Interpreting Schenkerian Prolongation

[Chopin's] replacement of implicative or causal classical structures (such as

antecedent-consequent) with a reliance on discrete `analogy' ± on parallelsegments and layers ± . . . turns attention away from propulsive relationships tothe immediacy of the moment . . . The very system of tonal implication is used

against itself . . . to produce an effect of analogy that counteracts the force ofharmonic resolution. (Subotnik 1991, p. 157)

[T]he choosing to employ the twelve-pitch-class syntax for composing, thoughnot easily formulable as the replacement of `tonal axioms' by `serial axioms', stillis formulable at a fairly general and deep level as the replacement of the

analytical and synthetic notion of prolongational parallelism (`Schichten') bythat of transformational parallelism, extensible to inter- as well as intra-dimensional parallelism, to multidimensional imaging. The syntactic analogycan be pressed even further (prolongations induce transformations of structural

functions; transformations induce prolongations of ordered intervallicstructure), but a different syntax has been created, just as a different geometrywas created, susceptible to different adaptations and applications. (Babbitt 1997

[1999]), p. 132)

Music is, by a natural inclination, what immediately receives an adjective

[predicate] . . . [This predication] . . . has an economic function: the predicate isalways the rampart by which the subject's image-repertoire protects itselfagainst the loss that threatens it: the man who furnishes himself or is furnishedwith an adjective is sometimes wounded, sometimes pleased, but always

constituted; music has an image-repertoire whose function is to reassure, toconstitute the subject who hears it. (Barthes 1985, pp. 267±8).

Mozart, String Quartet in D minor, K. 421, Menuetto

Some time ago I worked with an analysis class on the opening of the Menuettoof the third movement of Mozart's String Quartet in D minor, K. 421 (Ex. 1a).One group analysed the passage as extending the tonic and setting up acadential dominant, prepared by the `strong' subdominant on the downbeat ofbar 9 (Ex. 1b and Fig. 1b). The other group focused on the cadential functionof the `dominant' six-four harmony on the downbeat of bar 8 and its five-threeresolution in bar 9 (Ex. 1c and Fig. 1c):

Music Analysis, 22/i±ii (2003) 51ß Blackwell Publishing Ltd. 2003. Published by Blackwell Publishing, 9600 Garsington Road, Oxford OX4 2DQ, UK

MARIANNE KIELIAN-GILBERT

INTERPRETING SCHENKERIAN PROLONGATION

I later discovered that Allen Forte and Steven Gilbert had analysed thispassage along the lines of the second reading shown in Ex. 1c (and Fig. 1c) andhad commented on the relative appropriateness of other readings:

The prolongation of f2 in m. 8 is worthy of comment, since this kind of situationmay still cause difficulty to the analyst. In the worst case, this would be read as adescent from 3̂ÿ 1̂ ± an arrival on 1̂ two measures too soon ± in which case e2 in

m. 9 would be (mis)understood as some kind of neighbor note. In fact, what wehave here is an idiomatic foreground prolongation of six-four. The bass of thesix-four is a on the downbeat of m. 8; the resolution of the six-four occurs on the

second quarter note of m. 9 over bass a, with a dissonant passing note f1, insecond violin. Prior to its resolution, the six-four is prolonged first by thedescending motion in parallel sixths between descant and bass that occupies all

of m. 8 and then by the flagged lower neighbor note g on the downbeat of m. 9which delays the return of the bass a and the resolution of the six-four to five-three. (Forte and Gilbert 1982, pp. 363±4, my emphasis).

But is this musical situation actually as fixed or obvious as their text seems tosuggest? Is it the case that anyone hearing a tension between a tonic groupingand a dominant extension in these bars is, at best, naive and inexperienced?Could the ènergy' from the six-four be played out several times in these bars,so to speak: in bar 8, in bar 9 and, in retrospect, in the span from bars 8 to 9?What role does the contrapuntal organisation of this passage play in suchperceptions? In the light of these questions, it is not which reading is right orwrong, but how the òscillation' of different readings of harmonic-thematic(and contrapuntal) patterns and groupings might characterise the elements inquestion. Indeed, Forte and Gilbert's text is designed more to circumvent thepossibility of hearing an arrival on tonic on the third beat of bar 8 ± àn arrivalon 1̂ two measures too soon' ± in which case, one would hear bars 9±10 as somekind of an echo or suffix (this less preferable hearing is shown in Fig. 1d; Ex.1d).

bars:

upper line:

bass line:

figs: 5

D

A

1/3 4 5 6 7 8 9 10

A G G F E D E A C DF

C

6—

C

5

B

6

B

5

A G F

6 6 64

G A A

6 8 76 5

— —–

D

8

readings:

b) RN:

c) RN:

d) RN:

e) RN:

i

i

i

i Gr+6

Gr+6

Gr+6 V

V i

(i) ii

ii

(+ suffix)

V i

i

i

64 3

5

V

Fig. 1 Mozart, String Quartet in D minor, K. 421, Minuetto, bars 1±10

ß Blackwell Publishing Ltd. 2003 Music Analysis, 22/i±ii (2003)

52 MARIANNE KIELIAN-GILBERT

I was in a group that initially heard reading 1b (Ex. 1b) and subsequentlythe other readings (Exs. 1c and 1e). Having to choose one and eliminateanother, or to say that one was less valid than the other, did not satisfy our

6

Ex. 1a Mozart, String Quartet in D minor, K. 421, Menuetto, bars 1±10

1 3 5 7 9

( )

Ex. 1b Extension of tonic, bars 1±8

Music Analysis, 22/i±ii (2003) ß Blackwell Publishing Ltd. 2003

INTERPRETING SCHENKERIAN PROLONGATION 53

1 3 6 8 104

Ger+

Ex. 1c Extension of dominant six-four/five-three, bars 8±9

1 3 7 8 105

Ex. 1d Anticipation of tonic arrival, bar 8

1 3 5 7 9

Ger+

Ger+

Ex. 1e Extension of pre-dominant function, bars 7±10



perceptions of the passage. In our discussion it was helpful to think thatalternative perceptions ± that of a delayed tonic and/or an extended dominant ±contributed to the particular rhythmic and tonal èffect' of this passage, and toplace these perceptions in some theoretical context. It helped to `hear multiply'rather than to reduce our experience by eliminating or ranking perceptions.

Emerging in the `postmodern climate' of the 1990s, the question arises as tohow the temporality of different hearings might be construed and experienced.Not only are multiple readings sometimes ± often ± possible, they may also be asignificant way to render the specificity of a particular reading or the dynamicof a progression over time. Might the sense of an òscillation', a back-and-forthof different hearings, characterise the relationships of such conflicting and/ormultiple harmonic readings over time? Should we be wary of the fact that ourtheoretical tools often compel us to make ìmpossible' unitary decisions, orshould we welcome the fact that they force them, impossible as they are?1

Temporal Process, Interpretative Understanding and Theoretical-Experiential (In)determinacy

This study pursues issues of temporal process and theoretical-experiential(in)determinacy in music by way of investigating the relationships and tensionsbetween prolongational and translational relationships in tonal hearing andanalysis. Crucial here is a sensitivity to the changing temporal extents andlevels of musical perception. Distinctions between prolongational (back-to-front, orientations of conceptual depth) and translational relationships (left-to-right, orientations of linear succession) are fundamental in construing andrelating aspects of conceptual understanding and moments of temporal/qualitative experience.2 The temporalities of such effects as `holding on',ànticipation', `deflection', `delay', èarly or late arrival', `movement towards',or `movement from X to Y' (e.g. `pivot-chord' experience), come under theumbrella of descriptions that relate the determinate qualities of ongoingpurposeful change with conceptual understanding. A larger issue, to beconsidered later, concerns relationships between the kinds of ambiguity(multiple perceptions and interpretations) that we encourage in the sphere ofanalysis and the ambiguities that postmodernism encourages in opening upmultiple realities and subjectivities, and in stressing reader-orientatedresponses.

The play of presentation and response, perception and interpretation, is partof the dynamic temporal character of music. Alternative responses andinterpretations can hone experience, point to the `strangeness' of `fresh'perspectives, or characterise the effects of ongoing temporal experience. Theyopen up ways of (re)hearing and (re)thinking, and allow for the play of(in)determinacy and the sharpening of perception.



The notion of determinacy registers the extent to which a particulartheoretical angle or level can model a musical experience. Aspects of music aremore or less determinate ± registered and made intelligible ± through theorientations of particular theories. In this sense, theories are ways ofconceptualising, describing and hearing. Temporal hearing draws on aparticular relationship of conceptual (abstract) and presentational (music-temporal) experience ± the varying senses in which the angles of a theoryprovide a `determinate feeling' or `syntactic depth' to an experience.3 In turn,this `determinate feeling' can nuance or change a theory. Thus, a theory is likea musical instrument that one takes up to play a piece and allow it to sing,rather than a medical instrument or tool that one might use for a particularfunction, such as surgery.

To some extent, all interpretative-experiential situations embody anappreciation of theoretical-experiential (in)determinacy. The act of selectingone set of meanings may have an effect on another set of values. Particulardistinctions may become fluid when experienced from a different angle ofunderstanding. Differentiation varies with the interactions of subject/perceiverand emerging object(s) of perception. For example, the Heisenberg principle ofindeterminacy (1926) states that one cannot know or determine both positionand momentum at the same time, and moreover, that the act of measuring onedisturbs the other. The more precisely one tries to measure position, the moreone perturbs momentum, and thus the less one can measure momentum. Theposition of the observer directs and determines the nature of physical eventsfor perception and analysis. This is in contrast to classical mechanics, whichmaintained that it is possible to measure simultaneously the position and themomentum of any body. If a particle, however, has, or is regarded as having,some of the properties of a wave, then the uncertainty principle is a necessaryconsequence.4

Interpretative-experiential (in)determinacy is related to, though distinct from,vagueness (not enough information available for interpretation) and ambiguity(information available for multiple interpretations that are comparably plausible)in the ways that it mediates categorisation and lived temporal experience.5 The(in)determinacy of gender, for instance, suggests that categorical distinctions(though not irrelevant) are inadequate or variably nuanced. Experiential-theoretical (in)determinacy allows for a listener's disposition to construedeterminate relations as `disturbed by' or `contingent upon' one's livedexperience ± and thus modifiable by alternative perceptions and by the effortnecessary to hold certain conceptions in relation to others in and over time. Thesealternative (non-simultaneous) relational orientations are, to some extent,mutually implicated though not necessarily equally weighted. For example, justas prolongation (`composing out') describes a `way of listening' that characterisesthe degree of willingness to hold onto one event while hearing another,6 it also



includes the sense of the relationship of a later to an earlier event that enlivensthat earlier event (and vice versa). It is a relational process that projects andembeds structural functions and part-whole relationships. To experienceprolongation is to differentiate content at different levels of specificity.

The experience of prolongation may embody alternative perceptual andconceptual groupings at different levels or temporal distributions (e.g. thesituation of prolonging a suspension, Schenker's account of the consonantpassing-note). Although the implication of a prolonged harmony (e.g. a tonic)extends to events within its temporal span, prolonging harmonies (e.g. adominant) can, and with expressive consequences, condition, nuance or evenreconstitute the prolonged harmony. The latter situation is not rare: itmotivates a perceptual-conceptual situation in which one confronts paradoxicalor seemingly contradictory prolongational relationships. In this article, I willnot only argue for the value of such alternative perceptions, but I shall alsosuggest that the presence of these perceptions is one way of experiencingbroader motions or progressions in temporal flux, of experiencing theirtemporal process and expression.

