Schenkerian analysis is probably the most disseminated approach in order to analyse Western tonal music, at least in the English-speaking world. In the last decades, there have been many attempts to apply Schenkerian analysis to other musical traditions than the one it was created for;that is, Western art tonal music. These attempts include Western art medieval and Renaissance music, Western folk music, non-Western music and Western popular music.

However, most of Schenker´s theory;as expressed in his late writings, such as Free Composition (Schenker 1979), published in 1935 shortly after his death; is culturally, stylistically specific: the availability of just a few forms of the fundamental structure, the voice-leading principles, and the emphasis on triads, among other constraints, make it applicable just to a very specific repertoire. In fact, Schenker only analyses German instrumental music of the 18th and 19th centuries, mainly by Händel, J. S. and C. P. E. Bach, Haydn, Mozart, Beethoven, Schubert, Mendelssohn, Schumann, and Brahms. The only (remarkable) exceptions are the foreign composers Chopin and Scarlatti and the vocal music by J. S. Bach (chorales) and Schubert and Schumann (lieder).

In spite of this fact, Schenker assumed his theory to have universal validity. As based on nature;the harmonic series; it would be applicable to any good music. Therefore, Schenker believes that only the music above mentioned is good music. He usually dismisses non-Western music and Western folk music as primitive; considers Western music before 1700 to be just a early stage which would lead later to "true" music; rejects the composers of his own time; and scorns most European non-German music;especially Italian opera.

These aesthetic implications are hardly assumed nowadays by those who practice Schenkerian analysis. They acknowledge Schenker´s theory to be culturally specific and, as such, only applicable to a very limited repertoire. Attempts of application to other kinds of music are usually deemed to require important adaptations in the theory. In this article, I will examine some significant Schenkerian analyses of popular music in order to obtain conclusions about the applicability of this kind of analysis to this music, and, in general, to other repertoires than Western art tonal music.

Schenker did not attempt to apply his theory to modern;that is, Americanized or jazz-influenced; popular music. To be sure, he would have considered such an attempt aberrant. His theory was only concerned with "masterworks", and his judgments about popular music was very negative. Jazz was the closest to the popular music of our time that he was acquainted with in his own time. These are some of the opinions he wrote about it: "jazz possesses as little genuine rhythm as a metronome or a train wheel" (Schenker 1994-97: III-7), and "Jazz stirs the bones, not the mind" (Idem: III-77).

Despite Schenker´s scorn of other kind of music than Western art music from J. S. Bach to Brahms, there have been attempts to apply Schenkerian analysis to popular music, which include American popular ballads (Forte 1995) and songs by Gershwin (Gilbert 1984 and 1995), Jimi Hendrix (Brown 1997), the Beatles (Everett 1986, 1987, 1992, and 1995, and Moore 1997), K. D. Lang (Burns 1997) and Paul Simon (Everett 1997).

No one of these analyses intends to apply the whole Schenker theory. At least, the aesthetic implications of Schenker´s theory are not assumed in them, since they usually try to "demonstrate" the aesthetic value of the popular music they are dealing with2 : "The aim of this essay is to expose the musical means of expression of geniality and exuberance in the Beatles´ simple early song, 'She Loves You', using the 'serious' tools of academic analysis that pertain to issues of voice leading and harmony." (Everett 1992: 19); and "The popular music with which this book is concerned enjoys an international reputation as an American cultural artifact of highest quality. Not all the popular music written in the period 1924-50 is worthy of consideration [...] In a very real sense, these songs are the American 'Lieder' of a particularly rich period in popular music." (Forte 1995: 3).

However, the amount of Schenkerian principles adopted in these analyses varies broadly among them; some try to apply most of them, whereas others can hardly be called Schenkerian analyses.

