Exploring the ‘Sound-box’ in Radiohead’s

“Paranoid Android”

David R. Sears⇤

October 15, 2011

Abstract

In the analysis of popular music, transcription remains the mostcommon method for the visualization of musical information. How-ever, Western notation often fails to adequately represent parame-ters that remain essential both to the perception and composition ofrecorded music, parameters such as dynamics, tempo, texture, timbre,and spatial position. In an attempt to provide such a visualization,Dockwray and Moore (2010) conceptualized a stereophonic track interms of the ‘sound-box’, a four-dimensional virtual space consistingof the dimensions laterality, register, prominence and temporal conti-nuity. They did not provide, however, a method for extracting thesefeatures directly from audio. Using Radiohead’s “Paranoid Android”as a case study, I first explore alternative approaches for the visualiza-tion of dimensions of the sound-box. Taking methods for the extrac-tion of stereo panning information as a starting point, I then considerhow compositional parameters related to the lateral dimension of thesound-box contribute to the articulation of formal sections.

Introduction

In the analysis of popular music, transcription remains the most commonmethod for the visualization of musical information. Of course, the choiceto privilege Western notation in music analysis is not necessarily a poor

⇤Email: david.sears@mail.mcgill.ca

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one; the attributes it most clearly represents—melody, harmony, rhythm andmeter—also happen to be those attributes listeners most readily perceive andremember (Meyer 1998, 8). That music scholars often identify the score asthe primary object of study also reflects the expectation that, at least in thepre-recorded era, the score represents an immediate artifact directly originat-ing from the pen of the composer. This kind of thinking lends support to thebelief that an analysis of the formal design of, say, the first movement of theEroica Symphony might relate in some manner to Beethoven’s own concep-tion of the movement’s form as he was composing it. In the case of popularrecorded music, however, artists very often do not begin (or end) with thescore, instead choosing to produce, by various technical means, a recordedaural object. While transcriptions therefore still provide very useful visualrepresentations for popular music research, they fail to adequately representfeatures of the recorded audio that remain essential both to its composi-tion and reception, such as dynamics, tempo, texture, timbre, and spatialposition, nor can they visualize parameters over which engineers and pro-ducers have direct control, such as panning, equalization, and compression.Musicologist Albin Zak explains,

By now, there is a widespread consensus that pop records are con-structed artworks, which has begun to suggest a growing slate ofquestions about compositional techniques and criteria. Scholarshave their own traditions and it is reasonable to seek help in an-swering such questions from older compositional practices withlong histories of thought and articulated principles. But sincesuch traditions developed in a pre-electric era where the enablingtechnology was limited to musical notation, we must also imaginenew approaches to criticism and analysis that move beyond thecustomary concerns of musicologists and music theorists. (Zak2007, n.p.)

In an attempt to move beyond the attributes Western notation so wellrepresents, Ruth Dockwray and Allan Moore conceptualized a stereophonictrack in terms of the ‘sound-box’, a four-dimensional virtual space consistingof the dimensions laterality, register, prominence and temporal continuity(2010).1 Using the sound-box representation, the authors sought to trace the

1The four dimensions roughly correspond to stereo space, pitch (or frequency) space,loudness, and time, though the prominence of a sound source is also a↵ected by charac-

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development of normative procedures for the composition of music in stereospace, culminating in the identification of a taxonomy of the most prevalentmix types. Given their desire to generalize across a large sample of tracks,however, they did not provide a method for considering variations within atrack’s sound-box over time, instead simply producing a single, cumulativevisual representation for each track.

Recent interest in developing methods for the visualization and analy-sis of recorded audio is not unique to musicological and music-theoreticalscholarship. Over the last decade, research in the music information re-trieval (MIR) and digital signal processing (DSP) communities has yielded anumber of promising methods for the extraction of musicologically relevantfeatures directly from audio (e.g., key-finding, beat extraction, and harmonicand formal analysis). Yet, given the increasing attention these disciplines de-vote to the recorded object, it is perhaps somewhat surprising to note a lackof similar interest in the development of methods for analyzing features ofproduction. This fact reflects, in large part, the immaturity of the MIR andcomputer music disciplines, rather than the explicit dismissal of productionas a relevant domain of study. Indeed, in the last few years a handful of stud-ies have provided a method for deriving stereo panning information directlyfrom audio (Avendano 2003; Tzanetakis 2007; Sarro↵ and Bello 2008, 2009).However, methods for extracting dimensions of the sound-box have yet to beapplied in music-theoretical discourse.

In a recent article concerning the application of signal processing tech-niques in record production, Jay Hodgson laments the inherent contradictionunderlying current pop music discourse. He writes,

Even as musicologists and theorists turn their analytic attentionsto pop records, and even as many are compelled to reject whatDavid Brackett calls the ideological and aesthetic baggage’ of‘musicological discourse’ to do so, they remain largely fixated onmusical details which can be notated—formal contour, harmonicdesign, pitch relations, metered rhythm, and so on. (2010, 294)

Rather than reject the trappings of musicological discourse outright, I hopeto demonstrate that the analysis of production techniques derived from the

teristics of the physical space in which it is recorded, its distance from the microphone(s),the type(s) of microphone(s) employed, as well as any e↵ects applied by the engineer afterrecording.