For some repertoires `prolongation' is a problematic concept, encompassingapparently different approaches and conflicting views. Even in conventionaltonal situations, one can alternately experience the qualities and status of notesas consonant or dissonant. What is `prolonged', for example, when asuspension is embellished? In an ornamented suspension, the ornaments arealso heard in relation to the suspended note(s). We construe dissonance as apassing motion experienced in relation to a conceptually deeper `background'configuration that defines and prolongs a consonant interval. In whatsituations, or to what advantage, might a `dissonant' element project analternative sphere of influence, one that might hold both consonant anddissonant elements in abeyance, or extend another element as `dissonant'? Onecannot resolve these questions, except by reference to levels of hearing, to theprocess of defining progressions, or to rhythmic-metric presentation andtemporal process.7 Here, I explore these issues by examining what I shall referto as the relationships and tensions between prolongational and translationalrelationships in tonal analysis.

Revisiting Mozart, K. 421, Menuetto

Do we need to choose between two or more readings of the Menuetto fromMozart's D minor String Quartet? In Forte and Gilbert's hearing of anextended dominant six-four function as initiated by the six-four (Ex. 1c; Fig.1c), once the German sixth moves to the six-four in bar 8, the cadential mode isoperational, and the interpretation is finalised. In part, convention directs anunderstanding of the following six-four harmony as the dominant `resolution'



laid, am laid in earth, may my wrongs cre ate No

10

Larghetto [ . = ]

sempre

guest. When I am

Viola

sempre

Violin II

very soft

38Violin I

very soft

1

1

1st time

2nd time

trou ble, no trou ble in thy breast, When I am

Ex. 1f Purcell, `Dido's Lament' from Dido and Aeneas



of the augmented sixth (bar 8, as a metrical `downbeat').8 What is interesting isthat Forte and Gilbert go to some length to explain the bass motion as a passingmotion from a down to f, encompassed within a larger neighbour-note motion(a±g±a). Their reading thus leaves open the question of whether the neighbour-note motion is `deeper' than the passing motion.

The extended tonic reading (Ex. 1b, Fig. 1b; Ex. 1e, Fig. 1e) preservesaspects of melodic parallelism between the first violin of bars 1±2 (f2±e2±c]2±d2)and that of bars 8±10 (or bars 7±10, this upper-line pattern can be heard withinbar 8 and also extending between bars 7 and 10). Notice that if the suspensionon beat 1 of bar 2 is incorporated into the mapping of patterns, both possibilitiesof motivic-thematic harmonisation ± of the six-four (bar 8) as extendeddominant or anticipated dominant ± are embedded in the opening bars(bracketed in Ex. 1a). Both readings allow for different `waves' of f2±e2±c]2±d2

in bars 7/8±10 (and in relationship to the counterpoint of the d1±c]1±e1±d1

pattern of the viola in bars 7±8). Significantly, though perhaps less metricallyaligned at the surface, the combination of hypermetric groupings would suggestreading an extension of pre-dominant harmony in bars 7±9 (thus the Germansixth becomes part of an extension of the initial tonic ± see Ex. 1e; Fig. 1e).9 Inthis reading, the German sixth extends throughout the harmonies of bars 8±9.This connection highlights the contrapuntal repetition of the cello line (b[±a±g±f, bars 7±8) in the viola in bars 9±10 and the `voice-exchange' between theGeman sixth and the iio6 harmonies of bars 7 and 9 respectively (B[±G]/G±B[).

Consequently, claims of motivic parallelism cannot provide a basis forchoosing one reading over the other. Rather than arguing for the efficacy ofunitary choice, the specificity of the particular effects of a musical passageoften emerges through multiple, alternative or contradictory readings: that is,one might engage in multiple readings to characterise the tonal-temporal effectof a passage. For example, the progression to the tonic sixth chord of bar 8deflects the energy of the previous six-four as dominant, continuing the energyof the descending bass line, showing that the six-four's possible function asdominant is still in process and not fixed. Events are determinate in separatetime frames, rather than fixed or captured in a unitary determinate reading.Attention is drawn and deflected; deciding between `still' and `again' is theperceptual issue that is at the crux of these kinds of situations.10

The topos of the opening phrase embodies a Baroque lament pattern (cf.`Dido's Lament' from Purcell's Dido and Aeneas, Ex. 1f), a characteristic bassline that descends from 1̂ to 5̂, followed by a skip and stepwise ascent to 5̂: D±C]±C±B±B[±A±F±G±A±(D). One could read Mozart's bass line as a manipula-tion of this pattern in several ways: 1) following reading 1c, by drawingconnections between the two instances of `A' in the bass, G is a lower neighbournote and F is a consonant skip from the first A; or 2) foregrounding theextension of tonic via an arpeggiation of D±A±F, with the chromatic filling-in of



the initial fourth, suggested by readings 1b or 1e. I do not intend to suggest thatalternative readings are always or never equally weighted, or that a conventionalreading should be assigned a `background' priority. I simply wish to emphasisethe potential of leaving open a many-to-one relationship of foreground/experiential hearing and a background or conventional construct, whether thatconstruct is a `convention,' in this instance modelled on the lament outline, orwhether it is a basic pattern, e.g. a chromatic descent from 1̂ to 5̂.

In these examples, it is notable that the (temporal) oscillation of inter-pretative perceptions is a function of construing alternately the phenomena ofharmonic and thematic repetition in music. By òscillation' I mean a back-and-forth motion or a repeated change (fluctuation) of patterns and/or implications.As evident in the Mozart example, the apparent alternation of I and Vharmonies (in bars 1±3, 7±8, 8±9, 8±10) presents a play between differentgroupings and degrees of articulation and arrival. Such oscillations may projectdifferent qualities (experiential effects) depending on the degree of depth(`vertical', back-to-front play between levels of abstraction and prolongationalgroupings), the time extent of the process of alternation (`horizontal,' left-to-right presentation of translational, i.e. melodic, parallelism), and the numberand rate of reversals or alternations (the degree and rate of change).

In the examples that follow, the concept of oscillation and its attendantsound qualities suggests ways to construe the dynamic aspects of movingbetween different states or conditions. These qualities include senses ofrocking or vacillating, fluctuating or wavering, or fluctuating attentionbetween different states or courses of action. They also include conditions ofcontinued reversal ± swinging, rapid alternation (fluttering, quivering,jiggling, hovering) and flickering.11 As we shall see, aspects of oscillation canapply both to alternative levels of musical perception that are non-simultaneously active, as well as to alternating events in a series. Byprojecting different kinds of fluctuation ± conceptual (vertical, depth), linear(horizontal) or fast-slow (varying rates), alternating relationships may beconstructed as ongoing and processive rather than as discrete clicksassociated with a specific moment in time. These perceptions call fordescriptions that mediate between what has already happened and what isabout to happen.12

Schenkerian Prolongation: Effects, Òbjects' and Dubiel `Motions'

Teaching Schenker's theory as a process of `reduction' stems in part fromAllen Forte's 1959 article, the implications of which have been described byWilliam Rothstein and Robert Snarrenberg in terms of the Àmericanisationof Heinrich Schenker'.13 Others have noted that prolongation and reductioncan be related as different aspects of the same process (Neumeyer and



Tepping 1992; Cadwallader and GagneÂ 1998), though Schenker's orienta-tion is notably from `earlier' (deeper) to `later' (more determinate) levels ofunderstanding.14 Fundamental to the latter conception of prolongation aselaboration are the various kinds of note-relationships that obtain betweenevents at earlier and later levels (Schichten). One tendency of the `reductive'stance is to attempt to account for relationships between levels in terms of anote-for-note mapping of events, or a one-to-one relationship, between theevents of different levels and events represented by a score.15 By contrast,viewing Schenkerian prolongation as elaborative, as `composing out', leadsto the idea that the object of prolongation can be a process or rule, inaddition to the background `normalisation' or verticalisation of a chord orinterval. The conception of prolongation as a process, `rule' or function ± ora `motion' between structural harmonies ± maps events of earlier and laterlevels in many-to-one relationships.16 Joseph Dubiel has demonstrated thatthis idea ± of making motions or rules the objects of prolongations as much asharmonies or notes ± finds confirmation in Schenker's cryptic arguments andexamples in Counterpoint:

[In Schenker's view, deviations in word order of a sentence from Faust do not]

constitute an offense against German grammar [but] only prolongations of themost ordinary grammatical laws. (Counterpoint I, 13) . . . [This] reveals, first ofall, that the kind of entity that gets prolonged is a rule ± which is to say that little

in this book supports the standard latter-day application of the concept topitches and harmonies. (Dubiel 1990, p. 293)

Dubiel also makes the point that Schenker's theory of prolongation, whetherfrom the perspective of elaboration or reduction (invoking particular functionsor motions to explain a harmonic progression), attributes musical `effects' toparticular combinations of notes (ibid., p. 297).17 In this view, Schenkerianprolongation is extended to encompass motions, processes or `rules', as well asnotes and chords, and the effects that result from working out those motions orrules in particular ways over time.18

The sketches shown here suggest different strategies of listening. Firstly,they present interpretations singly and in combination. In the case of theMozart K. 421 examples, each sketch depicts a different temporal distributionof harmonies and the musical effect is the result of the alternation (oscillation)between the different, non-simultaneous perceptions. Secondly, they showharmonic areas in conjunction with non-aligned and repeated motivic patterns(in brackets). Here the effect is that of a tension between a thematic repetitionand a goal-orientated harmonic progression. Thirdly, they show a succession ofalternating (oscillating) harmonic-thematic patterns. In this strategy, the effectcaptures a hearing of a deeper harmonic motion that is expressed by more thanone reiteration of that progression.



The next part of this article explores how such conceptions of prolongationas the `temporal' process of structural functions can characterise the dynamicnature of `fluctuating', ànticipating' and `delaying' music event-perceptions.

The Proctor and Riggins/Rothstein Exchange

In their article À Schenker Pedagogy' (Proctor and Riggins 1989), GregoryProctor and H. Lee Riggins analyse a portion of a figured Bach Chorale(No. 47, `BeschraÈ nkt, ihr Weisen' ± Ex. 2a) as a `deceptive' extension thathighlights the èffect' of a dominant prolongation in bars 4±6 (Ex. 2b). WilliamRothstein, in a subsequent letter to the editor of the Journal of Music TheoryPedagogy (Rothstein 1990b), criticises their reading as `mechanical', and arguesfor an alternative, more `musically' viable interpretation of the pattern as anextension of tonic harmony in bars 4±6 by means of a 10±5±10 voice-leadingpattern derived from a species model (Ex. 2c). If one considers both thesereadings as alternative middlegrounds that work out the implications of anearlier level, namely the `process' of an eventual `motion' from I to V, then thetwo readings can function as alternative levels that are non-simultaneouslyactive (oscillating), though apparently contradictory, as in the Mozart K. 421example. These levels compose out the `deeper' temporal process of a motionfrom I to V.

From this perspective, each reading is coherent as articulating the more`local' effects of a broader temporal motion in process from I to V. Suchapparently contradictory readings are expressions of non-simultaneousmultiple foreground readings, each a configuration of a broader temporalprocess represented in a deeper middleground reading. Several questionsresult from this kind of àllowance' or `suspension': to what extent is itdesirable or possible to construe the temporal motion 1) in relation to a singlereading, 2) in relation to an oscillation of two or more readings in tandem, or 3)as one reading of a deeper, less determinate level that includes both of the moredeterminate interpretations (see Ex. 2d as a possible representation of this idea,i.e. with implications of a line from 5̂ (Proctor and Riggins) and/or a line from 3̂(Rothstein) in the harmonic area of the dominant).

Might the musical èffect' of the passage result from the interaction of bothtemporal process and conceptual distinctness? Does the deeper levelaccommodate both aspects as alternating or co-existing at later, more locallevels? These later levels thereby contribute to the determinate musical èffects'of a background conception of the passage ± the èffects' of a contrast betweensenses of apparent arrival or delay ± and are evidence of an oscillation ofrelations that stem from a temporal process (motion). Are these èffects' bestcharacterised as a `slow motion' oscillation of several hearings or as a singlehearing that registers determinate, but individually incomplete readings by



way of reference to an `abstraction' of a higher/earlier level? Does the sense inwhich the `locally determinate readings' (Figs. 2b and 2c) are mutuallyexclusive preclude the possibility of hearing bars 4±6 as an area of oscillation orprocess that extends a deeper harmonic progression, or does it stimulate thatperception?19 The ideas presented here would suggest the latter position.

