of the highest-profile films of recent decades, and has set the model for the kind of music expected of such films, particularly in the genre of escapist action-adventure epics. Among the more recent successes in this genre has been the Harry Potter film franchise. John Williams composed the soundtrack for the first three three of the eight films, and while each of the three remaining composers for the franchise created additional themes and cues – sometimes replacing some of the cues created by Williams – Williams’ signature style contin continued ued to have its impact felt right through to the end of the series. Because of the ubiquity and popularity of Williams’ music, it is no surprise that his music has also been amongst the most thoroughly studied music of Hollywood. Hollywood. Certain aspects of his musical vocabulary have been studied particularly closely, notably by Frank Lehman, 1 including his treatment of the motives and cues representing the primary antagonists of the films that he has scored, which follows a tradition reaching at least as far back as Richard Wagner’s Ring Cycle. Cycle. This paper will examine another another such cue, from the Harry Potter franchise, representing the franchise’s primary antagonist, Tom Riddle (known also as the Dark Lord, Voldemort, and “He who must not be named”). The process will be to first examine the piece in search of those elements whose presence we might anticipate (based on the existing studies of his work), and then to perform further analysis to find additional interesting characteristics that contribute to the repres entation of evil in this cue. As a matter of transparency, a brief disclaimer is in order: the music to be analysed is not the cue as it appears at any given moment within the film, but rather an arrangement 2 that can be taken as representative of the cue in its various forms. The sheet music compilation refers to this arrangement as Voldemort Voldemort;; however, Jamie Webster, in her

1

Frank Lehman, “Reading Tonality Through Film: Film: Transformational Hermeneutics and the Music of Hollywood” Hollywood” (PhD dissertation, Harvard University, 2012). 2 John Williams, “Voldemort”, in Harry Potter: Sheet Music from the Complete Complete Film Series, Series, arranger not specified (Van Nuys, CA: Alfred Music Publishing Publishing Co., Inc.), 39-41. NACE 1


dissertation on the music of the Harry Potter franchise, 3 identifies at least three distinct motives found in this arrangement as representative representative of “Mystery and the Rise of Evil”; 4 these cues are identified as “Something’s Odd” (Example 1 below), below), “Evil Rising” Rising” (Example 2), 2), and “Voldemort” “Voldemort” (Example 3).5

Webster describes these cues,

collectively, as follows:

Example 1 "Something's Odd"

“Something’s Odd” is the first motive in the Voldemort arrangement. Voldemort arrangement. Note that the C-sharps in the melody are displaced from the following augmented augmented triads (wherein it appears in the tenor). My transcriptions vary slightly from Webster’s, to agree with the sheet music that I will be analysing; c ompared to the said sheet music, I have enharmonically respelled the D-flat in the third measure from the given C-sharp to better reflect the apparent triad that I have labelled.

3

Jamie Webster, “The Music of Harry Potter: Continuity and Change in the First Five Films” (PhD dissertation, University of Oregon, 2009). 4 ibid.,, 441. ibid. 5 ibid.,, 423, 426, and 427, respectively. ibid. 6 ibid.,, 422. ibid. NACE 2


Example 2 "Evil Rising" Rising"

“Evil Rising” is the second motive present in the Voldemort arrangement. Voldemort arrangement. Note that I have identified the diminished triad on the second beat of the second measure as E-sharp to imply the usual #vi o7 that would typically precede a dominant chord (which is perhaps implied but omitted here ) before the return to i; however, as we shall see, much of the music to be analysed does not submit well to traditional Roman numeral analysis, and this diminished triad, and indeed, much of the harmony throughout, should probably not be considered functional in the traditional sense. For this same reason, although I shall shall consistently try to select the most most traditionally meaningful names for ambiguous chords, all apparent chords, including those that ar e transitory, shall be labelled, and no consideration shall generally be made for inversions. Example 3 Voldemort

“ Voldemort” Voldemort” is the final and eponymous motive in the Voldemort arrangement. Voldemort arrangement. Here, again, I have respelled respelled some chords from the sheet music to reflect the the apparent chords. Note also that the half-diminished chords are both lacking thirds, and therefore might equally viably be interpreted as dominant seventh chords with lowered fifths; however, minor thirds dominate this arrangement and should probably be inferred here, if indeed it is at all meaningful to infer traditional chords on these transient sonorities. NACE 3


This decision to analyse this arrangement is justified by the following observations: (1) it is inordinately difficult to gain access to actual scores of film music; 7 (2) the focus of the analysis in this paper will be the motives, more than the arrangement; and (3) film music cues do not always have a definitive form 8 (motives are repeated, sometimes frequently, throughout the film series, with developmental changes accruing).

II.

TRANSFORMATIONAL TRANSFORMATI ONAL METHODOLOGY

Before proceeding with the analysis, it must first be determined the nature of the transformations to be employed in the analysis, based on the nature of the music itself. Williams’ music is approximately tonal in the basic respects: there is a key centre of g-minor that is maintained maintained quite consistently throughout the arrangement, and the vast majority of the chords are major and minor triads, especially in metrically strong positions, with a substantial number of other tonally traditional chords ( e.g. e.g.,, augmented triads, diminished and seventh chords, etc. etc.)) largely relegated to metrically weak positions, and only a handful of sonorities of dubious tonal identity, also in metrically weak positions. On the other hand, as Webster has noted, it is heavily chromatic. This chromaticism comes from the fact that chords used, despite being of qualities traditionally used in tonal music, are almost invariably not drawn from the key signature of g-minor, and the phrase model contains no functional dominants until very near to the end of the arrangement (a kind of lose recapitulation in which the “Something’s Odd” motive and the “Voldemort” motive are reharmonized, presumably for precisely that reason: to add functional dominants, dominants, followed by a concluding cadence). Clearly, a neo-Riemannian approach would have substantial benefits – except, of course, that neo-Riemannian theory has difficulty with dissonant chords, and the methodology will need to be adapted somewhat. The familiar case of the hexatonic pole, an absolute progression 9 that in traditional neo-Riemannian theory is designated LPL, 10 sometimes abbreviated H, shall serve as an example to elucidate these adjustments.

7

Lehman 2012a, 14 f.n. 1. ibid. 9 For a detailed discussion of absolute progressions in the film scores of John Williams, see: Tom Schneller, “Modal Interchange and Semantic Resonance in Themes by John Williams”, Journal of Film Music 6.1 (2013): 49-74. 10 Note that, unlike many compound neo-Riemannian operators, like Slide, the hexatonic pole is a palindromic composition of an odd number of contextual inversions, and so it shares most the basic properties of the three standard neo-Riemannian operators: it is an involution, it is mode-reversing, mode-reversing, and pitches move by only a single semitone; the only exception is that it contains no common tones – it is an Extravagent Relation is Relation is the sense defined in: Robert Cook, “Parsimony and Extravagance”, Journal Extravagance”, Journal of Music Theory Vol. Theory Vol. 49, No. 1 (2005):109-40; esp. 116-7. 8

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Lehman, in his dissertation, combines the mainstream neo-Riemannian operators with a variant of the canonical TnI operators. The problem (at least with respect to to major and minor triads) with traditional inversion is that the index of inversion is anchored to the space, rather than the chord; in this notation, the hexatonic pole from C-major to ab-minor is T 3I, but the hexatonic pole from G-major to E-flat-minor is T 5I – hence, the operator is not uniform, in the sense described by Julian Hook 11 – that is, it does not behave identically or intuitively on each starting chord, and the differences between indices does not clearly represent the differences between starting chords (or between ending chords). In the case of major and minor triads, an inversional procedure anchored to the chord, and more specifically to the chord root, is arguably arguably more meaningful than inversion anchored to the space. Lehman substitutes the neoRiemannian Parallel contextual inversion for the more traditional I inversion, creating the isomorphic T nP group;12 proving that T nP is isomorphic to T nI is trivial, as P is equivalent to I with a compensatory index added to the index of transposition (T nP = T n+xI). The resulting T nP operator measures the distance between chord roots, and either reverses the mode of the chord or not. not. In this notation, the hexatonic pole is invariably represented as T 8P – this is a substantial improvement. Reference has already been made to the the concept of uniformity, as described by Hook. It is worth observing at this point that this T nP formulation is fundamentally equivalent to Hook’s Hook ’s notation for ‘uniform triadic transformations’:: <±, ±n> is equivalent transformations’ equivalent to T n / TnP.13 It has the advantage, however, of being more familiar or intuitive. intuitive. It is also approximately equivalent to the S n/W n Schritt/Wechsel group, group, but again is more familiar. However, Scott Murphy has drawn attention to another limitation of the neo-Riemannian notation in the context of film music: neo-Riemannian analysis is designed to handle chord successions consisting of of major and

