Aldo Clementi’s System; and an original composition, Variazioni su AlDo ClemEnti for chamber orchestra
A Dissertation
Presented to
The Faculty of the Graduate School of Arts and Sciences
Brandeis University
Music Theory and Composition
Yu-Hui Chang and Allan Keiler, Advisors
In Partial Fulfillment
of the Requirements for the Degree
Doctor of Philosophy
by
Michele Zaccagnini
August 2014
The signed version of this form is on file in the Graduate School of Arts and Sciences.
This dissertation, directed and approved by Michele Zaccagnini’s Committee, has been accepted and approved by the Faculty of Brandeis University in partial fulfillment of the requirements for the degree of:
DOCTOR OF PHILOSOPHY
Malcolm Watson, Dean Graduate School of Arts and Sciences
Dissertation Committee:
Yu-Hui Chang, Music
Allan Keiler, Music
Eric Chasalow, Music
Joshua Fineberg, Music, Boston University
Copyright by
Michele Zaccagnini
2014
Acknowledgements:
I would like to express my deepest gratitude to the Brandeis University music faculty in particular to Allan Keiler for his invaluable guidance in writing this dissertation; Yu-Hui Chang for the insights; Eric Chasalow for his positivity; Martin Boykan for the all the years of help and wisdom and David Rakowski for his competent humor.
This project could not have been successful without the help of my uncle Guido Zaccagnini whose passion for Clementi’s work and message has inspired me to undertake this task. I would like to express my gratitude to Anna Clementi for granting me access to Aldo’s sketches, Garbiele
Bonomo at Suvini Zerboni for the initial inputs, Maria Rosa De Luca at Università di Catania and Manuele Morbidini.
On a personal level I am grateful to have had the support of my family, my parents Paolo and
Antonella, my brothers Carlo, Davide and Giovanni and my partner Zeynep Soysal.
iv ABSTRACT
Aldo Clementi’s System
A dissertation presented to the Faculty of the
Graduate School of Arts and Sciences of Brandeis University
Waltham, Massachusetts
By Michele Zaccagnini
The composer Aldo Clementi left a significant body of work behind, which holds an important place in the musical landscape of the second half of the twentieth century. The research assesses the work of the composer within the musical landscape of the post-war avant- garde as he quickly parted from the aesthetics of his contemporaries to form a peculiar “third way” out of the musical impasse. In the transformed socio-cultural landscape of his times,
Clementi articulated a clear musical thought loaded with eschatological implications about the new role of music. Clementi incorporated in his composition some of procedures derived from a visual approach. An important explanation of the workings of the “magic square,” a pseudo- cartesian compositional tool is, therefore, contained in the research.
The research focuses on one piece, Aus Tiefer, composed in 2004 as an homage in memory of composer Luigi Nono, assessing possible implications of Clementi’s idiosyncratic approach in today’s computerized world and compatibility with the so-called algorithmic composition. In particular, the paper will point out the most compelling aspect of the composer’s oeuvre: its fascinating exploration of boundaries between simplicity and complexity at a perceptual level. A
v seemingly far-fetched parallel with mathematician Stephen Wolfram and his work on “cellular automata” will describe Clementi’s particular approach to the simple/complex dichotomy.
The original composition Variazioni su AlDo ClemEnti relates to Clementi’s aesthetic in its attempt at avoiding a linear-chronological flow of musical events. Both components of my dissertation, the essay and the original composition, are linked at their core in their dealing with the general idea of discursiveness in music.
The original composition creates stasis in the form of repetitiveness as opposed to simple, verbatim repetition. The repeating musical elements are algorithmically organized and continuously rearranged to convey a sense of “dynamic stasis” or “static motion.”
vi Table of Contents
Aldo Clementi’s System
1. Chapter 1
1.1. Introduction p. 1
1.2. Biographical notes p. 2
1.3. Music’s loss of innocence p. 3
1.4. Clementi and Adorno p. 6
1.5. Survival of the craft p. 8
1.6. Going visual p. 10
1.7. Erasure of time p. 15
1.8. Conclusions: The (ir)relevance of the composer’s philosophical views p. 17
2. Chapter 2
2.1. Aus Tiefer: a case study p. 21
2.2. Saturating intervals through the “magic square” p. 27
2.3. Visual appeal of the magic square p. 33
2.4. The algorithm p. 36
2.5. Conclusions p. 54
3. Chapter 3
3.1. Un dolce naufragio p. 57
3.2. Repetition and musical narrative p. 59
3.3. Aus Tiefer: a narrative of deception p. 61
3.4. Different layers of repetition p. 63
3.5. Conclusions: Clementi’s sonic automata p. 73
4. Original composition: “Variazioni su AlDo ClemEnti” for chamber orchestra p. 80
vii List of illustrations
Fig. 1 Chorale's theme, divided into fragments p. 22
Fig. 2 Second theme varied. p. 22
Fig. 3 Organ's chorale p. 22
Fig. 4 Canon levels (III) (courtesy of ed. Suvini Zerboni, Milano) p. 25
Fig. 5 An example of a sketch of the Magic Square p. 28
Fig. 6 First theme's numbering (pitch level 7) p. 28
Fig. 7 Transformation matrixes p. 29
Fig. 8 First theme represented in the square p. 30
Fig. 9 Layering of the 1st theme on levels F# and G p. 31
Fig. 10 Intervallic densities (from X to XIX they repeat as a palindrome) p. 35
Fig. 11 Gradual increase of density p. 36
Fig. 12 Translating a melody into a set of intervals with OM p. 38
Fig. 13 The self-intersection matrix algorithm p. 39
Fig. 14 First theme setting p. 43
Fig. 15 First theme and its inversion on F# p. 44
Fig. 16 Poly-intersection matrix's algorithm p. 46
Fig.17 Second theme's setting p. 53
Fig. 18 René Magritte, The Treachery of images. 1929. Oil on canvas. 63.5 cm p. 73 × 93.98 cm (25 in × 37 in) Los Angeles County Museum of Art, Los Angeles, California
Fig. 19 - Cellular automata p. 76
Fig. 20 - Aus Tiefer (courtesy of ed. Suvini Zerboni, Milano) p. 76
viii
List of Tables
Tab.1 Palindromic organization of themes p. 23
Tab. 2 Numeric system p. 28
Tab. 3 Self-intersection matrix (1st theme) p. 40
Tab. 4 Poly-intersection matrix: first theme and its inversions p. 47
Tab. 5 Self-intersection matrix 2nd theme p. 50
Tab. 6 Poly-intersection matrix 2nd theme p. 51
Tab. 7 Repetitive/deceptive constructions p. 64
Tab. 8 Sonic shape similarities p. 69
Tab. 9 mid-macro equalities p. 69
ix Aldo Clementi's System
Chapter 1
1.1. Introduction
Italian composer Aldo Clementi, who passed away in 2011, has left us with a substantial oeuvre. Though not a household name in the contemporary music scene, he maintains a solid reputation as a consistent and uncompromising composer whose musical thought never waivered through the decades.
This work explores Clementi’s compositional process with an unprecedented attention to the minutia of its workings.1 It will also attempt an assessment of the composer’s oeuvre in today’s musical landscape. My research has been blessed with a crucial and unprecedented privilege. Anna Clementi has let me into her father’s studio,2 free to explore his sketches, the collection of which has been recently acquired by the Sacher Foundation in Basel.
I will begin by describing the composer’s general aesthetic. Understanding the composer’s aesthetic, mainly through his own words, will be helpful in understanding his modus operandi. To
1 The existing scholarship that dealt with the composer’s process, mainly Gianluigi Mattietti’s monographic research (Gianluigi Mattietti,. Geometrie di Musica: il Periodo Diatonico di Aldo Clementi. Lucca: Libreria musicale italiana, 2001) have fallen short of correctly describing compositional techniques such as the “magic square,” which the composer often mentions as a go-to place to begin his work. This research makes up for the lack of scholarship on the matter. 2 Accessing the composer's workshop on the Via Cassia in Rome has been an exalting experience, rich in findings and discoveries a sort of “treasure island” moment for the contemporary music scholar. For such privilege my unlimited gratitude goes to the composer's daughter, Anna Clementi. I also wish to acknowledge and thank Guido Zaccagnini, one the composer's pupil and, incidentally, the uncle of who writes, for the crucial guidance throughout my research.
1 better observe the composer at work, I will focus on one particular piece, Aus Tiefer, an
important work of the composer’s late period.
To assess the composer’s legacy is possibly the most ambitious goal of this research, which
will be articulated along two different lines of thought. Firstly, I will describe possible implications
of Clementi’s idiosyncratic approach in today’s computerized world and compatibility with the
so-called algorithmic composition. To do so I will recreate the composer’s compositional process
through a software simulation3.
Secondly, I will point out what I believe is the most compelling aspect of the composer’s
oeuvre: its fascinating exploration of boundaries between simplicity and complexity at a
perceptual level. A seemingly far-fetched parallel with mathematician Stephen Wolfram and his
work on “cellular automata” will describe Clementi’s particular approach to the simple/complex
dichotomy.
1.2. Biographical notes
Aldo Clementi was born in Catania, Sicily, in 1925, where he received training in both
piano and composition. He died in Rome on March of 2011. A gifted pianist, he pursued both
the path of piano performance and composition, to eventually dedicate himself solely to the
latter.
His first composition teacher, Alfredo Sangiorgi, the only Italian composer to have been a
pupil of Arnold Schoenberg, introduced him to the atonality of the Second Viennese School.
3 I have used Open Music an algorithmic composition tool. The procedures can be easily replicated in other software environments or programming languages. While the composer positively proceeded with the sole help of pencil and paper, the use of the computer greatly and effectively helped expedite and filling in the gaps of my research material. In today's computerized world anybody can perform highly complex operations in real time. In music, composition programs have been developed to take advantage the capabilities of computer's processors to present composers with results that would have taken weeks or months to develop on paper.
2 After earning his diploma in 1954, he moved to Bolzano and then to Rome, where
Goffredo Petrassi, an internationally renowned composer and teacher, and a sort of “father figure” of the contemporary music scene4, invited him to attend his advanced composition classes at the Santa Cecilia Conservatory.
Another influential composer, Bruno Maderna, introduced Clementi to new techniques of composition. The Internationale Ferienkurse für Neue Musik in Darmstadt, which he attended between 1955 to 1962 is now considered a focal point of musical avant-garde. In Clementi's own
Sicily, a similar venue took place between 1960 and 1968: the Settimane internazionali Nuova Musica of Palermo which is now regarded as the Southern European twin of the Darmstadt festival. A very active composer at the time, Clementi presented several pieces in both venues. These experiences aesthetically forged his early compositions.
In the Darmstadt school and on a lesser level in the Palermo festivals, the prevailing aesthetic was one of total organization of the musical material. The idea of total control over the material was instigated by thinkers like Theodore Adorno and concretized in music by composers such as Olivier Messiaen, Luigi Nono, Pierre Boulez and Karl-Heinz Stockhausen: the compositional processes took the name of “serialization” and composers who used such process defined themselves alternatively as “post-Webernians” or “hyper-structuralists”.
1.3. Music’s loss of innocence
It's true: art and music are dying of saturation. Therefore either one has the courage to be silent, or can continue to do things […] that express the agony and the dissolution of the represented object.5
4 Among his pupils we find Franco Donatoni and Ennio Morricone in Italy, but also international figures such as Elliot Carter and Peter Maxwell Davis. Carter, in particular, dedicated more than one piece to his former teacher. 5 “E’ vero: l’arte e la musica stanno morendo per saturazione. Allora, o si ha il coraggio di stare zitti, oppure si continua a far cose […] che esprimono proprio l’agonia e il dissolvimento dell’oggetto espresso” Michela
3
In interviews and writings, Clementi often explained how music as an art-form capable of universal masterpieces was in a state of dissolution; such conviction came about gradually but inevitably and eventually became the centerpiece of his aesthetic.
In retrospect, the bleakness of this idea, put in the context of the composer’s musical fortunes, seems striking. Clementi had been blessed throughout his musical education and career with many fortunate encounters and an enviable amount of recognitions. From Petrassi to
Maderna to Adorno, Clementi received a musical education that could have hardly been more rich and refined. His personal relations with intellectuals of the caliber of Cage and Nono, provided him with precious interlocutors. Furthermore, since the early sixties the composer’s work had been gaining an increasing well-respected reputation. Yet, despite such an enviable position as a contemporary composer of his times, his pessimism never receded from the relentless tones of the above quote.
To be fair, pessimism and mistrust in the socio-economic transformations of the post-war years was a widespread sentiment among European intellectuals. The transformations that mass- production and technological advancements brought into the various art-forms did not go un- noticed.