Schenker´s theory aims to explain the organic coherence of the "best" pieces of the so-called "common-practice" tonal music;though Schenker did not use this term. In short, this coherence is mainly achieved through directed tonal motion;where the relationship between dominant and tonic harmonies is the basic principle; as synthesised in the fundamental structure. Therefore, the main assumption Schenker makes is the subordination of some sounds to others as their elaborations, and the recursivity of this phenomenon at different levels of musical structure; this assumption permits Schenker to represent music in a hierarchy of levels from foreground to background;or to generate music from background to foreground, as he does in his Free Composition. Other important assumptions' by Schenker concern: the nature of structural harmonies, which must be triadic and diatonic; the fundamental line, which must be a step-wise descent from ^8 , ^5 or ^3 to ^1 in an octave (obligatory register); and the application of the rules of counterpoint;such as the generation of dissonances from motions between consonances and the prohibition of parallel fifths and octaves; at all hierarchical levels.

I have already commented that Schenker believed these constraints to be universal, as based in the physical phenomenon of the over-tones. The majority of Schenkerian analysts acknowledge the style-specificity of this set of principles as a whole and they feel free to change some of them in order to apply Schenker´s theory to popular music. The less the analysts consider that the music they are dealing with shares features with "common-practice" tonal music, the more important these changes will be. At the same time, there is a certain resistance among theorists to renounce to Schenker´s principles, and sometimes the discrepancy of such principles with the features of the music analysed leads to unconvincing analyses;this point will be dealt with below.

Therefore, it seems that the application of Schenkerian analysis to popular music is less problematic when the music shares the main features of "common-practice" tonal music;that is, when this music is tonal since it uses basically the same chords, though maybe modified, and in the same way, so that directed motion based in dominant-tonic relationships can be clearly perceived; hence, there is a certain tendency among analysts to favour this kind of music. This fact is overtly acknowledged by many analysts, even if they think that some changes must still be made in Schenkerian analysis in order for it to be applied to this music. So, for example, Walter Everett chooses to analyse "She Loves You" because "The Beatles ardent early works cohere by virtue of a greater degree of structural tension than is heard in most of their later work." (Everett 1992: 19). Allen Forte says: "Many of the concepts and techniques covered in this chapter derive from the writings of Heinrich Schenker [...] In this book, the primary relation between Schenker´s remarkable and path-breaking work is to be found in the analytical approach, not in any shared interest in musical repertoire, except insofar as the American popular ballad exhibits the basic structural characteristics of classical tonal music. Although I wish to acknowledge Schenker´s influence, I emphasize at the same time that the adoption of the linear-analytical procedures he developed is modest in scope and does not begin to engage the full range of his formulation." (Forte 1995: 42). Lori Burns claims. "While the application of Schenkerian analysis to a popular song may raise methodological questions, I believe that the analytical results prove the validity of this approach. Tonal harmonic function carries with it a code of predictable idioms and relationships. This popular song ["Johnny Get Angry"] works within and plays upon well-known harmonic conventions" (Burns 1997: 99). And Steven E. Gilbert states: "Since Gershwin wrote basically tonal music, it is reasonable that we adopt a modified Schenkerian approach." (Gilbert 1984: 423).

The above cited analyses by Forte, Gilbert, Brown, Everett and Burns in fact apply most of Schenker´s principles. Some adaptations are needed. According to Gilbert, "the main point of difference is that in Gershwin´s harmonic language the dissonance had at least been partially [...] emancipated. The triad was still necessary for closure, but dissonances such as ninths and so-called thirteenths did not require resolution." (Gilbert 1984: 423). There are some other "irregularities" in the songs analysed by Gilbert. For instance, in the end of " ´S Wonderful", scale degree ^2 of the fundamental line is lacking, and there is not a structurally supported ^3 in the vocal line; the same happens in "I Love You, Porgy", where there is a missing scale degree ^2 (Gilbert 1995: 21-22). This forces the analyst to consider "implied notes" in order to maintain the Schenkerian fundamental line, which can be problematic: "The matter of implied notes is open to question, more so in twentieth-century music than in the standard tonal repertoire of the eighteenth and nineteenth centuries." (Idem: 13). But, at least for the mentioned examples, "Implied notes under these circumstances [...] should be understood as logical (or intellectual) rather than aural phenomena." (Idem: 22). Another interesting issue in Gilbert´s analyses is the use of some of the Schenkerian means to achieve organic coherence in music, such as concealed repetitions3 : "Whether conscious on the composer´s part or not, concealed repetitions such as these contribute greatly to the organic structure of a composition. The opening of Rhapsody in Blue, no doubt an intuitive creation, is nonetheless rich in concealed repetitions." (Idem: 18). These are mainly found in Gershwin´s "serious" compositions, but there are also some instances of motivic relationships between different levels of the music structure in such songs as " ´S Wonderful" (see Idem: x); Gilbert adds: "Such features make for an organic piece of music and demonstrate that the composer lavished the same care on his songs as he did on his concert works." (Ibidem).