11

Julian Hook, “Uniform Triadic Transformations”, Journal Transformations”, Journal of Music Theory Vol. Theory Vol. 46, No. 1/2 (Spring – Autumn, 2002): 57-126. 12 Notice that, in spite of the addition of a neo-Riemannian transformation, which traditionally uses rightward orthography, I am using leftward orthography here, and will do so consistently throughout this paper, everywhere where neo-Riemannian operators are combined with non-neo-Riemannian operators (in case of potential confusion, I will add the symbol ∙ only in cases of leftward orthography); however, compound operations consisting exclusively of neo-Riemannian operators will still be given in the traditional rightward orthography. 13 Note that Hook’s formulation contains an ordered triple <±, n, m>, where n and m are different indices of transposition depending on the mode of the beginning triad; in this notation, the hexatonic pole from C -major to Aflat-minor is <-, 8, 4>; however, since the transformations we shall deal with in this paper are involutions, n and m are mod 12 complements, and so the notation ±n ± n serves equally well for both n and m, m, and and is simpler. NACE 5


minor triads, but without reference to any key-centre ; in film music, there often is a key-centre, or at least momentary points of stability that behave similarly to centres; 14 one is tempted to borrow a little Schenkerian terminology, and think of one chord as a kind of stuffe stuffe,, against which the other behaves more contrapuntally than harmonically (of course, this analogy is quite shallow, and should not be taken to imply an ursatz ursatz). ). Under the standard neoRiemannian definition of the hexatonic pole as LPL, there is no distinction between the expressions

svi

–

I and i - SIII . While these expressions certainly have something in common, there is also a substantial difference in the world of the absolute progression as used in film music, with the affective associations that they entail. Murphy proposes an alternative notation to designate progressions in which one chord behaves as a point of relative stability compared to the other. This notation takes the form MnM, MnM, where the first M, as either capital or miniscule, represents the mode, not of the first first chord, chord, but rather, of the tonicised chord, chord, while the case of the second M represents the mode of the less less stable chord. Hence, the expression svi

i

–

I is described as M8m, while

– SIII mode of the chords SIII is described as m4M. The relationship between these is relatively clear: the mode

is reversed, and the indices are mod12 complements. However, the distinction is also clearly evident.15 However, the notation does have a few disadvantages – not the least being that it is generally unfamiliar and unintuitive. In particular, that the first M represents the stable point, and not necessarily the first chord, is extremely unintuitive. I propose a slightly different notation, which presents the same information, but in a more intuitive or familiar form. I suggest the notation T ±n{P/p/E/e}. This notation is extremely intuitive, intuitive, given that it resembles T nP,

14

Scott Murphy, “Transformational Theory and the Analysis of Film Music”, in The Oxford Handbook of Film Music Studies,, edited by David Studies David Neumeyer (Oxford: Oxford University Press, 2014), 2014), 485. 15 This notation also avoids a limitation in neo-Riemannian notation, which does not affect the hexatonic pole, but does affect the similar Tarnhelm progression (to be defined in the next section), which may be defined as either LP or PL, depending upon the context, and equivalently, either composite may or may not represent a Tarnhelm, depending on context. In the new notation, m8m is invariably a Tarnhelm, and although m4m might also be defined as invariably a Tarnhelm (though it is not the traditional understanding of the progression, i t does correspond to the LP and PL definitions), it represents a distinctly different kind of Tarnhelm with a distinctly different kind of sound – and ultimately should probably be given a different name (just as IV-I plagal cadences cade nces and I-V half cadences contain the same voice-leading, but are understood differently in context, and are given different labe ls). NACE 6


which, as already described, is an obvious variant of T nI. P, as a representation of the the Parallel operator, designates a mode-reversal, and can be given in either majuscule or miniscule to identify the mode of the more tonicised chord; the same can done with the E (identity) transformation for those chords that do not cause mode-reversal (though this may not be necessary is some cases, where the mode of the chords does not substantially influence the meaning of the progression – certainly it is not necessary for for subsequent repetitions of an oscillating progression). Although the index numbers are mod12, and therefore negative index numbers are not typical, under my proposed system, a negative index would represent the case where the the second chord is the tonicised tonicised chord. Hence,

would be represented as T+8P and svi

I would be represented by T – I

-8P.

I

–

svi

This notation has the benefit of

being extremely easy to read by anyone familiar with T nI and neo-Riemannian operators,16 and also shows that the forward and reverse forms of the same progressions are obviously linked (the indices are the same absolute number, ignoring the sign). On the other hand,

i

– SIII SIII would be described as T

+4p,

and SIII

– i i

would be described as T-4p, which is also very intuitive. Notice that positive index index numbers should be indicated distinctly as such; in that way, an index that is missing the positive sign would be understood as neutral with respect to which chord is more stable or tonicised tonicised (or when no claim is being made regarding the stable stable chord). As a bonus, the symbol ± can be used to designate an oscillation between the two chords, which is a common feature of chromatic absolute progressions in film music. 17

III.

THE TARNHELM

All of this is to provide the t he necessary background to most effectively define the Tarnhelm progression, which Lehman describes as one of the most characteristic progressions of John Williams’ film scores, specifically representative of villains.18 The Tarnhelm progression is an absolute progression that can be described as T±8e [T±8 describes oscillation between a quasi-tonic and another chord whose root is eight semitones above, while e (as

16

In fact, a substantial benefit of this notation is that it is “backwards compatible”; that is to say, if an analysis is done in this notation, and musician unfamiliar with this new notation (but familiar with the old) reads the analysis while ignore the unfamiliar elements, that musician’s interpretation of analysis, while less informative, is still correct. 17 For the ubiquity of oscillation, see Lehman 2012a, 32. 18 Lehman 2012a, 135-44. NACE 7


opposed to P) denotes that the progression is mode-preserving and, as a miniscule, denotes that both chords are minor]. Notice that it is quite similar similar to the hexatonic pole T±8P – it is part of the same hexatonic system (along with the minor-key leittonwechsel and and a major lowered-sixth chromatic mediant, all of which are quite similar), 19 and it even shares the characteristic that it contains both the upper-leading-tone to the dominant scale-degree (associated with the minor subdominant chord) and the (enharmonically respelled) leading-tone to the tonic (associated with the dominant chord);20 the only significant difference is that both chords are minor, while the hexatonic pole is modereversing. The locus classicus for this progression is Wagner’s Ring Cycle, Cycle, in which it is the harmonic leitmotif 21 representing the eponymous Tarnhelm Tarnhelm,, a helmet that renders the wearer invisible, as well as granting the ability to change shape and teleport.22 Although it is merely a tool, its use is ultimately ultimately associated with all of the most tragically fateful actions taken on all sides; although the eponymous ring is to be understood as the central ultra-powerful object that corrupts absolutely, the tarnhelm tarnhelm is is a close second – almost a kind of junior junior partner to the ring. According to Lehman, after its use in the Ring Cycle, Cycle, it spread rapidly through both the art music tradition and the film scoring tradition.23 The quintessential example of the Tarnhelm progression in film scoring is The Imperial March, from the scores to the Star Wars film franchise, once again by John Williams; as would be expected, this march represents Darth

19

For the concept of hexatonic systems, from which the hexatonic pole is derived, see: Richard Cohn, “Maximally Smooth Cycles, Hexatonic Systems, and the Analysis of Late -Romantic Triad Progressions”, Music Analysis Vol. Analysis Vol. 15, No. 1 (1996): 9-40; esp. 18-30. 20 This characteristic of the hexatonic pole is described in: Richard Cohn, “Uncanny Resemblances: Tonal Signification Signification in the Freudian Age”, Journal of the American Musicological Society Vol. Society Vol. 57 No. 2 (Summer (Summer 2004): 285-324; esp. 306-8. See also: Bribitzer-Stull, BribitzerStull, Matthew, “From Nibelheim to Hollywood: Hollywood: The Associativity of Harmonic Progression”, in The Legacy of Richard Wagner: Convergences and Dissonances Dissonances on Æsthetics and Reception, Reception, edited by Luca Sala (Lucca: Turnhout, 2012), 157-183. Bribitzer-Stull also notes notes the following following set-theoretical characteristics of the Tarhelm Progression: Progression: the collective pitches form SC 5-21 [01458], which is the same set-class formed by the closely related I-sVI progression, which has similar but less negative “otherworldly” connotations; it is the only only pentachord abstractly included in the so-called so- called “magic” all-combinatorial all-combinatorial E hexachord 6-20 [014589], and its most salient trichord is [014], also noted for its dark connotations (op. ( op. cit. 161 & 163). 21 I have chosen to reserve the use of the term leitmotif for for the Wagnerian opera tradition for which it was developed, and have stuck to the more generic term “motive” for the elements of a modern film score, on the basis of observations about the appropriateness of the term in: Stephen Meyer, “ ‘Leitmotif ’: On the Application of a Word to Film Music”, Music”, Journal Journal of Film Music 5.1-2 (2012): 101-8. 22 Bribitzer-Stull, 158. 23 Lehman 2012a, 135; Lehman cites the coining and description of the Tarnhelm progression in Bribitzer -Stull 2012. NACE 8


Vader, one of the franchise’s primary antagonists. The use of the Tarnhelm progression in the Imperial March is given as example 4. Example 4 Imperial March Tarnhelm Motive

The main motive of the Imperial March from John Williams’ scores to the Star Wars film franchise is harmonized exclusively by an oscillation of the Tarnhelm progression.

Lehman discusses the Tarnhelm interpretation of this theme at considerable length. 24 It seems reasonable to identify the Tarnhelm progression as a critical element of Williams’ style for cues representing primary antagonists, and it likewise seems reasonable to look for it within the Voldemort Voldemort arrangement from the Harry Potter score. Bribitzer-Stull notes several occasions when the Tarnhelm is used in the second and third films, 25 but makes no note of any use in the first film, or the elements of the Voldemort Voldemort arrangement. arrangement. However, before looking for it, it is worth scrutinising the assumption that the guiding principle behind the Williams’ composition of the Imperial March is, March is, in fact, the Tarnhelm Progression. Ordinarily, in analysis, it is fallacious to challenge challenge an analysis on the basis of the composer’s intentions; however, when attempting to identify elements of a composer’s style, it can be well worth questioning the composers intention to use the Tarnhelm progression, lest in doing so we misattribute a different intention. For instance, double leading-tones of the

svi chord might support an alternate interpretation as a

kind of displaced dominant (Lehman gives the notation DOM’∙T1 and T11∙DOM).26 However, there is an even more convincing explanation.