20

10 15

5

25 30

Ex. 2a Bach, Figured Chorale, No. 47, `Beschrankt, ihr Weisen'



( ( ))

5

2

4 3 2 1

3

‹ ‹‹ ‹ ‹ ‹ ‹

)(

Ex. 2b After Proctor-Riggins 1989 (bars 1±8; Fig. 1a, 11): bar 4ff as extension ofthe dominant

3 2

‹ ‹

Ex. 2c After Rothstein 1990 (bars 1±8; no example): bars 6±8 as extension of thedominant

3 2

‹ ‹

4

‹

5

‹

3

‹

2

‹

3

‹

2

‹

1

‹

(E: *

A: ( ) )(

(E: 5

‹

4

‹

3

‹

2

‹

1

‹

) **

)

v.

A: 3

‹

2

‹

( ) ( )

* Rothstein** Proctor-Riggins

Ex. 2d Local oscillation, scale degrees 3̂±2̂



Rothstein's reading highlights the melodic `parallelism' and contourtransformation of the upper line (see brackets, bars 4±5, C]±B±A±B±C]; andbars 5±6, B±A±G]±F]±G]±A). Proctor and Riggins's reading calls attention tothe alternation of I and V harmonies in both passages (bars 1±2, I: I±V±I6±V±I;and bars 4±6, V: (I)±V±I±V±I). In this reading one can hear the melodicpattern of the bass in bars 3±4 in relation to the rhythmically expanded andharmonically re-orientated pattern in the bass prior to the structural cadence ofbars 7±8 (bracketed in Ex. 2b).

Other examples of `perceptions' that can be characterised as specificrelations of (conflicting or contradictory) èffects' include irregular resolutions,deceptive relations, the `consonant passing note', deflected/delayed six-fourresolutions, subdominant v. dominant contexts (e.g. I: I±IV [C±F] v. IV: V±I[C±F]), functional substitution (six-four functional orientations as I or V;German sixth as tonic or pre-dominant), and so on. These perceptions fusemultiple and conflicting experiential orientations, each with an appreciablemusical èffect' that contributes to the determinate perception of the passage.In particular, the conflicting orientations draw alternately from parallelismscreated by prolongation (embedded structural functions) or by the repetition ofmelodic patterns (linear succession, pattern translation).

Such responses are not to be taken as an advocation of a relativistic orindiscriminate application of a particular theoretical position, Schenkerian orotherwise. The unitary decisions encouraged by certain theories can alsofunction to encourage an attention to specifics, so as to highlight the tensionbetween normative and compositional presentation. In this sense,presentational ambiguities of various sorts are often carefully handled withinthe confines of a particular theory, such that the musical context can `clarify'which of a range of situations a composer might intend.20 In these cases, thetheoretical indeterminacy of more determinate levels (levels focused on one oranother interpretation) may be understood as a process that crystallises theconceptual-temporal configuration of an earlier, more abstract level. Or itmight be possible to maintain a range of possibilities such that one orientationmay prevail, and then another.21

The extent to which oscillating readings and perceptions are possible ordesirable invokes the familiar rabbit/duck or old woman/young woman figures.Different viewings are mutually exclusive, but the `composite' figure or èffect'includes the structural orientations and aspects that make possible the flip inperspective from one figure to the other. Each view depends on a different axisof orientation.22 A similar example in a painting by Georges Braque isdiscussed by Rudolf Arnheim:

The shape of the profile line changes entirely, depending on which face it is seento belong to. What was empty becomes full; what was active, passive . . . the



objects create the illusion of being materially present, only to change withoutnotice into something completely different but equally convincing.23

In a musical context, one orientation might yield prolongationally embeddedpatterns, another orientation might suggest melodic groups that projectrepeated melodic patterns. Such different musical readings can be mutuallyexclusive but their composite representation can incorporate the `effects' ofalternative hearings. However, one aspect of this analogy between image andmusic that may not be comparable is the perceptual strength of the figures andthe perceiver's ability to switch between them at will. The ability to changemusical orientations seems to be more fluid, and available to the consciouscontrol of the listener; in comparison, the viewer's control of the image seemsless predictable.

In an oscillating process or experience, the outcome may be impossible todecide, suspended until the final element has appeared. In tonal (Schenkerian)perception we often choose the first element (e.g. the tonic) as that whichdirects the structural progression.24 A variety of factors can make this situationtemporally and musically interesting: the addition of new elements, varying thelength of oscillation, shifting rhythmic or melodic emphases within the periodof formation, or shifting between prologational and melodic (translational)orientations. These possibilities suggest different ways of experiencing theeffects of repetition as a means of extending and nuancing conceptually deeperstructural progressions.

How or at what level do we `back up' to locate the `ground' for alternativereadings of the sort considered here?25 And do we undertake `backing up' witha related loss of determinacy? There are, of course, artistic, political andpersonal issues at stake on all sides. Does one side really need to claim theprimacy of the `depth' of musical experience, eschewing the application ofmechanical rules and procedures? Need another side appeal to reasonablepedagogy, to rational analytical approaches to `the music'? Nothing precludesthose holding contrasting positions from invoking a lineage of analyticaltraining to establish credibility or to silence the `untrained'. A `method' can bethe province of those with years of specialised education. It can also be used asa means of highlighting the distinctiveness of particular readings, of evaluatingtheir relative degrees of fit (or lack of fit) with experienced musical passages, orof incorporating the means to reconcile different interpretations within theconfines of a particular theory. What is significant in the context of thisdiscussion is that sometimes differences of interpretation, rather than being afunction of the relative expertise of an interpreter, stem from the possibility ofhearing different or alternative expressions of a background level in foregroundlevels, or from hearing in terms of different orientations. Such differencesreflect a tension between prolongational and translational relationships and



hearing. Thus, an awareness of particular orientations and approaches canchange power relationships between analysts, or between the analyst and thepiece.

This is not the same as saying that there is no `right' analysis, or opting for asufficiently general set of rules such that any analysis that fits them is equallyapt. Rothstein raises the problem of what happens when an ànalysis is one ofan indeterminate number of ``correct'' analyses, all of them equally uncon-cerned with the music and hence equally uninteresting' (Rothstein 1990b,p. 297). As I have argued, the interest lies in the interactions of theory andexperience and in the sensitivity to music's temporal processes. Thus, whetherone formulates conflicting prolongational-motivic readings as oscillatory (oreven as simultaneously operative, as Martin Scherzinger does at times in hisanalysis of the Adagio fromMozart's Piano Sonata in F major, K. 280) may notmatter as much as developing the implications of this oscillation for listening,analysis and interpretation.26

One frame for mediating various positions in Schenkerian analysis is theòrganic context' of the whole: `which of the two lines is primary ± and thuswhether G]4 or E4 rules at the cadence ± can only be determined by thesubsequent course of the chorale' (Rothstein 1990b, p. 297). Yet one way ofreading the Bach chorale às a whole' might be as a large-scale working out ofthe tension between hearing an extending tonic in bars 4±5 (delaying tonic andthus delaying a move to V, see Ex. 2c) or hearing an initial reference to V (seeEx. 2b). Thus, the Rothstein-adapted orientation of Ex. 2c might endorse ahearing of the F] minor area of bars 21±4 as supporting a delay of tonicharmony until the return of the tonic in bar 29. The Proctor and Riggins-derived orientation of Ex. 2b (initiation and extension of V) might endorse ahearing of the influence of V in bars 4±8 extending to the return of V in bars25±8, and thus hearing the thematic repetition of bars 17±20 (IV) in bars 25±8(V) and the repetition of F]±E±D±C] in the upper line of bars 3±4 in bars 21±2as part of a progression extending the influence of V.

Rothstein cautions analysts to avoid a `preconceived idea of what they willfind [that] easily blinds them to what actually occurs in the music. [In suchcases:] Theory wins, music loses.' (ibid.) Yet distinctions and differences ofinterpretations are not to be passed over: `Recognized, acknowledged,challenged, they [can] serve as points of articulation, departure, transforma-tion, and significantly, mutual implication and definition' (Kielian-Gilbert1997, p. 254). One must be able to try out alternative readings within particulartheoretical contexts; and the disjunctions between readings can open a spacefor positions that are both sympathetic and biting. The theoretical orientationis not the music and thus the differences that obtain can be illuminating fromboth the perspective of the theory (and its logical constraints) and that of `themusic' with its performed and experiential contingencies.



Leaving aside the question of what brings credibility to an analyst, the largerissue here is how to sustain the potential of alternative readings and how tobring various readings into contact with each other without the need forcompetition, without the need for one reading to depose another.27 The nextsection takes up distinctions of prolongational and translational parallelism as ameans of pursuing this issue.

Prolongational and Translational Parallelism

Schenker's well-known remarks at the beginning of Harmony on the artisticsignificance of repetition in art bring together two èxperiments': the role ofrepetition in determining the identity and association of motives, and a tonalsystem that can allow for the èxpansion' of the motive:

Thus the motive constitutes the only and unique germ cell of music as an art. Itsdiscovery had been difficult indeed. No less difficult, however, proved to be thesolution of a second problem, viz, the creation of a tonal system within whichmotivic association, once discovered, could expand or express itself. Basically

the two experiments are mutually dependent: any exploration of the functionsof the motif would, at the same time, advance the development of the tonalsystem, and vice versa, any further development of the system would result in

new openings for motivic association. (Schenker 1973, p. 20)

The progression, direction and force of a succession of Stufen (harmonicscale steps) express the working out, or paths, of a structural harmonicprogression. Harmonic Stufen manifest themselves in the progression andtransformation of structural functions at different levels of determinacy(Schichten) with respect to the articulations of the musical foreground. Theselevels establish prolongational parallelisms that articulate and transform goal-directed structural progressions through successive elaboration (composingout).

The role of thematic restatement in this orientation is often one of delayingthe completion of the structural harmonic progression. Dubiel also makes thispoint, noting that Schenker conceives interruption or a divided ìnner form'(3̂±2̂//3̂±2̂±1̂) as an undivided structure at a deeper level (3̂±2̂±1̂).28 The point ofinterruption of the structural progression is fixed specifically by the structuralarticulation of the dividing dominant and requires the tonal-thematicrestatement. Oswald Jonas describes it in this way:

A most powerful urge to repeat is created by initiating a certain movementwhose starting and concluding points may be unequivocally presumed by thelistener, then to interrupt this movement at the crucial moment ± say, justbefore the concluding step. A tension is thereby created which can be relaxed

only by a repetition, this time without interruption, running its full course to asatisfactory conclusion. (Jonas's Ìntroduction' to Schenker 1973, p. xxiii)



In a related way, the extension of Schenkerian conceptions of prolongation tosituations of harmonic oscillation (e.g. motions between Stufen) is to express thesemotions at more foreground levels of the process of composing-out. As we haveseen, these are often cases of exact thematic repetition where the structuralimplications of the first harmony prevail at a deeper level during the repetition.The second thematic presentation, to the extent that it re-articulates the initialstructural progression, is thus a marker for the ongoing process of the progression.The completion of the repetition or restatement can also signal the continuation ofthe progression. The deeper level harmonic motion thus also holds the first Stufe(harmonic area) in temporary abeyance during the oscillation, and at the end of thethematic restatement that initial motion is eventually completed.29

The direction and force of the prolongational transformation of a structuralprogression thus contrasts with the `stasis' of melodic-thematic repetition.This contrast is aptly characterised by Milton Babbitt in his distinctionbetween the prolongational parallelism of `tonal axioms' ± prolongations thatìnduce transformations of structural functions' ± and the transformationalparallelism of `serial axioms' ± transformations that ìnduce prolongations ofordered intervallic structure' (Babbitt 1997 [1999], p. 132). Rose Subotnikidentifies the latter process in Chopin's repetitions as `producing an effect ofanalogy that counteracts the force of harmonic resolution' through its apparentstasis (Subotnik 1991, p. 157). Operating in contrast to prolongationalparallelism, translational parallelism is the successive repetition of melodic orharmonic òrdered intervallic structures', a concept that links Babbitt'stransformational parallelism with Schenker's account of motivic identificationthrough successive repetition.30

Prolongational parallelism projects the temporal transformation of astructural function. Pattern and copy are of different temporal lengths (seeFig. 2) and include back-to-front projections of deeper-level patterns in moredeterminate, temporally shorter presentations.31

A translational parallelism is one that moves a configuration over in space-time. To translate is to `transfer' or `transport' a body or form of energy fromone point of space to another without rotation (or from one person, place orcondition to another). The term `translational' also stems from a symmetricaloperation or motion that duplicates a configuration by spatial repetitionthrough a fixed distance. Translational parallelism in a musical contextinvolves a left-to-right movement (duplication) of a pattern, shifting theoriginal configuration to a new spatial-temporal location, thereby moving someof the initial aspects as well. The temporal length of pattern and copy is thesame or functionally equivalent. In the following discussion, I explore howtranslational parallelism allows for or extends the notion of motivic (andharmonic) repetition into the conceptual framework of Schenkerian sub-surface and cross-level parallelism (and vice versa).



