Saturday, November 6, 2010

Recital Program notes

As part of my masters program at V.C.A.M. I will give a 45 minute recital on December 2nd at 6.30pm, at Federation Hall, Melbourne.
Unfortunately I cannot exceed my word limit of 1000 for my program notes. Hence I am publishing the 'extended version' here. Enjoy!


Marc Hannaford - piano

Scott Tinkler – trumpet

James McLean – drums

* * * * *


90+ - Elliott Carter

Anda Two {trio version} – Hannaford

More (than Nothing than Ever Before) – Hannaford

Rumination - Hannaford

Anda Two {solo version} – Hannaford

90+ {modelised version} – Carter/Hannaford

To do, having learned, is an intellectual prejudice. To learn, having done, is an absurdity. What is real is the synchronism of to learn while doing and to do while learning.”[1]

Jankelevitch’s perceptive passage regarding improvisation demonstrates the circular nature of this art form. Our own artistic development relies on the synchronised interplay between ‘doing’ and ‘learning.’

By coming into contact and beginning to play with Australian improvisers Scott Tinkler, John Rodgers, Ken Edie and Elliott Dalgleish, I realised my “doing” was not sufficiently developed to have what I felt were meaningful music discourses with them.

In 2006 I was introduced to the musical language of American composer Elliott Carter (b. 1909). Firstly, I feel that my analysis and implementation of many of Carter’s compositional techniques has allowed me to develop a musical language whereby I can improvise with these people with probity and conviction.

Secondly and more recently, Carter’s rhythmic language as used in 90+[2] and Two Diversions[3] has led me to create frameworks for improvisation that are dually related to the notion of form in the jazz tradition and the notion of structural polyrhythm in Carter’s music. Thirdly, using some of Carter’s scores as a reference, the variety of ways these rhythmic frameworks may be realised in a performance in relation to the traditional roles of those instruments in an ensemble (particularly in relation to the jazz tradition) has led me to question, re-evaluate and develop my own attitudes to ensemble playing.

The structural basis of Anda Two (Marc Hannaford) is the juxtaposition of two polyrhythmic pulsation streams. The pulsations are at intervals nineteen and twenty-three semi-quavers, respectively. This composition grew out of my investigation of mid-range polyrhythms in Elliott Carter’s music and his choice to often avoid prime numbers in the generation of polyrhythmic streams. It is interesting to me that, while non-prime numbers provide a greater number of discrete realisations of a single polyrhythm in terms of simultaneous primary pulsation (what most people would call ‘the beat’) division and grouping, polyrhythmic streams containing prime numbers have only one realisation; that is, each polyrhythmic stream is generated by grouping a common primary pulsation division. The coincidences of these polyrhythmic pulsation streams provide the beginning and end of the form on which to opening melody and subsequent improvisation is performed.

In this program, this piece is presented twice, once for solo piano and once for trumpet/drum kit/piano trio. The reason for this double-presentation is two-fold. Firstly, I hope it will give the listener a chance, if they so desire, to hear the rhythmic framework of the composition. In my experience as a listener, hearing multiple realisations of the same work may result in the active listener perceiving common motifs. In this case that motif is the underlying rhythmic framework mentioned above. Secondly, each realisation presents challenges in term of improvising what, in the musicological terminology used to analyse Carter’s rhythmic language, is called the surface rhythm. While there is some continuity between the challenges in solo and group realisations, the different orchestrations of what is essentially a similar musical vocabulary result, in my experience, in unique challenges. Playing solo allows the performer to make all choices regarding musical material, but burdens them with the responsibility of being the sole maintainer of the larger rhythmic structure, resulting in the need to balance improvisatory freedom with compositional structure at a high level. This is a theme I will return to in this essay at a latter stage. The trio realisation presents challenges that also balance freedom and structure; whilst some trio members may maintain the large rhythmic framework others are able to improvise without the inhibition of the possibility of losing track of where in the framework they are, but also means that individual’s improvisations may introduce unexpected materials, possibly resulting in the other member’s disorientation regarding the improvisatory framework. This problem has been ‘solved’ in my research by developing the materials for improvisation as a group in rehearsal, ensuring a kind of clarity improvisation that allows for more improvisatory freedom.