24

Lehman 2012a, 137-40. Lehman also notes that Murphy and Bribitzer-Stull have likewise identified the Imperial March as the quintessential modern example of the Tarnhelm. 25 Bribitzer-Stull 2012, 168. 26 ibid., 138. ibid., 138. Note that the transformation DOM implies that the first chord behaves as the dominant of the second, resolving back to its tonic; hence, DOM’ implies a tonic progressing to its dominant; due to the importa nt functional NACE 9


The hexatonic pole, which is similar to the Tarnhelm progression, can once again serve as an example, or more accurately, as a counterexample, to elucidate elucidate the concern. The hexatonic pole is a good good example of an absolute progression that can reasonably be assumed to be the guiding principle behind a compatible selection of chords, whether or not the composer compose r is aware of the literature surrounding the use of the progression, as there are very few other ways in which this this progression might come come about. The Tarnhelm progression, on the other hand, differs in respect that turns out to be very significant: it is mode-preserving (both chords are minor); this means that the Tarnhelm progression can just as easily be produced via the technique of chromatic planing. It should, of course, be remembered that, regardless of how it is produced, an absolute progression is an absolute progression, and the associations produced by that absolute progression still come along for the ride; but even so, if it we re instead to have been produced through planing, this observation would be more insightful than simply the use of the absolute progression per progression per se. se . Thus, it is worth taking a moment to see whether or not not planing would be a more appropriate analysis. As it turns out, it may very well be a superior analysis. Minor triads represent approximately ninety percent of all the chords (counted by chord changes; the percentage is even higher if counted by duration), even though none are diatonic to the key of G-minor (except, obviously, obviously, the G-minor triad itself). The only exception to monochromatic minor chords is the occasional E-flat-major triad, which is, in fact, diatonic to the key of G-minor, and is simply a chromatic alteration (intensification?) of the ubiquitous ubiquitous E-flat-minor triads that that have already been presented. (See example 5). Example 5 Minor Triad Planing in the Imperial March

implications of these terms, I will use this type of transformational label only when the appropriate function is actually implied, and will stick to T nP or neo-Riemannian labels where no function is implied. NACE 10


Nearly all the chords are minor. The E-flat-major chords (circled in red) are chromatic alterations of the previously presented E-flat-minor chords. The E-flat-minor chord over a C in the bass (circled in blue) could could be interpreted as a half-diminished seventh chord, but given that the figure is only a slight variation of the presiding motive, this label seems more meaningful, making it just another example of the ubiquitous minor triads (with an underseventh). The C-sharp-minor triads (in green) are an example of the Minor Tritone Progression (discussed in Section IV below).

Interestingly, the E-flat-major turns out to be significant in more ways than this: the E-flat-major triad is also outlined by the primary melodic motive – that is, the melody me lody outlines the leittonwechsel of of the tonic harmony, which is approximately symmetric around the first chord. This transformation, traditionally designated L, can also be be designated (in the minor key) as T ±8p, demonstrating, yet again, a close relationship to the Tarnhelm and the hexatonic pole.27 As will be seen, this relationship will again come into play in the analysis of the Voldemort arrangement. More immediately, however, however, it remains to support the interpretation that the Imperial March was was composed by planing a minor triad along its L transformation. In fact, this is not the only time that that Williams generates a theme from a similar transformational process. For instance, Lehman elsewhere describes the Rebel Fanfare, Fanfare, also from the Star Wars franchise, which he describes as being ultimately derived from another absolute progression that is ubiquitous to Williams’ style: the so-called

27

It is interesting to note that the hexatonic pole is simply a complete mode-reversal of the minor-mode leittonwechsel – that is, perform a leittonwechsel on a minor triad, then reverse the modes of both triads. NACE 11


“Cowboy Half -Cadence” sVII

-

V that Williams had previously used in the main theme for the film (see

Example 6).28 Example 6 Rebel Fanfare Derived from Star Wars Main Theme

This figure is an approximate reproduction of Example 19 of Lehman 2013 (see f.n. 28), showing how the Rebel Fanfare is an expansion of the “Cowboy Half -Cadence” from the end of the Star Wars Main Theme. However, it is equally convincing to see it as a major triad planed to harmonize a melody that outlines a diminished triad. But is this really the best explanation for this passage? Once again, the passage consists entirely of a single type of chord quality – in this case, major triads – planed to harmonize a melody that outlines a standard tonal chord type – here, a diminished triad that is literally symmetric around the first triad. What is particularly interesting about this observation is that it means that the motive representing the Rebellion is a kind of major-mode antithesis to the minor mode Imperial March that represents their arch-enemy. This shows an even deeper debt to Wagner Wagner than has thus far been indicated, because Wagner does does something rather similar. According to Lehman, “[David] “[David] Lewin’s insight is that portions of both motifs’ [ i.e., i.e., the the Tarnhelm and Valhalla, which represents the Gods, and by extension, the forces of good – that is, the antithesis of what is represented repr esented by the Tarnhelm] harmonic substance are eq uivalent when inversional equivalence of major and minor is taken into account.” 29

28

Frank Lehman, “Hollywood “Hollywood Cadences: Music and the the Structure of Cinematic Cinematic Expectation”, Music Theory Online Vol. 19 No. 4 (2013): 4.13. 29 Lehman 2012a, 171, citing: David Lewin, “Some Notes on Analyzing Wagner: The Ring and Ring and Parsifal ”, 19 ”, 19th Century Music 16.1 Music 16.1 (1992): 49-58. NACE 12


Example 7 Comparison of the the Imperial March and the the Rebel Fanfare

The Imperial March is harmonized almost exclusively by minor chords, and the melody outlines a major triad approximately symmetrical around the first pitch; its antithesis, the Rebel Fanfare, is harmonized exclusively by major triads, and the melody outlines a diminished triad exactly symmetrical around the first pitch; even the contour is related; note that the B-flat-major triad in the Rebel Fanfare is a passing tone harmonized by the same planing.

This similarity in the music is particularly interesting, given that the similarity of the plots of the two epic cycles is also such a ubiquitous observation as to have become a virtual pop-culture cliché, as a can be readily verified by a quick web-search. NACE 13


Example 8 Hedwig's Theme, Section III

Hedwig’s Theme is the principal theme of the Harry Potter film franchise. Note that when chromatic planing is explained as neighbour tones and appogiaturas, the rest of the theme is relatively tonal, though the only non-minor chord is the final dominant (even the lowered supertonic, implying a Neapolitan, is harmonized as a minor triad – since this transformation [T±1e] will recur, I shall refer to it by the slightly inaccurate but convenient term “Neapolitan Minor”). Minor”).

Williams’ use of this planing technique tec hnique is not limited to his scoring for the Star Wars franchise. Indeed, the same technique is clearly evident in the Harry Potter scores’ best known cue, Hedwig’s Theme, especially in the portion of the theme that Webster identifies as “Section III”. 30 In the case of Hedwig’s Theme, it is far less clear that a harmony is being outlined by the melody; rather, the changing harmonies reflect neighbour-tone motion and appogiaturas; nevertheless, all of these motions are supported by planed minor triads.

30

See Webster 2009, 514-5 for segmentation of Hedwig’s Theme. NACE 14


It should be observed at this point that we are observing this partial similarity of the observations made about the Star Wars score, not to the Voldemort arrangement (representing evil), but to the principal theme of the film, where no such agreement was necessarily to to be expected – and indeed, once the chromatic planing is explained awa y, the rest of the cue is surprisingly tonal (as demonstrated in the multilevel analysis of Example 8), as we would expect of a main theme. Clearly, this kind of triadic planing is a larger element of Williams’ overall technique.

IV.

TRITONE PROGRESSIONS AND THE LYDIAN

S4

Another pair of progressions that are noted elements of William’s compositional technique is the use of the Lydian mode31 and the so-called so- called “Major Tritone” progression (any two major triads that are a tritone apart). 32 Neither of these elements is directly tied to the associations that we should expect to find in the Voldemort Voldemort arrangement; arrangement; however,, they share a common element that is more broadly intrinsic to Williams’ style, which certainly occurs however throughout the Harry Potter soundtrack, and might well be ex pected to make its influence felt in i n some shape or form in the Voldemort arrangement: the frequent use of the S4 scale degree; less widely cited is the “Minor Tritone” Tritone”

progression,33 which also shares this characteristic. The Major Tritone progression takes the form T ±6E. Scott Murphy argues quite persuasively that its primary association is with wit h “outer space and/or images of celestial objects”, 34 or at the very least, with science fiction; 35 he proposes that the “distance” between the chords themselves is reflected in the vastness of the setting being represented,36 which might imply that this progression might also usefully be applied to other extremely vast (but ultimately terrestrial) vistas.