Such issues became the object of a famous trilateral dialogue between two philosophers of the Frankfurt’s school of critical theory, Walter Benjamin and Theodore Adorno, and the playwright Berthold Brecht. The mechanical reproduction of art-works resulting from technological advancements such as photography, pre-recorded music and cinema undermined what Benjamin defined the “aura”6 of the work of art. Renzo Cresti’s in his monographic work
Mollia, Autobiografia della musica contemporanea (Cosenza: Lerici, 1979) (my translation) 48-55: 48. 6 The term comes form another major exponent of the Frankfurt school of Critical Theory: Walter
4 on Clementi, interpreted the preoccupations of contemporary artists:
The language becomes functional, similarly to the one of advertisement and it becomes “anti-critic;” a language based on stereotypes that proceeds with tautologies and labels so to be better integrated with industrial and political power.7
According to these thinkers, if music and art in general were to be inserted into the mechanisms of mass-production, their very nature would undergo a radical transformation: they would eventually be turned it into commodities. In today’s context, looking at the ways music is marketed, we notice how such preoccupations were more than justified. To take a concrete contemporary example, the most recent developments in music marketing techniques, such as the online store ITunes, relentlessly promote accessibility. But easing access generates compartmentalization, i.e. the organization of music into categories and subcategories to facilitate consumers’ access. The composer who aspires not to be included in any genre, i.e. to deliver a universal message not related to the utilitarian logic of the commodity, is therefore forced to duck and zig-zag through the stereotypes and labels of the “culture industry” in a desperate attempt not to fall into the anonymous wheels of mass-production.
Clementi seemed to agree to the general terms of the discussion:
Not anymore is the musician a beacon that guides the whole of humanity, as in the beautiful Romantic era. Mankind does not seek art anymore but only comfort, practicality, pleasure and entertainment. One has to have the courage to admit that there is no more need for art.8
Benjamin. Benjamin famously addressed the issues discussed in these paragraphs in the essay “The Work of Art in the Age of its Technical Reproducibility.” (London: Penguin, 2008) While a mention of Benjamin’s seminal essay cannot be omitted here, a thorough discussion of the matter and interpretation of Benjamin’s though is beyond the purpose of this research. Nonetheless one can safely assume how the composer was familiar with the writings and thought of Benjamin. 7 “Il linguaggio viene funzionalizzato, secondo una tecnica molto simile a quella publicitaria, e diventa irremediabilmente anticritico, un linguaggio stereotipato che procede per tautologie ed etichette pe rmeglio integrarsi col potere industriale e politico” Renzo Cresti, Aldo Clementi: studio monografico e intervista. (Milano: Edizioni Suvini Zerboni, 1990)(my translation and italics) 8 “Il musicista non é più una specie di faro che illumina tutta l'umanità, come ai bei tempi dei romantici. L'uomo non cerca più l'arte, ma il comfort, la praticità, il piacere, il divertimento. Bisogna avere il coraggio di
5 1.4. Clementi and Adorno
Clementi’s pessimism can be traced back to his early years’ feeding grounds: “if my music lacks theatrics, effects, neoclassical optimism and any useless positivity, it is mostly because of the influence explicit or implicit of Adorno’s thought.”9
As we will see throughout this research, Clementi was greatly influenced by Adorno.
Clementi’s first encounter with Adorno’s thought dates back to when he attended the philosopher’s lectures in Darmstadt in the late fifties and early sixties. It seems appropriate to outline some of Adorno’s thoughts about music in order to understand Clementi’s aesthetic.
Adorno, applying his own brand of the Hegelian dialectic (defined as “negative dialectic”) saw no other alternative for the modern composer but to choose complete isolation from the principles of mass-production. The composer had to emancipate his role from the logic of mass- production and principles of profit and pursue the telos of music – which is vaguely identified by the philosopher as the pursuit of truth and progress.
The new aesthetic the philosopher had in mind was that of the Second Viennese School.
This latter was built on the rational idea of series and showed overt fascination with complexity.
In the first chapter of Philosophy of New Music, “Scheonberg and Progress,” but also in Thomas
Mann’s Doctor Faustus, the philosopher described the goal of this new kind of music as the goal of knowledge: “[Art] as knowledge […] becomes radical in that moment in which is no longer content with itself as such” furthermore “only in the sphere of necessity […] is art able to
ammettere che di arte non c'e' più alcuna necessità” Enrico Cavallotti, Aldo Clementi: verso la morte della musica. (In Il Tempo, Roma, 22 dicembre 1977) (my translation) 9 For further reading about the influence of Adorno see Meditazioni sulla musica offesa Raffaele Pozzi in Maria Rosa Luca, Canoni, Figure, Carillons: Itinerari della Musica di Aldo Clementi : atti dell'incontro di studi, Facoltà di lettere e filosofia, Catania, 30-31 maggio 2005. 1. (Milano: Suvini Zerboni, 2008)
6 appropriate the power of objectivity that ultimately makes it capable of knowledge.”
The inevitable consequence for the Adornian composer was to be in strident opposition with the general taste. In fact, according to Adorno, an inevitable consequence of the new aesthetic was that the general public would not accept this new kind of music.
After laying out the general principles of his new music aesthetic, though, Adorno sent out mixed signals about the procedures that the composer was to adopt. While he authoritatively stated “[the artist] is no creator” and the composition is “nothing but solution to technical puzzles and the composer is the only one who knows how to decipher them and understand his own music,” he then went on to harshly criticize the extreme rationality of those who extended
Shoenberg’s idea of series to all the controllable musical parameters, not only pitches but also rhythm and dynamics. It was probably hard for the composers that called themselves post-
Webernians to read how, in his essay The aging of New Music, Adorno dismissed all that had been produced by the Darmstadt experience as a betrayal of New Music's mission: because of the excessive reliance on mechanical processes compositions had been reduced to mere acts of
“scholasticism.”
Even if in the meantime the raw material of composition was purified of slag and unhomogenous vestiges of the past, […], it is still questionable whether such a purification of all disturbing intrusions would be of service to the cause of music, and not simply to a technocratic attitude, in whose eager concern for consistency something entirely too binding, violent and unartistic announces itself.10
According to Adorno the dismissal of past canons and establishment of a new rational
“technocratic” rule for composition was therefore not enough to open the door to a “brave new
10 Theodor W. Adorno, Richard D. Leppert, and Susan H. Gillespie. Essays on music Theodor W. Adorno ; selected, with introduction, commentary, and notes by Richard Leppert ; new translations by Susan H. Gillespie.. (Berkeley, Calif.: University of California Press, 2002)
7 world” of music: thus far such procedures had produced “no valid accomplishment, no rounded masterpiece.”
The application of Schoenberg’s idea of series to all of the musical parameters (not only pitches but also durations, dynamics and timbers) had transformed the work of the composer to the one of the compiler.
Clementi’s early aesthetic is indebted to the hyper-structural Darmstadt aesthetic. It was perhaps out of frustration for the confusion generated by Adorno’s powerful but unclear words that he decided to embark on a different path. While he saved the Adornian negative view of the fruition of art in modern society, he did not buy into any of his progressive views. Clementi thus subtracted teleology from the Adornian equation metaphorically – thereby sealing Pandora’s box before Hope could come out. Compared with the high stakes that Adorno put on the role of the modern composer, Clementi saw his act as fundamentally useless: an utterly decadent, almost inglorious practice of fiddling with remnants of a formerly glorious art-form.
1.5. Survival of the craft
The composer writes:
There exists no contradiction between a pessimistic and apocalyptic view on the future of art and the need to correctly put notes together to continue a precious musical craftsmanship. For many the crisis of art becomes an alibi.11
Clementi was consistent with his negative aesthetic when he abdicated his role of a composer and humbly, degraded his role to the one of an artisan assembler of musical objects.
11 “Non c'è contraddizione tra una visione pessimistica, o apocalittica, sul futuro dell'arte e l'esigenza di mettere bene insieme le note, il desiderio di continuare un prezioso artigianato musicale. Per molti la crisi dell'arte diventa invece un alibi” Cavallotti, Aldo Clementi
8 In other words, given the asserted impossibility of creating truly new art works in the field of music, Clementi settled for a lower form of art: artisanship.
In truth, though, the supposed reconciliation between an apocalyptic view of the future of music and the justification of the need for a compositional craft is, logically speaking, a contradiction. After all, if the future of music was hopelessly doomed, then why bother composing? In other words, if the crisis of art were an alibi for modern composers’ lack of exactitude, wouldn’t craftsmanship, however correct and precious, be an alibi itself in the face of an inevitable extinction?
Clementi’s claim that such artisanship should be “correct” seems even more contradictory. In this vague characterization, it is easy to spot an un-resolved love affair with the
Adornian modernistic aesthetic of the composer’s early years.
Before I proceed further on this line of thought, let me take a step back and put the composer’s words in their appropriate context. These were words spoken from an artist’s own manifesto: they are meant to assert a worked-out aesthetic point of view and clarify its nuances.
Therefore it would not be correct to simply dismiss them as contradictory.
To fully understand this contradiction is to understand Clementi’s originality against the two mainstream aesthetic of the second half of the 20th century: modernism and postmodernism.
The exclusion of any possible teleological goal or progress of music marked Clementi’s rejection of modernist orthodoxy, while the need for correctness stands in sharp contrast with the postmodernist aesthetic.
9 Perhaps Clementi’s music should be considered in its own aesthetic category. In this regard, David Osmond Smith cleverly defined Clementi’s pieces as “monuments to the death of music.” The word “monument” might be a bit misleading since there is no actual celebration of past glories of music: for this reason Clementi, who considered the romantic era the apex of music, always refrained from using themes form his favorite Romantic composers. But the imagery of a monument is illustrative of another aspect of Clementi’s music: the chisel-work and planning that characterized their construction. The reconciliation of the seeming contradiction happens within the aesthetic of the monuments to the death of music.
Ultimately, the reconciliation of the dichotomy of a dying art and the need for a continuing craftsmanship happened within the meta-musical realm that Clementi created.
1.6. Going visual
It was because I was acquainted with the Informel and Materism in paintings, of which I could not see a correspondent in music, with their abolishment of contrasts […] that I considered a start from scratch.12
Clementi’s infatuation with visual arts dated as far back to his studies with Petrassi, an art lover and connoisseur himself. Since his young years, he entertained friendships with painters such as Achille Perilli (whose paintings are generally labeled as Geometric Abstractism, a movement related to Supermatism) and Piero Dorazio. Clementi, as one can infer by the above quote and other interviews, was convinced that visual arts had in somehow surpassed music in their quest for an aesthetic re-invention.
12 “Furono l'Informale e il Materismo in pittura (di cui non vedevo un reale equivalente nella musica) e i relativi postulati circa l'abolizione dei contrasti (a compartimenti stagni lungo l’arco formale) e della dialettica dell'articolazione – tutti stanchi residui di una mentalità ancora fondamentalmente neoclassica – a farmi seriamente considerare la necessità di un riinizio da zero” Mario Bortolotto,. “Intervista con Aldo Clementi.” (In Lo Spettatore Musicale, 5, 1967) (my translation)
10 The intersection between the musical and visual was certainly not a new idea and had often been of fecund consequences in the past.13 Regarding this relation in the post-war years,
Gianfranco Vinay notices:
Since at the beginning of the past century painting renounces to figurative representation and music to tonality […] the [subsequent] sense of vertigo […] brought a need for mutual verification and support [...].14
Clementi’s rigorous aesthetic played a major role in the implementation of the cross- disciplinary aesthetic. Some of the elements of the paintings that fascinated him became the means, the nuts and bolts, colloquially speaking, with which he executed his negative convictions.
But how to aurally represent the erasure of music? Which visual procedures could the composer incorporate and imitate in his own process?
Clementi developed different approaches, which ultimately defined the periodization of his oeuvre. Such periodization was agreed upon (if not stipulated by) the composer himself.
i. Structural: 1956-1960
ii. Materic informal: 1961-196415
iii. Optical a-formal: 1966-197016
iv. Diatonic: 1970-2011
The first period is indebted to the Darmstadt experience of which I have already talked
13 The case of Debussy’s impressionism or Schoenberg’s passion for Kandinsky’s abstract paintings is significant in their temporal proximity with our case. 14 “All'inizio del secolo scorso, la pittura rinuncia alla figuratività e la musica alla tonalità e ai princìpi elaborativi fino ad allora vigenti, il senso di vertigine determinato dall'infrazione di precedenti convenzioni ed equilibri, ha creato esigenze di verifica, mutuo sostegno ed enfatizzazione”. Gianfranco Vinay in Gianmario Borio, L' orizzonte filosofico del comporre nel ventesimo secolo: [collection of papers from the conference "L'Orizzonte Filosofico del Comporre nel Ventesimo Secolo - The Philosophical Horizon of Composition in the Twentieth Century", Venezia 2000]. (Bologna: Società Ed. Il Mulino, 2003) 397-405 (my translation) 15 The terminology here is derived from visual arts as a combination of “materic painting” (Achille Perilli) and “non formalized art” (Michel Tapié). 16 Again here the reference is to visual arts as enacted by painters such as Piero Dorazio, Victor Vasarely.
11 about.
The Materic-informal period contains three major pieces: Informel 1 in 1961, Informel 2 in
1962 and Informel 3 between 1961 and 1963. In 1961 his theatrical work Es was staged in Rome with the visual contribution of his friend Achille Perilli.
It was, again, Adorno’s influence that pushed the young Clementi to embrace the informal aesthetic. In 1961 his Darmstadt lecture “Vers un musique informelle,” Adorno had proposed for the composers to embrace the so-called “Art Informelle.”17 The expression was not new, the philosopher had appropriated the term from Michele Tapié who used it to describe a certain aesthetic that characterized the American movement of Abstract Expressionism (Jackson
Pollock, Willelm De Koonig and Mark Tobey) and the European Tachisme (derived from the
French word tache (stain) included Jean Fautrier, Hans Hartung and Serge Poliakoff), and translated it into music. He aimed at instigating the production of a kind of music that had not been produced yet and had to have “no form”, refusing any of pre-given aesthetic code including the one that emerged from Darmstadt.