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audio representation might both complement and clarify analytical readingsarising from the notated score.

This paper consists of three parts. In part one I present an analysis ofboth the form and the harmonic processes underlying the first section of Ra-diohead’s “Paranoid Android,” which leads to the identification of a tonalconflict that prevents a straightforward formal reading. Part two describesmethods for the analysis of stereo panning techniques, including the appli-cation of Carlos Avendano’s equations for deriving stereo information fromaudio. It concludes with a discussion of how techniques for the extraction ofeach of the dimensions of the sound-box might clarify the formal interpreta-tion provided in part one. Finally, part three provides an example of howproduction constraints concerning the manipulation of the sound-box alongthe lateral (stereo) dimension result in important compositional consequencesfor the artist/composer.

Part 1. Formal Ambiguity in “Paranoid

Android”

Since “Paranoid Android’s” 1997 debut as the first single from Radiohead’sthird album, OK Computer, its reception, like that of the album, frequentlyconsisted of allusions to British rock acts like Pink Floyd and The Beat-les, with many critics appealing to the commercial success of OK Computeras evidence of prog-rock’s revival in the British music scene (Letts 2010,29). Aware of the characterization of “Paranoid Android” as “neo-prog-rockgrandiosity,” members of the band reacted somewhat dismissively: “Ignorethat. That was just a Pink Floyd cover” (30). Despite Radiohead’s beste↵orts, however, it isn’t surprising that, given the song’s duration of over sixminutes, as well as its three-part formal design, the prog-rock label persistsnearly fifteen years later (e.g., see Gri�ths 2004; Footman 2007; Letts 2010).

Even the formal design of the first part (shown in example 1), whichappears at first glance to be the least problematic of the three parts, defieseasy description.2 The first part (0:00-1:18) consists of an instrumental intro-duction, followed by a verse and its repetition. The unchanging lyric in thefollowing phrase, “What’s that?”, provided in example 2 and labeled in the

2Gri�ths (2004) understands the return of the second part as a fourth part in a 4-partformal design. I, however, interpret this section as a coda.

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Example 1: Form Diagram of the first part of “Paranoid Android.”

form diagram as Bridge/Chorus (hereafter labeled B/C), clearly indicates arefrain, thereby suggesting the first part follows the standard verse-chorusformal type.3 Yet, the harmonic progression underlying the refrain lyric failsto support such a reading. Provided in a voice-leading reduction in exam-ple 3a,4 the A section of the verse begins with the harmony of c minor.The presence of an F in the following chord suggests a major-minor seventhsonority with F as the root, in this instance functioning as a substitute forthe dominant of g minor.5 However, this chord might also substitute for anA half-diminished seventh chord, as the prolongation of c minor through 5-6

3For a discussion of rock formal types, see Covach 2010. Identifying a passage as arefrain or a chorus is often somewhat tricky. Jay Summach resolves this issue by invokingconcepts of length and completeness to distinguish between the two formal labels (2011,n.p.). In this case, the invariant lyric is extremely short, yet the duration of the passageat over twenty seconds is nearly equal in length to the verse, suggesting a chorus. For thesake of simplicity, I will refer to the lyric as exemplary of a refrain, but for the passageitself I will retain the term chorus.

4A number of scholars have questioned the validity of applying a Schenkerian approachin popular music analysis (for example, see Middleton 1990, 195), and they generallyo↵er two complaints. First, a strict Schenkerian analysis fails to accommodate modalharmony, a feature that pervades much of rock and popular music (Biamonte 2010). Ratherthan interpret modal syntax as a deviation from the so-called normative tonal paradigms(e.g., the Ursatz ), I suggest that, following Burns (2000), the notion of prolongation isstill applicable in modal harmony, though the syntactic relationships found therein areadmittedly much less clear. Second, many popular songs resist attempts to provide a globaldirected voice leading structure, instead oftentimes presenting a number of harmonicallydisconnected sections—verse, chorus, bridge (Capuzzo 2009, 157). Burns’ response is totreat each section independently, permitting her to “avoid an Ursatz interpretation,” anapproach that I adopt here (219).

5Certainly, the F7 is understood in tonal syntax as V7 in Bb, but resolved deceptivelyin this figure to the submediant of g minor. However, I would suggest the resolution of thetritone to Bb represents a strong departure from Radiohead’s harmonic language; instead,I interpret the F7 as bVII in g minor, which functions as a kind of pre-tonic. Indeed,De Clercq and Temperley provided evidence from a corpus analysis of one hundred rocksongs that IV, V, and bVII represent the most frequent pre-tonic harmonies in rock music(2011, 61).

