With the sound of Stockhausen's Gesang der Jünglinge ringing in his ears from a radio broadcast, György Ligeti fled Soviet-invaded Budapest in November 1956. He arrived in Cologne a month later to work with Stockhausen himself in his studio at Westdeutscher Rundfunk, where this piece and others had been realised. From this key location, Ligeti was thrown into the middle of European high modernist composition, which was still preoccupied with the development of a post-Webernian serial method. Although Ligeti was in close contact with such figures as Boulez, Maderna, Nono and Stockhausen, conventional wisdom states that that he found little interest in the methods of integral serialism, preferring instead to forge his own path. However, in his first year in Cologne, he published his seminal analysis of Boulez' Structure 1a. It seems clear that serial method held some particular interest for him, at least at this early stage. In fact, his investigations of it almost took precedence over his composition at this time: Apparitions was not completed for a further year, and the electronic piece Glissandi was realised only a few months before the Structure analysis was published in 1958. In his 1974 article charting the origins of the total serial method, Richard Toop claims that the analysis was suggested by Stockhausen, then editor of Die Reihe, as a way to help Ligeti earn money. This may well be the case, but the modest financial rewards from publication in an avant-garde music journal do not by themselves account for the devotion and thoroughness lavished by Ligeti on his analysis. It seems reasonable to say that his earliest experiences with total serial music held some great fascination for Ligeti, a fascination he was eager to satisfy. Yet the question, also formulated by Toop, remains: why should such an apparently un-serial composer as Ligeti undertake such a piece of work at all, and to such a high degree of apparent enthusiasm?

In an attempt to clarify Ligeti's relationship to total serialism through the late 1950s and 1960s I will be investigating the influence the Bartók analyst Erno Lendvai had on Ligeti and his music, and contextualising this influence within high modernist Cologne. My purpose is to help to clarify Ligeti's compositional development in light of his parallel work as an analyst both in Cologne and in Budapest before his emigration.

Before he left Hungary, Ligeti had been Professor of Analysis at the Liszt Academy for six years. Lendvai was amongst his colleagues, working as a visiting lecturer from 1954. At this time, Lendvai was writing his two early, defining, works on Bartók, An Introduction to the Analysis of Bartók's Works and Bartók's Style, both published in 1955. It seems improbable that the two men did not share at least some of their ideas at this time. Indeed, in an interview with Péter Várnai published 1983, Ligeti states that he "was in complete agreement" with Lendvai's analyses. For all Hungarian composers of the 1950s Bartók, who had only recently died, was an inescapable spritual mentor, influence and challenge. Lendvai's analyses were the first successful attempts to reach a full understanding of his compositional technique. They have therefore held a certain fascination for a generation or more of Hungarian composers. In a currently unpublished paper given by Simone Hohmaier at the first international conference on György Kurtág at Balatonföldvár last year, the music of both Kurtág and Péter Eötvös was shown to have certain roots in common with a number of Lendvai's Bartók analyses. In particular Hohmaier drew attention to aspects of symmetrical construction and pitch expansion in the works of both these composers, which finds certain parallels in Lendvai's work. Perhaps the simplest example of this is in Kurtág's own 'Hommage à Bartók' from book 1 of his Játékok, [EXAMPLE] in which the symmetry of contrary motion is pursued rigorously outwards from middle C.

Further examples of Lendvaian thinking can be found in compositions by other composers such as László Sáry, who employs a Fibonacci series to determine the rhythmic proportions of his piece Csigajáték ('Snail Play') of 1973. While it would be rash to suggest at this point that Lendvai's writings served as some sort of compositional treatise for these individuals, it is true to say that as the first clear analyses of Bartók's compositional style they held an importance for anyone following in the composer's footsteps. While their worth to analysts today is debatable, there is little doubt in my mind of their value as a compositional resource and encouragement to young Hungarian composers. Far more than almost any other composer, the unique and revolutionary achievements of Bartók cast an overwhelming shadow over any composer succeeding him in Hungary. By turning to analyses such as Lendvai's, composers could fathom some of the fundamentals of Bartók's composition (at least as Lendvai himself saw them), and exploit or avoid them as they chose. As I now hope to demonstrate, Ligeti, at least for a time, chose to freely adopt a number of the theoretical models demonstrated by Lendvai.

Because the points I wish to make about Ligeti's employment of ideas derived from Lendvai are general ones applicable to much of his music of the period under discussion, I shall draw examples from a few pieces rather than focus on one individual piece in greater depth. These pieces are Apparitions of 1958-9, Atmosphères of 1961 and Continuum of 1968.