To better understand the aesthetic of the Informel in visual arts, let me refer to the description that Gianmario Borio gives in his paper “Tangency between music and painting: the
Informel”. Describing the New York school of Abstract Expressionism, Borio characterized it as a product of a synthesis of two European tendencies: expressionism and surrealism. From the first the New Yorkers took the gestural character and the expressive force that emanates from the work. The impulse, Borio continues, is generated not by a deformation of reality like in Klee or
Kandinsky but by the matter itself, by the vitality of the act of painting:
The acceleration of the painting gesture excludes mental processes and commonly known
17 For more information: Manuele Mobidini, Musiques informelles. Il concetto adorniano e l'opera di Aldo Clementi. (Università degli studi di Siena, 2010)
12 images. The canvas becomes a seismograph that captures the psychical motions in their immediateness. Mobility is then one of the distinctive features of the informel.18
The aesthetic of the Informel fascinated Clementi for its negative qualities of complete erasure of (recognizable) forms. There existed a possible overlap then between the Informel and
Clementi’s macabre representation of the end of music, and Clementi attempted at exploiting it.
In particular the idea of contiuum that the non-formalized aesthetic encompassed seemed to enthrall the composer. Clementi’s new mission became then to translate continuum into music: the composer ultimately concretized this general idea into an actual procedure of complete abolishment of contrast in his music. The “start from scratch” mentioned in the quote refers to this very compositional procedure; the following quote shows the degree of commitment that the composer put into this task:
The misunderstandings are generated by those who think, if sub-counsciously, of music as “discourse” inadvertently making it a caricature of an arch that describes a useless orgasm. Exaltation and depression are close chapters, no matter how disguised they might be, they are modest symbols of an extinct dialectic. A forte followed by a piano, a high note followed by a low one, a “sweet” timber followed by a “raw” one are in themselves a sonatistic cell of the greater Sonata Form [...].19
In this quote the composer’s view is evident as radical as it is uncompromising enumerating all the different instances of contrast that his music had to avoid: dynamics, timbric colors, pitches cannot be used as “effects” to surprise the listener to establish a dialogue between elements.
To achieve his goal, the composer had to completely restructure his method of composition, but the so-called “magic square,” a compositional technique that he learned from
18 “L'accelerazione dell'attività pittorica permette di mettere fuori gioco processi mentali e immagini condivise; la tela diventa un sismografo che coglie I moti psichici nella loro istantaneità” Borio, L' orizzonte filosofico del comporre nel ventesimo secolo (my translation). 19 “Gli Equivoci nascono solo da quanti, anche inconsciamente, pensano la Musica come discorso e quindi, non accorgendosene, come caricature di un arco che descrive un inutile orgasmo. Esaltazione e depression sono capitol chiusi” Mollia, Autobiografia della musica contemporanea. 48-55: 48 (my translation)
13 Maderna and that he used throughout his serialist period remained an important part of his process. The study of the workings of this technique will occupy the majority of the next chapter.
For the moment, let me briefly explain its logic to notice how this technique had in itself a strong visual appeal. The square consisted of a twelve by twelve space traced on checkered paper; in such space, musical ideas could be graphed by means of their intervallic content, visualizing them as shapes capable of being flipped, rotated and transformed. It would not be far-fetched therefore to say that the magic square had been the first germ for Clementi’s expanding visual approach.
But, as the above periodization suggests, a systematic incorporation of visual procedures into his work began only in the early sixties. These procedures allowed the composer practically incorporate the aesthetic achievement of Abstract Expressionism and Geometric Expressionism into his work. This is notable in the use of large sheets of graph paper where he drew shapes that would contain musical textures. To achieve the desired textures he made extensive use of the magic square. Practically speaking, while the square allowed the composer to gain control over the most intricate textures at a microscopic level, the graph paper planimetries provided a plan for the juxtaposition of the shapes. The music produced by means of such procedures consisted of innumerable strata of dense polyphony. Informel 3 is a single-sheet score in which there can be found seventy-two real parts of imitative counterpoint. While the details where carefully worked out the totality often resulted in massive keleidoscopic textures.
Clementi’s visual approach can also be noticed by looking at some of his scores since in many of these, the entire piece consisted of a single page. This particular layout became possible since the composer started writing pieces that required the repetition of one page several times.
In some case the repetition was accompanied by a gradual imperceptible decelerando, like in the case of Madrigale for four-hand piano and prerecorded tape; in other cases the tempo was fixed and the number of repetitions was left to be decided by the performers, like in the case of
14 B.A.C.H. for solo piano.
The single page layout was suggestive of the visual work of art and could easily to be associated to a canvas, rather than a piece of music unfolding through multiple page turns.
1.7. Erasure of time
So far in our discussion, we looked at Clementi’s “aurally inscrutable” techniques to bridge the musical and the visual. In other words, while the scholar and the performer would benefit from observing the composer’s compositional techniques or appreciating the original layout of his scores, the unaware listener would be completely left out of the subtlety of the composer’s multidisciplinary approach. But while those are precious elements that describe the details of Clementi’s work, they were instated for reasons that surpassed the academic interest they could arise. Clementi’s goal was to concretely, if illusionary, create an aesthetic syncretism between the two spheres of perception.
Clementi was neither the first nor the only one interested in building a relation between the visual and the auditory. In his essay “On Some Relationships between Music and Painting,”
Adorno already explored possible consequences of the contamination between the visual and the musical:
Music that “paints” […] nearly always suffers a loss of temporal organization, [...]; and paint that behaves dynamically as if it were capturing temporal event, as the futurists desired and many abstract painters attempt to do with circling figures exhausts itself, at best, in the illusion of time.20
In other words, when music and the visual arts collide then somehow, time and space, which are the natural domains of music and the visual arts, also overlap and get confused.21
20 Theodor W. Adorno, "On some relationships between music and painting." In The musical quarterly. (Oxford: Oxford University Press, 1995. Vol. 79, No 1) 66-79. 21 Painting acquires one of the defining elements of music “time” and undergoes a process of
15 Perception of time was the variable that Clementi used as a trait d’union between the visual and the auditory. The idea of continuum and the consequent erasure of dialectical contrast became the procedure he used to operate against the linearity of time, which is the natural musical dimension.
Practically speaking, a piece deprived of any inner contrasting character would suffer from a loss of linear narrative. Negating a traditional diachronic musical narrative would, consistently with the composer’s aesthetic, represent music’s negation of itself. It would also deprive or at least distort the piece’s diachronic temporality.
The compositional tool to bring about this paradoxical overstepping of one discipline into another is the simple idea of repetition. Clementi used repetitions of single elements to create dense masses of sound which effectively eliminating a demarcation between background and foreground like in the paintings of Pollock or Dorazio. The listener recognizes the single repeating element as familiar, without being able to aurally extricate it from the totality which they form: the single elements are absorbed by extremely articulated sonic masses from which they sometimes emerge faintly but never really raising to the role of “themes.”
In this regard, Borio notices:
The juxtaposition and overlap of elements that remain identical in their successive apparitions contributes to neutralize the concept of musical form as an unfolding of time and let the space surface as perceptive dimension of music.22
Similarly to a painting of the Abstract Expressionism then:
The listener acts as someone who looks through the lenses of a camera which at regular intervals focuses a single detail, bigger portions or the whole object.23
“temporalization” while music, while loosing its traditional relation to time, starts to unfold through an “imaginary space” Gianmario Borio when describing such a tendency in Ligeti's Athmospheres rightfully specifies that the composer's interest lays in the construction of a “imaginary space” rather than in the exploration of physical space through a specific disposition of the sound sources. 22 Gianmario Borio in De luca, Canoni, Figure, Carillons. 15-31 23 ibid. p. 21
16 For the sake of completeness, let us discuss for a moment the inverted process of the temporal within the visual. In paintings, the relation between the detail and the totality of the work seems create a “temporalization” of the visual experience. In respect to the works of Tobey,
Cage noticed how the observer experiences a continuous mutation of prospective starting “from an almost indistinct totality to reach a vision of the particular, to then link it to the other parts in a research for a unifying principle, which he perceives without being able to clearly identify.”24
This mutation of prospective gives the viewer an illusion of time. Cage himself makes the connection between such aesthetic with music.
One can look at one part first then at another one and have as much as possible an experience of the whole. But the whole is done in a way that doesn't seem to be completely included in the frame. It seems that those things could have a continuation outside of the frame. If we were talking about music instead of painting, it would be a piece that doesn't have a beginning a middle section and a conclusion, deprived of a center of interest.25
1.8. Conclusions: The (ir)relevance of the composer’s philosophical views
It's true: art and music are dying of saturation. Therefore either one has the courage to be silent, or can continue to do things […] that express the agony and the dissolution of the represented object.26
Indeed, it can be challenging to, both, believe the composer when he speaks his mind about the end music and to consider his oeuvre as a positive contribution.
Clementi on several occasions expressed his belief that music is a doomed art-form whose past glories cannot be replicated. The composer noticed how the role of music in society had
24 ibid. p. 21 25 “L’individuo può guardare prima una parte e poi un’altra e, per quanto gli sia possibile, avere un’esperienza del tutto. Ma il tutto è fatto in modo che non sembra essere completamente incluso nella cornice. Sembra che quelle cose lì possano avere una continuazione al di là della cornice. Se parlassimo di musica anziché di pittura, sarebbe un’opera che non ha un inizio, una parte mediana e una conclusione, che non ha alcun centro di interesse” Richard Kostelanetz, Conversing with Cage (New York: Limelight Editions, 1994) 175 26 “É vero: l'arte e la musica stanno morendo per saturazione. Allora o si ha il coraggio di stare zitti, oppure si continua a fare cose- io stesso ne faccio pochissime, al massimo due l'anno- che esprimono proprio l'agonia il dissolvimento dell'oggetto espresso” Cresti, Aldo Clementi. 45
17 been diminishing as a consequence of mass-production mechanisms and the culture of comfort and entertainment. If, in the past centuries and notably in the Romantic era, music had been a source of inspiration for humanity as a whole, being invested with a role of moral and spiritual guidance, alas, this was no longer true in the 20th century.27 Clementi believed these changes to be irremediable.
Many intellectuals agreed28 - in different terms and to different degrees - on the severe crisis affecting the art-world as a consequence of the cultural shocks and the technological advancements of the 20th century. Clementi found an original “way out” of the cultural impasse by attempting to systematically incorporate those very sentiments of loss and disruption into his music.
As a first, ideal step Clementi stressed the importance of craftsmanship, as one element that could be saved from the critical moment:
There exists no contradiction between a pessimistic and apocalyptic view on the future of art and the need to correctly put notes together to continue a precious musical craftsmanship. For many the crisis of art becomes rather an alibi.29
He argued that the modern composer would never be able to reach the peaks of his past peers. Yet, he could still find comfort in a meticulous work of artisanship.
But, if on the one hand craftsmanship granted him a reason to continue his work, on the other hand art had been deprived of its higher meaning and function. What the composer was left to
27 Not anymore is the musician a beacon that guides the whole of humanity, as in the beautiful Romantic era. Mankind does not seek art anymore but only comfort, practicality, pleasure and entertainment. One has to have the courage to admit that there is no more need for art. “Il musicista non è più una specie di faro che illumina tutta l'umanità, come ai bei tempi dei romantici. L'uomo non cerca più l'arte, ma il comfort, la praticità, il piacere, il divertimento. Bisogna avere il coraggio di ammettere che di arte non c'è più alcuna necessità” (Cavallotti, 1970) 28 Theodore Adorno and Walter Benjamin were among the most outspoken in addressing the crisis of culture. 29 “Non c'é contraddizione tra una visione pessimistica, o apocalittica, sul futuro dell'arte e l'esigenza di mettere bene insieme le note, il desiderio di continuare un prezioso artigianato musicale. Per molti la crisi dell'arte diventa invece un alibi” Cavallotti, Aldo Clementi
18 represent was the very emptiness and disruption of modern music. The idea of a meta-narrative of the end of a medium described by the same medium is an idiosyncratic feature of Clementi’s aesthetic apparatus that also links his thought to other artists of his times: from Pirandello’s meta- theater to Cage’s questioning of the role of the artist.
As I will point out throughout this research, the pessimistic, almost apocalyptic, streak that transpires from the composer’s words stands in sharp contrast with the ultimate aesthetic aim of his music. Arguably, Clementi’s music deliberately attempts to redefine some of the paradigms of musical narrative. It is infused with a modern fascination for static textures and their “inner life”. Clementi’s music is grounded in something other than a linear, narrative based on the dialectic of contrasts; it perceptually explores a continuous and minute rearrangement of identical objects. Starting from 1971’s B.A.C.H Clementi’s music became what is now best known for: an apparently unchangeable stream of sounds. His unremitting aesthetic path has left many listeners baffled with the aimlessness of its musical results. But those who appreciate the composer’s unmistakable style, understand his music as an experience deprived of feelings such as excitement, suspense or despair; one that, instead, leads the listener into a meditative state.