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Verse 1

(Please could you stop the noise, I’m trying to get some rest

From all the unborn chicken voices in my head

Refrain

(What’s that? (computer voice: I may be paranoid, but not an android)

What’s that? (computer voice: I may be paranoid, but not an android)

Verse 2

(When I am king, you will be the first against the wall

With your opinion which is of no consequence at all

Refrain

(What’s that? (computer voice: I may be paranoid, but not an android)

What’s that? (computer voice: I may be paranoid, but not an android)

.

Example 2: Lyrics from the first part of “Paranoid Android.”

Example 3: A. Voice-leading reduction of the verse. B. Voice-leading reduc-tion of the 5-6 motion of c minor and g minor. C. A possible continuationof the verse, shown after the dotted vertical line, of the descending fourthsroot motion through C, G, and D.

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motion, shown in example 3b, undermines the status of F as a root (for em-phasis, the F has been placed in brackets). This claim is further supportedby Radiohead’s choice to retain the 5-6 motion of the opening c-minor sonor-ity in a model-sequence that descends by fourth. Shown in example 3c, if Fhad been the intended root mediating the harmonies of c and g minor, a Cshould have appeared as the root of bVII in a continuation of the sequencedescending from g to d minor. Although Radiohead does insert the neces-sary E-natural in both the bass line of the acoustic guitar and the descendingmelodic line in Thom Yorke’s vocals, no instrument provides the necessaryC. Instead, Radiohead prolongs g minor for the duration of the verse usingan E half-diminished seventh chord.

The absence of a clear tonal center is a particularly remarkable featureof this opening. Does “Paranoid Android” begin in c minor? The extendedduration of g minor, achieved by repeating the B section of the verse, suggestsg minor as a more viable tonic. Moreover, in the B section the lead electricguitar descends from 5 to 1, resolutely confirming g minor. However, thepresence of the E-natural in the bass, the raised sixth scale degree of g minor,undermines the sense of G as a stable root.6 That the E-natural is givenso much weight in the outer voices, then, serves to destabilize the senseof g minor as a definite tonic, thereby creating a conflict between the twopossible roots of E and G that necessitates resolution in subsequent material.7

Example 4 provides a voice-leading reduction of the B/C. To resolve theambiguity the E-natural presents in the verse, Radiohead modulates to a keyin which the E is tonally stable. The g minor harmony underlying the E-natural is therefore transformed from a tonic function in the key of g minorto bvii in the key of a minor. The subsequent harmonic progression, bvii-iv6-V7, prolongs the dominant by way of descending parallel tenths.8 Following

6The prevalence of scale-degree flexibility, particularly in the minor mode, might indi-cate the E-natural is not particularly dissonant or unstable, or that it simply representsan inflection of the dorian mode. However, in this figure the E-natural undermines thesense of g minor as a tonic precisely because it appears in the bass; its status as a viableroot creates the harmonic conflict that the B/C later resolves.

7Although I’m claiming the verse is in g minor, I’m reluctant to suggest that it neces-sarily begins in g minor. At first listening, the opening progression from c to g suggests amodel-sequence, but the extended duration of the g minor sonority leads me to retrospec-tively reinterpret the opening c minor chord as iv in g minor.

8In a strict Schenkerian sense, the voice-leading sketch in example 4 asserts that theroot of the first chord in the B/C is in fact E, not G, suggesting that the E half-diminishedseventh functions as a chromatic alteration of the dominant. This point is perhaps some-

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Example 4: Voice-leading reduction of the end of the verse, followed by theB/C after the barline.

Deborah Stein, Guy Capuzzo refers to this particular transformation of theunderlying harmony from tonic function to non-tonic function as exemplaryof directional or progressive tonality (2009, 158).

Given the lack of tonal stability underlying the refrain lyric, perhapsthis section more clearly functions as a bridge, as it e↵ects a modulationto a contrasting key, provides harmonic and melodic contrast, and perhapsmost crucially, ends on the dominant in the new key, thereby providing theretransitional function necessary to proceed to the second part in the new keyof a minor. However, it is hard to dispute that Yorke’s vocals in the bridgeare indicative of a refrain, suggesting an analytical dissonance between thetwo formal readings, resolved either by choosing to place greater analyticalpriority on one or the other reading, or by suggesting a synthesis of thetwo functional types: a kind of form-functional fusion. Given the privilegedposition accorded to the syntactic parameters of music (i.e., melodic andharmonic content), I would suggest that only appealing to the refrain lyricdoes not provide su�cient analytical weight to privilege the chorus reading.

what minor, but it has implications for determining precisely when the transformationtakes place: at the beginning of the B/C, or at the arrival of the dominant in root posi-tion? This is a tricky distinction, but I would suggest that, because of the emphasis ofg minor in the B section of the verse, it is di�cult to suddenly hear the first chord atthe beginning of the B/C as an E half-diminished seventh in first inversion. Instead, I’dsuggest the G remains the root, as it functions as a pivot between the tonic of g minorand the subtonic of a minor. The phenomenal experience of the transformation of theE-natural from raised sixth to stable root doesn’t actually take place until the bass arriveson E-natural at the end of the progression.