The fundamental principles of Lendvai's analyses of Bartók are built on the divisions of the golden section, and the fibonacci series of numbers to which this is related. From this position, Lendvai describes many of the scales, harmonies and formal structures of Bartók's compositional style. Lendvai is also concerned with symmetrical systems - something he believes is a rare common feature of both Eastern and Western European music - as evidenced in his development of the axis theory and its deployment in Bartók's music. Another striking, if contrived, image of symmetry is that produced when an ascending scale based on the intervals of the golden section is superimposed upon a descending acoustic scale. [EXAMPLE] My purpose here is not to provide a critique of Lendvai's methods, but to isolate those conclusions he reached which may have been of interest to a composer such as Ligeti. As I have said, there does seem to be a case for stating that a number of these analytical conclusions fed into the compositions of Ligeti and his contemporaries. What isolates Ligeti is that he was the only one of these composers, because of his emigration from Hungary, to carry these models into the late serial environment of Western Europe.

The use of golden sections in Ligeti's music is briefly documented elsewhere - Michael Hicks in his analysis of 1993 highlights the presence of one dividing the two main sections of Continuum at bar 126, a point musically highlighted by a change in figuration from narrow scales to broad arpeggios, and the first registration change of the piece. [EXAMPLE] However, in his analysis, Hicks also draws attention to other musical elements which would not look out of place in one of Lendvai's analyses of Bartók. These include a number of key harmonic fields, shown in example 4 [EXAMPLE]. In the first half of the example, Hicks isolates what he, and the composer, call a 'typical Ligeti signal', occuring at two key formal points of the work - at the start and the beginning of section two at bar 50. Hicks highlights the parallels between the beginnings of these two sections. I would further add to this the observation that the so-called 'Ligeti signal' is also a classic harmony of Bartók's drawn, as Lendvai argued, from the intervals of 2, 3 and 5 semitones - all numbers from the fibonacci series. Furthermore, the two 'signals' are related symmetrically to one another.

In his next paragraph, Hicks isolates another harmonic field, shown in the second half of example 4. This chord is described as being cadenced onto after a period of intervallic blurring throughout the second section, and is of structural significance because of its place as the final harmony of this section of the piece. However, if one puts aside for the moment the central blurring, the chord itself is a Bartókian major-minor chord, or gamma chord, familiar once more from Lendvai. Hicks even goes so far as to derive this chord's construction from the Ligeti signal chord as a pair of symmetrical 'unfoldings'; I would like to suggest that the connection between these two chords may find its precedent in Lendvai's writings.

Ligeti's pieces written immediately after his emigration from Hungary should show the greatest use of Lendvai's principles, since they would be freshest in Ligeti's mind. Indeed, in his interview with Péter Várnai, Ligeti talks of how the idea of applying the golden section as a principle of construction to his music was in his thoughts. He attempted to realise a work in the Cologne studio in which the proportions of the golden section were applied to harmonic partials, but the piece failed musically and was abandoned. However, the prevailing mood of total musical organisation which inspired this electronic experiment fed into his acoustic compositions of the time, not least of which was his first great orchestral work Apparitions. Ligeti himself acknowledges his use of golden sections in the construction of the first movement, which I will clarify here.

There are a total of 234 crotchet beats in the first movement, just one more than the perfect fibonacci number of 233. Since the quotient of two adjacent numbers in the fibonacci series approaches the golden ratio of their sum, for 233 crotchets the golden section falls at either 89 or 144 crotechets. Thus, the golden section of this movement of 234 crotchet beats falls at very slightly more than 89 or 144 crotchet beats in. Counting beats, then, we find that the 144th crotchet falls in bar 71, at the basses' tremolando. By Ligeti's own description, this movement falls into two parts: the first in the low register, the second in the high, with the golden ratio determining the lengths of the respective sections. At the point of the golden section, the music has come to the very lowest reaches of the modern orchestra: a bottom C on the double basses. However, as so often in Ligeti's music, this note is heavily blurred: in this instance by the C sharp one semitone above. This C sharp is itself lowered microtonally in the following bar, and both notes - at such a narrow interval and in such a low register - collapse into near noise, particularly with the addition of tremolo markings. The music disappears from the bottom end of the orchestra's compass, and even from the boundaries of discernible pitch to prepare the beginning of the second, higher register, section. This begins at bar 73 and features sustained pitches throughout its length as high in the orchestral range as the previous bass notes were low. [EXAMPLE] The golden section therefore marks the conclusion of the first section of the movement, and is highlighted by an extrapolation of both its register and its blurring of the noise/sound dichotomy.

Further examples of the use of a golden section to locate key structural points may be shown briefly on the following diagrams. [EXAMPLE] At bar 80, for example, the final section of 89 crotchets divides further into the fibonacci numbers 34 and 55, and this point is marked by a rapid outburst on harp, percussion and keyboards, after which the piece dissolves into little more than a single sustained cluster fading out to the work's end. The second diagram illustrates similar divisions which may be found in another orchestral work from this period, Atmosphères.

However, both of these works are considerably more complex than Continuum, and further analysis of the presence of golden sections falls outside the scope of my paper here, although Ligeti's own comments regarding Apparitions especially suggest that more may be found underlying the work's fundamental structure.

At this point, having established what elements of Lendvai's thinking Ligeti brought to his music in Cologne, I wish to investigate how these ways of thinking influenced his confrontation with total serialism.