One can simply reconcile the apparent contradiction between the outspoken pessimism about the future of music and a positive research into the realm of simple-complexity by simply considering the former as the spark that generates the latter, which in itself becomes a true impetus. Figuratively speaking, the composer put himself into a corner from which he eventually had to escape.
In other words, Clementi also used the cultural crisis of the 20th century as “an alibi”. Not an alibi that allowed him to be “less careful” in his creative act, something he condemned in the music of other composers, but one that allowed him to create in a “free space” deprived of any
19 narrative obligations. Therefore, the radical acknowledgment of “the end of music” was a necessary step he took in order to legitimately explore the complexity of static musical objects; such an exploration had to completely disregard most of the traditional narrative elements of music. Clementi, maybe because of his vast knowledge and respect for the musical canon and repertoire, decided to eschatologically characterize his abandonment of a traditional musical narrative as “inevitable,” something independent of his own free will. But, as tortured as they might have been, these decisions granted him the freedom to engage in the exploration of static textures.
But how are the idea of static textures and the idea of music coming to an end reconciled for the composer? Clementi used the pessimist hypothesis as a “set of instructions” to generate his modus operandi. In particular, Clementi identified the germ that most strongly defined the music of the past, i.e. the dialectical features generated by contrasts and the mechanism of tension and release, to then mercilessly deprive his music of all of those dialectical features.30
Therefore, Clementi, starting from the year 1971, drastically and abruptly renounced writing pieces that contained a narrative based on a dialectic of contrasts, development and variation.
But once music is deprived of all of its dialectical vestiges, what are we left with?
Clementi’s music provides one possible answer to this very question.
30 Arguably, the only surviving narrative is afore-mentioned meta-narrative which takes place through devices other than dialectical.
20
Chapter 2
2.1. Aus Tiefer: a case study
Aus Tiefer was written in 2004 and dedicated to Luigi Nono. It calls for a female chorus (4 soprani, 4 mezzosoprani, 4 contralti) and 12 instruments (3 flutes, 3 oboes, 3 B flat clarinets, and
3 French horns in F).
The piece is a collection of 19 panels, each of which present a particular combination of melodic fragments taken from the Lutheran choral Aus Tiefer Not. Clementi builds the entire piece, almost thirty minutes long, using just two melodic fragments and their inverted forms, layering them through canonic constructions. These fragments, once presented, do not change throughout the entirety of the piece. In fact the melodic fragments, their transposition levels, instrumentation, orchestration and dynamic levels are all immutable from beginning to end. The melodic fragments are repeated within each of the 19 panels and panels repeat at different points of the piece. The way fragments and entire sections are repeated in the piece does not let the listener infer that any transformation of the material is actually taking place: its basic elements are never really varied or re-contextualized. One can safely say that the dynamic-transformative quality of these elements seems to be amiss. The idea of development or even the more basic idea of variation is clearly not part of the piece’s narrative.
21 A) Material
The theme of the original chorale is subdivided in two fragments, as shown below.
Fig. 1 Chorale's theme divided into fragments
Throughout the nineteen canons, the piece employs these two fragments either in their original form or in inversion, either alternatively or simultaneously.31
Other than the two thematic fragments and their inversions, two more thematic elements are found exclusively in canon IX and XI: the varied 2nd theme and the organ's theme.
Fig. 2 2nd theme varied
Fig. 3 Organ's chorale While the varied theme can also be seen as a hybridization of the first and second themes, the organ's chorale stands as a foreign object in the tight thematic organization of the piece. It is taken from a later setting of the Aus Tiefer psalm 130 and is played by the organ “with its own tempo” as the score reads.
Table 1 below represents which theme (1st, 1st inversion (1st'), 2nd, 2nd inversion (2nd' ) or the
31 Other forms of transformations, retrograde and retrograde inversion, while present in Clementi's sketches are not employed in the piece's final version.
22 organ's theme) appears in the nineteen canons. By looking at the chart the reader can appreciate the specularity of the thematic organization of the piece. In considering the appearance of the themes and their juxtapositions we can observe two main structures:
i. the outer I to VIII and XII to XIX
ii. the core IX-X-XI
The two identical outer structures repeat as palindromes around an inner structure, which is also a palindrome .
organ ◊ ◊
2nd+2nd ◊ ◊ ◊ ◊ ◊ ◊
1st' ◊ ◊ ◊ ◊ ◊ ◊ ◊ ◊ ◊ ◊ ◊
1st ◊ ◊ ◊ ◊ ◊ ◊ ◊ ◊ ◊ ◊ ◊
I II III IV V VI VII VIII IX X XI XII XIII XIV XV XVI XVII XVIII XIX
Tab .1- Palindromic organization of themes
The axes of symmetry consist of a substructure which encapsulate canon X between IX and XI which are uniquely constructed with thematic variations. Around the central structure we find two symmetrical outer structures32.
B) Layering
Clementi exclusively uses canonical procedures in Aus Tiefer. While the technique calls for simply stacking same lines by offsetting their entrances in time, Clementi achieves a remarkable level of nuance in his own canonic construction. In his pieces there are different levels of canons
32Clementi's proverbial fixation with symmetry can be interpreted with Cage's words “ Symmetry […] itself suggests zero” is consistent with his aesthetic of erasure.
23 that work simultaneously. They are organized with a russian-doll-like procedure: smaller canonic structures are incorporated in increasingly bigger ones.
Depending on which of the nineteen canons we look at, we can find different levels of canonical organization. One way to hierarchically organize these levels starting from a simpler canonical construction to more complex ones would be as follows:
! First level33. The same theme is played at same pitch level and same rhythmic values.
! Second level. The same theme is played on a different pitch level and with same rhythmic
values.
! Third level. The same theme is played on different pitch levels and with different
rhythmic values either augmented or diminished proportionally. While first and second
level canons do not appear by themselves in the piece but nested within other canonic
structures, third level canons do appear by themselves, thereby constituting the thinnest of
the canonic setting of Aus Tiefer.
! Fourth level. Different themes are played on different pitch levels and with different
rhythmic values. This level consists in juxtaposing two third level canons as shown in
figure 4 . The added variable of complexity at a fourth level canonic construction is the
introduction of theme transformations which in Aus Tiefer is limited to the theme's inversion.
One can already start appreciating the coherence and consistency of Clementi's methodology.
Each level of the canonical construction has an added variable, which adds complexity. The canons are far from being simply a stacking of different voices; rather they are a collection of separate entities consistently built to form lager structures.
33 “Shadowing” canon: This trick allows for a first aural blurring of the line. This role is played by the instruments in the case of Aus Tiefer which are to play softer, i.e. shadowing the vocal line.
24 Fig. 4- Canon levels (III).
25
C) Shapes
Aside from the fragmental content, another element that varies between each of the panels is their “shape”. In each panel the voice entrances are organized according to shapes such as a
• Triangle pointing upwards,
• Triangle pointing downwards
• “Hourglass” shape
• Rhombus
The last two shapes are compound structures that can be obtained from different juxtapositions of the first two. To clarify how these shapes work in organizing the rhythm of the panels let’s consider for instance the upward-pointing triangle. In this case, the bottom voices will enter first, middle voices second and top voices last. Alternatively, in the hourglass-shape, top and bottom voices will come in (almost) simultaneously while middle voice will come in last. All these shapes share one common characteristic: they produce symmetrical sound masses with the point of maximal density at their center, producing a gradual increase/decrease of sound. While their rhythm might be different their ultimate perceptual result is very similar (yet not identical).
26 2.2. Saturating intervals through the “magic square”
In studying the composer's sketches it appears how two main kinds of sketching work occupied his compositional process. The first took place on checkered workbooks.34 As I later found out and will explain shortly, this sort of preparatory work dealt with the choice of the transposition levels that each of the canons was to contain both in number of voices and pitch levels. The second kind employed large sheets of graph paper onto which the composer assembled cut-offs of manuscript paper. This latter kind of work accounted for the rhythmic organization of the canons in their shapes, i.e. the chronology of the voices’ entrances.
The quaderni di lavoro (i.e. workbooks) only occasionally show sign of traditional music notation. If Clementi needed to have a notated version of a theme, he quickly and freehandedly drew a pentagram without switching to a manuscript paper. What the quaderni mainly contain instead is a remarkable amount of pseudo-Cartesian graphs (see fig. 5). He often referred to such graphs as “magic square” in his interviews, without ever revealing the details of its workings, preventing the square's secrets, its “magic”, to be revealed.
Leaving the folkloristic appellation aside, the technique of the square which was introduced to him by Bruno Maderna in the sixties, by the composer's own admission, had changed his way of writing and thinking about music. [quote] In my research, I was not able to learn what Maderna actually taught his pupil; on the other hand, through a careful study of his quaderni I deciphered how such technique was implemented by Clementi.
34 Those workbooks were stacked in his studio and were differentiated by cover inscriptions indicating the dates and titles contained .
27
Fig. 5- An example of a sketch of the Magic Square
To work within this graphic environment the composer had to first translate the theme into a series of numbers from 1 to 12 each representing a note of the chromatic scale.
The numbering is always consistent and independent of the octave placement.35
C C# D D# E F F# G G# A A# B
1 2 3 4 5 6 7 8 9 10 11 12 Table 2. Numeric system
Fig 6. First theme's numbering (pitch level 7)
Once the composer had translated a theme into a number series he proceeded to build
35 F1 and F3 would both correspond to number 7
28 matrixes of the twelve transpositions for each of the four specular transformations: original, inversion, retrograde and retrograde inversion.36
Fig7- transformation matrixes
He then chose which level of transpositions and which of the transformations could work together in a canon. And this is when the magic square technique plays its crucial role.
In fact beside the four matrixes without fail one can find an implementation of the square.
Let me illustrate the workings of the technique through an example. Given the theme of figure 6 and its numeric translation {7, 12, 7, 8, 7, 3, 5, 7} I can “map” the theme's intervals as dots (or plus signs or xs etc. as in fig. 6) in the 12 by 12 square. In order to do so, the theme has to be divided it into a set of intervals:
{(7 12), (12 7), (7 8), (8 7), (7 3), (3 5), (5 7)}
In Fig. 8 each point represents an interval (for example the coordinates (7 12) represents F#-B, a
36 In Aus Tiefer the composer ended up using only the originals and the inversions
29 descending perfect fifth, or an ascending perfect fourth37). The graph can thus be used to chart the theme's intervallic content38.
Graphically the theme above will then have a rendering of the sort
Fig 8. First theme represented in the square
This way of visualizing a melody through dots in a square allowed the composer to quickly grasp the intervallic content of a theme.
A question now arises: why would the composer go through the trouble of a graphic mapping of the intervals? As I have already mentioned, these graphs were far from being just a trifle the composer adopted to occupy his spare time. On the contrary, Clementi heavily relied on them to make his choices.
Only after the composer had mapped the themes into these squares he would be able to settle on certain levels of transpositions and transformations39. To clarify the importance that the choice of a level of transposition plays in Clementi's writing let me stress how Aus Tiefer's thematic material, as shown in table 1, is limited to two themes and their inversion (excluding the
37 One of the “flaws” of the magic square is its inability of representing the direction of the interval. 38 By intervallic content I refer to its horizontal intervals, namely, the intervals between each pair of successive notes. 39 In particular one can see in fig 7 a marker inscription quoting “Buono!” (i.e. Good!) that comes after pages filled with squares and matrixes reworking the same theme.
30 exceptions of IX and XI). Furthermore these themes usually appear separately. This exasperated, self-imposed economy of materials, forced the composer to work exclusively with elements such as transposition levels of the same theme and their rhythmic organization. In particular, the selection of the levels of transposition and transformation of the same theme occupied most of the composer's process.
Clementi used two “rules” to achieve the “perfect” combination of levels, one positive:
• saturate the intervallic space with multiple versions of the same theme
and one negative:
• avoid repetition of the same interval at the same level by different lines40.
Let me explain what I mean by intervallic space looking at figure 8. The dots in the graph represent the intervals of one level of transposition of the first theme (F#). These dots partially fill the graph. If I add another transposition of the same theme seven more dots will be filled in the
12 x 12 space (144 slots in total). To the theme on F#, graphically represented on figure 8, I can then add another version of it, say on level G, obtaining a graph such as the one below:
Fig. 9- Layering of the 1st theme on levels F# and G.
40 The F# - B interval that opens the theme in fig. 6 cannot be replicated in Clementi's system by any other line. Another perfect fifth like C – G is though allowed.
31 Such operation will accomplish a higher degree of saturation.
But this sort of layering cannot happen freely: different levels of transposition cannot replicate the same interval.
As an example let's take the above mentioned first themes on levels F# and G: their interval content would be numerically represented as:
F#: {(7 12), (12 7), (7 8), (8 7), (7 3), (3 5), (5 7)}
G: {(8 1), (1 8), (8 9), (9 8), (8 4), (4 6), (6 8)}
The two sets of intervals don't have any element in common. But if I add level G# instead of G an intervallic intersection will be created:
F#: {(7, 12), (12, 7), (7, 8), (8, 7), (7, 3), (3, 5), (5, 7)}
G#: {(9, 2), (2, 9), (9, 10), (10, 9), (9, 5), (5, 7), (7, 9)}
The interval 5 -7 (E – F#) is in fact present on the two different levels. F# and G#
Avoiding intervallic overlaps of different levels of transposition is the second rule that the composer strictly followed in building his canons.