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In part 2, I will attempt to redress this imbalance by appealing to the sound-box.

Part 2. The ‘Sound-box’

The extraction of meaningful information directly from recorded audio repre-sents an extraordinarily di�cult task. As Nicholas Cook explains, “if West-ern notation is extremely selective as a representation of musical sound, therecorded object is perhaps just the opposite” (2009, 226). Recording en-gineers and producers seeking to visualize parameters of production oftentake a fairly pragmatic approach, deriving a representation of stereo spacesimply from careful and informed listening. In his book The Art of Mixing,David Gibson provides visualizations of the sound-box in a manner simi-lar to Dockwray and Moore’s model to illustrate mixing techniques relatedto each of the dimensions.9 To visualize each dimension in time, WilliamMoylan (2007) presents two-dimensional plots to evaluate sound accordingto characteristics such as pitch, spatial elements, and loudness. Moylan’sSound Location Graph provides a particularly useful method for visualizinginstruments placed both in stereo space and time.10

A Sound Location Graph for the first part of “Paranoid Android” ispresented in example 5. The verse begins with hi-hats, a cabasa, and othernon-pitched percussion panned to either side of the stereo space, with anacoustic guitar, snare and kick drum panned to the center. The entrance of anelectric guitar on the left provides stereo width, as the remaining instrumentscover a relatively narrow range of the stereo space.11 The arrival of the B/Cmarks the entrance of the bass guitar in the center and another lead guitarpanned to the right. Together these instruments e↵ect a dramatic expansionof the stereo space, thereby articulating the formal boundary between theverse and the B/C.

Unfortunately, useful as these representations can be, the lack of precisioninherent in determining both the location and width of each instrument in

9Dockwray and Moore also cite Gibson as an important inspiration for their own visu-alization (2010, 183).

10For an example, see Moylan 2007, 182-184.11Achieving stereo width in one instrumental voice is accomplished by a variety of

technical means, many of which relate to methods for delaying the signal. I will discussthis issue in greater detail in part 3.

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Example 5: Sound Location Graph of the first part of “Paranoid Android.”The y-axis indicates stereo position and the x-axis indicates measure num-bers.

the space makes visualizing each dimension of the sound-box particularlydi�cult. In a paper providing techniques from DSP for audio analysis, CarlosAvendano (2003) proposed a series of equations that derive a stereo panningspectrogram (SPS) from stereo audio. Avendano’s equations take as theirstarting point the digital signal of the left and right channels each decomposedinto a number of frequency bins, also known as a spectrogram. Example 6displays the three most common visual representations of audio for the firstpart of Radiohead’s “Paranoid Android”: the time-domain representationprovided at the top, the frequency-domain representation in the middle, andfinally the spectrotemporal representation (or spectrogram) at the bottom.

Before going further, a brief explanation of each visualization might beuseful here. The time-domain representation simply visualizes a line plot ofthe intensity in normalized amplitude of each sample of both the left andright signals over the duration of the entire excerpt, shown here in seconds(digital audio is generally sampled at 44.1kHz). To visualize a signal inthe frequency domain, a short-term Fourier transform (STFT) of the signalsdetermines the intensity at each k frequency bin, with intensity given herein decibels (note the sharp cuto↵ of both signals at around 18kHz). Finally,to consider how the frequency spectrum varies over time, this decompositiontakes place over a given m time window that moves along each signal at aparticular step size, resulting in a matrix of m time frames and k frequency

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Example 6: Three representations of the first part of “Paranoid Android.”Top: Time-Domain representation of the audio waveform, with the x-axispresenting time in seconds, the y-axis presenting normalized amplitude. Mid-dle: Frequency-Domain representation of the spectrum with the x-axis pre-senting frequency and the y-axis presenting intensity in dB. Bottom: Spec-trogram with the x-axis presenting time in seconds, the y-axis presentingfrequency, and intensity in dB color-mapped (red denotes frequency bandswith high intensity).

bins. The bottom representation therefore retains time on the x-axis andfrequency on the y-axis. Intensity in dB is color-mapped, with red indicatinghigh intensity.12

(m, k) = 2|Xl(m, k)Xr(m, k)|

|Xl(m, k)|2 + |Xr(m, k)|2 (1)

Avendano’s first equation simply compares the matrices of the left and rightchannels at a given m time frame and k frequency bin. It assumes thatsimilar intensity values between the two channels result in a center-pannedevent.13 The equation then yields a new matrix of values falling in a range

12The spectrogram at the bottom of example 6 was calculated with a Hamming windowof 50ms and a step size of 25ms.

13Putting it simply, if a guitar is panned to the center of the stereo space, then each ofthe stereo channels should possess the same degree of energy at the same frequency and

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between 0 and 1, with 0 indicating events panned to the side (labeled “wide”in the figure) and 1 indicating events panned to the center. This matrix ofpanning values can be visualized as a spectrogram, provided at the top ofexample 7.