Ligeti's reading of the methodology of total serialism may be inferred from his analysis of Structure 1a. He very quickly abandons point-by-point description and analysis of pitch relationships, to consider form, duration, density and texture. In this analysis, the actual content of the row is pushed further and further into the background, to be eventually replaced by monochrome blocks on graphs [EXAMPLE] in which the global character of each statement of the row is considered, and not the details within each of those statements. Of course, the passacaglia-like nature of Boulez' piece, in which the row is successively stated in all of its inversions and transpositions, lends itself to such an analysis. However, it is not the only necessary reading of the piece. Marc Wilkinson's analysis, published in the same year as Ligeti's, takes a very different approach. Although his analysis is not as thorough, Wilkinson deals much more carefully with the consequences deriving from the local details of the row itself - certain symmetries arising from notes a major third apart, for example - making the content of the row the focus of his study, and not the greater structure in which the row functions, as Ligeti does. If we imagine a number of levels of compositional construction - analogous to a Schenker diagram - in which a composer may impose his will to a greater or lesser extent, then Wilkinson deals principally with the lowest levels of this structural hierachy: the pitch and duration content of the row, and the melodic-harmonic interactions which result. Ligeti's analysis however focusses on the central levels: once he has made the necessary comment that Boulez' row is a quotation from, and homage to, Messiaen, he almost entirely disregards the pitch and durational content of the row. (Although towards the end of the analysis he does draw attention to some local detail, this is generally with a view to illustrating a more global point.) And aside from very general, and somewhat unsatisfactory, observations on the fluctuation of densities with each restatement of the row, scant attention is paid to the very highest structural level of the piece. Alongside the obvious interest and admiration for the workings of the piece's intermediate structural levels, there seems an inferred dissatisfaction with its most local and most global structural elements, and their interaction within a top-to-bottom compositional process.

The sense one gets from reading Ligeti's analysis is that Structure 1a is a piece which functions in a way similar to a clockwork toy: once it has been wound up, it is switched on and left to run automatically until the end. This is a criticism often levelled at the piece. Ligeti himself has never been averse to using pre-compositional procedures in his music (even once, in Poème symphonique for 100 metronomes, picking up on the clockwork analogy), but he has never employed integral serialism even though as a young and impressionable man he was surrounded by its leading practitioners. I believe that the reason for this may be found between the lines of his Structure analysis.

Returning to Lendvai, behind his belief in the golden section as a key musical building block is his assertion of the difference between arithmetic and geometric series. The example he gives of the difference between the two is as follows. In the case of a Mozart theme, for example, in order to attain balance there is a symmetrical division of phrases into two- and four-bar lengths: this follows arithmetic laws, as each phrase is created by the addition of regular units. However, the use of the golden ratio to divide a phrase follows geometric principles, since it cannot be expressed as a rational fraction, and is best expressed as a geometric shape. More interestingly, when employing a geometric system such as the golden section, one is able to begin from a total duration and subdivide down to the smallest level of construction, ie top down; or start from the smallest unit and work up to a total duration, ie bottom up to the highest structural level. The point is that the golden section principle can be applied on all levels of the composition - as Lendvai suggests it may be in Bartók's music and as we have seen between a number of Ligeti's pieces. In this respect it provides a much more satisfactory and rigorous global process than the arbitrary arithmetic of integral serialism. After all, although the length (and highest structural determinant) of Structure 1a is governed by the repetitions of the row in all of its 48 standard permutations, even this number is fairly freely chosen: why not use just the 12 transpositions, or the even just the four inversions to each achieve an equally 'complete' effect? In a work such as Continuum I have hopefully illustrated how Ligeti uses as a basis for this music a much more thorough compositional process than that provided by integral serialism, one in which the same rules govern the local harmonies and the most global structures: both the lowest and highest structural levels of composition find their parallels in Lendvai.

Much of the interest in Ligeti's music is found in the tension between process and invention, and the exploration of this is the stated aim of his Structure 1a analysis. That article is subtitled 'Decision and Automatism', and Ligeti's thrust is to find the points in Boulez' system in which the composer, or chance, have intervened. This is the 'clocks and clouds' duality alluded to later in Ligeti's output. What I would suggest is that in integral serialism Ligeti found a method which was paradoxically not systematic enough at its core for him to make use of. In order to create the tensions felt in a slowly decaying and flawed system - an aspect of Ligeti's music which has persisted throughout his career - the background system must be as rigorous and determined as possible. Ligeti's analysis describes Structure 1a as relatively indeterminate at its highest and lowest structural levels, and perhaps this is the root of his dissatisfaction with serial method per se. His reading of the piece would certainly suggest a frustrated intrigue with the methods he draws from it. Dissatisfied with the compositional implications his own analysis of European integral serialism has uncovered, Ligeti seems at this moment of confrontation to have turned to an apparently more thorough and flexible methodology derived in part from his background in Hungarian analysis, and the world of Lendvai and Bartók.