31

Lehman 2012a, p. 14, fn. 2 and passim. and passim. Scott Murphy, “The Major Tritone Progression in Recent Hollywood Science Fiction Films”, Music Theory Online Vol. 12 No. 2 (2006): 7. 33 Schneller 2013, 50. 34 ibid., 2 and passim. 35 As implied by the title of his article (see f.n. 32 above). 36 Murphy 2006, 17. 32

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Murphy begins his discussion of the Major Tritone progression in the now familiar way: with the soundtrack to Star Wars. In this case, T±6E occurs in a cue shortly following the main title scroll, 37 which Lehman also describes, and identifies as “Escape Pod Drop” from Imperial Attack .38 Murphy notes that Williams’ score to Star Wars Star Wars as helping “to restore the orchestra as the primary performing ensemble for science-fiction and adventure scores”’; scores ”’;39 it is perhaps possible that the association with outer space was less firmly instilled in Williams than in those who followed him (whose associations were influenced by his work). There is something slightly ominous ominous about the scene in question, and it is possible that this progression might also invoke something of the ominous for Williams. According to Lehman, the Lydian progression implies, among other things, “the extraordinary and otherworldly”.40 This often takes on an aspect of amazement and wonder, wonder, but can also take on darker hues.41 Williams’ use of this effect is ubiquitous. ubiquitous. 42 The characteristic element of the Lydian mode is the S4 scale degree,

as it is the only element of the scale not shared with the basic major scale. As such, we might suppose that these darker hues related to the extraordinary and an d otherworldly might be intensified by maintaining the

S4 within the

context of a darker mode (such as an overall minor tonality). This is a reasonably apt description of the Minor Tritone progression, T ±6e, which is a minor-mode analogue to the Major Tritone progression; Schneller describes it thus:

37

ibid., 7. Lehman 2012a, 130-3. 39 Murphy, 40 Lehman 2012a, 31; Lehman cites: Mervyn Cooke, A Cooke, A History of Film Music (Cambridge: Music (Cambridge: Cambridge University Press, 2008), 227-33. 41 Lehman 2012a, 32; here, Lehman cites: Janet Halfyard, “Music Afoot: Supern Supernatural atural Horror-Comedies and the Diabolus in musica”, musica”, in Music in the Horror Film: Listening to Fear , edited by Neil Lerner (New York: Routledge, 2010): 206-23 206-23 [21-37]. 42 loc. cit. f.n. 23 supra. 38

NACE 16


Example 9 The Ark Theme from from Indiana Jones: Raiders of the Lost Ark

The Ark The Ark Theme Theme from from Indiana Jones: Raiders of the Lost Ark begins begins with two measures of an oscillating Minor Tritone Progression [blue], which (due to the repeat) make up half of the excerpt. Not surprisingly, the remainder of the excerpt contains three Tarnhelm Progressions [red] (two of which are from the dominant, rather than the tonic; an absolute progression is defined compared to the more tonicised chord, chord, and not necessarily a true tonic), two circle of fifth progressions, and a number of minor-third root relationships. In addition, all triads in this excerpt are minor triads, planed so that roots of consecutive triads largely outline traditional triads; the r oots of these larger triads also generally share the same relationships found between surface-level triads, including the single descending minor second.

Clearly, the use of the

S4 scale degree is an important element of John Williams’ scoring style , regardless

of the emotional affect intended by the passage, and more specifically includes the minor tritone progression to

43

Schneller 2013, 2; Schneller makes the following citations: Murphy 2014, 488; ‡ Frank Lehman, “Music Theory Through the Lens of Film”, The Journal of Film Music 5 Music 5 Nos. 1-2: 179-98. †

NACE 17


represent mortal threats and dangers; clearly, we should expect expe ct to find some reflection of this element of Williams’ affective vocabulary in the Voldemort arrangement.

V.

WILLIAMS’ SIGNATURE SIGNATURE IN VOLDEMORT

Having now identified the most important elements of Williams’ compositional style that would be expected to appear in the Voldemort Voldemort arrangement arrangement (i.e. (i.e.,, the Tarnhelm Progression, the use of the

S4 scale degree, especially

as the Minor Tritone Progression, and the use of chromatic planing, especially of minor triads), we are now prepared to analyse the arrangement for evidence evi dence of Williams’ musical fingerprints. A clean copy of the complete arrangement is attached to this paper as an appendix; due to the need to develop additional analytical syntax to represent these analyses on the score, graphical analysis will be postponed to a later point in this paper. The first eight measures of the arrangement are based on the “Something’s Odd” motive (presented as example 1 on page 2 above). The first thing that is immediately obvious is that this this motive is not pure planing of minor triads, and that the Tarnhelm progression is not used in this motive. This may not be entirely surprising; given the title of the motive as “Something’s Odd”, this motive, which functions as a kind of introduction to the arrangement, behaves rather like foreshadowing, and the direct use of a motive representing evil and a primary antagonist might be a bit much. On the other hand, the Minor Tritone Progression, as a representative of dark magic, would make perfect sense here. In its most prototypical form, it is absent, but already on the second beat of the arrangement, we have a C-sharp in the melody, which is the S4 scale degree that is the Minor Tritone Progression’s most salient fea ture, suggesting

that we should perhaps look a little closer. The first chord is a G-minor triad, meaning that the the next required chord would be C-sharp-minor; instead, we get (based on spelling and voicing) an F-augmented triad. However, augmented triads are, of course, symmetrical, and since the arrangement as a whole is not particularly respectful of chord inversions, this chord can be just as easily identified as C-sharp-augmented; this is a tritone t ritone progression, at least, even if it is not exactly the one we were expecting. Additionally, it is also also interesting to note that an augmented triad is NACE 18


only a semitone away from a minor triad – which means that it is only a semitone away from the minor triad planing we were looking for. The second half of the motive behaves in very much the same fashion, except that virtually all the chords are expanded to augmented triads; while the first phrase p hrase was based around G-minor, the second phrase is dominated by D-flat-augmented, which could be interpreted as a D-minor triad expanded by lowering the tonic by a semitone; under this description, the G-sharp in the following C-sharp-augmented triad would constitute a

S4 scale degree

by comparison. By comparison, the “Evil Rising” motive (presented as e xample 2 on page 3 above) is shorter, just a single fourmeasure period (beginning measure 11), but it is easier to deal with. The first measure consists of an alternation between G-minor and E-flat-major – not quite the Tarnhelm we are waiting for, but close. Also, the decorative chords in between, which serve to harmonize an escape tone, are A-dominant-seventh chords (without their fifths), which again carries the

Minor Tritone Progression. S4 scale degree, and is reasonably close to, but not quite, a Minor

The

second measure is not particularly interesting either, unless we count the diminished triads as approximately minor for the purposes of chromatic planing (they both share a minor third, but this is a stretch). The third measure is effectively a repeat of the first. More importantly, however, the fourth measure of this motive, which serves as the full cadence of the period, consists of an E-flat-minor triad r esolving to a G-minor triad – at last, a clear and indisputable Tarnhelm Progression; from this point, the Tarnhelms, while not as ubiquitous as might have been expected, begin to turn up with with substantially greater frequency. Also of note is the the A-diminished triad that decorates the E-flat-minor triad; here, the A root is a clear S4 relative to the E-flat, and notwithstanding

the diminished fifth of the triad, is once again a fair approximation of the Minor Tritone Progression.

The overall harmonic plan of this motive is |

contains i | vii - i | i | svi - i |. This contains

an interesting element not yet seen as an a n element of Williams’ Williams ’ style, but which will recur in this arrangement: the use NACE 19


of the minor triad (rather than a diminished triad) on the leading tone as a substantial harmony, behaving as a kind of weak dominant. It alternates with the minor tonic, so it is a fair fair candidate for the description T ±11e.44 With the “Voldemort” motive proper, we begin to see much of what we expected. It shares a similar overall harmonic design to the “Evil Rising” Rising” motive: |

i - - -

- - - sii | i - svi - i |.

sii | i - vii - i | i

In both motives, the the basic design is a measure of minor minor

tonic, a measure controlled by a leading-tone minor triad, another measure of tonic, and the final measure cadencing on the Tarnhelm progression. This motive, however, also includes the the Neapolitan Minor previously seen in the Ark Theme of Theme of Raiders of the Lost Ark and in Section III of Hedwig’s Theme from Harry Potter ; this progression is T ± 1e, and serves as a balance for the T ±11e of the leading-tone minor. No evidence of the minor tritone progression this time, though. There are plenty of C-sharps ( S4), but this

time, they are the result of planed minor triads, which are ubiquitous even among the passing tones (all of which are instances of T 1 and T11), certainly for the antecedent phrase, and also to a lesser extent in the consequent phrase, in which a few of the passing tones are replaced by less easily classifiable chords (but the C-sharp remains common). Immediately following the presentation of the primary theme of “Voldemort”, a two -measure secondary theme is presented that will serve for developmental material (Example 10). This theme is characterised by semiquaver triplets (which had previously been seen as simple connective material in the bassline of “Evil Rising” and the primary theme of “Voldemort”). Other than being the source of development, development, the secondary theme itself is not particularly interesting, but it does contain a rather substantial and interesting Tarnhelm progression; this Tarnhelm is an illustrative case because it operates on the subdominant (i.e., (i.e., iv

– sii rather than i – svi),

44

This progression also joins with the Neapolitan Minor and the hexatonic pole as the three Extravagant Relations (see Cook 2005, loc. cit. f.n. 10 f.n. 10 supra supra), ), all of which appear as significant relationships in the Voldemort Voldemort arrangement, arrangement, as will be seen. NACE 20


yet is still clearly a Tarnhelm based on its chord qualities qualities and root distance, and it still used to evoke the same affective associations.45 Example 10 Theme II of Voldemort

This second theme serves as the source of development for the remainder of the arrangement; it contains a substantial Tarnhelm progression prolonging a pitch-level other than the tonic (in this case, a plagal subdominant).