The aesthetic aim of Gilbert´s analyses is overtly acknowledged: "I also believe that Schenker provided not only an analytic method, but a test of quality;in that a good piece of music will be rich in the kind of organic, hierarchical relationships that were the focus of Schenker´s work. The result is that the best of Gershwin´s melodies submit very well to the scrutiny of a Schenkerian (or at least Schenker-influenced) analysis;and it is hoped that the examples presented here have shown precisely that." (Gilbert 1984: 455-456). This belief in the power of Schenkerian analysis to demonstrate aesthetic value seems to be implicitly assumed by most theorists.

Allen Forte, in his study of the American popular ballad, also modifies Schenker´s assumption that every structural harmony must be a consonant chord: he allows for an extension of Schenker's concept of consonance, speaking of "in the case of our vernacular repertoire, a consonant chord that is enhanced by one of the stable dissonances, such as a ninth." (Forte 1995: 43). Again, Schenkerian fundamental line do not always fit in these songs. Forte´s attitude to this is less scholastic, so to speak, than Gilbert´s one; instead of resorting to implied notes, he simply states: "some ballads may have long-range melodic configurations that are not stepwise lines" (Idem: 51). Forte´s analyses try to demonstrate that large-scale melodic structures "contribute in the most elemental fashion to the shaping of the ballad and to its detailed affects, often down to the level of the setting of individual components of the lyrics." (Idem: 333).

Gershwin´s songs and American popular ballads can be seen as somehow close to the "common-practice" tonal harmony; at least, there is a clear feeling of directed tonal motion in this music. Things can be different when we are dealing with pop or rock4 music. Though tonal harmony can be useful to describe some rock music, much jazz and rock harmony is probably better explained as modal. Modal system is widely used by jazz and rock musicians and by analysts who deal with this kind of music. Allan Moore in particular, advocates a modal approach in his book Rock: The Primary Text (Moore 1993: 47-50). However, other analysts try to apply functional tonal harmony to the rock music they are dealing with.

Among the Beatles´songs, it is not always possible to find the clear directed tonal motion that Schenkerian backgrounds represent. Walter Everett has devoted a number of articles to analysing some Beatles´ songs. In general, he tries to make a rather strict Schenkerian analysis. Sometimes, this stance leads him to conclusions which are distant from the actual music. Thus, for example, in his analysis of "She´s Leaving Home", he builds a Schenkerian background where the final structural dominant is a non-existent (elided) chord (Everett 1987: see graph in page 10). Something similar happens in his analysis of "Strawberry Fields Forever", where "the cadential V is minimized nearly to the point of not happening", and the fundamental line progression "^2-^1 actually occurs above I" (Everett 1986: 372-373); in fact, the strong sense of directed tonal motion that Everett´s background suggests (Idem: 372) does not seem to correspond to the music.

Things are rather different in Everett´s analysis of side two of Abbey Road (Everett 1995). Though Allan Moore claims that "The most recent example of the strict Schenkerian approach is probably Walter Everett´s reduction of the entire second side of the Beatles´Abbey Road to an Ursatz [fundamental structure]" (Moore 1997: 88, footnote 4 to chapter 4), in fact Everett is forced here by the features of the music and the obvious intuitions in its hearing to move away from a strictly Schenkerian background. Probably the clearest example is the end of "You Never Give Me Your Money", where the bass line in Everett´s reduction finishes with the chords C major, G major in the first inversion, and A major;a progression which is not at all explainable through functional harmony; in parallel octaves with the fundamental line (Everett 1995: 218). Everett offers the following explanation: "The pentatonic system does not know the harmony of the major-minor system; triads are usually all major [...] because they are simply heard as doublings, in natural overtones, of the pentatonic 'roots'. These do not normally have harmonic/contrapuntal relationships between them, other than the powerful but primitive passing functions [...] and neighbor functions [...] Therefore, the song can end with ^3-^2-^1 in parallel octaves (a doubled single voice) in the outer 'parts'. " (Idem: 221).