Note two important di↵erences between this representation and a tra-ditional spectrogram: (1) intensity in the traditional spectrogram has beenreplaced by a center/wide coe�cient, and (2) the center/wide spectrogramdoes not o↵er any information regarding the direction of the pan. This figurereveals a considerable increase in the number of frequency bins panned tothe side in the B/C (between 0:47-1:07).

l(m, k) =|Xl(m, k)Xr(m, k)|

|Xl(m, k)|2 r(m, k) =|Xl(m, k)Xr(m, k)|

|Xr(m, k)|2 (2)

�(m, k) = l(m, k)� r(m, k) (3)

�(m, k) =

8><

>:

1 if �(m, k) > 0

0 if �(m, k) = 0

�1 if �(m, k) < 0

(4)

l(m, k) = [1� l(m, k)]�(m, k) (5)

Equations 2-5 retain panning direction in the next iteration of the panningspectrogram. Equation 3 simply subtracts the right from the left signals cal-culated from equation 2, resulting in a new signal in which the direction ofthe sign indicates whether the event was panned to the left (positive) or tothe right (negative). Equation 4 simplifies the resulting matrix of di↵erencedvalues by replacing each positive or negative integer with its directional sign.Finally, equation 5 multiplies each value of the center/wide matrix calcu-lated in equation 1 by this direction coe�cient, resulting in a Stereo PanningSpectrogram (SPS), shown at the bottom of example 7.14

at the same moment in time. If a guitar is panned to the right, the right channel shouldpossess significantly more energy at the appropriate frequency bins.

14Rather than calculate the SPS using the spectrogram representations shown in exam-ple 7, I applied two additional constraints to the initial spectrogram calculation to reducecomputational complexity and more closely account for the psychoacoustic constraints ofthe auditory system. First, I applied Terhardt’s outer ear model (1979), which attenuatesthe lower and higher registers of the spectrum and emphasizes the spectrum at around2-5kHz (the range in which speech information is generally carried). Second, I replaced a

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Exa

mple

7:Top

:Center/W

ideSpectrogram

ofthefirstpart.

Bottom:StereoPan

ningSpectrogram

ofthe

firstpart.

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Example 8: Time Series Plots of the first part. Top: Stereo Width in blue. 2indicates at least two frequency bins possess energy at opposite ends of thestereo spectrum, while 0 indicates all of the frequency bins possess energyin one location of the stereo spectrum. Middle: Register in red, measuredin midi note numbers (piano keys = 21-108). Bottom: Loudness in green,measured in sones.

The SPS of “Paranoid Android” clearly visualizes the entrance of the left-panned electric guitar in the verse, as well as the entrance of the right-pannedelectric guitar in the B/C. Given the high degree of information reflectedin the SPS, a time series representation of stereo width might provide aneasier method for visualizing the lateral dimension of Dockwray and Moore’ssound-box. Taking the SPS as a starting point, I calculated a simple metricof stereo width by determining the range of panning values present acrossall of the frequency bins at a given m moment in time.15 Provided at thetop of example 8, the time series of stereo width is bounded by a maximumvalue of 2, indicating that a panning value resides at each extreme of thestereo panning space, and a minimum value of 0, indicating that all of thefrequency bins possess the same panning value. Each of the peaks in theverse, for example at 18s and 30s, visually represents the entrance of the

linear frequency scale with Zwicker’s Bark scale (1961), which redistributes the frequencybands along critical band rates, thereby making the critical band a scale unit (each tickmark on the y-axis represents one critical band).

15To smooth the resulting time series, I applied a 1-second moving average and thendownsampled to 2Hz (2 values per second).

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Example 9: Time series of sound-box expansion for the first part. Each timeseries from example 8 was first range normalized between 0 and 1, and thetime series were then averaged.

left-panned guitar.To determine a measure that displays the registral dimension of the

sound-box, shown in the center of example 8, I simply converted the high-est and lowest registral pitches to midi numbers, then calculated the rangeof register values present at a given moment in time. The verse displaysa narrow range of roughly two octaves. However, the entrance of the bassand lead electric guitars at the beginning of the B/C dramatically increasethe range of registral space, as indicated in the plot. Finally, the bottomfigure presents loudness, measured in sones (Moore et al. 1997). To visualizea single time-series plot of sound-box expansion, example 9 represents theaverage of the three time series placed on a scale from zero to one.16

The time series in example 8 clearly demonstrate that the beginning of theB/C features an expansion of the sound-box along every dimension. Yet, eachof these examples fails to capture the in-time experience of an expanding andcontracting sound-box. In fact, George Tzanetakis, the designer of a MIRsoftware framework called Marsyas, recently created a tool called MarPan-ning that visualizes the SPS in real time (2009). His vision of the sound-boxconsists of stereo space on the x-axis, frequency on the y-axis, time on the

16To compare the three dimensions, each of which has a di↵erent scale, each time serieswas first range normalized, which placed the range of values between zero and one. Thethree time series were then averaged.

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z-axis, and intensity color-mapped. Paranoid Android SPS.mov presents theanimation of the first part of “Paranoid Android” using MarPanning.