Prolongational parallelism Translational parallelism(mutually related)

· projects the `expansion' orenlargement of the motive

· projects identity and repetition orrestatement of the motive

· pattern and copy are differentlengths

· pattern and copy are the same orof functionally equivalent lengths

· underpinned by goal-directedstructural progressions.Emphasises transformations ofstructural functions (e.g. I-V-I):a) nested, embedded patternsb) successively presented

patterns

· repetitions project periodicity,temporal balance and/or thefunctional equivalence of orderedinterval patterns. Emphasisespattern repetition.

· thematic repetition delays orextends harmonic completion:

· thematic repetition is reiterativeanalogical; it suggests:

a) end of repetition signals thecompletion of theprogression

a) a potential equilibrium ofemphasis; highlights imitativecounterpoint

b) primacy to the initiatingharmony

b) `chess board' effect ofemphasis, i.e. potential foralternate rhythmic groupingsbased on grouping initial orsubsequent harmonies

· cross-level or sub-surfacerelationships between parallels

· functional equivalence of parallels

· `motivic parallelism': theprolongational application of atranslational (transformational)process; projects hierarchy

· motivic/thematic-harmonicrepetition: translationalapplication of a prolongationalprocess; tends towards asuspension of hierarchy

· temporal transformation(embedding; prolongation) of astructural function

· temporal duplication (translation)of a prolongational process orfunctional succession

· goal-directed (hierarchical),`homophonic', vertical, abstract,back-to-front

· spatial (non-hierarchical),`contrapuntal', horizontal, linear,left-to-right

· potential for translationalcombination, i.e. overlappingchains or groupings

Fig. 2 Tendencies of prolongational and translational parallelism



Though mutually interdependent, the two processes have distinct tenden-cies. An analogue of spatial or planar geometry, translational parallelism relatessuccessively articulated musical patterns on or at the same level of determinacy(syntactic-semantic depth): the patterns have functionally equivalent lengthsand are related through successive temporal presentation. They extend (viarepetition) ordered interval structures and are thus temporally `static'. Incontrast, incorporating dimensions of conceptual-syntactic `depth',prolongational parallelism connects patterns at different levels of abstraction:the related patterns have different temporal lengths, and they are eitherembedded one within another or presented successively. They extend andtransform structural functions and are thus temporally `progressive'.

In Schenkerian terms `motivic parallelism' is a prolongational application ofa translational process. Conversely, `motivic and/or thematic repetition' is atranslational application of a prolongational process (as for example, inimitative textures).32 `Harmonic oscillation' can articulate both prolongationaland translational functions.33

As a way of hearing the differing temporal effects of such `parallelisms' morespecifically, consider Allen Cadwallader's reading of Mendelssohn's SongWithout Words, Op. 62 No. 1 (his Ex. 1.1 and 1.3 are shown in Ex. 3b).34 Thepassages in question are bars 5±10 and 22±35 (see Ex. 3a). His reading of bars5±10 shows the modulation from G major to B minor accomplished by theextension of a G major harmony (in bars 6±8) via the German sixth of B minor(bar 8), progressing to the structural dominant six-four of bar 9. Similarly, hisreading of bars 26±35 (Ex. 3b) extends the subdominant harmony (C major) ofbar 27 via a 5±6 exchange to the chromaticised II65 (V/V) of bar 32, progressingto the structural dominant six-four cadence at bars 33/34±5.35

My alternative readings (shown in Exs. 3c and 3d) acknowledge theharmonic oscillation between G major and B minor harmonies in bars 6±8 and8±10 (bar 6, G major and bar 8, B minor (first inversion); bar 8, French sixthand bar 10, B minor, see Ex. 3c), and the harmonic oscillation between IV orV6

5 of V to the cadential six-four in bars 24±9 and 30±35, respectively (see Ex.3d). In particular, these readings highlight the repetition of the melodic line inboth these passages (bracketed in the upper line); the melodic line states andthen intensifies the basic elements of the progression from G major to B minor.In the first instance the melodic phrase happens twice (bars 6±8 and 8±10), thefirst time without a cadence but clearly establishing B minor as the goal for acadence, the second time achieving the cadence but doing so through arepetition of the first phrase. If we associate the move to B minor with onemoment in time, Schenkerian practice, with its emphasis on delay, woulddirect us to pick the later one with the cadence and treat the preceding music aselaborating the transitional harmony. In contrast, taking account of thetranslational parallelism of the melodic statements contributes an alternative



reading, in tandem with the previous reading. The sense of oscillation betweenthese readings characterises the processive aspects of moving from I to III andof interrelating thematic and harmonic aspects.

Similarly, one can hear the thematic return of the opening in bar 22fftransformed by the change in the consequent phrase of the opening melody inbar 26ff (compare bar 4ff, bar 22ff and bar 26ff: in bar 26 the consequentphrase begins with a descending perfect fifth, d2±g1 (!)). The continuationextends the motion of I (bar 22) to IV±V again by a process of harmonicoscillation (of IV or V6

5 of V to V) that is marked by the direct thematicrepetition of bars 26±30 in bars 30±34 (bracketed in the upper line of Ex. 3d).The climactic repetitions of bars 26±9 and 30±35 coincide with the dominantsix-four harmony. It is worth noting that these thematic repetitions project D±E±D neighbour-note motions in the upper part that also relate to the

cresc.

dim.

cresc.

Andante espressivo

cresc.

4

7

10

cresc.

Ex. 3a Mendelssohn, Song Without Words, Op. 62 No. 1 i) bars 1±10



dim.

34

cresc. dim.

31

dim.

28

cresc.

25

cresc.

22

cresc.

38

Ex. 3a (continued) ii) bars 22±41



3 3 3 3

‹‹‹‹

(2)

‹

1 4 8 10

a

* * * * * * *xxx

x = D–C–B

y y

(= bars 1–2)

G:

antecedent consequent

= B:

+ +

+

A1

Ex. 3b Cadwallader 1990 (`Form and Tonal Process'), Ex. 1.1, bars 1±10 and Ex.1.3, bars 22±35

3 3‹‹

b

* * *xx

y

+

2 8 10

A2

G:

* * * * * *x

x modified(3)

24 26 27 30 32 34 35

‹

‹

3 2

‹

1

‹

(CP)

CP

P

N

NN N

( )



translational parallelism of the D±E±D pattern offset in the bass (both Ds inthe bass articulate a six-four `cadential' dominant).

Thus, in both passages, the thematic restatements correlate with processesof harmonic oscillation. They relate the translational parallelisms of thethematic/harmonic repetitions to the prolongational parallelisms of local anddeeper harmonic levels.

Oscillation and Alternative Emphases

In contrast, consider the different situation where the ordered relationshipbetween the structural harmonies changes during the period of oscillation.How does the eventual move towards completion of the structural progressionoccur?36 How might thematic presentation, and prolongational and/ortranslational parallelism, participate in this process? Three different analyticalcontexts show different compositional approaches to this issue: Schenker'sanalysis (via Drabkin) of the role of the consonant passing note, Dubiel'sanalysis of conflicting middleground readings in a Brahms concerto, and myaccount of shifting tonic-dominant and dominant-tonic groupings in a Chopinprelude.

( )

3

‹

2

‹

( ) 3

‹

3

‹

2

‹

1

‹

( ) 3

‹

( 2

‹

1

‹

)

1 2 3 4 5 6 7 8 9 10

Ex. 3c Bars 1±10

N

!

22 24 25 26 29 30 33 35

Ex. 3d Bars 22±35



Schenker's formulation of the consonant passing note is instructive,particularly for its insights into the possible relationships of levels and theways that structural functions can be transformed. William Drabkin providesan eloquent account of multiple contexts of Schenker's view of thesubdominant harmony: I±IV±I±V±I (3̂±4̂±3̂±2̂±1̂) understood as [(I±(IV±I))±V±I] or as [I±IV8±7±V±I] (see Ex. 4a which reproduces examples from Drabkin1996, pp. 149±50). According to Drabkin, `These two interpretations arefundamentally opposed to one another' (ibid., p. 150).37 Since `Schenkerunderstood all dissonance as arising from consonance, so that a crucial way inwhich music develops is by dissonances at a higher level being made consonantat a lower level, through an enriched bass; . . . this process in turn enables newdissonances to emerge at the lower level' (ibid., p. 152). The `tonic' can thusappear in the course of the connection of IV and V harmonies such that thedominant, not the tonic, is the goal of the progression. However, Schenker alsorecognised cases in which one might argue in either direction:

We are not dealing with a simple case of Schenker offering differentexplanations of the voice-leading of similar passages of music, a difference

attributable to what is sometimes referred to as `the development of histheories'. It is a contradiction that derives from viewing the subdominant fromthe perspective of the tonic, on the one hand, and viewing the tonic from the

perspective of a IV±V progression, on the other. (Ibid., p. 174)

The phenomenon of the consonant passing note characterises a situation inwhich a consonant harmony is interpolated as a passing harmony in a higherlevel prolongation of a `dissonant' or less stable harmony, which in turn findsresolution at a still higher level. In the case of hearing a consonant passing note,a higher-level extension of the second element of the progression colours theperception of subsequent consonant harmony (at a lower level) whichfunctioned initially as the first element of the structural progression. Ratherthan hearing the consonant passing harmony as a `violation' of the logic of aprolongational succession, one can re-orientate one's hearing in terms of thatsuccession at a deeper level.38 In this case, hearing the consonant passing noteas a lower-level inflection of a higher-level move (IV±V) suggests a particular`colouring' of the (subordinate) tonic harmony at a later level such that thesecond element (IV) colours the first. Such colourations result from differentways of hearing an oscillating succession of harmonies.

It is also worth noting that the temporal perceptions of contradictoryreadings, or of linking alternative readings at different levels, can be nuanced indifferent ways. These differences are both related to and separate fromcontextual presentation. Thus, Steve Larson's strict neighbour-note reading ofthe g1 of bar 6 (shown in Ex. 4b) is supported by rhythmic presentation andimmediate context (projecting the translational parallelism of G±F±E in bars



1±4 and 5±8) (Larson 1997, p. 107).39 My alternative reading is not unrelated torhythmic context: it renders a different rhythmic unfolding (i.e. distribution)of the upper line pattern G±F±E, hearing the translational parallelism of bars5±6 and 7±8 (A±G±F, G±F±E).