The problem in using Schenkerian backgrounds when dealing with music where modal relationships are important is the fact that Schenkerian backgrounds emphasise dominant-tonic relationships while relegating any other ones. These relationships are essential in "common-practice" tonality, but in much rock music, the dominant chord is not more important than others. So, for example, in the very usual twelve-bar blues pattern I - I - I - I - IV - IV - I - I - V - IV - I - I , there seems to be no reasons to think that the V chord is more important than the IV one, and there is not a strong feeling that the V chord must resolve directly into the I one, as it happens in the omnipresent full cadence of "common practice" tonality.

Therefore, no good results are obtained when a strict Schenkerian analysis is imposed on such music as blues. In his analysis of "Little Wing" by Jimi Hendrix, Matthew Brown claims: "blues pieces essentially conform to the principles of common-practice tonality" (Brown 1997: 161), so the compositional strategies of Jimi Hendrix would be limited by the rules of tonal harmony and counterpoint. This belief that Hendrix´s music is governed by the rules of tonal harmony leads to an implausible interpretation of a eight-bar blues open-ended pattern | e | G | a | e | b | a | G F | C d | as a I-IV-I-V-I background in E minor (Idem: see graph in page 162). If it is possible to consider the III chord (G) of bar two as a neighbouring chord in relation to the IV chord (a) in bar three, it is much more unconvincing to consider the whole second half of the pattern as a prolongation of the V chord (b); moreover, this V chord (b) is a minor chord, so that its intended role as a dominant harmony is much more arguable.

A very different attitude to Schenkerian analysis is that of Allan Moore in his book The Beatles: Sgt. Pepper´s Lonely Hearts Club Band (Moore 1997): "much of my graphic vocabulary is borrowed from Schenkerian analysis. The diagrams are not, however, intended to function as Schenkerian analysis of these songs" (Idem: 27). His analyses do not attempt to reduce the musical surface to a Schenkerian background and do not even show a large-scale structure based in dominant-tonic relationships. So, directed tonal motion is not supposed to be in the music as a prerequisite. In fact, songs are usually classified according to the modal system. One can not even speak of backgrounds in these analyses, since the reductions are not carried out at deep levels: Moore presents just a middleground quite close to the musical surface. The criteria to make these reductions are only partially the same as those of Schenker's theory. He favours triad and triad-derived chords, recognises such basic voice-leading principles as neighbouring and passing tones and selects stressed or "salient" tones;for example, the tonic is identified by means of "metric, rhythmic and accentual modes of stress" (Moore 1992: 77).

In which sense can all these analyses be called Schenkerian analyses? We have seen how in its applications to popular music the principles of Schenkerian theory have been considered as axioms that may or may not be used, according to their fittting in the stylistic features of the music. But there are still some important Schenkerian principles that remain even in the least Schenkerian of these analyses. First, Schenkerian symbols, graphs and terminology prove to be useful in all these analyses. Second, there is still a search for consistent, mainly step-wise lines;especially in the upper-voice or melody; which in fact is meant to provide some coherence to the music. Third, hierarchical, generative, transformation-based structure of music is assumed by all of them in some degree, since some sounds are always selected as being more important than others, which elaborate them. However, this hierarchy is looser in the freest Schenkerian analyses: the number of possible structural chords and of possible combinations of them grows; the voice-leading rules are not so strict; and there is not a strict hierarchy of sounds;that is, diatonic triad are not necessarily more important than other chords, and neither dominant harmonies nor step-wise descents in the upper voice are emphasised in, for example, Moore´s analyses. Therefore, hierarchies can not be so easily applied to deep levels of the musical structure. Another kind of hierarchy is the reduction of music to two main lines, the bass and the upper voice, which is the same in all these analyses as in Schenker´s theory.