How might a better understanding of the sound-box a↵ect the two formalinterpretations of the B/C presented earlier? The expansion of the sound-boxappears to serve two functions: first, it clearly delineates formal boundariesbetween the verse and the first B/C, thereby isolating the B/C from thesurrounding material, and second, the initial increase across the sound-boxis followed by relative stasis, in which each of the dimensions reaches a plateauuntil 1:09, at which point a significant decrease in each dimension signals thebeginning of the next verse. The lack of mobility present in the sound-boxwithin the B/C therefore provides a crucial, stabilizing force, suggesting theB/C represents an important arrival that coincides with Yorke’s refrain lyric.Although the dominant at the end of the B/C undeniably serves a retransitionfunction, the relative stasis of the sound-box provides su�cient weight tocounterbalance this tonal motion. In light of both the presence of the refrainlyric and the stability provided by the sound-box, the transformation of theE-natural from unsettling dissonance to stable root represents a significantarrival that severely weakens the expectation for the resolution of dominantharmony.

Hence the first iteration of the B/C is, in my view, a chorus, albeit withbridge-like characteristics. But what about the second iteration of the B/C?On the surface, the two di↵er only in that the second B/C actually precedesthe second part of the song, thereby successfully resolving the dominantharmony to the tonic in the key of a minor. In fact, the second B/C ismarkedly di↵erent. Part 3 considers how attempts to manipulate stereo spacein record production result in interesting textural and metric consequencesthat serve to distinguish the two iterations of the B/C.

Part 3. Compositional Consequences of the

‘Sound-box’

Perhaps one of the great compositional strengths of the recorded mediumlies in the artist’s ability to create performance spaces that could not be du-plicated live, leading Theodore Gracyk to term such spaces “virtual perfor-mances” (1996, 38). Moreover, “non-veridic” applications of various signal

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processing techniques take full advantage of headphones,17 as the mediumproduces a sharper stereo image and can render sound localization withmuch greater precision than loudspeakers (Dockwray and Moore 2010, 184).Engineers and producers achieve these virtual spaces through a variety oftechniques, such as equalization, reverb, and delay. Alexander Case writes,

Equalisation is likely the most frequently used e↵ect of all, reverbthe most apparent, delay the most diverse, distortion the most se-ductive, volume the most under-appreciated, expansion the mostunder-utilised, pitch shifting the most abused, and compressionthe most misunderstood. All e↵ects, in the hands of a talented,informed and experienced engineer, are rich with production pos-sibilities. (2007, xix-xx)

Richard Middleton claims that the application of these techniques in head-phone music results in the listener’s involvement as “a gestural subject, whois assimilated into the textural space,” producing an immediate and immer-sive environment in which the artist can continuously manipulate texturalspaces (quoted in Moore and Dockwray 2010, 220).

The B/C of the first part of “Paranoid Android” presents one instancein which Radiohead and their engineer/producer, Nigel Godrich, endeavoredto surround the listener in an immersive environment by expanding each ofthe sound-box dimensions. Sound-box expansion along the lateral (stereo)dimension also achieves an important compositional goal: the independenceof multiple instrumental voices in a rich and highly complex acoustic sig-nal. David Huron has already demonstrated the important role played byprinciples of auditory streaming in both producing and perceiving complexpolyphonic textures (2001). Given that polyphony is generally attributed tomusic that predates the birth of the recording studio, it is not surprising thatHuron lists onset synchrony, timbral di↵erentiation, and source localizationas auxiliary principles in achieving the perceptual independence of multiplevoices, yet each of these principles can be easily manipulated in a recordingstudio environment.18

17John Andrew Fisher coined the term non-veridic in reference to the use of signalprocessing techniques to produce a recorded object that doesn’t sound as though it was,or even could be, performed live. See Hodgson 2010, 284.

18I am not suggesting that these principles are not evident in polyphonic music, onlythat the recording studio a↵ords the artist/engineer greater freedom in manipulating amix according to these principles.

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To achieve stereo width at the B/C, rather than introduce a new instru-mental part, Radiohead chose to place the same guitar part on either sideof the mix, with Jonny Greenwood playing on the left and Ed OBrien onthe right. If Godrich had simply duplicated the original guitar part, thenplaced the original and duplicate signals in the left and right channels, re-spectively, the auditory system would interpret the two parts as originatingfrom directly in front of the listener, panned to the center. Engineers oftensolve this problem by slightly delaying one of the two signals. If the delayis shorter than around 30ms, the auditory system cannot resolve the timedi↵erence between the two signals, and so the listener perceives one signalstretched across the stereo field; producers term this technique ‘fattening’(Gibson 2005, 23). If, however, the delay is longer than 30ms, the listenerwill hear two separate signals on either side of the stereo plane. The audiofiles 1.1-4.mp3 illustrate this e↵ect by delaying the guitar part from Radio-head’s “Reckoner” by 0ms in 1.1 (no delay), 10ms in 1.2, 50ms in 1.3, andfinally by 100ms in 1.4. Even with a delay as small as 10ms, the guitarappears to have moved to the left of the stereo space.19 Engineers also of-ten apply mirrored equalization, which gives instrumental parts with similarfrequency components complementary spectral shapes to minimize maskingbetween the two signals (Hodgson 2010, 287). Jay Hodgson writes, “whenapplied to tracks spread to either side of the stereo plane, mirrored EQ canenhance the perceived width of a mix. Rock engineers often equalize elec-tric guitar parts di↵erently and, when appropriate, they pan the tracks toopposite sides of the stereo spectrum” (287).