“Voldemort” then returns to the primary theme for one more phrase that begins parallel to the original antecedent, but cadences differently from either of the previous two iterations: this da capo capo cadences cadences from E-flatItalian-sixth to G-minor. This is quite similar to the Tarnhelm Progression, Progression, in that the penult penult begins begins on the lowered sixth (i.e. (i.e.,, root motion is by T 8); however, the penult the penult is is not a minor triad; it is, in fact, an augmented sixth chord (not only in terms of quality, but also in terms of position relative to the tonic). As an augmented sixth chord, it is somewhat unusual that it does not resolve to the dominant, but rather to the tonic; however, augmented sixth chords frequently resolve through the tonic to the dominant, and this is very much in the spirit of neo-Riemannian theory: chords are defined by immediate motion between subsequent chords (governed by voice-leading), rather than longterm motion governed by function. (It could also be described as implying a dominant that is ultimately skipped). It is, of course, little more than an extended leittonwechsel ,46 and it is possible to identify the chord as a dominant seventh chord rather than an augmented sixth chord (we have thus far not been shy about enharmonic reinterpretations compared to the given score). However, leaving it as an Italian sixth chord draws attention to one

45

This was previously seen in the Ark the Ark theme theme from Indiana Jones: Raiders of the the Lost Ark – Ark – see example 9. The use of a leitonwechsel as a variant on a previously presented Tarnhelm as the end of a theme approaches was previously seen in the Imperial March (highlighted in red in Example 5 above). 46

NACE 21


important fact for our analysis: it contains a S4. This chord blends elements of both the Tarnhelm and the tritones

that we have been tracking as elements of Williams’ style for antagonists. antagonists. It hardly needs to be said that the earlier portion of the phrase (which parallels the antecedent) still displays the planing, Minor Leading Tone and Neapolitan Minor progressions that I have proposed as additional elements of Williams’ style. The next seven measures represent a brief development, based primarily upon the t he “Voldemort” motives. motive s. It contains one Tarnhelm, several near-Tarnhelms, and a reasonable prominence of

S4, as well as additional

examples of the same Italian sixth progression just described. Following this, there is a kind of recapitulation, with anoth er presentation of the “Something’s Odd” motive; however, the pitch-level of the melody is a minor third lower (beginning on the tonic, rat her than the mediant), with an accompanying reharmonization. This time, the chord alternation with the tonic G-minor is D-augmented – only one semitone away from the E-flat-minor chord needed to produce the Tarnhelm progression, but rooted at a true dominant, which is to be expected as we approach the final cadence of the arrangement. A partial restatement of the “Voldemort” motive follows, eliding (via another Tarnhelm) into a four measure extended final cadence that contains virtually every characteristic discussed over the last few pages: a Tarnhelm, a Minor Leading-Tone, lots of

S4s, an Italian sixth, and even a Hexatonic Pole, along with the one and only true

dominant seventh chord in the arrangement (which does, in fact, resolve correctly as an authentic cadence). Section V Summary: The Voldemort arrangement does, indeed, contain the previously identified elements of Williams’ style (viz ( viz., ., the Tarnhelm and approximations on the Minor Tritone Progression, perhaps better defined as the ubiquity of

S4 in tonally uncharacteristic forms), in progressively denser concentrations as the arrangement

progresses towards a characteristically evil climax. It also contains some degree of the minor minor triad planing that I have identified in Williams’ other work, especially esp ecially the use of the Minor Leading-Tone triad and the Neapolitan Minor triad, as well as the developmental reharmonization of a Tarnhelm into a more traditional leitonwechsel . NACE 22


VI.

OTHER ANALYTICAL TECHNIQUES

Although we have developed a whole whole new notation for identifying identifying absolute absolute progressions, there there is no no doubt that the fundamental methodology is an extension of a neo-Riemannian philosophy, and it shares some of the fundamental limitations of neo-Riemannian theory. For instance, the methodology discussed thus far is limited to major and minor triads. It does not accommodate augmented or diminished diminished triads, nor any form of seventh chord. chord. This is because of a fundamental assumption built into most forms of transformational theory, and made explicit in David Le win’s Le win’s manifesto of Transformational Theory, Generalized Musical Intervals and Transformations. 47

Lewin gives the

following definition:

What this effectively says is that a transformation transformation (and (and also, the more restrictive operation operation)) changes an object into another object within the same family (sc. ( sc.,, of the same kind); neo-Riemannian operators are transformations (and indeed, operations operations)) of this kind because they operate on the group of all twenty-four equal-tempered major and minor triads – the elements of set class 3-11 (037) – and produces the same group of twenty-four equal-tempered major and minor triads. In this context, augmented augmented and diminished triads cannot be achieved in neo-Riemannian theory because they are elements of a different set class – hence, any transformation upon the group constituted by (037) that would produce an augmented triad [set class 3-12 (048)] or a diminished triad [set class 3-10 (036)] – or, for that matter, seventh chords – would violate the condition of group closure. What is needed in order to allow allow a transformation between major/minor triads and augmented/diminished triads is to widen the original family S ( from Lewin’s definition) to include (037), (036), and a nd (048).

A. Klumpenhouer Networks One of the more common methods for relating sets of differing set -classes is through Klumpnhouer Networks (henceforth K-Nets). In a K-Net analysis, analysis, a set is divided into two subsets; the notes within each subset are interrelated by transposition, while the two subsets are related to each other by a pair of inversions. The point of the

47

Lewin, David. Generalized Musical Intervals and Transformations. Transformations . (New Haven: Yale University University Press, 1987). ibid.,, 36. ibid.

48

NACE 23


analysis is to identify an isography – which generally means that the transposition labels are the same and the inversion labels are related to each other in the same way (that is to say, if the two inversions in the first set are I n and Im, then the two inversions in the second set are I n+C and Im+C, where C is common common to both). Then, the transformation labelling the isography is . An alternative, roughly equivalent definition, is that a K-Net is a dual transposition of a split set (i.e. ( i.e.,, the two sets are transposed by distinct and potentially differing indices). 49 K-Nets can be a very useful way to relate otherwise unrelated sets; however, it has not been typical to use KNets to analyse tonal or near-tonal music. The reason for this is not not difficult to suppose. Both major and minor triads contain a perfect fifth; suppose that we select the perfect fifth as one subset (in which the two notes are related by T7); then the chordal third would be the remaining subset, linked by the pair of inversions. If we move from a major triad to another major triad, then both the perfect fifth and the chordal third will transpose by the same distance, and the relationship will be the same. Since the index of inversion is equivalent to the sum of the two pitches involved in the transformation, the index of transposition for the tw o pitches is summed (which means, effectively, that the i ndex of transposition is doubled). A similar relationship holds for inversion, inversion, as is summarised below. Figure 1 Correspondence on TnI to Same Mode: T n =

Major-Minor: TnP =

Minor-Major: T nP =

Transformations between consonant triads of the same type are doubled to reach the isographic label; those of opposite kinds double and then increase or decrease by one, depending on direction. Clearly, then, selecting the perfect fifth as the common interval for a K-Net analysis is superfluous; it is effectively equivalent to a T nI label, except that it is less precise. A similar argument can be made for the neoneoRiemannian operators, corresponding to the idea of selecting either the minor third or the major third to preserve, while transposing the uninvolved pitch. These labels effectively describe the number of semitones shifted by the t he single note that moves, as is summarised below. Figure 2 Correspondence of K-Net Isographies to neo-Riemannian Operators

49

P

L

R

Minor to Major

Major to Minor

O’Donnell, Shaugn, “Klumpenhouer Networks, Isography, and the Molecular Metaphor”, Intégral 12 12 (1998): 53-80. NACE 24


K-Net isographies equivalent to neo-Riemannian operators effectively describe the number of semitones moved by the single moving pitch.

Once again, the K-Net analysis is both superfluous superfluous and less detailed than the neo-Riemannian analysis. In generally, and certainly for trichords, a K-Net isography selects a single subset as a benchmark, and disregards the transposition of that subset, then measures the relative relative transposition of the second set compared to its original relationship to that benchmark – it is thus a kind of measure of voice-leading parsimony; it will tell us nothing about major and minor triads that a neo-Riemannian transformation, combined with with a transposition, will not tell us. Hence, a K-Net analysis is of little value in a piece that uses e xclusively major and minor triads. However, the Voldemort Voldemort arrangement arrangement uses set-classes other than (037). It is worth considering whether or not the K-Net analysis would would reveal anything new. I have therefore subjected the arrangement to a K-Net analysis; a representative portion of that analysis is given of in Figure 3. The complete analysis is not provided because it failed to reveal any useful patterns beyond those already revealed by the analysis already described, and it is, of course, these patterns that are the purpose of a K-Net analysis. However, this does not mean that the K-Net analysis was entirely unrevealing. Indeed, the very fact that it is possible to perform a “complete” K-Net K -Net analysis is itself revealing. Not just any two sets will form a K-Net isography; isography; therefore, the fact that every single pair of adjacent chords in the Voldemort Voldemort arrangement arrangement can form an isography is an important observation. To begin with, the most obvious obvious (if slightly slightly banal) observation is that the entire arrangement is exclusively a three-voice texture; although there are a re no small number of seventh chords, they are ar e all incomplete; the same goes for the few sets that do not clearly correspond to traditional common-practice chords. More interestingly, interestingly, it speaks to certain tendencies of Williams’ style, not so much in terms of what he chooses to do, but rather, in terms of what he chooses chooses not to do. Although Michael Buchler notes that that most trichord setclasses are able to form isographies with most other trichord set-classes, 50 one important exception is the combination of augmented and diminished triads; no isography is possible between augmented triads and diminished triads, because they do not share a single interval in common. Although Williams makes substantial use of both types of sonorities, he never uses them back to back. Similarly, although he uses a few unconventional chords, he he also does not use them back to back. In the same way, although the seventh chords are incomplete, the missing notes do not

50

Buchler, Michael, Michael, “Reconsidering Klumpenhouwer Klumpenhouwer Networks”, Music Networks”, Music Theory Online Vol. Online Vol. 13, No. 2 (2007); par. 36. NACE 25


prevent the selection of a common interval class upon which which to base an isography. And in spite of the amount of of dissonance Williams uses, he never uses any dissonant chord that does not contain at least one common abstract interval with the previous and following chords (which, in this case, means that he never uses chords dominated by tritones or semitone clusters). In short, all of Williams’ chords share common abstract abstract intervals with the surrounding chords.