In short, the strong unity and coherence that Schenker´s theory reveals in music is retained in these Schenkerian analysis insofar as they are faithful to Schenkerian fundamental structure and voice-leading principles. So, when Schenkerian principles are partially left in order to approach other kind of music than the one Schenker dealt with, such unity and coherence must be either found by other means or given up.

So far, we have seen what Schenkerian analysts do when approaching popular music, but it is also interesting to see what they do not do. Some significant aspects of rock music are not emphasised by Schenkerian analyses because of their intrinsic limitations. First, rhythmic analysis of rock can hardly be carried out by Schenkerian analysis: the repetitive rhythmic patterns, the slight variations they undergo in the repetitions, and the contrast between, on the one hand, the rhythmic section and, on the other hand, the melody which avoid the beats by means of frequent syncopation, can not be properly addressed by a theory that sees rhythm as emerging from middleground pitch structure. Second, and more generally, all "secondary" parameters are considered just as "projecting" pitch structure, so that they can not be considered as much significant as they frequently are in rock music5 . And third, issues of form in rock music are neglected in Schenkerian analyses when form, as it often happens, does not emerge from large-scale linear-harmonically induced directed motion.

Schenker´s theory has been developed for Western art tonal music. It seeks to unveil a "deep structure" of the music which reduces a whole composition or movement;maybe twenty minutes long; to a few important "structural" events. This deep structure;the fundamental structure of Schenker´s background; symbolises a clear sense of directed motion from the beginning to the end of the piece.

We have seen how the attempts to extend Schenker´s theory leave its most obviously style-specific principles and try to retain the general structural framework of Schenkerian analyses;the hierarchical, generative, transformation-based structure; which is often implicitly understood as having some psychological, universal validity. However, much of what is usually assumed to be universally applicable, in fact originates from aesthetic norms tied up with Western art tonal music.

Schenker´s theory emphasises the fact that music tells us a story, with its beginning, development and end; a complete story, which does not need any other source than the music itself to be meaningful. But this kind of sustained musical flow is not characteristic of all music, but a historical contingency associated with absolute, autonomous Western "classical" music since the eighteenth century onwards.

However, even when dealing with this absolute music, there are some problems in the application of this theory. It focuses on harmony and voice-leading at a large level and consider any other musical parameters of musical form to be secondary or "surface" events. Now, the deep structure on which it is based, is not an obvious musical event: it must be discovered through analysis, and its effects on the music are not easily perceivable;except in the case of very short compositions. By contrast, the "secondary" parameters can be much more obvious. Therefore, these theories are the more useful when the "secondary" parameters of musical form enhance the deep structure; that is, when, for example, in the classical sonata form "the tonal plan [...] governs the disposition of themes and textures, the patterning of loud and soft and high and low, the pacing of climax and relaxation" (Cook 1994: 89).

But, since the second half of the nineteenth century onwards, simple, coherent deep structures of this kind are not so easily found. As an example, in his analysis of a passage from Stravinsky´s Concerto for Piano and Winds, Schenker himself "succeeded in proving;to his own satisfaction; that Stravinsky´s voice-leading, though it mimics tonal procedures, fails to create any kind of organic tonal hierarchy: the various prolongation spans just do not cohere at any level." (Fink 1999: 114). So, it seems that even for absolute Western art music, the search for deep structures by means of harmony and voice-leading is just one of the possible ways to organise large-scale structure. As for the repertory that Schenker´s theory focuses on, the existence of this kind of organisation of musical structure does not mean that music must be perceived in a way that emphasises this large-structure. Despite the efforts of analysts to show these non-obvious connections, most listeners seem to hear music in a way very much closer to musical surfaces6 : "The view of a Beethoven symphony as a chaotic and shifting assemblage of surface 'flows';transient, intense energy connections between 'partial objects', some in the piece, some in a listening consciousness; [...] does capture the fundamental contingency of musical experience." (Fink 1999: 137).