In addition to the techniques an engineer can apply to ensure sound sourceseparation, the musician might also choose to record the instrumental partagain and add it to the mix, resulting in minute temporal and spectral varia-tions that render the two signals distinct enough for the listener to distinguishthem in stereo space (termed overdubbing). In the case of the B/C of “Para-noid Android,” guitarist Ed OBrien applied an e↵ect pedal that placed hisright-panned guitar two octaves higher than Jonny Greenwood’s left-panned

19Klumpp and Eady (1956) demonstrated that the just-noticeable-di↵erence for timedi↵erences between two signals is optimally about 10microseconds or less, which suggeststhat the auditory system is extremely sensitive to the spatial position of sounds in theexternal environment. The psychoacoustics literature of binaural hearing, particularly inregard to sound localization, is extensive. For an overview, see Akeroyd 2006.

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guitar.20 Greenwood also went one step further in distinguishing the two gui-tar lines by applying rhythmic and melodic variations underneath OBrien’spart. Provided in example 10, their performance not only achieves stereowidth, as the earlier analysis revealed, but also produces a heterophonic tex-ture. To facilitate hearing instruments placed exclusively in the left or rightchannels of the space, all center-panned events (i.e., time points with equiv-alent energy at a given frequency in both channels) in BC1.mp3 have beenremoved from the final recording.

The top figure in example 10 visualizes the onsets of each of the twoguitar parts in the first B/C.21 The bottom figure plots the degree of onsetasynchrony between the left-panned and right-panned guitar parts. Here, Iam interpreting O’Brien’s right-panned guitar as the model and Greenwood’sleft-panned guitar as an elaboration of that model. This analysis reveals asystematic manipulation of onset asynchronies around the three-note chro-matic descending line Bb-A-G#, the top line of the descending parallel tenthsshown earlier in example 4. Shown in the transcription in example 11, ratherthan reproduce O’Brien’s melodic line exactly, Greenwood did not performany notes from the three-note line that emphasize the downbeat (i.e., anynotes either directly preceding or falling on the downbeat). He then delayedthe remaining instances of the three-note descending line occurring on thethird beat of each measure. The delay for each of these notes is too small tobe easily retained in a transcription of the passage, as the average deviationof around 130ms is far shorter than a sixteenth-note duration at the track’stempo (186ms). Yet, this delay is still much larger than the recognitionthreshold of listeners. The deviations of the remaining notes in the patternare comparatively small, resulting in an important perceptual e↵ect: thedelay between the guitar voices foregrounds the three-note descending line,thereby emphasizing the structurally salient melodic line played by both gui-

20It is somewhat di�cult to determine precisely which e↵ects pedals the two guitaristsused, as the band has rarely discussed these issues publicly. There have been a numberof attempts to reconstruct the e↵ects rigs used on OK Computer from secondary sourcesand interviews (for an example, see Randall 1994). In addition to possible productione↵ects applied by Godrich (e.g., compression, reverb), it is likely that at his entrance inthe B/C, O’Brien applied a Digitech Whammy pedal set to ‘Octave Up,’ an e↵ect thatallows the guitar to sound up to two octaves higher than the instrument can produce, andGreenwood probably applied an Electro-Harmonix Small Stone Phase Shifter, giving hisguitar the characteristic sweeping e↵ect.

21Guitar onsets were determined manually using Sonic Visualizer to facilitate acquisition(Cannam et al. 2010).

19

Example 10: Top: Plot of the onset times of the electric guitars on the right(red) and left (blue) in the first B/C. Bottom: Deviations from synchrony ofthe left guitar measured against the right guitar.

Example 11: Transcription of the electric guitar parts from the first B/C.

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tars.22

In the second B/C, shown in example 12, Greenwood’s melodic line nowpresents all of the notes from the three-note motive that he initially omitted,but also introduces an embellishing F in the pattern of the left guitar as wellas a rhythmic variation on the same pattern, resulting in a unique hetero-phonic texture in which the two voices slip in and out of phase. Provided ina transcription in example 13, Greenwood continues to deviate dramaticallyfrom O’Brien’s melodic line within each measure, but crucially returns tosynchrony at events occurring on the downbeat. The three-note descendingline therefore anchors textural activity to the underlying meter, restoring thetwo melodic lines from a state of heterophony within each measure to one oftextural monophony at the downbeat.