Aside from the technique itself, an original feature of Clementi's process comes into light: the composer's concern lies not in the single notes of a musical line but in its intervals. While repetition of notes across the lines are common in any of his canons, fragments cannot replicate the intervallic motion of one another (i.e. from that common note to another common note). The
“absolute value” of an interval, say a perfect fifth, can be replicated in different lines but not at the same pitch level.
A particular theme, and its determined set of intervals, will then contain the “constraint” by which the number of voices of the canon will be derived. These operations gave different results depending on the themes used, some being more prone to multiple-voice constructions than others. The experience that the composer acquired in this technique made him more aware of
32 the qualities of a melody in relation to its intervals. Many of the sketches in the quaderni are studies of themes to explore their polyphonic potentials according to Clementian rules.
The first fragment of the Aus Tiefer chorale proved to be one of the composer's favorite because it allowed him to build up to 12 real voices with no intervallic intersections between the original and the inversion.
This sort of operation, i.e. maximizing the number of voices while avoiding intervallic intersections, determined each of the canon's number of voices and levels of transpositions.
The reasons for adopting this particular graphic representation should now be clearer: the magic square provided a quick way to check different levels of transposition indicating whether they caused intervallic intersections with others; intuitively, in traditional notation this operation would prove more time consuming.
2.3. Visual appeal of the magic square
More in general, the square represents an abstract space that allows the composer to work almost as a visual artist, creating dense textures such as those he so admired in abstract expressionist painters. Clementi used the square as a pivotal procedure that lets him into a spatial rather than temporal dimension. While the technique clearly constitutes an efficient tool in mapping intervals, it also gives a synchronic representation of a melodic fragment: the theme appears as shape, disjointed from its temporal constraint. The post-modernist exploration of physical space operated by Cage and others, is reinterpreted by Clementi as exploration of a conceptual space created through compositional artifice and otherwise hidden to the listener.
In this kind of space, intervals constituted the bricks with which the composer proceeded
33 to fill all possible slots, as many as the intervallic-intersection constraint and the limited thematic material allowed. But filling the slots of the square was an operation of calculation, a puzzle, comparable to “compositional tetris”, rather than a free-hand, stream of consciousness act of creativity.
Below various graphs are illustrated in which a computerized rendering of the magic square is realized for each of the canon contained in the piece. Each of the dots represent an interval and each interval is played by one level of transposition only. The reader can so appreciate visually the textural difference between each canon.
In III, V and X (see figure below) we can appreciate how the composer achieved an almost complete saturation of the space, remembering that no dot is repeated and that only one theme is employed.
34 I II III
IV V VI
VII VIII IX
X Fig 10- Intervallic densities (from X to XIX they repeat as a palindrome)
35 In particular the construction of the three canons, which start the piece are built as a gradual stratification of one over the other. Canon I while having an intervallic content perfectly symmetrical with canon II does not overlap with it in any of its points so that canon III is obtained by the juxtaposition of one on top of the other without producing any repetition
+ →
I II III
Fig. 11 Gradual increase of density
2.4. The algorithm
In the material gathered, only some of the graphs and matrixes of Aus Tiefer were retrieved. This lack of material prompted me to reconstruct the composer's multi-step procedure with a computer algorithm that would reproduce the process behind the quaderni. This approach helped me test my assumptions about the composer's process with the outcome of his work: the score of Aus Tiefer.
Such an approach not only proved successful (the algorithms' results were consistent the canons of the piece) but offered insights about the algorithmic approach the composer adopted.
In this section I will rely on such algorithm and show the reader the different steps of my
36 analysis. The charts produced by the program Open Music41, while less visually appealing than the ones of our composer, will be neater and easer to read.
A) Monothematic canons
In my simulation I will focus on the process from the moment the composer chose his thematic material and started assembling it into his macro structures.
As we have already seen in discussing the magic square, the first step will be to subdivide the theme into intervals42. In doing so each note, except for the first and last, will be repeated twice since it will be both the arrival for an interval and the departure for the next.
For instance the first theme on level 5 (E) will be
{5, 10, 5, 6, 5, 1, 3, 5} while its intervals
{(5 10), (10 5), (5 6), (6 5), (5 1), (1 3), (3 5)}
41“OpenMusic (OM) is a visual programming language based on CommonLisp / CLOS. Visual programs are created by assembling and connecting icons representing functions and data structures.” OM allowed me to control and divide the process in different steps through what are usually called “patches”, i.e. algorithms that can be concatenated or nested into one another to produce operations of increasing complexity. 42 I will use Clementi's way of numbering notes from 1 (C) to 12 (B)
37
Fig. 12- Translating a melody into a set of intervals with OM
This is a pretty simple implementation of an Open Music patch that reproduces just the intervallic subdivision that I will need.
The two boxes “notes-> 1-12” and “intervals” contain simple arithmetic operations that allow the notes to be translated into couples of numbers. I can apply the same algorithm to the remaining eleven levels of transposition and obtain a total of twelve sets of intervals (same intervallic patterns on different levels).
Since the composer's idea is to fill the intervallic space with the use of a single line transposed on different levels avoiding intervallic intersections, I will proceed in building another algorithm to check which levels of transposition intersect with one another.
38
Fig. 13- The self-intersection matrix algorithm.
In particular, the Aus Tiefer first theme will intersect only some of its transposed peers.
The goal of the algorithm illustrated above will be to look for empty sets of intervallic intersections.
Fig. 13 shows the construction of the algorithm: the theme is transposed it onto twelve levels (sub- patch “transpositions”), which are then divided into intervals (“intervals”), then the sub-patch named “find-intersection” matches each of the transposed version of the theme with each of the others reporting any overlap in the intervallic content. The patch named “inters?” will “ask” whether there is any intersection between two levels transposition reporting the statement “true”
39 (“t”) if the answer is “yes” “false” (“nil”)43 if it's “no”.
Such an operation will result in a twelve by twelve matrix of t-s and nil-s:
C C# D D# E F F# G G# A A# B
C t nil t nil nil nil nil nil nil nil t nil
C# nil t nil t nil nil nil nil nil nil nil t
D t nil t nil t nil nil nil nil nil nil nil
D# nil t nil t nil t nil nil nil nil nil nil
E nil nil t nil t nil t nil nil nil nil nil
F nil nil nil t nil t nil t nil nil nil nil
F# nil nil nil nil t nil t nil t nil nil nil
G nil nil nil nil nil t nil t nil t nil nil
G# nil nil nil nil nil nil t nil t nil t nil
A nil nil nil nil nil nil nil t nil t nil t
A# t nil nil nil nil nil nil nil t nil t nil
B nil t nil nil nil nil nil nil nil t nil t
Tab. 3 Self-intersection matrix (1st theme)
I will call the resulting matrix the “self-intersection matrix” since it reports intervallic intersection between a theme and itself on different levels of transposition.
This matrix will possess specific qualities: rows and columns corresponding to the same pitch level will have the same content, in other words the matrix has an axis of symmetry in its diagonal; also the diagonal will always contain “true” statements since it represents the unison
43 “t” and “nil” stands for “true” and “false” in LISP programming language
40 transpositions44.
The matrix tells us that, in the case of the first theme (table 3), aside from the unison or octaves, for each level of transposition two more transpositions are to be avoided: the major second above and below45.
These results allow me to “simulate” the process the composer adopted to choose specific levels of transposition. These choice also determined the number of voices that could be included in seventeen of the nineteen canons46.
Once a starting level has been chosen there will be only a limited number of transposition that can be added without replicating intervals. In the case of the first theme the number is exactly six.
If we start from the level of the original Lutheran chorale B (figure 1) I will proceed adding one voice at the time. Each time I add a new voice I will have a further limitation in choosing the next transposition.
The levels that don't have any intervallic intersection with B and are therefore available to be utilized in a Clementian canon, will be indicated by the statement “nil” in the matrix. From the highlighted row in table 3, I can extrapolate the the following available levels:
C D D# E F F# G G# A# (B)47
Proceeding from right to left, if I keep adding levels of transposition A# will be added next producing a new set of available transpositions:
44 A theme will not only have some but all of the intervals in common with its own self. 45 A caveat to the matrix reported is that not all “true” statements are equal: the unison transposition will contain all of the intervals while those on the major second will only have two intervals in common, but that does not matter to the composer who wanted to avoid any overlap. 46 IX and XI represent exceptions, since they follow the rules only partially. 47 The note in parenthesis indicates the transposition level to which the t-nil string belongs to; the matrix will give a “t” statement since a unison transposition will create intersections.
41 C D D# E F F# G A# (B)
C# D D# E F F# G G# (A#) B
Remembering that I can only use levels of transposition that don't intersect any of the preceding ones, the next level available will be G since A would create an intersection with B while G# with
C.
Adding G I will get:
C D D# E F F# G A# (B)
C# D D# E F F# G G# (A#) B
C C# D D# E F# (G) G# A# B
And so on...
Proceeding until no other level is possible without creating an intersection I will have:
C D D# E F F# G A# (B)
C# D D# E F F# G G# (A#) B
C C# D D# E F# (G) G# A# B
C C# D D# F (F#) G A A# B
C D (D#) E F# G G# A A# B
C# (D) D# F F# G G# A A# B
D D# F# G A# B
I will be able to pick only those levels that contain no intersection with all of the preceding ones which are indicated by the string of notes. Reading the columns of the preceding table those levels are, starting from level B, D, D#, F#, G and A# .
Once the sixth transposition is added, no further addition will be available without
42 creating intersection with one of more of the preexisting ones. The layering has to stop at six real48 voices. In the figure 14 canon II is shown with levels of transpositions consistent to my
analysis. These levels are kept throughout the entire piece when the first theme is played.
Fig 14- II. First theme setting.
48 Twelve including the same level's “shadows”
43 B) Polythematic canons
The canon of figure 14 which appears in different “shapes” on II, VII, XIII and XVIII is what I referred to previously as a third level canon. Moving up the ladder of canonic levels the composer started adding new thematic material to thicken the canonic strata. In fact a whole new set of possible transpositions can be added if I introduce new themes. Clementi starts doing so by adding the theme's inversion:
Fig. 15 -1st theme and its inversion on F#.
Interestingly enough we can notice how, differently from what has been observed in the case of the self-intersection matrix, if taken at the same pitch level, a theme and its inversion do not cause any intervallic intersection.
In other words the set of intervals:
{(7 12), (12 7), (7 8), (8 7), (7 3), (3 5), (5 7)} has no element in common with the set:
{(7 2), (2 7), (7 6), (6 7), (7 11), (11 9), (9 7)}
Let me remind the reader here how the composer's concern resided in a theme's intervals rather than its single notes the elements. It was the intervals not the notes that had to be unique to a line. Comparing the two lines, while the number 7 will appear multiple times in both lines it will never be approached or left the same way between the original and the inversion: the
44 elements of the sets are couples rather than single numbers. But if the same level is allowed for the first theme and its inversion, other levels of the inverted theme will create intersection with each level of the original.
We can proceed to look for those intersections in a way similar to the self-intersection matrix.
The algorithm used before can be tweaked to allow for more than one theme to be analyzed.
This slightly different algorithm will compare two different themes and find intersections at different levels of transposition.
45
Fig. 16- Poly-intersection matrix's algorithm
As the figure shows the algorithm is able to start from one input, the theme, invert it through the patch “inversion” and then similarly to what has been showed before, translated both the original and the inversion in numbers (patch “notes 1->12”), produce all possible transpositions both the originals and the inversions (patch “transposition”), break them into sets of intervals (patch
“intervals”) and eventually match each of the original with each of the inversions to look for intersections.
46 I will call to the resulting matrix the “poly-intersection” matrix, and I will differentiate the inversion's level from the original with an apostrophe.
C' C#' D' D#' E' F' F#' G' G#' A' A#' B'
C nil t nil nil nil t nil nil nil nil nil nil
C# nil nil t nil nil nil t nil nil nil nil nil
D nil nil nil t nil nil nil t nil nil nil nil
D# nil nil nil nil t nil nil nil t nil nil nil
E nil nil nil nil nil t nil nil nil t nil nil
F nil nil nil nil nil nil t nil nil nil t nil
F# nil nil nil nil nil nil nil t nil nil nil t
G t nil nil nil nil nil nil nil t nil nil nil
G# nil t nil nil nil nil nil nil nil t nil nil
A nil nil t nil nil nil nil nil nil nil t nil
A# nil nil nil t nil nil nil nil nil nil nil t
B t nil nil nil t nil nil nil nil nil nil nil
Tab 4.- Poly-intersection matrix. First theme & its inversions.
The statements of the preceding matrix should be read as follow: the theme on row C will have no intersection with inversions C' , D', D#', E', F#', G', G#', A', A#', B' while it will have intersections with C#' and F'.
We can now proceed with the simulation of the composer's process and start adding new voices using the theme's inversion. In doing so I will have to make sure that those new voices do not intersect any of the preceding voices, which, as a reminder, are D#, D, F#, G, A# and B.
The matrix will help us in this process. For each of those original levels I will report all the
47 inversion corresponding to “nil” values.