B. Augmented and Diminished Triads in Neo-Riemannian Neo-Riemannian Theory Another approach would be to extend neo-Riemannian transformations to accommodate the other other set-classes. Although it would be quite simple to proclaim, “Let there the re be a transformation from a major triad to an augmented triad!”, triad !”, for most methods of doing doing so, we would not see that it was good. In traditional Roman numeral analysis, labelling chords is barely the first step; true analysis begins after the chords have already been labeled. labeled. Likewise, in Transformational analysis, the mere labelling of transformations does not, of itself, constitute a valuable analysis; the more valuable analysis is the identification of patterns or allusions guiding the selection of transformations. It follows, then, that for a newly defined transformation to be of value, it should be capable of participating in the same kinds of patterns. Two of the three neo-Riemannian operators, the parallel and and the leittonwechsel , share the basic characteristic that it is possible to transform from a major triad to a minor triad with only a single semitone change ( parallel by by mode-reversing the chordal third, leittonwechsel by by exchanging the root of a major triad tr iad for the fifth of a minor triad). The same can be said of converting either major or minor triads into either augmented triads triads or diminished triads. A major triad is transformed into an augmented triad by raising the chordal fifth, and the minor triad is transformed into an augmented triad by lowering the root; similarly, the major triad is transformed into a diminished triad by raising the root, and the minor minor triad is transformed into a diminished triad triad by lowering the fifth. As a consequence, it is possible to step from a major triad to a minor triad by passing through an augmented or diminished triad en route,, by retaining the third, and altering the root and the fifth one at a time; both of these are essentially equivalent route to Lewin’s SLIDE transformation, with the modality (augmented or diminished) of the intermediate ste p determined by which chord tone (root or fifth) is altered first. With respect to the augmented triad, this observation is clearly

NACE 26


apparent in the Cube Dance figure presented by Douthett and Steinbach, 51 which links each augmented triad to three major and three minor triads (three in each of two adjoining hexatonic systems). Figure 3 Cube Dance Dance

Reproduced from Douthett and Steinbach (1998), Figure 9 (p. 254), with annotations added [blue] identifying the hexatonic systems.

In order to proceed with an analysis, we need to do two things: (a) we need to define the transformations that will take us from major and minor chords to augmented and diminished chords in a way that is consistent with the behaviour of the other neo-Riemannian operators (ideally in terms of the parsimony described above); and (b) we need to redefine the existing neo-Riemannian operators so that they can operate upon augmented and diminished

51

Douthett, Jack, and Peter Steinbach, “Parsimonious Graphs: A Study in Parsimony, Contextual Transformations, and Modes of Limited Transposition”, Journal of Music Theory 42.2 (1998): 241-63. It is not clear how this diagram should be ci ted. Douthett and Steinbach credit its name to Carol Krumhansl “at the 1993 meeting of the SUNY-Buffalo Working Group,” Group ,” (Douthett and Steinbach 1998, 262, f.n. 11), but they do not credit its conception, nor is it clear clear who should be credited with the first published description. It is also described by Richard Cohn a few pages later in the same journal: Richard Cohn, “Square Dances with Cubes”, Journal Cubes”, Journal of Music Theory 42.2 Theory 42.2 (1998): 283-296. NACE 27


chords in a way that is analogous to the way that they operate on major and minor triads and yet is consistent with the existing definitions. There are multiple ways to define and conceptualise the three standard neo-Riemannian operators that all produce effectively the same result. If we focus on function, then R transforms a major triad to into its relative minor and a minor triad into its its relative major. If we focus on voice-leading, voice-leading, then R preserves the lower third of of a major triad and shifts the fifth up by a tone, while it preserves the upper third of a minor triad and shifts the root down by a tone. If we take the contextual inversion approach, then R causes a triad to invert such that the major third maps onto itself. However, to make these transformations compatible with augmented and diminished chords, they must be redefined exclusively with reference to the characteristics shared by all. The characteristics common to major, minor, augmented, and diminished triads are: (a) they contain only three tones, arranged in thirds; and (b) the thirds that make up the chords are exclusively major and minor thirds. Although there are several possible ways to define define the neo-Riemannian operators on these terms, the simplest and most intuitive is along the lines defined by Hook as uniform triadic transformations. For Hook, the neo-Riemannian operators can be defined as <-, ±n> such that P = <-, ±0>, L = <-, ±4>, and R = <-, ±9>. To extend these operators to apply to augmented and diminished triads, we need to specify the following properties: (1) augmented triads are approximately major (by virtue of the major third between root and third), and so will take the positive transposition, as major triads do; (2) diminished triads are approximately minor (by virtue of the minor third between root and third), and so will take the negative transposition, as minor triads do; and (3) mode reversal means to switch all major thirds to minor thirds, and all minor thirds to major thirds, while keeping the root static. This definition, of course, has no impact on the application of the neo-Riemannian operators to major and minor triads, and creates an equivalent set that tha t looks very similar for augmented and diminished triads: root motions are equivalent, they contain mode-reversal between them (without overlapping with major and minor triads), and they are all involutions; it is likewise possible to generate all twenty-four possible augmented and diminished triads through repeated application of the RL transformations in a cycle.

The one difference is that they are not not

parsimonious (parsimony in the sense of a single semitone shift between chords is not possible between augmented and diminished triads), but they do create the most efficient types of voice-leading possible between these types of chords. NACE 28


All that remains is to define transformations to move from major and minor to augmented and diminished, and vice-versa. The simplest solution here is a half-mode-reversal; that is to say, we reverse the mode of one third, but not the other. We will define the transformation α ( alpha alpha)) to mean that the upper third (compared to the root, not the voicing) is reversed while the lower third is preserved, and β (beta ( beta)) to mean that the lower third ( sim. sim.)) is reversed. Thus, applying both α and β in sequence would result in a complete mode reversal as found in the traditional t raditional neo-Riemannian operators.

These operators behave in equivalent but opposite ways on each type of

major/augmented and minor/diminished triads, so that it becomes possible to move from any triad type to any other triad type (ignoring root motion) 52 in a single transformations. Table 1 summarises the actions of each transformation on each type of triad: Table 1 Effects of Redefined Neo-Riemannian Neo-Riemannian Operators on All Triad Triad Types C+

C

c

co

P

co

c

C

C+

L

eo

e

A ≤

≤+ A ≤+

R

ao

a

E≤

E≤+

α

C

C+

co

c

β

c

c≥o

C+

C≤

Combining α and β to either a major or minor triad, regardless of order (sc., ( sc.,regardless regardless of whether we pass through an augmented triad or a diminished triad), produces the SLIDE transformation (sometimes denoted S ). ). However, since the augmented triad is symmetrical, and since neo-Riemannian theory takes no account of roots, through the concept of double-emploi double-emploi,, we can transform into an augmented triad, then redefine the root, and transform out in a different direction (this can be notated simply as γ γ for for first inversion, and γ’ and γ’ for second inversion, inversion ,

52

It is, of course, possible to combine these operators with a transposition level, as in the tradition neo-Riemannian operators, to create pairs of half-mode-reversing transformations that combine to be equivalent to each of P, L, and R, but there is little point creating six transformations when two will suffice. NACE 29


if they need to be notated at all), 53 resulting in two other possible outcomes: the Nebenverwandt Nebenverwandt (N) and the observation is quite equivalent of the Relative transformation (αγ’β ( αγ’β[C] [C] = γ’β = γ’β[C+] [C+] = β[A ≤+] ≤+] = a = R[C] ■). This latter observation

and β on the Tonnetz Tonnetz,, while simultaneously solving an existing useful, as it gives us a convenient way to represent α and critique of the Tonnetz Tonnetz:: that motion along two axes (P and L) are ar e parsimonious, but motion along the third (R) is not. The solution is to add infinitely long strips along the R ax is that represents the augmented triad, such that performing the R transformation involves passing through the augmented strip first; I say infinitely long strips because of the symmetry of the augmented triad, which makes it possible for one to step into the augmented strip from one adjacent triangle, and step out of it in any other adjacent triangle, no matter how distant, while still counting only two steps (as far as parsimony is concerned). Figure 4 shows this this extended Tonnetz Tonnetz.. Figure 4 Extended Tonnetz

This extended version of the Tonnetz Tonnetz shows the augmented triads a strips dividing triads from their Relative transformations. These strips behave as though though infinitely long, long, such that one can enter an augmented an augmented strip from near the bottom of the Tonnetz and Tonnetz and come out of it from near the top just as easily as entering it and leaving it at the same level (as ( as with a Relative transformation) and count it as the same distance in terms of voice-leading parsimony. This is effectively a kind of equivalent representation to the Cube Dance diagram, unfolded and laid out as a net; as such each coloured diagonal row represents one of the hexatonic systems (labelled above, according to the traditional cardinal directions).

Passing through the diminished triad does not display this property. Although the diminished diminished triad is symmetrical within itself, it does not evenly divide the e ntire octave, and so the root is distinct (unlike the diminished

53

I am using the letter γ ( gamma) gamma) to to represent rotation, rather than the more traditional R, because the use of R conflicts with the usage of R for the Relative transformation. NACE 30


seventh chord – we will deal with seventh chords shortly). As such, there is always one one clear root of a diminished triad, and so applying α and and β consecutively always results in the the same SLIDE transformation. For simplicity, for the purposes of tracing a path on the Tonnetz Tonnetz as as a spatial network, we can represent this diminished chord as overlapping with the node across which the the SLIDE transformation proceeds – the node representing the pitch that is held common between the two chords (the chordal third). Figure 5 shows the extended Tonnetz Tonnetz with with the labels removed, which gives a clearer view of this Tonnetz Tonnetz.. Figure 5 Simplified Extended Extended Tonnetz

This depiction of the Tonnetz is Tonnetz is simplified by having the labels removed; in addition, the nodes where chords meet represent diminished triads. This diagram allows for a clean spatial network network upon which a path can be traced that incorporates augmented and diminished triads along with the major and minor triads.