Example 12 clearly illustrates that the left-panned guitar repeatedly slipsan eighth note out of phase. At the end of the second B/C, the left-pannedguitar suddenly slips further and further out of phase, first by an eighth note,then a quarter, and finally a dotted quarter, before returning to synchrony inthe last iteration of the four-note rhythmic motive G#-D-E-D. These devia-tions from synchrony can be expressed around the edge of a circle, in whichthe 360 degrees represent a measure of music. Phase Animation.mov ani-mates these deviations on a circle above the figures presented in example 13.This particular visualization naively assumes the deviations from synchronyrepresent what Harald Krebs termed a displacement dissonance (1999, 34),a form of metric dissonance in which the two parts are presented in the samemeter but are displaced in time (i.e., out of phase). In fact, what began asan example of a heterophonic texture in the second B/C ends as an exampleof grouping dissonance, in which the two parts present the final four-noterhythmic motive in a four against three hemiola-like pattern, displayed inbrackets at the end of the transcription in example 13.

Where the first B/C is characterized by relative stasis in each of the sound-box dimensions, the second B/C is marked by two important di↵erences.First, the melodic embellishments in the left-panned guitar of the second

22It is important to note that these timing di↵erences are not due to the physical de-mands of playing the instrument. The di↵erences in timing never occur at chord changes,so altering the position of the left hand on the fretboard for each chord change has little tono e↵ect on deviations between the two guitarists. Moreover, the durational rest precedingeach note in the three-note motive is more than su�cient to provide both guitarists thenecessary time to play the out-of-phase notes simultaneously.

21

Example 12: Top: Plot of the onset times of the electric guitars on the right(red) and left (blue) in the second B/C. Bottom: Deviations from synchronyof the left guitar measured against the right guitar.

Example 13: Transcription of the electric guitar parts from the second B/C.Brackets indicate rhythmic grouping.

22

B/C suggest a shift to a clearly heterophonic texture.23 Second, the presenceof metric dissonance near the end of the second B/C propels the listenerforward, generating clear expectations for the arrival of the second part ofthe song. I would suggest that these textural and metric di↵erences, initiallyresulting from a desire to create stereo width and promote the identificationof each of the instrumental parts in the mix, are more indicative of thecharacteristics found in a bridge than in a chorus, which is more likely tobe homophonic and rhythmically regular.24 The dimensions of the sound-box therefore play a crucial role in articulating the form of the first part,initially providing a stabilizing force to counteract tonal motion, and laterproducing textural and metric dissonances that support the tonal motion ofthe dominant as it resolves to tonic at the beginning of the second part of“Paranoid Android.”

The choice to create an immersive sonic environment results in interest-ing compositional consequences, as Radiohead and their producer appliedmethods, both in performance and production, that could achieve the im-pression of stereo width, but that also resulted in the introduction of metricdissonance and the manipulation of textural space. The recorded mediumtherefore a↵ords artists the capacity to control parameters of both compo-sition and production that could not be realized in performance. As LelioCamilleri explains, “not only are sound and space used to transmit the tradi-tional parameters of melody, harmony, rhythm, and meter, but they becomeorganizational in their own right” (2010, 200). The recording studio there-fore serves as a powerful compositional tool, which has yet to be su�cientlyconsidered in music scholarship.

Conclusion

At a conference on the art of record production, Albin Zak explained that“among the problems inherent in establishing an academic discipline aimed atilluminating record production, then, is the need for a fundamental aestheticreorientation as well as new modes of analytic description” (2007). I hope

23These textural distinctions are not necessarily categorical, but can instead lie on acontinuum, a concept suggested by Huron (1989).

24I’m associating textural, harmonic, and rhythmic instability as features expressed bya bridge, not a chorus. However, this claim remains unverified and necessitates furtherstudy.

23

to have provided a few techniques for the analysis of stereo audio that canboth complement and clarify existing modes of description either derivedfrom or reliant on the score. However, though my analysis was admittedlymyopic, covering only two minutes of music, I nevertheless hardly scratchedthe technical surface in attempting to describe and explicate the processingtechniques employed in the production of “Paranoid Android.” There iscertainly no question that audio represents an enormously di�cult challengefor the analyst, and methods for determining processing techniques usingonly audio remain in their infancy. The desire by musicologists and theoriststo sidestep a discussion of record production is therefore understandable. Butperhaps music scholars might also benefit from following artists and engineersinto the studio. Popular music analysis demands a great deal of expertise,and in an ideal world, a better understanding of the common techniquesapplied in record production might usefully inform subsequent analysis, beit either by transcription, or by applying DSP techniques. In order to gobeyond mere description and begin to consider questions of function andmeaning, such a comprehensive, inter-disciplinary approach to the analysisof popular music might represent the best way forward.

Acknowledgements

This study was funded in part by the Fonds de recherche Nature et tech-nologies Quebec. I’d like to express my gratitude to Nicole Biamonte, whoseilluminating seminar on the analysis of rock music inspired this research. Ialso o↵er thanks to Rene Rusch and Meghan Goodchild for their commentsand suggestions on portions of this manuscript.

24

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