Surface events also seem to be more important than deep structures in most popular music. In rock music, for example, the continuous repetition of a short musical structure;usually composed of versus and refrain; and the use of very short harmonic and melodic patterns, guarantees a strong, obvious unity that does not need to be emphasised by means of any hidden relationships. As we have already seen, the absence of directed tonal motion in much of this music makes problematic the application of Schenker´s theory. Modified Schenkerian theory still develop hierarchical models based on harmony and voice-leading and they also focus on musical parameters which for popular music could in fact be considered as "secondary": when the music repeats the same harmonic and/or melodic patterns over and over again, the "surface" parameters become the more important. Thus, it can be said that this kind of analyses, and the aesthetic evaluation they imply, "leaves untouched those very factors where rock can be seen at its most interesting (and complex and profound): timbre, textures, sound manipulation, performance practice etc." (Moore 1993: 18).

Popular music has frequently been despised by Western theorists because of its "too" obvious unity and coherence, which is achieved by means of incessant repetition. The same can be said about most Western folk music and non-Western music, where "cyclical" forms -;that is, based on the continual repetition of a fragment; are widespread. But in these musical cultures, the aesthetic value probably does not lie in the unfolding of a "musical" story from the beginning to the end; rather, the pleasures people obtain from listening to music lie in the slight but important variations performers make on the basic patterns. The limits on the universality of such theories based on the characteristics of Western art music as Schenker's, then, are fundamentally those imposed by the model of the unified and coherent narrative.

However, maybe this is not even the most important point. Music is not always meant just to be listened to. Our Western art tonal music is the product of a music culture which approach music aesthetically;that is, which "interpret it in terms of a specific interest in sound and its perceptual experience" (Cook 1992: 7); and this is a "distinctly restrictive approach to music" which "leads to an unbalanced interpretation [...] of ritual, religious, and easy-listening music;all of which are intended not so much to be listened to, as to be experienced within a larger social context from which they derive much of their significance. Again, it finds little use for a great deal of Renaissance and baroque music, whose interest lies in the playing rather than the listening. And it is not even adequate as an approach to twentieth-century art music [...] While a work such as this [one of Stravinsky´s serial compositions] can be experienced simply as a succession of sounds, it is evident that the composer´s aesthetic attention was directed as much to the imaginary musical object delineated by the sounds as to the sounds themselves. It may be impossible for the listener to grasp this musical object without an analytical reading of the score." (Idem: 8).

Thus, music fulfils several different functions, and the function of "aesthetic enjoyment" is just one of the possible ones7 . It seems that our evaluation of music is related to how well it serves particular functions: "many of the arguments concerning the relative merits of different musics can be resolved into arguments concerning the relative merits of different functions, which thus becomes an ethical rather than an explicitly musical issue. 8" (Moore 1993: 27).

Therefore, the idea of analysis focusing almost exclusively on purely musical;audible; facts which lies at the core of Schenker´s theory, is strongly cultural-specific, and the translation of this idea to other musical cultures creates the risk of neglecting more important features of their music.

NOTES

1. Most of this article is taken from my dissertation "Universality versus Cultural Specificity in Analytical and Perceptual Approaches to Music: the Case of Unity and Coherence" (MA diss., University of Southampton, 1999). I am profoundly indebted to my supervisor Nicholas Cook because of the many suggestions he made for it, some of which were included literally.

2. To be sure, this analysts usually assume Schenker's aesthetic implication that their analyses reveal, at least in part, the aesthetic value of the music, as we will see below. What they do not assume is that only music from Bach to Brahms is aesthetically valuable and that only this music can be successfully analysed by means of Schenkerian techniques.

3. According to Schenker, repetition is one of the "forms of organic relationship which occur in true diminution" (Schenker 1979:98); for him, concealed repetitions -that is, the motivic relationships in the middleground or even between middleground and foreground that Schenker points out in his analyses- are more important than obvious repetitions in order to achieve organic coherence in music: "it was precisely these concealed repetitions which freed music from the narrowness of strict imitation and pointed the way to the wiedest spans and most distant goals" (Idem: 99)

4. These terms will be used here without distinction.

5. Shenker's theory focuses on pitch structure, especially harmony and voice leading. Therefore, other musical parameters -such as timbre, dynamics, texture, rhythm, register and so on- are usually considered as 'secondary' parameters in Schenkerian analyses.

6. This argument is widely developed in Cook 1992.

7. Alan Merriam proposes ten categories of function of music in Merriam 1964: 217-218.

8. Simon Frith develops a similar argument in Frith 1998.

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