D#: C' C#' D' D#' F' F#' G' A' A#' B'
D: C' C#' D' E' F' F#' G#' A' A#' B'
F#: C' C#' D' D#' E' F'' F#' G#' A' A#'
G: C#' D' D#' E' F' F#' G' A' A#' B'
A#: C C#' D' E' F' F#' G' G#' A' A#'
B: C#' D' D#' F' F#' G' G#' A' A#' B'
C#' D' F' F#' A' A#'
The theme's inversion levels capable of being stacked with the preceding third level canon will then be : A, A#, C#, D, F and F#.
Is this enough to put the theme and its inversion together? “Not so fast” Clementi might say. There is a further test that these inverted themes will need to satisfy in order to comply with the no intersection rule. What we learn from the above results is that those levels of inversions don't intersect with their original counterparts on D, D#, F#, G, A#, and B but we would also need to check whether they produce intersection among themselves.
Sparing the reader another tedious demonstration, I will just mention how the self- intersection matrix built on the inversion of the theme will be identical to the one of the original theme (the intervals are the same, only inverted, as we have noticed earlier the square technique does not account for the direction of the interval). On the self-intersection matrix reported earlier one will discover how no intersections are to be found among levels C#, D, F, F#, A and A#.
Now we can put the six plus six voices together being certain that no interval is repeated among different levels of transpositions.
We can now go back to figure 4 and appreciate the construction of the twelve real voices
48 canon which with the addition of the 12 instrumental “shadows” form a sonic mass that hides such a refined constructing principle.
C) The “Second Theme”
The second theme is taken from the second part of the chorale theme in its original form
(figure 1).
This fragment proved much more resistant to Clementi's method of construction since it easily creates intersections with its own transpositions or its inversions
This will become immediately clear once we extract the now familiar self-intersection matrix of the second theme. We can observe the far higher number of “true” statements in respect with the self-intersection matrix of the first theme.
49 C C# D D# E F F# G G# A A# B
C t nil t nil nil t nil t nil nil t nil
C# nil t nil t nil nil t nil t nil nil t
D t nil t nil t nil nil t nil t nil nil
D# nil t nil t nil t nil nil t nil t nil
E nil nil t nil t nil t nil nil t nil t
F t nil nil t nil t nil t nil nil t nil
F# nil t nil nil t nil t nil t nil nil t
G t nil t nil nil t nil t nil t nil nil
G# nil t nil t nil nil t nil t nil t nil
A nil nil t nil t nil nil t nil t nil t
A# t nil nil t nil t nil nil t nil t nil
B nil t nil nil t nil t nil nil t nil t
Tab. 5 Self-intersection matrix 2nd theme
Starting from level B and making the same set of operation already done on the first theme I will select A# as my second level and then G. After adding the third level there will be no more transposition possible. Similar results will be reached starting from the other levels.
C D D# F G G# A# (B)
C# D F G A (A#) B
C C# D# E F# (G) G# A# B
G A# B
Given the limited amount of levels available, the composer decided to increase the thematic variance. To compensate the lack of a thick polyphonic layering, in setting the second
50 theme, the composer chose to use two levels of the original second theme against one of its inversion. The only instance of the second theme inversion also appears on B: similarly to what we have seen in regard with the first theme, the second theme also allows for setting one level of transposition with its inverted form at the same level. This is shown in the poly-intersection matrix below
C' C#' D' D#' E' F' F#' G' G#' A' A#' B'
C nil nil nil nil t nil t nil nil t nil t
C# t nil nil nil nil t nil t nil nil t nil
D nil t nil nil nil nil t nil t nil nil t
D# t nil t nil nil nil nil t nil t nil nil
E nil t nil t nil nil nil nil t nil t nil
F nil nil t nil t nil nil nil nil t nil t
F# t nil nil t nil t nil nil nil nil t nil
G nil t nil nil t nil t nil nil nil nil t
G# t nil t nil nil t nil t nil nil nil nil
A nil t nil t nil nil t nil t nil nil nil
A# nil nil t nil t nil nil t nil t nil nil
B nil nil nil t nil t nil nil t nil t nil
Tab. 6 Poly-intersection matrix 2nd theme
If we assume then B and B' (transposed) as our starting levels then I can extrapolate the set of available levels of the original theme from the B' column:
51 B: C D D# F G G# A# (B)
B': C# D# E F# G# A A# B
The next original level will be D#.
Once I add the D# level no other levels can be added since from the self-intersection matrix I get as available levels:
C D (D#) E F# G A B which exclude the G# A# levels available from B and B'.
Even in the case of the second theme on canons IV, VIII, XII and XVI, the choice of number of real voices and levels of transposition is strictly dictated by the composer's system.
52 Fig.17 Second theme's setting.
53 2.5. Conclusions
From his early years to the end of his life, Aldo Clementi proceeded to form a clear aesthetic thought which has been illustrated in the previous chapter. The philosophical tone of his many statements and their eschatological implications form a truly complex apparatus of aesthetic convictions.
The composer's view of contemporary music and of its future, so potently negative, results into a radical abandonment of traditional musical narration and discourse. He recuperates some elements of musical tradition, but only as object trouvé: like a survivor of a lost civilization rummaging through remnants of the past, playing with relics whose original purpose has long been forgotten, he employs themes from the past and uses canonical constructions depriving them of their original nature. This aesthetic operation is in itself a representation of the desolate future that Clementi takes the modern composer to face. Frustrated by the impossibility of replicating the glorious past, Clementi uses the same tools but in a “wrong” way. His operation is similar to that of drawing a caricature: some elements of the subject, while still recognizable, are exasperated to create an eerie effect. Differently from a caricature, though, the effect is hardly comical but rather daunting. In Clementi's output and in particular with one of his major later work, Aus Tiefer, contrapuntal textures remindful of the glorious baroque era are exasperated to the point of deliberate unintelligibility.
Clementi's all-encompassing world view is matched by a compositional process which does not indulge in any coup de coeur, heat of the moment decisions, but is based on strictly predetermined procedures. The first goal of this chapter has been to unfold how the composer operates in the smallest procedural detail. It goes beyond the goals of this research to establish a nexus of necessity between Clementi's aesthetic thought and his output. But in this chapter I have
54 attempted to draw certain connections between Clementi's aesthetic ideas and his musical and procedural method. In particular, one can find the germ of such a connection in Clementi's musical ideas of proliferation of a single element, and of self-erasure, both being pervasive in his aesthetic and musical thought.
The second aim of this chapter has been to bring out a feature of Clementi's composing process that makes him a precursor of a particular type of contemporary composition technique, known as “algorithmic composition”. In broad outline, algorithmic composition is the use of algorithms or formal procedures in composition, often without human intervention (say by the use of computers). Generally, algorithmic composers focus their attention on the procedural content of their piece, leaving the musical outcome to be the indirect outcome of the process, almost a byproduct of it.
This idea contains both the Cagean idea of the composer becoming a listener of the results of his own procedures and the modernist fascination with complex structures49. Clementi refrained from any intervention in the end result of his process, thus incorporating chance operations in his work. Of course, it should be said upfront that Clementi never used any kind of computer software in his process. His complex procedures only take place on paper; nonetheless, they inevitably achieve an absolute level of exactitude characteristic of computer aided algorithmic composition.50
Clementi like a modern day algorithmic composer concentrated his focus on the workings
49 Clementi's syncretic connection between post-modernist and modernist aesthetic, the reader might recall, has been one point of last chapter's discussion. 50 In today's computerized world anybody can perform highly complex operations in real time. In music composition programs have been developed to take advantage the capabilities of computer's processors to present composers with musical result that would have taken weeks or months to develop on paper. This is one reason why some overlook such the deployment of computer software to compose as a product of “laziness” on behalf of the composer in the best cases or even abdication of the role of creator in favor of mechanized procedures. What these criticism fail to address is the choices that the algorithmic composer has to make in order to create the process. Choosing one mathematical or logical operation over another will produce different results that will represent the composer's idea or fail to do so.
55 of the process, perfecting them as a clockmaker. His machinery was built accurately and with a clear aesthetic direction. Whether the product of such procedures successfully achieved his aesthetic goal is a question that can only be answered by the reader/listener. What I cared to demonstrate here is how the composer translated his aesthetic conviction in precise procedures and calculations and how, while the choice of a procedure over any other was a creative act, the outcome of such a procedure was the product of mechanical calculations. In my analysis, this algorithm built in Open Music proved to be extremely accurate in predicting the composer's choices
56
Chapter 3
3.1. Un Dolce Naufragio
In this chapter I intend to push my research beyond the investigation of the composer’s motives and process, leaving aside the composer’s perspective and aesthetic thought in order to tackle what is probably the thorniest topic of all: the assessment of the end result, the music. In other words, the goal of this chapter is analyze the listener’s perception of Clementi’s music.
Even though I am about to step into the muddy territory of subjectivity, one should not forget how Clementi’s music represents an almost unique case, for it possesses an aesthetic consistency rare amongst most composers. The assessment of the listener’s experience can be then considered not in a vacuum but against the background of the composer’s intentions to eventually notice whether a listener’s response is consistent with the intended goals.
The goal of this chapter, and ultimately of the entire monographic research, is to notice how Clementi’s late production, while a cosmically pessimistic act, is far from constituting a moot point in the development of musical aesthetics51. On the contrary, Clementi’s music revisits the very premises of musical narrative and carries the listener into a particular and original kind of musical experience. If, generally speaking, a piece’s narrative is found in the dialectic of contrasts and/or the more sophisticated idea of development, Clementi’s complex sound artifacts appear
51 Regardless, that is to say, of what the composer wants to say about it.
57 to have no such a thing as narrative. Instead, a fascinating and striking feature of
Clementi’s late production is the apparent calm of the musical surface as it contrasts with its indiscernible core. In particular, Aus Tiefer perfectly exemplifies both the un-narrative qualities and simple/complex dichotomy of Clementi’s late production. The apparent simplicity of its traditional themes, as they are voiced in canons, the textural, contrast-free layering of familiar material gently carries the listener into familiar territories of traditional music. Subtly but inevitably, the simple elements that started the piece undergo a gradual and hypertrophic layering that transforms what seemed as discernible or even predictable surface into an incomprehensible maze of sound. Ultimately, the listener’s legitimate expectations for a musical discourse are frustrated. This chapter will illustrate how Aus Tiefer’s perceptual experience can be described as a game of deception in which the music ceases to exist as narration and starts to exist as an inanimate and complex sound artifact.
Aus Tiefer and all of its “diatonic period” peers appear as a wondrous collection of sound experiments in which the most simple initial states are able to create fascinating results of unpredictable complexity.
In Giacomo Leopardi’s poem L’Infinito a simple hedgerow stands between him and the obscurity of an indiscernible unknown. Similarly in Aus Tiefer a simple melodic fragment is all it takes to represent the limits of musical understanding; by simply following the themes presented, those willing to abandon the moorings of a dialectical musical narrative are destined to a sweet shipwreck, un dolce naufragare, such as the one described by Leopardi.
To simplify the complex aesthetic Clementian apparatus into discrete steps, we can observe how Clementi’s music perceptually unfolds along three lines:
• It appears as familiar and easily predictable
57 • It subtly but inevitably reveals itself as deprived of a paramount feature: its
narrative
• It ceases to exist as a pseudo-language and presents itself as a complex object of
sound
In the first step, the listener’s attention is engaged through a game of false references and unfulfilled allusions. Secondly, the systematic removal of contrasts and the idea of development, i.e. the pillars of musical narrative, undermine the dialectical unfolding of the piece. Finally, the listener is left to contemplate music for what it is at its most primitive level: an object of sound.
Once the listener accepts her diminished role as a “contemplating observer” of objects rather than the interpreter of a narrative, she discovers the fascinating nature of the objects that are being presented to her. The kaleidoscopic constructions are striking because their apparent simplicity is intertwined with an inner life of complexity.
As I mentioned, one of the premises of the chapter is to disregard the composer’s own observation about his music to approach the music from a listener’s prospective. But is important to notice how, since Clementi’s pieces are products of automated processes that come into existence autonomously, independently of the composer’s will, Clementi’s role is not strictly of a composer but of a composer/listener. Clementi operates as a Deus ex machina who sets the rules of the game according to a general aesthetic idea, to then take a step back and observe the product of his machinery come into existence. The impetus behind Clementi’s production is an original and extremely modern fascination with complexity as it generates from simple initial states and rules. To fully appreciate and understand Clementi’s legacy one has to see is efforts as a sort of musical scavenging: his pieces are experiments devised to explore the unknown complexity of sound as it relates to perception and expectation.
58
3.2. Repetition and musical narrative
The year 1971 represents a turning point in Clementi’s production. In the compositions that immediately preceded 1971, during the course of the so-called Informelle period, Clementi develops an aesthetic fixation for “shapelessness” achieved by means of a thorough erasure of any sort of contrast: in dynamics, melodic material, timbres, harmony or rhythm. Simply speaking, his Informelle pieces can be described as “blurs” or “stains” of sound.