Joseph Dubiel, in a subtle discussion of the opening ritornello of the firstmovement of Brahms D minor Piano Concerto, looks at `abnormal' inflectionsof the opening D minor tonic by a B[ triad ± abnormal, because these

Ex. 4a Drabkin, `The Consonant Passing Note' (1996), Exs. 1±3

N

3 2 1

‹‹‹

(— — )

P

3 2 1

‹‹‹

Ex. 4 A contextually unstable octave embellishes a contextually more stable seventh

Ex. 4b Larson, `The Problem of Prolongation' (1997), Ex. 4, and an alternativereading

G A

A F

F

F

G

G

E

E



references fuel situations that conflict with the larger tonal norms of themovement in which they occur (Dubiel 1994, pp. 82±3).40 According toDubiel, the way to `maintain both that the tonic inflects the B[ chord and thatthe B[ chord inflects the tonic' is `by not maintaining both interpretations ofthe same objects at the same time' (ibid., p. 85). Understanding theìnterpretative timing' of the events is crucial to Dubiel's distinction, that is,attending `to the temporal frames of the perceptions they entail' ± when suchperceptions become relevant and for how long they are the leading possibilities(ibid., p. 87, his emphasis). In Dubiel's hearing of the Brahms movement,constructing schematic middlegrounds for tonal norms and motivic àbnorms'means showing one or the other (but not both) às an explicit reappearance of asonority present all along, or as the return of a sonority temporally displaced',i.e. as non-simultaneous prolongational readings (Ex. 5 gives Dubiel's (a)normal and (b) abnormal schematic middlegrounds for the opening ritornello):the àbnormal span is uncovered when the D minor span inside it ends; butthen this span reaches back to the beginning' (ibid., p. 87). The B[ chordbecomes a `point of reference for what will eventually resolve it' (ibid., p. 85).

Dubiel's distinction is that although transformational relations interact withand motivate the tonal (prolongational) progression, the two middlegrounds donot find a deeper level of co-existence because of the non-simultaneity of theirrhythmic organisation. In hearing the piece in this way, the two incompatibleprolongational readings undoubtedly inflect each other, though their musicallevels, temporal extents and effects can be quite different. In the Brahmsmovement, the local rhythmic elaborations of the normative progression (inmodel A, a2 spawns b[2 as a neighbour-note to a2 at later levels) are referentialfor a distinct and àbnormal' middleground reversal (in model B, b[2 spawns a2

as a neighbour-note to b[2, initiating an oscillation with a2). This underscores

appogg. appogg.

appogg.

nb

baEx. 5 Dubiel, `Contradictory Criteria' (1994), Ex. 3.1



the idea that instances of harmonic-thematic oscillation can create notablydifferent musical effects in particular musical contexts.

In his analysis Dubiel demonstrates that non-simultaneous conflictingmiddlegrounds can arise from the temporal experience of music in differentconceptual (prolongational) spaces or temporal (translational) spans (tonal andmotivic). In a similar way, David Lewin's model of perceptual-contextualdescription tracks musical perceptions at different stages of temporalexperience.41 Lewin's model characterises the conceptual experience of musicas moments or stages that have different or changing temporal extentsdepending on the set of implications upon which they draw. Each contextdepicts a temporal NOW of experience, namely a set of events that organisesperceptions, including past retentions and future protentions (possibilities)framed in relation to a specific Language L. Musical perceptions are temporal`windows' that motivate the conceptual contexts for a perception (theseinclude: a set of EVents, a ConteXT for that set, a Perception-Relation-LIST,and a Statement-LIST). The contexts range from individual `slices' thatinclude single conceptual entities in the Language (e.g. various potential tonalorientations of a chord) and passages before or after these instances that shapethe context of hearing. Particular temporal extents variously position thechord-sound in the conceptual-experiential framework of Language L. BothDubiel and Lewin show that `similar terms can refer to rather differentconceptions at particular historical moments' (Lewin 1986, p. 115). They drawattention to the ways that the categorical formulations of a theory (its `PlatonicTHEs') can constrain or motivate music perception, and vice versa.

Chopin, Prelude in D[ Major, Op. 28 No. 15

Chopin's D[ major Prelude (Ex. 6a) is a study in the tensions and alternationsof the tonal-harmonic forces of prolongation and the melodic forces oftranslation. The Prelude creates the effects of a temporal oscillation oralternation of musical spans in the context of alternate groupings of repeated I±V±(I) patterns. The musical analogue is the ambiguity of temporalredistributions of prolongationally distinct (conflicting) functions and spansof tonic or dominant influence. Consider the analogy of two differentgroupings found in an oscillating series abababababababa such that both `ab'and `ba' orientations are possible and operating at `different musical times' orare linked (chained) together in an overlapping fashion (Fig. 3). I have labelledthis overlapping of two different (alternative) translational groupingstranslational combination. We are aware of these conflicting orientations in anon-simultaneous fashion (related to the visual problems of the orientations forthe rabbit/duck or old woman/young woman perspectival figures). Thealternate groupings of tonic and dominant pairs infuse the Prelude.



Previous examples have investigated situations in which the initialprolongational function (i.e. tonic) governs the succession of harmonies atdeeper levels. This analysis explores the implications of the second harmonicfunction (i.e. dominant) to condition or nuance the first over varying timeextents.42 That is, the function of the dominant conditions, nuances and evenreconstitutes the tonic notes (in six-four configurations) in different temporalframes. This temporal redistribution of different harmonic functions makespossible the continuation of aspects of the nocturne-like A section of thePrelude in its funeral-like B section.

Fig. 3 Alternating series and translational combination

a b a b a b a b a b a b a b a

(1) a b a b a b a b a b a b a b a

versus:


versus: (translational combination)


I V I V I V I V I V I V I V I

(1) I V I V I V I V I V I V I V I

versus:


versus: (translational combination)




24

20

7

15

10

5

Sostenuto

7

Ex. 6a Chopin, Prelude in D[ Major, Op. 28 No. 15, bars 1±57



48

cresc.

cresc.

43

38

33

cresc.

cresc.

28sotto voce

53

Ex. 6a (continued)



Exs. 6b and 6c show respectively the tonic and dominant extents orimplications of the phrase, the six-four sonority implying a tonic or dominantorientation over the course of the opening phrase. In Ex. 6b, tonic orientationssuggest a hearing of the melodic g[2 as a neighbour to an extended (deeper) f2.In Ex. 6c dominant orientations suggest hearing g[2 as initiating a third span toe[2 at the end of the melody within which the f2 works as a consonant passingnote in an extension of dominant harmony.43 The double neighbour-notefigure of the upper line suggests a redistribution of scale-degree functions of 3̂±2̂±4̂±3̂ (F±E[±G[±F), with 5̂±4̂±6̂±5̂ (A[±G[±B[±A[) in an inner voice.44

This temporal overlapping or redistribution of alternative harmonic functionscontinues in the subsequent sequential patterns of bars 9±20 in two ways. Ex. 7ashows how the G[ major harmony of bar 10 extends the tonic orientation of bars8±10. In contrast, Ex. 7b shows the G[ major harmony of bar 10 in the context ofan extended dominant function (the tonal region of A[ major/minor). Theseorientations project the double neighbour-note figure F±E[±G[±F in distinct

F E G F3

‹

2

‹

4

‹

3

‹

1 4

Ex. 6b `Tonic' implications of the phrase, bars 1±4; melody g[2 as neighbour toan extended f2 [F±E[±G[±F]

F E G (F)3

‹

2

‹

4

‹

(3)

‹

1 4

E

( ) ( )(NB The repeated a 1 calls the functional status of tonic into question on beat 3, and specifically in bar 2.)

Ex. 6c `Dominant' implications of the phrase, bars 1±4; melody g[2 as initiating athird span to e[2 [F±E[±G[±E[±(F)]



temporal distributions. Significantly, each figure is connected in harmonicallyconflicting (non-simultaneous) temporal extents. Such temporal overlapping ofdistinct I or V prolongational spans continues throughout the Prelude.

In the subsequent contrasting `b' section of the aba structure of bars 1±27,two sequentially related sub-phrases melodically project A[ minor in bars 11±12 and B[minor in bars 15±16. The 10±5 linear pattern now recalls the openingmelodic scale-degree pattern 5̂±4̂±6̂±5̂ (with 3̂±2̂±4̂±3̂ in an inner voice) in eachtonal area. These bars variously suggest B[ as a neighbour to A[ (Ex. 8a) or A[major as a neighbour to B[ minor over the span of bars 9±20 (Ex. 8b). Theperception of this temporal redistribution of harmonic functions is emblematicof the alternating relationship of the eight-six-four and nine-seven-threeharmonies over the A[ pedal of the opening bars. In particular, the melodicdouble neighbour-note patterns give the first reference to the chromatic notesC[ and F[, notes that will feature prominently in the contrasting C]/D[ minormode of the B section.

Significantly, hearing the reference to B[ in bars 15±16 as a neighbour to A[invokes further scale-degree implications: the pattern F±E[±G[±F, now shadedas 6̂±5̂±7̂±6̂ in relation to A[ minor/major (with D[±C±E[±D[ as 4̂±3̂±5̂±4 in theinner voice). In contrast, the A[ tonal area can be heard as a neighbour to B[, inthe context of an internal expansion of the double neighbour-note f2±e[2±g[2±f2, 3̂±2̂±4̂±3̂. These multiply determinate possibilities, the product of a 10±5

8 10 127

Ex. 7b `Dominant' implications, bars 7±10

8 10 12

Ex. 7a `Tonic' implications, bars 8±10



linear pattern over the course of bars 9±20, colouring the melodic grouping ofE[±F±E[, by that of F±E[±D[/F.45

A similar mix of orientations, and tonal scale-degree shadings, is played outover the entire expanse of the texturally contrasting minor-mode and funeral-like B section. The oscillations present the C]-minor harmony alternately as afive-three extension of tonic function (C]/D[minor) (Exs. 9a and 9b), and/or asa six-four extension of dominant functioning G] minor (Ex. 9c).46

In a similar way, the scale-degree orientations surrounding C]/D[ as tonicand G]/A[ as dominant reverse the temporal and scale-degree orientations thatwere projected in the first section (Exs. 9a and 9d): C]±B]±D]±C], as 1̂±7̂±2̂±1̂of C] minor, in a translational combination, overlapping with a grouping thatemphasises C] as an extension of the dominant G] minor, D]±C]±E±D] as `5̂±4̂±6̂±5̂' (with C]±B]±D]±C] as 4̂±3̂±5̂±4̂) (see Ex. 9d).

(N)

D :

9–12 19

‹

2

‹

4

‹

3

‹

5

‹

4 6 5

‹‹‹

3

a :

Ex. 8a B[ as neighbour to A[, bars 9±19: A[ minor double-neighbour figure, bar12

N

D :

9–10

20

‹

2

‹

4‹

3‹

5

‹

4 6 5‹‹‹

11–12

1–81613

3

‹

2

‹

b :

3

3

‹

4

‹

( ( ))

)(*

* parallel to a area in Ex. 8a

Ex. 8b A[ as neighbour to B[, bars 8±20: B[ minor double-neighbour figure, bar16



Analogous to the role played by B[ minor as vi in D[ or as a neighbour to A[(V of D[) in the first section, the striking articulation of E major in bars 40±43(and again in bars 56±9) functions alternately as major VI in A[/G] minor or as

C B D C

D C E D C CDB

E D F E ! )( D C DE

5

‹

4

‹

6

‹

5

‹

g :

c :

v.

2

‹

1

‹

3

‹

2

‹

28 30 31 33 35

Ex. 9a Double-neighbour patterns, bars 28±35

C CDB

28 30 31 33 35

i + V

Ex. 9b C] as articulation of `tonic' function: double-neighbour pattern, bars 28±35

D DEC

28 30 31 33 35

i + V

or( )

Ex. 9c C] as `six-four' articulation of `dominant' function: double-neighbourpattern, bars 28±35



`neighbour' to D[ minor (by third relation).47 In perceptual terms, then, is E aneighbour to D] over G]/A[ as sustained dominant (Ex. 10c), or is E/F[ anextension/subsitute for the tonic, projecting the tonic compass of the passage(Exs. 10a and 10b)? The oscillating significance of E major as tonic substituteor as part of a six-four extension of G] minor dominant48 opens up a tension ofhearing non-simultaneous, prolongationally conflicting readings over thetemporal course of the passage, rather than a development of conflictinginterpretations. Although the identities of tonic and dominant are not inquestion, their attendant functions are in temporal flux or oscillationthroughout the entirety of the B section. The funeral-march B section relates,and transforms, the temporal processes of the nocturne-like A section, therebyinterconnecting nocturne and funeral march.49 This overlapping also nuancesthe similarities and ambiguities of the `dividing' dominants of bars 26±7 and74±5 (see Ex. 10c (part d1), bracket below the stave, and Ex. 10d), the latter ofwhich is coloured by the continued oscillation of v and i harmonies.