90+ (Carter) is built around a stream of ninety, evenly spaced polyrhythmic pulsations. This stream provides a structural framework around which shorter polyrhythms and surface rhythms of various speeds are composed. A great variety of character and speed is achieved by the use of metric modulation, which alters the speed of the primary pulsation whilst maintaining the polyrhythmic pulsations at a constant speed of 18 b.p.m. . Carter’s magnum opus in this vein is Night Fantasies written in 1980. Using a systemised approach to rhythm and harmony, Carter creates a ‘series of continuously changing moods’ that ‘capture the fanciful, changeable quality of our inner life at a time when it is not dominated by strong directive intentions or desires – to capture the poetic moodiness that, in an earlier romantic context, I enjoy in works of Robert Schumann like Kreisleriana, Carnaval, and Davids-bündlertänze.”[4] 90+ is demonstrative of the trend in much of Carter’s later music being less systemised than the works composed around the time of Night Fantasies. However 90+ maintains the sense of interplay between foreground and background: “Its foundation is rigorous and regular; its musical surface is improvisatory and changeable.”[5]

This sense of the musical surface being improvisatory in character creates an obvious connection with my own study of improvisation. Indeed, one main challenge in my performance-lead research has been the aural assimilation of the local polyrhythms and surface rhythms Carter composes.

What may not be so obvious, given Carter’s obvious rigor in constructing compositional frameworks and developing a harmonic language, is his connection to a time in western art music when improvisation was still considered a valid form of artistic expression.

The polyrhythmic streams Carter generates in his works are orchestrated in such a way as to emphasise polyphonic texture; multiple voices sounding simultaneously that develop linearly.

This reference has been extremely useful in my analysis of Carter’s works. Roeder used this technique to analyse the rhythmic streams of Schoenberg’s music.[6] In his paper, Roeder is able to parse Schoenberg’s music into rhythmic parts and offer an analysis, in terms of pulsation streams, of each. "Pulse streams are considered to be distinct continuities, not levels or groupings of each other, so this approach does not involve meter in the exclusive and hierarchical . . . Rather, it analyses an irregular surface as the sum of several concurrent regular continuities . . ."[7] The only difference in applying this method to Carter’s music is that the pulsation streams become polyrhythmic, whereas in Schoenberg’s they generally are not.[8] Roeder’s comments are perceptive and useful in understanding the role this rhythmic structures play in this music: “In music that deemphasizes traditional harmonic or linear processes these pulse streams may integrate the accents of local rhythmic figures synergistically into compelling large-scale continuities. The nature and the interactions of these continuities -the synchronization of pulse streams and rhythmic motives relative to each other-create rhythmic form in the music."[9]

My program contains 90+ in its fully notated version, as well as a modelised version. In discussing the multiple realisations of a single piece of music in the central African music tradition, Simha Arom states: “While the score of a work of cultured music is the link between the abstract thought of the composer and its materialisation, the score of music from an aural tradition is the link between living musical reality and an abstraction of it. In both cases, the score links a message with a code, but in one, its purpose is the reproduction of the message from the code, while in the other, it is the discovery of the code through a study of the message or set of messages; and after the code has been determined, the score remains indispensable for showing the relationships between the code and the multiplicity of messages it is capable of engendering. In most music from aural traditions . . . there is no definitive text. Two performances of a given piece will differ, often considerably, even though the users treat them as identical. There is a text, but not a univocal one."[10] A modelised score represents this underlying “code” and can be used to generate multiple realisations of the same piece. The modelised score of 90+ contains only the ninety evenly spaced polyrhythmic pulsations that form the structural foundation for Carter’s improvisatory surface rhythm and local polyrhythms. For my realisation of the modelised version of 90+ I will improvise this surface and local polyrhythmic activity while maintain the ninety polyrhythmic pulsations. While Carter may not be easily linked with the music of central Africa, the connection between Jazz and African music is well known and documented. My connection to both the Jazz and western art music traditions facilitates this exchange, then, as I am able to use the ethnomusicological approach to analysing central African music to relate to Elliott Carter’s music through improvisation.