In 1971, the year of B.A.C.H., something changes. This short piece for solo piano consists of a single page to be repeated at least three times52. There are repeating elements such as a broken chromatic scale, a small fragment of Bach’s C minor fugue, and the notes corresponding to the baroque composer’s last name. Clementi calls this moment a “start from scratch.”53
As in to their Informelles precedents, pieces form the “diatonic period” such as B.A.C.H.,
Madrigale or Aus Tiefer (only to name a few54) do not seem to possess inner developments: their melodic, harmonic, dynamic material is fixed throughout the entirety of the piece. What perceptually separates the production of the “diatonic period” from the earlier non-formalized
(Informel) pieces is the striking presence in the former of aurally recognizable repeating melodic
52 The possibility of increasing the number of iterations is left to the performer. 53 “After a period of intense work that followed the acquaintance of Maderna and the attendance to the Darmstadt school, I was “saturated” [...] . I already knew the paintings of Fautrier, Tápies, Pollock and the textures of Dorazio, Tobey etc. The idea of continuum fascinated me. [...]I could not see a correspondent of the Informel and the Materistic painting in music. Their prescriptions of abolishment of contrasts [...] and of the dialectic of articulations, all of which were tiresome residuals of a mentality still indebted to neoclassicism, made me seriously consider the need of a start from scratch (my emphasis)” “Furono l'Informale e il Materismo in pittura (di cui non vedevo un reale equivalente nella musica) e i relativi postulati circa l'abolizione dei contrasti (a compartimenti stagni lungo l’arco formale) e della dialettica dell'articolazione – tutti stanchi residui di una mentalità ancora fondamentalmente neoclassica – a farmi seriamente considerare la necessità di un riinizio da zero” Bortolotto, “Intervista con Aldo Clementi.” 16
54 As I have observed in chapter 2 in Aus Tiefer, one finds both local level repetitions of melodic fragments and structural level repetition of entire sections of the piece; these sorts of repetitions can be also observed in different degrees for all the works between 1970 and 2011. In other words, the multilayered repetitive construction remains a constant of the composer’s modus operandi throughout the last four decades of his life.
59 fragments. The pieces from the “diatonic period” are perceptually very different from their
Informelle precedents since they provide the listener with aurally clear repetitions of fixed elements; on the other hand, formally speaking, the Informelle and the diatonic pieces do not achieve anything different, since they both create static sonic textures.
Before I delve into the specifics of repetitiveness in Aus Tiefer then, let me offer in a general assessment of what I refer to as repetition. It is not easy to define what repetitiveness in music is and how it works in general terms. It seems safe to observe, though, that the function of repetitiveness is to perceptually “ground” music through memory. Simply put, when patterns of pitch sequences, rhythms and even timbres or dynamics are repeated, the listener actively recalls them, noticing whether or not some of their features have changed55. This process engages the listener’s attention, turning her into an active part of the musical experience. Surely, in general, for an element that is repeating, for instance a sequence of pitches, the listener is also presented with others that on the other hand change, for instance rhythm, harmony, lyrics etc. The changing elements re-contextualize, vary or transform the repeating element so that it will not be perceived exactly as it was.
Whatever happens in a piece of music is the endless reshaping of the basic shape … there is nothing in a piece of music but what comes from the theme, springs from it and can be traced back to it; to put it still more severely, nothing but the theme itself56
Behind Schoenberg’s idea of Grundgestalt, the basic shape, we can identify a bifurcated process in which for an element that repeats - the “thread” the listener can trace throughout the piece - others undergo transformations (in a way the repeating components are instrumental for the listener to perceive the ongoing transformations of their surroundings.) Without the repetitive
55 How much of this process is conscious and how much it isn’t is a thorny matter that will not be delved into this research. 56 Arnold Schoenberg and Leo Black. Style and idea. Selected writings of Arnold Schoenberg. Edited by Leonard Stein. With translations by Leo Black. (London: Faber, 1975) 290
60 quality of some elements, there would be no solid grounding for the perception of the reshaping process. A piece’s narrative can then be described in broad terms as the interrelations between the static-repetitive and dynamic-transformative elements.
These general observations are necessary to point out how Clementi’s music attempts to undermine the very perceptual process just described. The purpose of the following sections is to demonstrate how in Aus Tiefer, while the repetitive-static component of the narrative is not only present but overbearing, the dynamic-narrative component is virtually absent. More precisely, the subtle variable qualities that Aus Tiefer possesses can be found in elements other than the traditional carriers of narrative: while melodic material, harmony and basic rhythmic structures are written in stone, very subtly other elements, such as the sonic girth and “shapes,” undergo slight, hardly perceivable changes.
3.3. Aus Tiefer: Narrative of Deception
As I just mentioned, while in a traditional musical narrative elements such as pitch patterns, rhythm, harmony, dynamics, timbers, inevitably, if in different degrees, change over time, in Aus Tiefer all of those elements are fixed: once presented they stay the same throughout the entirety of the piece. In fact the four melodic fragments, transposition levels, instrumentation, orchestration and dynamic levels are all immutable from beginning to end. It would be very hard to argue how over time, any “reshaping”57 of the kind described by Schoenberg is taking place.
The way fragments and entire sections are repeated in the piece does not let the listener infer that any transformation of the material is actually taking place: its basic elements are never really varied or re-contextualized. One can safely say that the dynamic-transformative quality of
57 Ironically, though, one element that does change between panels is the actual “rhythmic shape”, i.e. the way the canonic entrances are organized. This variable element however is hardly perceivable given that all of the other elements are constant.
61 these elements seems to be amiss. The melodic fragments are repeated within each of the 19 panels and panels repeat at different points of the piece. From an audience’s prospective, the repeating elements dull any attempt to trace a dialectical evolution of the piece.
Counter-intuitively, it is exactly the dullness of Aus Tiefer’s repetitions and its hollow narrative that shows us how deeply Clementi is interested for his piece to deliver a specific perceptual outcome. Nevertheless, preventing the listener from engaging in a dialectical musical narrative happens by means of a convoluted process. While many elements, such as the melodic fragments and the canonic construction, lead the listener’s perception in the familiar grounds of musical tradition, others such as repetitiveness and lack of contrast seem to negate the existence of the paramount feature of a traditional piece, i.e. a narrative of contrasts. In a way, the presence of familiar elements constitutes a testimony of a “former” nature of the piece, a nature that, given the lack of its narrative raison d’être, is no longer present. This complex mechanism can be described through the words of Jaques Derrida:
The trace is not a presence but is rather the simulacrum of a presence that dislocates, displaces, and refers beyond itself.58
Aus Tiefer’s traditional features are a “trace” of musical narrative.
Before I get too entangled in the complex aesthetics of the representation of an erased object, let me stop and go back to the true goal of this chapter: to the investigation to the perceptual outcome of Aus Tiefer. To simplify the discussion and observe the workings of the piece form a listener’s prospective, we can reduce “the representation of an absence” to a game of deception in which the listener is firstly allowed to believe in a presence of something and then denied that very existence. Once and if this perceptual outcome will be correctly spotted in the
58 Jacques Derrida, Speech and phenomena: and other essays on Husserl's theory of signs. (Evanston: Northwestern University Press, 1973) 156
62 piece, the connection between Clementi’s abstract thought, illustrated in chapter 1, and the actual experience of the listener will be established.
3.4. Different layers of repetition
At its core, Aus Tiefer’s deception starts from the presentation of simple material layered in an equally simple repetitive fashion. These elements lead the listener to believe how the outcome, i.e. the piece, will also be fairly simple and predictable. And while neither the material nor its constructive principle change over the course of the piece, its sonic outcomes slowly but inevitably appear to be obscure sound masses where all sense of dialectical clarity is lost59. In other words, the supposed simplicity of a repetitive process added to the plain-sounding melodic fragments are perceptual “baits” for the listener’s deception to take place. It will be the goal of the following section to observe how repetition and deception operate in tandem: the former being the constructive principle and the latter being its sensorial outcome.
For the sake of understanding the detail of the repetitiveness and deception in Aus Tiefer, I can distinguish four different levels of construction. For each of the four levels there are distinct repeating elements and a counteracting, deceptive force that works against the clarity of the repeating mechanism.
59 To observe in detail how Clementi’s music relates to Wolfram’s research in its fascination between simplicity and complexity, see the last section of the chapter.
63 Level Where Element How Deceptive
element
Micro Within panels Melodic fragment Repetition at Thickening different pitch politonality levels Middle Adjacent panels Number of Gradual Rhythmic voices/fragmental content increases/decreases shapes Macro Overall structure Middle structures Nested Palindromic palindromes Construction Meta Musical tradition Melodic fragments/ Historical Absence of canon/text/instrumentation references narrative Tab. 7. Repetitive/deceptive constructions
A) Micro-structural
The repeating element at the microstructural level is the melodic fragment. There are two-plus-two melodic fragments in Aus Tiefer: theme one, theme two and inverted forms. It speaks for the general repetitiveness of the entire piece that these four short fragments are literally the only un-varying sonic cells that form a piece of almost thirty-minutes. Aside from the basic transformation that connects the original forms of theme 1 and 2 to their inversions, nothing happens to the material whatsoever: the pitch and rhythmical content of the fragments is immutable. The fragments are layered at different pitch-levels and given different entrances in time.
If we leave aside panels 9 and 11, all the other panels contain either one or two fragments60: theme 1 and its inversion appear either separately or together each with their fixed transpositions. Each version of theme 1 is constructed of 12 voices and 6 transpositions (the instruments simply shadow the voices without being given a different pitch level). When theme one appears in its two forms simultaneously they are simply stacked one on top of the other creating a 12+12 voices and a 6+6 levels of transposition. Theme two appears always with its
60 Panels 9 and 11 contain a short organ interjection that uses melodic material from another setting of the same psalm.
64 inversion with a fixed level of transposition and a fixed number of voices: 2 transposition levels for the original form and 1 for the inverted form, for a total of three. This, of all settings, is the one with the least amount of transposition levels. The number of voices for the second theme’s setting is always 24, making it dense in term of sheer sound level, but thin in terms of harmonic density.
With regard to rhythmic construction, for each of the panels the voices entrances are canonical, i.e. not simultaneous. The center of each panel is unmistakably the point of maximum concentration of sound, where music becomes an indiscernible maze of sound and not a single fragment or harmony can be securely separated from the other.
At a micro-structural level, deception lies in the simplicity of repetition of identical, easily identifiable, melodic fragments as perceptually contrasting with the striking complexity of the sonic masses that their iterative layering gradually generate. We can notice at this point how this perceptual oxymoron, i.e. simple, verbatim repetitions and their complex sonic textures, functions as an ideal bridge between the composer’s abstract aesthetic and the listener’s actual experience: slowly but inevitably the simple, easily recognizable melodies create a chaotic, indiscernible sonic texture that carry the listener into a maze of sound where no solid grounding in terms of harmony, rhythm or dynamic punctuation is provided.
As shown in chapter 2, Clementi plans his indiscernible textures with great care through the use of the negative-constraint algorithm. To know how the process works in detail is to appreciate how the deceptive construction is accurate even at its smallest level: each of the transposition levels is chosen because of its negative qualities, not repeating any interval of any other fragment. The reason behind the choice of using the negative constraint should now become apparent: the clear tonal quality of each of the fragments is perceptually contradicted by the stratified sound outcome since each of the canonic entrances will stay clear of repeating any
65 of the previous entrances’ intervals. By repeating intervals among different voices, a specific,
“defined” harmony could be reinforced, becoming a “grounding element” for the listener to grasp. In other words, melodic fragments, while solidly diatonic in themselves, do not harmonically coordinate with one another, as would be the case in traditional counterpoint.
Rather, they work to each other’s detriment. The slow layering of transpositions with non- repeating intervals slowly but irreparably undermines the tonal transparency of the fragments61.
The ultimate result of a simple layered construction of the same, simple, diatonic fragment is, therefore, a blur of sound in which no specific harmony can be heard and no specific beat can be felt. At a perceptual level the listener’s legitimate expectation for what looks and acts like traditional counterpoint is negated.
As Procaccioli notices,
[Clementi] […] deeply changes the nature and meaning of counterpoint and turns it into a symbol, in an evocative, abstract manner: counterpoint as symbolism62
Mattietti rightly notices how Clementi’s aesthetic is deeply related to Escher’s absurd constructions. Escher’s drawings feature familiar elements such as staircases, absurdly rearranged, creating a perceptual game of deception, as accurately described by Douglas R.
Hofstadter in Gödel, Escher, Bach: an Eternal Golden Braid :
Those staircases are “islands of certainty” upon which we base our interpretation of the overall picture. Having once identified them, we try to extend our understanding, by seeking to establish the relationship, which they bear to one another. At that stage we encounter trouble.63
In Clementi as in Escher repetition is deeply intertwined with its perceptual counterpart-
61 Just to speak of their openings: theme 1 and its inversion feature a perfect fifth leap, while the second theme features a leading tone neighboring motion. 62 Procaccioli in Albertson, Aldo Clementi: mirror of time 237 63 Douglas R.. Hofstadter, Gödel, Escher, Bach: an eternal golden braid. (New York: Basic Books, 1979) 97. For more on the influence of Hofstadter on Clementi see Mattietti, 2001
66 deception.