Finally, the plagal reference to F] minor (G[ minor) via [VI (B[[) (orNeapolitan sixth of V, B[[/A major) in bar 63 and V7/IV in bar 71 harks back tothe plagal ambiguity of bars 9±10 (and the question of D[ as a consonantpassing note in bar 10). Throughout the Prelude, the oscillating relationshipbetween A[ and B[ (along with their various scale-degree and tonal-harmonicshadings) resonates in bar 3 (inner voice A[±B[±A[), in the A[ minor±B[ minorrelationships of bars 11±19, in the G]±A] oscillations in the upper voice of bars64±7 and 72±5, in the `echoes' of the B[±A[ dyads of bars 8±12, and in theconcluding six bars of the piece. (For example, is the a[2 on beat 2 of bar 82 aconsonant passing note between B[ and G[, and/or is B[±G[ an inflection of thedominant A[?)

These translationally parallel, prolongational patterns ± as interlockinggroupings of tonic and dominant harmonies ± counterpoint the alternation of

c : 1

‹

7

‹

2

‹

1

‹

g : 5 4 6 5

‹ ‹ ‹ ‹

d :( )3 2 4 3

‹ ‹ ‹ ‹

Ex. 9d Overlapping (translational) statements of the double-neighbour patterns:C]±B]±D]±C] and D]±C]±E±D]: C] as `tonic' v. C] as `six-four' articulation of`dominant' function



( )

C D E D (C )

28 40 41 42 43 44

Ex. 10a Bars 28±44: C] as articulation of `tonic' function

28 31 36 40 42 44 75

Ex.10b Bars 28±44: C] as articulation of `tonic' function

28 31 40 42 44 75

!

D C E D(d1)

( )

(E) D C E D

C B Dg :5

‹

4

‹

6

‹ ‹

( )5

75

70 73

6462

Ex. 10c Bars 28±44: C] as `six-four' articulation of `dominant' function

F E G E

DD EC(d2)

3

‹

2

‹

( 3!)

‹

24 26 27 28

Ex. 10d Overlapping (translational) statements of the double-neighbourpatterns: C]±B]±D]±C] and D]±C]±E±D]. C] as `tonic' v. C] as `six-four'articulation of `dominant' function



major and minor modes in the Prelude. For example, the A section embedsminor-mode tonal areas (A[ minor and B[ minor) within the context of amajor-mode tonic (D[ major), and the B section embeds a major-mode tonalarea (E major) within the context of minor mode tonic and dominant (C]minorand G] minor). From this perspective, these processes of oscillation andembedding offer ways to hear the B section as a musical `turning inside out' ofthe A section. These contrasts transform and interrelate aspects of the nocturnein the subsequent funeral march.50

Sonority, Structure and Genre

Rose Subotnik has written about Chopin's ìndividuality' of style, under-scoring its play or focus on sound as `pure' sonority (Subotnik 1991, pp. 141±65, esp. pp. 148±55). For example, in her analysis of the `transitional' passagefrom Chopin's E major EÂ tude, Op. 10 No. 3 (bars 54±62), she proposes that itseffects result from Chopin's suspending and lingering on multipleinterpretations of melody and harmony in either/both E major or/and B major(ibid., pp. 157±162; see the epigraph at the beginning of this article). Chopin'sìnnovation' is thus to create situations of thematic-harmonic analogy ratherthan (or in the context of) goal-directed harmonic progressions. The sensuousand cultural particularity of Chopin's music is not that of a `self-evidentintelligibility' or structure but of à particular individual in a particular culturalsituation', and thus contingent on matters of style (ibid., p. 152). Matters ofstyle and `sonority' are distinct from those of `structure', by which she meanslinearly directed, hierarchical relations and hearing.

In the terms outlined here, however, sonority is as much part of structure asstructure is part of sonority: back-to-front and left-to-right oscillating relation-ships connect sonic shading and syntactic continuity; translational parallelismsinteract with prolonged and, at times, overlapping harmonic progressions. Oneneed not construe sonic aspects as solely linked to style or as `natural',àutonomous' and set apart from structure. Bruce Horner has pointed out thatproperties of sonority are intimately linked with `specific practices of pro-ducing and signifying with sound', rather than with the idealising of `musicalessence' defined in terms of properties of the `medium of sound':

. . . the experience of music as possessing `dynamic sensuous fullness' is itself asocially produced effect of specific materially-conditioned listening practices

rather than a natural antidote to ideological pressures . . . By positing elementsof sound as the `natural' essence of music which fixed forms silence, rather thanas fully social and material, we contribute to just such mythicization [by thebourgeois culture] and its suppression of practical consciousness. (Horner 1998,

pp. 171, 184±5)51



Musical `structures' are likewise not immune to the effects of socially andmaterially conditioned listening and interpretative practices: they are vitallyconnected to social-cultural practices of producing and signifying.

In music-analytic terms, to understand Chopin's individuality is to describehis reworking of the oppositions of sonority and structure. To consider theways in which his music requires us to redefine such oppositions is to callattention to structure's intimate link with music's temporal process andcharacter ± and to Chopin's particular `temporalisation' (translation) of a depthof harmonic-tonal relationships. In his `temporalisation', opposite valuesalternate, oscillate, resonate, and thus come into contact. Often a feeling ofreconciliation may be mixed with a sense of nostalgia, morbidity of obsession,or promise of visionary reconciliation more implied than directly stated.52

Do accounts of varying syntactic depth paint music as a `radiant image oftranscendental significance ± that which is perfectly ordered without apparentsocial intervention'? (McClary 1988, p. xv) If Chopin's melodies seem to resistsocial interpretation, is it because we are too inclined to hear his melodic lines interms of a myth of philosophical progress or of a striving towards a heightenedideal?53 In this sense, both Subotnik's focus on Chopin's sonority and sonorousidentity apart from linear structural progression, and my account of his practicesof translational parallelism and harmonic oscillation, are strategies for arrestingor nuancing tonal outcomes by describing an activity in contrast to thedirectionality of rational progress. The music is, in this sense, `self-involved'.Are Chopin's apparent circularities a game of the surface of the piece, subject tomasterful and beautiful domination by the logic of progression at the end (or inthe `background')? Or does a sensitivity to Chopin's oscillations open up a field ofalternative temporal experience and interpretation, in counterpoint with thegender politics of Chopin's culture, to challenge a hearing of his music assomething divorced from life? Its temporal processes point to a music involved inthe world, articulating insights into the vagaries of being human.

Music theory ± construing (syntactic-semantic) relationships ± in this sense`does not diffuse the political consequences of ongoing material conditions but,rather, provides a means of constructing and understanding agency andsubjective identity in multiple locations'.54 In Chopin's music we might wellfind the play of dualities of meaning that take on different faces simply byvirtue of the person who listens and relates to them in her/his own way, butthese listeners, interpreters and music also write and are written upon in thefields of social practice.55 Acts of appropriation and theory construction can berevolutionary when done self-consciously, and thus `separation of the politicalfrom the non-political may be more a matter of degree than of kind' (Kielian-Gilbert 1997, p. 275).

Ambiguity or alternative interpretations in the sphere of listening andanalysis are not simply a breeding ground for an apparent postmodern



disregard of ethical or interpretative grounding. Particular contexts shape ourmusical perceptions and descriptions by drawing out different values of music.Observations may be persuasive or have validity from particular perspectives(interpretative selectivity). Similarly, music may present many values, andparticular interpretations may respond to some of those values and not toothers (interpretative incompleteness/gaps). It is thus helpful to examine whichvalues play a role in our perceptions.56

*

In the debate between Schenker and von Cube that Drabkin narrates, in thetemporal differentiations that Dubiel describes, and in the tonic-dominantoscillations of Chopin's D[major Prelude that I have examined, the `sounds' ofalternative musical contexts or of interrelating prolongational and translationalinterpretations are evident. Such interactive contacts have significant potentialto shape alternative hearings and stories; they do not simply muddy the `will ofthe tones'.

Interpretative positions may draw on or work from assumptions of`normative' conception(s) of tonal structure.57 Rose Subotnik argues that,although problematic, interpreting the tonality of classical music as a `universalnorm' furthers the sense in which relations and distinctions between style andstructure can be manipulated:

With Mozart and especially Haydn, however, it is often possible to entertain theillusion that the empirical particularity and arbitrariness of style have beenintegrated seamlessly with the universal necessity of an abstract musicalstructure, so that one could momentarily believe that the style is the structure

and that for this music, stylistic understanding (the stylistic perception or, in asense, the apprehension of structure as a surface) and structural understanding(the understanding of structural meaning or the apprehension of internal

structural connections) are identical. (Subotnik 1991, p. 118)

But Subotnik also stresses that conceptualisations of music and its structuresare deeply embedded in social-cultural-personal practices and processes ofconstruction and interpretation (a position evident in the epigraph by Barthesat the beginning of this article). Different possibilities of social and musicalengagement materialise in the forces of embedded and successive (repeated)musical relationships. And interactions of the tonal processes of prolongationand translation, of sonority (style) and structure, have particular analytical,pragmatic and political implications, and significantly project markedlydifferent experiential effects.

The variable orientations and interactions of harmonic oscillation andthematic repetition, and of prolongational and translational parallelism, offerdifferent ways of experiencing and construing the particular effects of temporal



function and theoretical (in)determinacy. Situations of harmonic oscillation ±in which the relative priority of initial and concluding structural functionschanges (as in the Chopin Prelude) ± call attention to the varying effects oftemporal translation on prolongation, and between thematic restatement andharmonic function. Issues of syntactic depth and semantic meaning are notseparate from social-cultural narratives; indeed, they shape and are theproducts of such narratives. Reconceiving their connections and interactions is,in fact, part of understanding and enlivening music's narratives and itspotential to resonate and touch our times and our lives.

NOTES

1. I am grateful to Joseph Dubiel for framing our discussion in these terms at onepoint in our comparison of alternative readings of Mozart's K. 421. I also want tothank Elizabeth Sayrs and Joseph Dubiel for their insightful comments on anearlier version of this article.

2. For a discussion of how left-to-right (linear, horizontal) and back-to-front(depth, spatial) metaphors align with different emphases of vertical andhorizontal dimensions of tonality in the theoretical positions of four theorists ±Marx, Riemann, Schenker and Reti ± see Ìnstitutional Values: Beethoven andthe Theorists', in Burnham 1995, pp. 66±111. Burnham regards the tension ofSchenker's juxtaposing the `left-to-right coherence of the Beethovenian motive-as-seed . . . with something like the background-to-foreground coherence ofSchenker's later theory' as crucial to the historical development of Schenker'stheory of tonality (ibid., p. 93).

In his review of Christopher Hasty's Meter as Rhythm (1997), Arnold Whittallcalls attention to Hasty's explicit foregrounding of processive (temporal) experienceand emphasis on projection as a mode of perception. Significantly, Whittall arguesthat theorising about listening is not simply an alternative or superior to theorisingabout reflection, but à necessary complement to it' (Whittall 1999, p. 360). In sodoing, he seeks to redress the problem of an asymmetrical weighting of eitherprocessive (left-to-right, linear) or reflective (back-to-front, conceptual) hearing.He thus calls attention to the `conceptual minefield which attempts to separateprocess from product can create' (the problematic separation of process and productof which Hasty is also well aware). For Hasty, Whittall argues, `the challenge ofworking with the opposition between process, conceived as something which is``presently going on'', and in which `̀ nothing is ever fixed'', and the familiarterritory of structure as ``product'' is entirely in keeping with a modern spirit ofintellectual enquiry and aesthetic curiosity' (ibid., p. 363).