C. Seventh Chords Having solved the challenge of incorporating augmented and diminished triads into the analysis in a way that is sufficiently consistent as to be able to generate pattern-based insight, we now turn to the problem of incorporating seventh chords into into the analytical system system (with the same provision). The solution to to this problem is not so convenient; unlike augmented and diminished triads, with same the same set cardinality as major and minor triads, seventh chords have a greater cardinality. How do we transform a trichord into a tetrachord in a way that is analytically insightful when combined with the neo-Riemannian opera tors and related transformations that will form the bulk of the analysis? NACE 31


There have been a variety of attempts to extend the techniques of neo-Riemannian analysis (and related systems) to accommodate seventh chords by Adrian Childs, 54 Edward Gollin, 55 Hook,56 and Douthett and Steinbach;57 however, the limitation of these is that they generally deal with relationships between between seventh chords, without approaching the problem of how to get from get from a a triad to to a a seventh chord. A few authors have approached the problem, usually as stop-gap measures in the context of papers dealing with other topics, but these solutions have not been entirely convincing, and have not caught caught on as any kind of standard methodology. For instance, Lehman simply deals with them as “near transformations”, and labels them * f (where f (where f represents represents the transformation being approximated, which is usually reckoned by truncating the the seventh chord into a triad). 58 Hook deals with the transition from triads to seventh chords through his “inclusion” transformation (symbolized by

). This transformation maps any member of set-class (037) onto the unique member of set-class



(0258) that contains it 59 – in simpler terms, a major triad is mapped onto a dominant seventh chord with the same root, and a minor triad is mapped onto the half-diminished seventh chord that shares a dualist root ( i.e. i.e.,, adds an under-seventh to under-seventh to the minor triad). In both cases, from a dualist perspective, the impact is simply to add a minor seventh to the existing triad. A draw-back to this solution is the arbitrary decision to limit transformati on from triads to seventh chords so that they always move to members of (0258). Minor seventh chords are arguably more common and useful, so it is curious to prefer the half-diminished variety – though his choice may be related to the fact that this set is a minimal perturbation of the symmetrical diminished seventh chord, just as (037) is a minimal perturbation of the symmetrical augmented triad, to which Cohn attributes their high degree of voice-leading smoothness. 60

54

Childs, Adrian, “Moving “ Moving Beyond Neo-Riemannian Triads: Exploration a Transformational Model for Seventh Chords”, Journal of Music Theory 42.2 (1998): 181-93. Chords”, Journal 55 Gollin, Edward, “Some Aspects of Three -Dimensional Tonnetze Tonnetze”, ”, Journal Journal of Music Theory 42.2 (1998): 195-206. 56 Hook 2002, esp. 116-8; he revisits the same analysis from a slightly different direction in: Julian Hook, “Cross “Cross--Type Transformations and the Path Consistency Condition”, Music Theory Spectrum 29 (2007): 1-3; his notation varies somewhat in the latter article. 57 Douthett and Steinbach 1998, esp. 255-6. 58 Lehman 2012a, ix. 59 Hook 2002, 117-8; 117-8; Guy Capuzzo follows Hook’s lead in his article of neo -Riemannian analysis of pop music: Capuzzo, Guy, “Neo-Riemannian “Neo-Riemannian Theory and the Analysis of Pop- Rock Music”, Music Music”, Music Theory Spectrum Vol. Spectrum Vol. 26, No. 2 (2004): 177-200; 191-2. 60 Cohn, Richard, Audacious Audacious Euphony: Euphony: Chromaticism and the the Triad’s Second Nature. Oxford: Oxford University University Press, 33-37. NACE 32


Hook’s example does, however, provide a provide a useful clue toward a better better definition. Hook is analysing the so-called omnibus progression. omnibus progression. This progression harmonizes a descending chromatic scale in groups of three chords for which two voices are obliquely preserved and the remaining voice moves chromatically upwards (i.e. ( i.e.,, contrary motion). This produces a single triad followed by two dominant seventh chords; the cycle then repeats a minor third lower (see Figure 6). Figure 6 The Omnibus Progression

Adapted from Hook 2002, Figure 12. The truncated triad of each ea ch seventh chord is related to the adjacent adjace nt seventh chord by leittonwechsel ; the seventh chords are then generated from these triads by the inclusion inclusion operation. Notice that the two F-seventh chords on either side of the A-minor are produce by chromatic voice exchange.

What is most interesting about this progression may not be the leittonwechseln and leittonwechseln and inclusion operations that Hook is drawing attention to, but rather the chromatic voice exchange that occurs from a seventh chord, through a minor triad, to the next seventh chord, which is of the same type, but moves from root position to third inversion; this voice exchange moves through the leading tone (for which the leittonwechsel is is named), but it also displays a critical observation: it is not merely a trichord, but rather a four-note multiset with three pitch-classes, one of which is doubled. The voice exchange through a shared passing tone is one of the time-honoured techniques of tonal theory, and one of its most obvious characteristics is that two voices in harmony with each other at both the beginning and end of the exchange temporarily come together to a unison ( sc. sc.,, they are temporarily not harmonizing each other). In the omnibus omnibus progression progression above, it is through this process that a measure of harmony is lost and then regained – that is, the cardinality of the set-classes is first decreased, then increased again. We shall return to this point. Another possible solution for transforming through sets of differing cardinalities is proposed by Clifton Callender (though his transformations are more broadly applicable to other problems in voice-leading) in the form of NACE 33


SPLIT and FUSE transformations. 61 The idea here is that a single note note can be split split into into two, with one a semitone above the original, and the other a semitone below, while a pair of notes a whole-tone apart can be fused into into a single note halfway between the two. Callender demonstrates his concept concept in pitch space, rather than than pitch-class space, so his splitting and fusing always occur from a second to a unison, rather than a tenth or sixth to an octave, but extending the concept into pitch-class space and applying these two transformations to the omnibus omnibus progression progression of Figure 6, the root and seventh of the root-position seventh chord can be FUSEd to the leittonwechsel triad, triad, the fifth of which is then SPLIT in the opposite direction to achieve the third inversion seventh chord ( and the completion of the voice exchange). Once again, a possible interpretation of the SPLIT operation is that that we are not so much creating a new note as we are taking two previously existing notes that were locked in unison and separating them out into distinct streams (and vice-versa for FUSE). Both of these methods imply a more general solution to the seventh chord problem, which comes from carefully examining neo-Riemannian analysis in its origins and applications, and observing what is not not required required in order for a neo-Riemannian analysis to be valid. First, we must note that there has never been a stipulation stipulation that a passage consist of a pure, three-part texture of complete triads with no doublings; subsequently, we must observe that although voiceleading [approximate] parsimony is a property of the neo-Riemannian operators in the abstract sense (and it tends to have been the mechanism by which passages benefitting from neo-Riemannian analysis have arisen), it has never been a strict requirement that the chord progressions so analysed actually be realised parsimoniously; a corollary of these two observations is that there is no obligation to lead a doubled tone tone in the same way in both voices. As a simple example, it is entirely normative to have a four-part texture in which the three upper voices move parsimoniously, while the bass line doubles the root of each triad (and consequently does not move in the same sa me way as the same pitch in the upper voices, nor does does it move parsimoniously). This is demonstrated in Figure 4. Figure 7 A Simplified but Normative Normative Neo-Riemannian Passage

61

Callender, Clifton, “Voice-Leading “Voice -Leading Parsimony in the Music of Alexander Scri abin”, abin”, Journal Journal of Music Theory Vol. Theory Vol. 42, No. 2 (1998): 219-33; esp. 224-226. NACE 34


This passage is a portion of the LR cycle. It is completely normative normative in its realisation: the majority of the voiceleading is [approximately] parsimonious (particularly the upper three voices), but the bass line consists of a doubling of the chord roots; it does not move the same way as the voices that it doubles, and it is non -parsimonious.

It is only a small step beyond these observations to recognise that any pitch in the chord, and perhaps all the pitches, could be assumed to be doubled, and that there is no reason why any one pair of doubled pitches ought to move in the same way. What we have, instead, is two (or, in principle, even an infinite number of) identical triads, locked together – as with the pitches that Callender splits and fuses – and we simply chose to separate these triads and apply to them two different triadic transformations. transformations. For instance, to create the omnibus omnibus progression progression of Figure 3, we begin with a C-minor triad, and split it into two copies; with one, we perform a leittonwechsel (to produce A-flatmajor), and with the other, we perform an a n α transformation transformation (to produce a C-diminished triad); the composite of these two triads is an A-flat-dominant seventh triad. triad. We can represent this transformation thus:

.