B) Mid-structural level
Within the whole macro-structural construction of the piece, analyzed in the next section, we find smaller, i.e. mid-structural level construction. At a mid-structural level the elements at play are adjacent panels or panels in close temporal proximity. The repeating elements at a mid- structural level are the number of voices or the fragmental material. Each panel contains (repeats) some elements of the previous and the succeeding one. The type of repetition that operates between panels concerns one of these two features. While some elements are left unvaried, some others are changed or added between one panel and the next. But this gradual change does not really affect the material in itself that returns unvaried. The changing element is, therefore, alternatively the number of voices employed in each panel, i.e. the texture’s girth, or, when that is left constant, the variety of melodic fragment(s) that grant its construction. Between panel 1 and 2 we find the same number of voices but two different versions of the first theme with 6 levels of transposition; then panel 1 and 2 are incorporated into panel 3 and is at the same time a simple sum64 of what has preceded it while introducing a texture made of 24 voices and 12 levels of transposition. Panel 4 keeps the number of voices constant, changing the melodic fragment to theme 2. The second theme panel acts in a way as a sort of climax, with the important feature of having the weakest harmonic layering of all panels: it only contains 3 transposition levels.
Panel 5 repeats the number of voices of panel 4 and the fragments of panel 3. Panel 6 and
7 revert to the number of voices of panel 1 and 2 and fragments of 1-2-3-5, creating a mid-level structural unit with a center in panel 4, which contains the second theme.
What has been described so far is a simple juxtaposition of the panels based on a principle
64 12 + 12 = 24
67 of gradual variation of sound quantities and material used. There is yet another subtle element that varies when panels are repeated in terms of fragmental material and number of voices (the transposition levels are always fixed) - their “sonic shape” as it has been illustrated in Chapter 2 p. 27.
At a mid-structural level, the listener is presented with gradual changes of textures. The deceptive character of this level consists in repeating some of the panels in all of their most recognizable features, such as fragmental material, transposition levels and number of voices in the case of panel 1 and 6, 2 and 7, 3 and 5 while changing their “sonic shape” a feature apparent when looking at the score but hardly recognizable, at least consciously, when heard.
C) Macro-structural level
The elements repeated at a macro-structural levels are the mid-structural level constructions. The macro-structure “imitates” the mid-level structures which are nested within it.
The macro-structure is a blown up version of the mid-level structure. This very idea creates a repetition at a “vertical” level, i.e. between levels of construction. There are three midlevel structures:
[1] : {1-2-3-4-5-6-7}
[2] : {8-9-10-11-12}
[3] : {13-14-15-16-17-18-19}
Structures [1] and [3] are an “imperfect” palindromes, imperfect since the first and second panels are repeated in sequence, rather than in retrograde. The “imperfection” at a mid level gets, in a way, “rectified” at a higher level since the last panel is, in fact, the same as the first and the next to the last is the second, etc. Also, while at a mid-structural level we only encounter
68 “imperfect” equalities such as the one between panel1 and 6 or 2 and 7, at a macro-structural level 1 and 19 the imperfection of their relation is, again, “rectified.” The perfect/imperfect quality of the equality lies not only in the panels having the same number of voices, fragmental material and levels of transposition in common (imperfect), but also their “sonic shape”65
[1] = [3] ? [2]
{1} ≈ {6} = {14} ≈ {19}
{2} ≈ {7} = {13} ≈ {18} ≠ {9} = {11}
{3} ≈ {5} = {15} ≈ {17} ≈ {10}
{4} = {16} ≈ {8} = {12}
Tab. 8- Sonic shape similarities
Mid-equalities Macro-equalities
{1} ≈ {6} {1} = {19}
{2} ≈ {7} {2} = {18}
{3} ≈ {5} {3} = {17}
etc. etc.
Tab. 9 mid-macro equalities
The deception at a macro level construction lies in this subtle game of similarities and perfect equalities between panels; these variations are hardly perceivable but, still, they exist.
Furthermore, following the same line of thought, one can notice how the particular kind of repetitiveness that a palindrome possesses - the traceability of a repeating event, such as the piece’s panels - is counteracted by the variable time span at which each of the repetitions happen.
65 In other words: while {1} ≈ {6}, {1}={19}
69 In other words, while each of the events will be repeated, the task of predicting when the repetition will occur will be not an easy one, especially given the length of the piece in question.
D) Meta-structural level
Repetitions within the three above-mentioned levels of Aus Tiefer are still not enough to fully convey the repetitive character of the piece. The clearly tonal, traditional fragment from the Lutheran chorale constitutes a meta-level repetition of musical tradition. The reference to the tradition of church music cannot be missed. Aside from its tonal character, the vocal setting, the canonical construction and the liturgical text are there to remind us of its origin and recreate its context.
Let me take a step back and observe how puzzling an effect Aus Tiefer and most of
Clementi’s late works might have on the unaware contemporary concertgoer. As a matter of fact,
Clementi, while known and appreciated by many, especially in Italy, never became during his lifetime a household name of the contemporary music scene, and while several reasons66 can be mentioned for the somewhat limited fame the composer achieved, one important factor might be traced to the puzzling aesthetic quality that pieces such as Aus Tiefer undoubtedly possess.
The historically familiar material, its endless repetition, unvaried from beginning to end, the highly controlled canonic layering can lead a listener to believe that the piece being played is:
66 In fact, there are indications that can lead us to believe Clementi to be the sort of artist who locks himself in an ivory tower and is indifferent to the audience’s reception of his work. I have never personally met the composer but I have had frequent encounters and discussion with close friends and family members of the composer. These encounters led me to believe Clementi to be a reclusive artist, generally indifferent to the “career” aspect of his profession. Aside from personal considerations, one can observe how the composer throughout his life seemed indifferent to elements that made contemporary music performances “appealing” to audiences and performers. Elements such as instrumental treatments, timbre exploration or interventions “on the stage” (by means of theatrical exploits by performers) the possibilities opened by computerized processes and sound analysis never really entered his compositions. Furthermore, from a performer’s prospective, his music lacked virtuosic qualities that are usually appealing to performers; in fact quite the opposite is true, Clementi’s pieces tend to relegate the performer to the role of a lifeless gear contained in a larger mechanism.
70 • A revival of past music, i.e. a piece à la Lutheran chorale
• A contamination between a past genre and new ideas
Ignoring the composer’s “spoken” intentions about the character that he intends his music to have, assessing the music solely from a listener’s perspective, one cannot make definite arguments against or in favor of one interpretation or the other. In the last issue of the
Contemporary Music Review dedicated to Clementi, Stefano Procacciolithrough a reductio ad absurdum notices how the composer’s work ends up in the same territory from which it so radically declared its departure. In his paper Procaccioli notes how Tre Canoni and, in general, the composer’s idiosyncratic style draws from “a cultural context in which the conceptual component of ‘serious’ music is quite present” but, paradoxically, given Clementi’s extremely controlled form
“one is strongly led to link Tre Canoni to the world of the classics.” 67
Procaccioli vaguely identifies contemporary “serious” music with the general category of conceptual art to eventually associate in an equally vague fashion Clementi’s work with the
“world of the classics.” Yet, these observations are not without value or insight. It would be hard to dismiss Procaccioli’s perception of an inherent classical character in Clementi’s music as inappropriate, wrong or even misled.
In Tre Canoni, one finds at least two facts that in spite of the original intentions, […] tend toward determining a reference to […] tradition: the use of contrapuntal relationships and the control of form
If a “bond with the past” is undoubtedly present, then are pieces like Tre Canoni or Aus
Tiefer mere celebratory homages to the tradition?
For many elements that are remindful of the tradition of music there are some important
67 Stefano Procaccioli Aldo Clementi, a Barometer of the Changes of Our Time? Some Observations after Listening to the Tre Canoni (but not only that. In Dan Albertson, Aldo Clementi: mirror of time II (Abingdon, Oxfordshire: Routledge, 2011)
71 deficiencies that prevent a straightforward labeling of Aus Tiefer as a celebratory revival. These deficiencies are not immediately apparent and their subtlety is an often-overlooked trait of
Clementi’s oeuvre. In fact if one lets the meta-historical fogginess created by the familiar fragments and canonic construction dissipate something else will become clear; there is something terribly amiss in Aus Tiefer, the horror of, in this case, a complete lack of a traditional musical narrative. The saturated repetitive textures of Aus Tiefer are immutable, as I just observed, at all levels of construction. The material does not change within the panels or among the panels, there is no structural arc, the piece does not unfold but rather “folds” onto itself, in a palindromic fashion.
In Aus Tiefer, the contrasting elements that perceptually contribute to form a musical dialectic are systematically eradicated through the use of the multi-layered repetitiveness. As a result of repetition there is no contrast at any of the different levels, whether micro, middle, macro or even meta. Counterpoint is deprived of its transformative qualities, while formal construction lacks its traditional dialectic of contrast. The absence of true contrast leaves the listener’s perceptions hanging because the mechanism of tension and release that music traditionally enacts is absent.
So many elements lead the listener to known territories of simple material and familiar sounding constructions only to leave her in a sonic space where even the simplest structural indication is missing. Nothing can be easier to perceive than something that is simply repeating itself, yet repetitions are working to each other’s detriment at all levels: the local level, through the layering of constrained transpositions, the mid-level, though a seamless expansion and thinning of textures, the macro-level through nesting.
In a sense, the piece is telling us not what it is but what it is not. If at the micro structural level the parallel with of Escher comes to mind, at the meta-structural level, Magritte’s non-pipe
72 seems to be the most accurate visual representation.
Fig. 18 René Magritte, The Treachery of images. 1929
3.5 Conclusions: Clementi’s legacy: Sonic Automata
Clementi’s pieces are striking for, on the one hand, they represent something they are not while, on the other hand, they appear as something new. By a slow, patient work of carving out, scratching the surface and sanding off all of the angles, Clementi leaves us music that has lost all of its dialectical and pseudo-linguistic functions and has gained new fascinating features. To better understand the latter aspect I would like to refer to the research of the mathematician
Stephen Wolfram.
It has been by sheer chance that, during the course of this research, I have stumbled upon
Wolfram’s book, A New Kind of Science published in 2002. This book, in a totally unexpected way, shed a new light on the work of Clementi. Stephen Wolfram’s work is concerned with the study of so-called cellular automata,68 the study of the behavior of simple programs. To oversimplify
68 A cellular automaton is a collection of "colored" cells on a grid of specified shape that evolves through a number of discrete time steps according to a set of rules based on the states of neighboring cells. The rules are then applied iteratively for as many time steps as desired. Von Neumann was one of the first people to consider such a
73 Wolfram’s magnus opus, A New Kind of Science describes how simple programs, i.e. a simple set of rules, can produce highly complex and unpredictable results. Wolfram like Clementi is fascinated by the observation of the outcomes that simple rules and initial conditions produce when they are run ad libitum. The image-rich book is ultimately a work of scientific research unconcerned with issues of aesthetics and artistic endeavors, but Wolfram’s approach to science can be easily related to Clementi, for the scientist becomes the wondering observer of simple experiments and their unpredictable results.
In the following quote, Wolfram describes his “eureka” moment that led him to embark in a long research of cellular automata:
[…] our everyday experience in building things tends to give us the intuition that creating complexity is somehow difficult, and requires rules or plans that are themselves complex. But the pivotal discovery that I made some eighteen years ago is that […] such intuition is not even close to correct.[…] what I found-to my great surprise- was that despite the simplicity of their rules, the behavior of the programs that I looked at had behavior that was as complex as anything I had ever seen.69
Wolfram’s fascination and experimental fixation with the world of simple programs and their occasionally unpredictable outcomes is easily relatable to Clementi’s own fixation for elaborate sonic masses springing from simple elements. Furthermore both Clementi and
Wolfram, instead of attempting to direct their experiments in a specific direction, controlling their calculations to guide them towards specific musical or scientific goals, let the “rules” run themselves ad libitum, to then observe their behavior.
Both Clementi and Wolfram70 founded their original studies on simple sets of instructions, and simple initial states. They both present a fascinated look at the way that these
model, and incorporated a cellular model into his "universal constructor."(http://mathworld.wolfram.com/CellularAutomaton.html) 69 Stephen Wolfram, A new kind of science. (Champaign, IL: Wolfram Media, 2002) 70 Wolfram sets up simple rules which determine how a cell will be on black or white according to its neighbors at successive states of iteration.
74 simple processes produce the complexity just by simple iterative procedures. Visually there is a striking similarity between the images in Wolfram’s book and the specific way Clementi represented his music. The triangular shapes of both the Automata and Aus Tiefer’s panels are an intriguing aspect of the odd couple Clementi-Wolfram.
75
Fig. 19 Cellular automata
Fig. 20 Aus Tiefer
To my knowledge, the composer never acknowledged Wolfram’s work among his
76 influences, though I would not be surprised to learn otherwise, given the multiple similarities71.
In conclusion, the modern field of Cellular Automata’s provides a fecund interpretation of Clementi’s legacy. Through the words of Wolfram we can appreciate how Clementi’s work tapped into a “New Kind of Music,” aimed at exploring rather than narrating, in which the composer, is an observer wondering about the origins of complexity.
[…]the Cellular Automata we set up are by any measure simple to describe. Yet when we ran them we ended up with patterns so complex that they defy any simple description at all. And one might hope that it would be possible to call on some existing kind of intuition to understand such a fundamental phenomenon. But in fact there seems to be no branch of everyday experience that provides what is needed. And so we have no choice but to try to develop a new kind of intuition. And the only reasonable way to do this is to expose ourselves to a large number of examples.72
“Exposing ourselves to a large number of examples” is what Clementi did for the last forty years, reinventing his role and opening new doors for aesthetic exploration.
71 Clementi did acknowledge the work of another mathematician Douglas Hofstadter as one of his influences. 72 Wolfram (2002)
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