3. This orientation is indebted to Chapter 4, Ànalytic Fallout', of Benjamin Boretz,Meta-Variations: Studies in the Foundations of Musical Thought (New York:Open Space, 1995). Boretz construes determinacy as syntactic depth. Ìn fact theSchenkerian notion is not denied but explicated by my characterization; for thenotion here is just that the ``levels'' constitute ± each individual level as well as allthe levels collectively ± a model of (all) the distinguishable data of the composition,



such that each level specifies a particular degree of (and kind of) determinacy forthat data' (p. 201). `[T]o be a ``thing'' in music is just to be a determinatestructure of determinable differences among observable aspects of elements andevents, the extent of particularity to which anything is a musical thing depends onthe extent to which, and the number of levels on which, not only the fact ofdifference, but also the nature of difference and the degree of difference (in thatorder) are cognitively determinable through perception' (p. 358).

4. See Walter J. Moore. Physical Chemistry, 3rd edn. (Englewood Cliffs, NJ:Prentice-Hall, 1962), pp. 481±2. John Cage explored different sides of (in)deter-minacy to mean: actions to bring about an unforseen situation, an absence ofhierarchy, or an awareness of the relatedness of all things and beings (and tosuggest that `this complexity is more evident when it is not over-simplified by anidea of relationship in one person's mind' (John Cage, `Indeterminacy (1959)', inSilence (Middletown, CT: Wesleyan University Press, 1961), p. 260). See also`Composition as Process, II, Indeterminacy', in Silence, pp. 35±40 (esp. p. 36);and Richard Kostelanetz, John Cage (ex)plain(ed) (New York: Schirmer, 1996),pp. 79±82 (esp. p. 81).

5. Kofi Agawu (1994) includes a bibliography of work by various writers onambiguity in music. He supports the paradoxical claim that within the confines ofan explicit music theory `the concept of ambiguity is meaningless' (ibid., p. 88).His focus, however, is on how the confines of a theory direct and dictate therendering of listeners' perceptions of tonal music. He does not explore howplausible readings in different (non-simultaneous) time frames might describe the`fusion' of particular musical effects in a passage, or the ways that musicalpresentations can make the constraints of a theory problematic.

6. See Dubiel 1994, p. 96. Various definitions of prolongation have also been proposedby such theorists as Joseph Straus (1987), Carl Schachter (1990), Allen Forte andSteven Gilbert (1982) and Richard Littlefield and David Neumeyer (1992).

7. Consider hearing, for example, the progressions in Debussy's PreÂ lude `BruyeÁ res'(Book 2, No. 5) in relation to a strict Schenkerian harmonic paradigm, in contrastto allowing different formal areas or pitch repetitions to dictate or constrain theemphasis. It is likely that such a hearing would differ from Felix Salzer's analysis.One can thus hear `progression' against the changes and emphases of section,register or formal relationships. Even in more conventional tonal situations suchemphases can be variously employed, though the usual tendency is to construevoice-leading events in a closer, mutually `characterising' relationship with thoseof formal design. See Felix Salzer, Structural Hearing, Vol. 2 (New York: Dover,1952), Debussy, `BruyeÁ res', Ex. 478, pp. 252±5.

8. The dotted quaver/semiquaver upbeat gestures of the inner parts (violin 2 andviola) that lead to bar 2, as well as to bars 4, 6 and 8 (in the cello), render bars 2, 4,6 and 8 as hypermetric downbeats. This hearing lends support to reading 1c (theeffect of an extended six-four/five-three dominant in bars 8±9), or to reading 1e(the effect of an extended tonic via a pre-dominant in bars 7±9). In contrast, thedotted quaver/semiquaver upbeat gestures of violin 1 that lead to bars 1 and 3, aswell as to bars 5 and 7, render bars 1, 3, 5, 7 and 9 as hypermetric downbeats.



This correlates with reading 1b (the effect of an extended tonic in bars 1±8), orreading 1e (the effect of an extended pre-dominant in bars 7±9), harmoniesfollowed by the dominant of bar 9.

9. See n. 8. Metric emphasis on odd bars stresses the parallel fifths of bars 3, 5 and7; metric emphasis on even bars stresses the parallel sixths in violin 1 and cello ofbars 4, 6 and 8, aligned with the falling perfect fourths of violin 1 of bars 4 and 6,though supported by chromatic notes (C] and B) in the cello.

10. My thanks to Elizabeth Sayrs for describing the issue in these terms.

11. See Oxford English Dictionary, s.v. òscillation' and `flicker'. The `function' of anoscillation is described by the upper and lower limits of the reversal; the `fusionfrequency' delineates the lowest rate or length of variation or point at which theoscillation (or flicker) is not perceptible.

12. Joseph Dubiel (2000) describes `flickering qualities' in the sounds of particularmotions between harmonies. His examples of a `paradox . . . where we have reasonto assert two different and ostensibily musically incompatible prolongationaldescriptions' are from the B[-flat minor prelude in Book II of Bach's Well-Tempered Clavier, the second movement of Beethoven's String Trio in G major,Op. 9 No. 1, the aria `Dove sono' from Mozart's The Marriage of Figaro, andBrahms's song ÀbenddaÈ mmerung', Op. 49 No. 5. Dubiel also explores the extentto which such musical encounters serve to transform (and even disunify) thetheory or conceptual framework òver various instances of its application' (ibid.,p. 9). I wish to thank Joseph Dubiel for sharing this work with me.

13. Rothstein 1990; Snarrenberg 1996, esp. pp. 315±19. See also Snarrenberg 1994.

14. See Snarrenberg 1996 on the latter point, esp. pp. 315±16. See also CarlSchachter: Ì should like to suggest a slightly different way of viewing back-ground structure. It becomes self-evident that any awareness of a backgrounddepends on its being embodied somehow in a foreground. And that ``somehow'' isextremely variable.' (Schachter 1999, p. 314)

15. In contrast to a Schenkerian orientation, Fred Lerdahl and Ray Jackendoff havepursued the theoretical implications of preserving this note-to-note connectionbetween levels in their reductions (Lerdahl and Jackendoff, 1983). Also seeEdwin Hantz's review of Lerdahl and Jackendoff, Music Theory Spectrum, 7(1985), pp. 190±202. Steve Larson discusses this issue in Larson 1997, to whichStraus (1997) and Lerdahl (1997) respond. Lerdahl clarifies his position byseparating the left-to-right ordering of èlements in a string' and the ìnternalcontent of an element' such that àt any prolongational level, only what is neededin that context is retained through a transformational operation'. He speculatesthat the nature of an event at a global level might involve an abstraction of tonalfunction rather, or more likely, than transformations of voice-leading (Lerdahl1997, pp. 148±51).

16. Also see Dubiel 1990 and 1994.

17. Robert Snarrenberg develops the idea of effects more specifically in relation toSchenker's verbal descriptions of music in Snarrenberg 1997. He writes of effects as



conceptual components that angle a perceptual response: a `concept to focus thelistener's attention' (p. 4); a pointer, hint or aid to train a listener's attention (p. 5);an ìnterpretive disposition' (p. 28); and a `reflective analysis of listener response' (p.7). A particular effect can combine a set of aspects; he does not examine therelationships between aspects. In one sense, I am exploring effects that achieve theirparticular result because of a tension of contrasting effects, i.e. effects spawned bytensions and interrelations of left-to-right and back-to-front perceptions.

18. See also Snarrenberg 1994, esp. pp. 324±8.

19. Frank Samarotto pursues a related argument (Samarotto 1999). He contrastsSchenker's construal of the rapport between deeper levels of tonal hierarchy ± onethat èmanat[es] from background to foreground' (ibid., p. 238) ± with thecapacity of more local rhythmic events to figure in deeper levels of a rhythmic-metric hierarchy. Ìt is perhaps essential to the nature of rhythmic analysis thatthe opposite seems to occur: immediate gestures penetrate to deeper levels anddisturb their stability' (ibid.). This disturbance is often articulated through`shadow metre', Samarotto's term for metric emphasis in contrast to the mainmetre (metre as written) (ibid., p. 235).

20. For example, in their discussion of various functions of the six-four chord,Edward Aldwell and Carl Schachter emphasise `how much the meaning of a six-four chord depends on context'; see Harmony and Voice Leading, Vol. 1 (NewYork: Harcourt Brace Jovanovich, 1978), pp. 261±80.

21. Also see the Schachter-Rothgeb exchange on Schubert'sMoment Musical, Op. 94No. 1, in Yeston 1977, pp. 171±201. Specifically, their disagreement centres onbar 10ff: Schachter reads the upper-line C of this passage as prolonged (with B asa neighbour note); Rothgeb argues that C is subordinate to B. Both readings havevalidity if one understands bars 8±15 as a process of working out an eventualmotion of upper line c1 (bar 8) to b1 (bar 12) as a motion of I to V. At lower levels,the oscillating process gives both interpretations validity and vitality (N.B. bothauthors draw on motivic aspects in support of their individual readings).

22. The ears and neck of the young woman in one view are alternately the eyes andmouth of the old woman in the other view (other aspects remain the same for bothfigures, e.g. the coat and scarf). See Henry Gleitman, Psychology (New York:Norton, 1981), p. 252.

23. See Rudolf Arnheim, Art and Visual Perception: a Psychology of the Creative Eye,new edn. (Berkeley: University of California Press, 1974), pp. 226±7. Braque'spainting is titled Cubist Woman (Lithograph, 10� � 14 in.) and can be viewed athttp://www.elinoffgallery.com/braque.htm [February 2002].

24. In a similar way, Scott Burnham has noted that, for Schenker, the `drama of theUrlinie' is primarily an orientation of delay àrising in the form of potentiallydramatic digressions and retardations of a fundamentally goal-oriented traversal'(Burnham 1995, p. 90). Offering an admonition to those who regard Schenker'stheory as exclusively focused on delay, Carl Schachter has noted that à knowinglistener judges the sequence of events, in a counterpoint exercise and also in acomposition, in relation to the possible choices open to the counterpoint student



or composer at that juncture of the exercise or piece. Awareness of this aspect ofthe Schenkerian enterprise serves as a corrective of the prevalent but mistakenopinion that Schenkerian analysis concentrates exclusively on a retrospectiveview of music without taking into account a moment-by-moment perspective.'Carl Schachter writing to the SMT discussion list (submitted by StephenSlottow, 18 September 2000); see http://www.societymusictheory.org/smt/

25. Pieter van den Toorn has noted that a `retreat' to deeper levels of abstraction maybe necessary to place more `determinate' readings in relief. See his discussion ofmotive in Music, Politics, and the Academy (Berkeley: University of CaliforniaPress, 1995), pp. 111 and 124. See also my rejoinder to include the specificity ofcategorisations as products of human motivation in Kielian-Gilbert 1997.

26. Scherzinger explores hearings `suspended between alternatives' as havingsubversive and potentially political consequences in his analysis and discussionof progression and motivic patterns in the Adagio movement. He relates theìndecisions' to departures from syntactical norms or stylistic conventions afterthe work of Dubiel (1994). See Scherzinger 1999 and 2002. Of the opening of theAdagio, Scherzinger writes: `But not letting one interpretation trump the other isalso subversive . . . And is this not a way of making those codes leak by pervadingour ears with every minority; with every detail and mutation . . . What issubversive about this kind of hearing is that it marks, and becomes fascinated by,those musical moments that reflect something that is out of kilter with what isreadily apparent as a syntactical norm or as a stylistic convention of the piece . . .These are moments that veer away from having the value of archetypes; momentsthat resist crystallizing into sedimented generality . . . moments that proliferate,not reduce, laws of combination' (Scherzinger 2002, p. 145).