This approach also provides us with a methodology for moving between seventh chords using the traditional neo-Riemannian operators (it is important that we should use these traditional operators, as it is in this way that we will be able a ble to draw significant insights about transformations, tra nsformations, irrespective of set-class cardinality). To accomplish this, we simply simply recognise that a seventh chord is merely a pair of triads that overlap by two pitches. The transformations in question, then, are merely the transformations that map the two triads of the first chord onto the two triads of the second chord. Note that this need not mean mapping mapping the upper triad onto the upper triad and the the lower triad onto the lower; there is, in pri nciple, no reason why the two triads shouldn’t switch places. In examining the nature of voice-leading, Joseph Strauss argues in favour of a concept t hat he calls total voice-leading62 - a measure of all the possible intervals between each note of the first sonority and each eac h note of the second sonority, expressed as

62

Strauss, Joseph, “Total Voice Leading”, Music Theory Online Vol. Online Vol. 20, No. 2 (2014). NACE 35


a multiset of intervals. Since neo-Riemannian transformations are effectively voice-leading constructs, we can reasonably apply the same procedure procedure for labeling the multiple transformations transformations between seventh chords: provide transformations from each component triad triad to each component triad, using a matrix notation. For instance, moving from ii& to V&, the upper triad of ii& moves to the upper triad of V& via RPR α α and and the bottom moves to the bottom via LRP; additionally, the top moves to the bottom via LRLR and the bottom to the top via PR α PR α . We can thus represent the transformation as

 , where the transformations take the following arrangement:

     ]. In this notation, the first three transformations of the omnibus [ omnibus progression progression are             given in Figure 5. Figure 8 The Omnibus Progression Progression in Matrix Notation Notation

 cm

-----------



[ ] A b7

-----------

F7

-----------

am

This is one possible interpretation of the omnibus progression in matrix notation; notice that the progression both begins and ends with the same transformation, and that the middle matrix provides two possible interpretations of the transformation between the two seventh chords, either one of which (or potentially both) may prove insightful, depending on the context.

Notice that although this method was developed for use with neo-Riemannian transformations, there is no particular reason why it ought to be restricted to them. An authentic cadence of V& - I in this form as

VII.

could easily be described

2 .  THE ANALYSIS

With the architecture in place, it is now possible to perform a complete analysis of the Voldemort arrangement. This analysis will be primarily graphical in nature, and will be divided into seven sections. Each section will be drawn on an extended Tonnetz Tonnetz,, as a special network that shows exclusively neo-Riemannian transformations; a few liberties are taken with respect to augmented triads in the same family in order to make the analysis analysis easier to read. Heavy dashed lines lead from one instance of a chord to another instance of the chord elsewhere in the network ( i.e. i.e.,, the identity transformation). Below the Tonnetz Tonnetz,, the analysis is re-interpreted as an event event network. In general, each NACE 36


measure will begin a new line (though in a few cases, two measures are placed on one line for space s pace reasons); reas ons); chords that appear off the main line are embellishing chords; heavy dashed lines are again identity transformations, and light dashed lines represent other relationships between important chords (relationships that are otherwise obscured by the embellishing chords). In general, neo-Riemannian transformations will be used when the relationship is close; for larger transformations, TnP relationships will be used; T nP labels will also be used for the absolute progressions discussed earlier in this paper; and DOM and SUB transformations are used only where the functions implied by them appear to have any meaning. meaning. Transformation labels are colour-coded colour-coded to help identify identify related transformations. In particular, Tarnhelm progressions (and progressions similar to Tarnhelm progressions, especially those whose off-tonic chord begins on the correct root) are shown in red; progressions emphasising the

S4 (especially

tritone root

relationships) are shown in cyan; minor leading tone progressions and Neapolitan minor progressions are given in magenta; and identity transformations and rotations of augmented triads are given in green.

[This space intentionally left blank]

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VIII.

CONCLUSIONS

Although it is difficult to draw conclusions conclusions from this rather fragmentary piece, these analyses have have shown that the characteristics that we have been tracking – the Tarnhelm, the

S4 of the tritone progressions, the minor

leading-tone, and the Neapolitan minor progressions (and approximations thereof) – permeate the Voldemort arrangement; this becomes even more apparent given the newly acquired ability to track related progressions with augmented and diminished chords, as well as tracking both the lower and (more importantly) the upper portions of seventh chords. Another interesting detail that becomes apparent from the analyses on the extended Tonnetz Tonnetz is that, throughout this arrangement at least, Williams seems to favour certain hexatonic systems: obviously, he most most strongly favours the Eastern system (in which the tonic is found); as we progress clockwise around the systems, Williams uses each new system less than the previous, scarcely drawing chords from the Northern system at all; Williams seems see ms to avoid moving counter-clockwise (upstream, as it were) around the systems, an observation not predicted prior to this analysis. Although this is only a single arrangement, and it would certainly be necessary to look for these new features – the minor leading-tone progression, the Neapolitan minor progression, minor triad planing, and a certain polarity with respect to the hexatonic systems – in other scores; however, I feel that I can reasonably suggest these as potential elements of Williams’ style for Antagonists themes.

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IX.

BIBLIOGRAPHY

Bribitzer-Stull, Matthew. “From Nibelheim to Hollywood: Hollywood: The Associativity of Harmonic Progression” Progression” . In The Legacy of Richard Wagner: Convergences and Dissonances Dissonances on Æsthetics and and Reception. Edited Reception. Edited by Luca Sala (Lucca: Turnhout, 2012): 157-183. Buchler, Michael. “Reconsidering Klumpenhouwer Networks”. Music Networks”. Music Theory Online 13.2 Online 13.2 (2007). Callender, Clifton. “Voice “Voice-Leading -Leading Parsimony Parsimony in the Music of Alexander Scriabin”. Scriabin” . Journal of of Music Theory Theory 42.2 42.2 (1998): 219-33. Capuzzo, Guy. “Neo “Neo-Riemannian -Riemannian Theory and the Analysis of Pop- Rock Music”. Music”. Music Theory Spectrum 26.2 Spectrum 26.2 (2004): 177-200. Childs, Adrian. “Moving Beyond NeoNeo -Riemannian Triads: Exploration a Transformational Model for Seventh Chords”. Chords”. Journal of Music Theory 42.2 (1998): 181-93. Cohn, Richard. “Maximally Smooth Cycles, Hexatonic Systems, and the Analysis of La te-Romantic Triad Progressions”. Music Progressions”. Music Analysis 15 Analysis 15.1 .1 (1996): 9-40. -----------------. “Square Dances with Cubes”. Cubes”. Journal of Music Theory 42.2 Theory 42.2 (1998): 283-296. -----------------. “Uncanny Resemblances: Tonal Signification in the the Freudian Age”. Journal of the American Musicological Society 57.2 Society 57.2 (2004): 285-324. -----------------. Audacious Euphony: Euphony: Chromaticism and the the Triad’s Second Nature . Oxford: Oxford University Press, 2012. Cook, Robert. “Parsimony and Extravagance”. Journal Extravagance”. Journal of Music Theory 49.1 Theory 49.1 (2005):109-40. Cooke, Mervyn. A History of Film Music (Cambridge: Music (Cambridge: Cambridge University Press, 2008). Douthett, Jack, and Peter Steinbach. “Parsimonious Graphs: A Study in Parsimony, Contextual Transformations, and Modes of Limited Transposition”. Transposition”. Journal of Music Theory 42.2 (1998): 241-63. Gollin, Edward. “Some Aspects of ThreeThree -Dimensional Tonnetze”. Tonnetze”. Journal of Music Theory 42.2 Theory 42.2 (1998): 195-206. Halfyard, Janet. “Music Afoot: Supernatural Horror Horror-Comed -Comedies ies and the Diabolus in musica”. In musica”. In Music in the Horror Film: Listening to Fear. Fear. Edited Edited by Neil Lerner (New York: Routledge, 2010): 206-23. 206-23. Hook, Julian. “Uniform Triadic Transformations”. Transformations” . Journal of Music Theory 46 Theory 46.1 .1 (2002): (2002): 57-126. ---------------. “Cross “Cross-Type -Type Transformations and the Path Consistency Condition”. Music Theory Spectrum 29 Spectrum 29 (2007): 1-39. Lehman, Frank. “Reading Tonality Through Film: Transformational Hermeneutics and the Music of Hollywood” (PhD dissertation, Harvard University, 2012a). ------------------. “Music Theory Through the Lens of Film” . The Journal of Film Music 5.1 Music 5.1-2 -2 (2012b): (2012b): 179-98. ------------------. “Hollywood Cadences: Music and the Structure Structure of Cinematic Expectation”. Expectation”. Music Theory Online Online 19.4 19.4 (2013). Lewin, David. Generalized Musical Intervals and Transformations. Transformations . New Haven: Yale University University Press, 1987. NACE 46


----------------. “Some Notes on Analyzing Wagner: The Ring and Parsifal” Parsifal”.. 19th Century Music 16.1 Music 16.1 (1992): 49-58. Meyer, Stephen. “ ‘Leitmotif ’: On the Application of a Word to Film Music”. Music” . Journal of Film Music 5.1-2 Music 5.1-2 (2012): 101-8. Murphy, Scott. “The Major Tritone Progression in Recent Hollywood Science Fiction Films”, Music Theory Online Vol. 12 No. 2 (2006). (2006). -----------------. “Transformational Theory and the Analysis of Film Music”. In The Oxford Handbook of Film Music Studies.. Edited by David Neumeyer (Oxford: Oxford University Press, 2014): 471-99. Studies O’Donnell, Shaugn. “Klumpenhouer Networks, Isography, and the Molecular Metaphor”. Metaphor” . Intégral 12 12 (1998): 53-80. Schneller, Tom. “Modal Interchange and Semantic Resonance in Themes by John Williams” . Journal of Film Music 6.1 Music 6.1 (2013): 49-74. Strauss, Joseph, “Total Voice Leading”, Music Theory Online 20.2 Online 20.2 (2014). Webster, Jamie. “The Music of Harry Potter: Continuity and Change in the First Five Films” (PhD dissertation, University of Oregon, 2009). Williams, John. “Voldemort”. Williams, John. “Voldemort”. In In Harry Potter: Sheet Music from the Complete Complete Film Series. Series . Arranger not specified (Van Nuys, CA: Alfred Music Publishing Publishing Co., Inc.): 39-41.

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Musical Transfiguration

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