In contrast, John Rothgeb emphasises the value of prioritising readingsresulting from different orientations (e.g. `pitch-to-rhythm' v. `rhythm-to-pitch'interpretations): Ìn several examples of competing and even conflictingassociations it may be in order to hear both associations . . . but to assign priorityto one of them.' (Rothgeb 1997, p. 183) `The norm in art music, however, issaturation of the musical surface with associations that are ``genuine'' (rather than``spurious'' . . .) and that compete, each of them with some degree of legitimacyfor the ear's attention' (ibid., p. 184). Despite this situation, `the ear' may be `tooeasily seduced' or `distracted' from apprehending relationships that ènric[h] thecontent': à different association will elude the ear that is too easily seduced by thefirst one . . . distrac[ting] the ear from a relationship that enriches the contentvastly more than it alone could possibly do' (ibid.). Rothgeb appears to position`the ear' between relationships of `content' and relationships that `distract' or`seduce'.

27. The issue of requiring a normative (single, best) reading in Schenkerian analysishas consequences beyond the pragmatic questions considered in this essay. See,for example, Littlefield and Neumeyer (1992), where they show how Schenkerianreadings can be directed or angled so as to `narrate' different things about amusical passage, giving priority to particular musical features, as for example,framing beginning and end, register, inner lines. This àngling' is made possibleby their reconceptualising the Ursatz as a middleground phenomenon. They also



stress that the choice of what to read in a musical passage is contingent andcontextual.

28. See Schenker's analysis of Chopin's `Revolutionary' EÂ tude in C minor, Op. 10No. 12 in Schenker 1969, pp. 54±5 and Schenker 1979, Fig. 12. This gives rise tovarying interpretations as to where the `point of interruption' occurs, with thearticulation of the dividing dominant or at the end of the prolongational extensionof that dominant (and thus with varying practices of positioning the doublesolidus marks (//) in a sketch to signal the interruption).

29. This correlates with the practice of omitting repeated passages in Schenkeriansketches.

30. The distinction between successive translation in linear time and conceptuallyembedded patterns can have other ramifications as well. Consider Edward T.Cone's analysis of `equilibrium' in the first movement of Stravinsky's Symphonyin C (Cone 1963) where he distinguishes between contrasting types of perceptionsand orientations. Rhythmic segments articulate a symmetry of axiallycomplementary pairs balancing the temporal units of the introduction (x) andexposition (y) around those of the development (z), recapitulation (y) and coda(x): x-y-z-y-x. These temporal spans are complemented by a scheme of transla-tional symmetry (parallelism), a presentation of corresponding thematic unitsbalanced through repetition and restatement. A similar distinction informs myanalysis of the first movement of Stravinsky's Octet; see Kielian-Gilbert 1991.

31. The terms `pattern' and `copy' are drawn from Burkhart 1978.

32. Patrick McCreless examines the expressive effects of semitone relations, asking ifmotion by a semitone is transpositional (translational in the context of this article)or prolongational (i.e. transpositional but within a prolongational framework). Hesuggests that often we can hear them either way, in chromatic (symmetrical) ortonal (asymmetrical) space. See McCreeless 1996.

33. For an example of this interaction, see the analysis of Clara Schumann, RomanceNo. 1, Op. 21 (1853) in Kielian-Gilbert 2000.

34. See Cadwallader 1990. This reading also appears in Cadwallader and GagneÂ ,1998, pp. 266±70. See also Carl Schachter's analysis of the same piece inSchachter 1995. Their interpretations of these passages are notably similar, andcontrast with those I present here.

35. In showing the deeper 5-6 exchanges of these passages, the readings byCadwallader and GagneÂ (1998) and Schachter (1999) highlight the recurringmotivic references to the voice-leading of the opening bars, a sixth moving to afifth above the bass, throughout the piece: F]±d2 to G±d2.

36. For an interesting example of how this move towards completion can be nuancedin situations of interruption, consider the indication to repeat the second part of abinary dance design. The `standard' interpretation might suggest that the `arrival'on the tonic occurs within, or towards the end of, the first statement of the Bsection (disregarding the impact and implications of the repeat). However, inBeethoven's Scherzo movement from the Piano Sonata in D major, Op. 28, the



repeat of the B section of the Scherzo poses the issue of hearing differentinterpretations (roles) of the `tonic' harmony. In the first statement of the Bsection the `arrival' of the concluding D major tonic can be reinterpreted inretrospect (undercut) as a potential extension or anticipation of the D six-fiveharmony at the beginning of the restated B section and thus as continuing the`span of implication' of the dividing dominant from the first section through tothe final tonic of the B section upon its second statement.

37. Richard Cohn (1992) and Carl Schachter (1990) have also discussed theimplications of conflicting or contradictory groupings of melodic lines andmotives in Schenkerian practice. For example, Schachter similarly describes thedifferent possible harmonic contexts of a descending fourth.

38. A famous case in point is Schenker's analysis of the C] of bar 2 of the second songfrom Schumann's Dichterliebe, Op. 48 as a consonant passing note connectingIV±V. This song is discussed by Drabkin (1996), Dubiel (1990), Forte (1977),Kerman (1994) and Neumeyer (1982). Arthur Komar, in his critical edition ofDichterliebe (New York: Norton, 1971) argues against Schenker's interpretation(see pp. 70±73), as does Forte, albeit in different ways.

39. In contrast to positions advocated by Straus (1997) and Lerdahl (1997), Larsonstresses the prominent function of presentational context in listeners' judgementsof pitch stability. In this example, however, the question of whether the octave Gor seventh F is `more stable' depends on how consonant and dissonantrelationships direct and influence the perceptions of specific interactions.

40. Dubiel uses the term abnorm to refer to `definably irregular events that becomecriteria of prolongation or succession in violation of larger norms of the pieces inwhich they occur'.

41. See Lewin 1986. Peter Smith has adapted Lewin's model to depict different`tonic' contexts in Schenkerian analysis; see Smith 1995.

42. A Lewin transformation, RICH, describes a pattern that undergoes an RIchaining transformation of elements such that the transformation of a pattern isboth a transposition and a retrograde inversion of the initial pattern withcomplementary common notes: `a RICH(s) is that retrograde-inverted form of swhose first two elements are Sn-1 and Sn, in that order . . .. if s � A±C±E[±E,then RICH(s) is E[±E±G±B[' (Lewin 1986, pp. 180±81). When this `translationalparallelism' is applied to a harmonic context, it can motivate a series ofinterlocked, mutually influencing prolongational contexts. For more on RICHtransformations, see Lewin 1987, pp. 180±88. Translational combination mayprovide one means of linking tonal (functional harmonic) and collectionalapproaches to pitch organisation in twentieth-century `tonal' music.

43. Charles Rosen has noted `the extraordinarily subtle ways in which Chopinprevents classical expectations from even coming into play . . . Chopin is amaster at weakening the force of his dominant preparations ± when he usesthem ± without, in fact, allowing any possibility of the final tonic to be indoubt. His technique does not admit any real ambiguity (that is, any convictionthat another tonic is imminent); what it does is remove some of the absolute



sharp-edged contour of tonic definition, and this endows the music with a lessangularly defined shape that allows Chopin's morbidity full play' (Rosen 1997,p. 396).

William Rothstein takes a different approach in his analysis of Chopin's E majorEÂ tude, Op. 10 No. 3, bars 16±17: ìn this instance the ambiguity of harmonicmeaning is especially remarkable . . . here two harmonic functions, V and I, stakevirtually an equal claim to the six-four chord'. Because of the continuation of thepassage (bars 17±21), he reads a tonic emphasis, `the concluding sequencerepresents an expanded final tonic'. See Rothstein 1989, pp. 225±6.

44. The status of E[ and G[ as part of a double neighbour-note melodic figure inrelation to D[ and F becomes apparent at this point: the e[2±g[2 pattern arisesfrom motion from an inner-voice a[1. Also implicit (realised later in the B section)is the scale-degree shading of these notes in relation to A[ (V): 6̂±5̂±7̂±6̂ (F±E[±G[±F) and 1̂±[7̂\±2̂±1̂ (A[±G[±B[±A[).

45. Jim Samson characterises the `b' section of the opening A section as typicallymore regular/periodic, sequentially structured, and deriving generically from astanzaic type rather than an aria type of melodic writing (as in the opening à' ofthe A section). See Samson 1996, pp. 169±72.

46. This reading positions the B section as initiating a subsequent minor-mode tonicbranch to the interruption at the structural cadence on the dominant thatconcludes the A section in bar 27 (interruption model) in relation to hearing the Bsection as a continuation or extension of the dividing dominant to the subsequentbranch of the interruption (major tonic) that marks the return of the A section inbar 76. The harmonic-functional oscillation revolves around the alternate statusof tonic and dominant functions.

47. Presumably Charles Rosen might lean towards this latter orientation: `Most ofthe later structures of Chopin assume that a minor key and its relative major areessentially the same tonality. Going from one to the other is a change of moderather than a modulation. This enables him to conciliate his need to move fromclosed to open effects with the more orthodox patterns that are largely irrelevantto his thinking.' (Rosen 1997, p. 398)

48. Among other things, the ramifications of this extended oscillation would argueagainst any shortening of the passage: Ìt is perhaps understandable that in thisfamiliar piece a cut is sometimes made of bars 43±58, but this can only reduce thepoignancy of the return to D-flat' (Thomas Higgins, `Notes Toward aPerformance', Norton Critical Score, Chopin Preludes, Op. 28 (New York:Norton, 1973), p. 66. In the interpretation offered here, even the issue of `return'would require qualification.

49. See Abraham's description of the B section of the Prelude as `monastery monksprocessing as in a funeral march'. Gerald Abraham, Chopin's Musical Style,quoted in Jim Samson, The Music of Chopin (London: Routledge and KeganPaul, 1985).

50. These shadings and implications of interrelated nocturne and funeral march arehighlighted when the A and B sections of the Prelude are featured as off-screen



music in the 1997 film, Face/Off, a film about role-reversal and alternativeidentity. See Kielian-Gilbert (forthcoming).

51. Feminist theory has also called attention to the connection between aestheticcontemplation (regarding texts as autonomous) and the sexual oppression thatderives from practices of `male gaze' in visual contexts. See Mary Devereaux,Òppressive Texts, Persisting Readers, and the Gendered Spectator: the NewAesthetics', Journal of Aesthetics and Art Criticism , 48/iv (1990), p. 342. CarylFlinn has also noted that `the notion of music ± and with it, woman ± sofrequently becomes cast in terms of profoundly imaginary pleasures of disorderedunsignifiability . . . [and risks] losing her and music to imaginary obscurity,meaninglessness and social ineffectivity.' See `The `̀ Problem'' of Femininity inTheories of Film Music', Screen, 27/vi (1986), p. 61; also Strains of Utopia:Gender, Nostalgia, and Hollywood Film Music (Princeton: Princeton UniversityPress, 1992), esp. Ch. 2, `The Man Behind the Muse: Music and The LostMaternal Object'.

52. For example, in the Fantaisie-Impromptu, the outer sections articulate fiery, andcircular, figurations of C] minor harmonies in contrast to the inner sections,which present a transcendental D[ major melodic line that articulates harmonicand melodic oscillations of A[ and B[. In the coda, the D[-major melody returnsin rhythmic augmentation, now in the bass as a left-hand melody. Thisorientation of the melody as a `harmonic' bass now underpins the figurativeright hand, and both suggests and suspends a sense of reconciliation betweentheir previous respective identities as figuration and melodic line.

53. For a different orientation to the reception of Chopin's music, see Kallberg 1996.

54. See Kielian-Gilbert 1999.

55. It is interesting to note that the Internet Movie Database lists 114 films between1931 and 2002 containing Chopin's music: see http://us.imdb.com/ (February2002).

56. See also Subotnik 1996, esp. pp. 65 and 115.

57. In contrast, Elizabeth Sayrs argues that traditional Schenkerian backgroundsdenote a `style' rather than a `measure' of tonality, along the lines of LeonardMeyer's conception of style as a set of compositional constraints. Her dissertationpresents a conceptualisation of Schenker'sUrsatz as a particular set of constraintson idealised voice-leading paradigms; see Sayrs 1997.

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Interpreting Schenkerian Prolongation

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