More (than nothing than ever before) (Marc Hannaford) is an exploration of local polyrhythmic materials used in Carter’s Two Diversions.[11] The various polyrhythms composed for the piano and drum kit intersect sparingly, roughly once every few bars, and consist of orchestrations of polyrhythms at various speeds, using a common primary pulsation division. The trumpet melody weaves through these two parts, remaining linked to them through a common primary pulsation, but utilising different and changing primary pulsation division so that it never coincides with either of the parts. The form on which the group improvises is a simplification of this idea, using a series of pulsations that gradually speed up and slow down in relation to the primary pulsation. Carter uses this notion of polyrhythmic speed in constructing each of the two voices in Two Diversions. In movement one, one voicing maintains a regular speed while the other articulates various polyrhythmic speeds around it (much like 90+) The opening of the second movement presents two polyrhythmic streams that are similar in speed. As the piece progresses one gradually speeds up while the other gradually slows down.

While at first glance Elliott Carter may not appear to have very much to do with the broader concept of developing an approach to playing Australian contemporary improvised music, closer inspection reveals some interesting philosophical links. While it is not at all my aim to imply that the American composer’s (whatever that may mean) socio-economic landscape at that time is the same (or even similar) to my own, I do feel that, in surveying Carter’s examination of the challenges he faced (faces?) in finding his own artistic identity, I may use some of the issues Carter raises to answer questions I have of my own situation.

Carter, in discussing the American composers’ landscape circa 1961 makes three particularly interesting statements:

“Paralleling the experiences of many Europeans, Americans have recently come to feel that this musical heritage does not furnish answers to many important new questions, necessitating a search for new answers outside the traditional approach."[12]

The “traditional approach” Carter mentions here is referring to the pedagogical/historical continuum of the European art music tradition.

"On the other hand, in large part because of the heterogeneous character of their country's heritage, American composers over the past fifty years have studied one European school of composition after another with great care, in their desire to express themselves truly and effectively. As a result, there can be no simply defined American tradition or style, and it is entirely possible that there never will be one."[13]

"To an American musician, the post-War European trends seem to have been directed toward the disintegration of the routines and formulae that characterised the highly accomplished techniques of all previous, great European composers. To us, this appears to have been undertaken in a spirit that is very thoroughgoing, even to the point of denying the fundamental reasons traditionally put forth for writing music. A definite break with the past on every level seemed urgent to the younger European composers."[14]

Each of these statements demonstrates a different aspect of the challenge Carter felt was facing him at this time. Seeing a generation of European composers develop personal approaches to music making that, through careful study of tradition, were able to question the role fundamental compositional techniques such as tonal harmony and rhythm played in creating ‘new’ music, perhaps Carter realised he too had to question the traditional approaches to music making so that he might develop a music that, while informed by tradition, was reflective of their unique cultural and geographic situation.

Faced with the established tradition of American Jazz that is itself embedded in the complex socio-economic-political framework that is North America, many Australian improvisers, in my experience, look for a way to adapt this language to reflect their own cultural and geographic situation. In light of this, and reflecting back to my first encounters with Scott Tinkler, John Rodgers, Ken Edie and Elliott Dalgleish, I can now infer that the solution I sought was not only related to my want to creating music with these people, as I described above, but was also part of a larger concern to develop an artistic voice, that, while informed by tradition(s), was my own. Indeed, it was this very process my mentors has gone through in their own lives.

In light of this is it is only natural that I should turn to traditional jazz forms as part of the process of assimilating Carter’s rhythmic materials. Lennie Tristano (b. 1919) provides an interesting case study in this respect. Firstly, he would often record standard jazz repertoire without stating the primary melody, instead using the underlying harmonic form as a point of departure for his own improvisations. This process is not unlike the ‘modelised score’ concept expounded by Arom above. Secondly, Tristano was keenly interested in developing rhythmic variety in his improvisations. The recording I am drawing on: Deliberation[15] demonstrates both of these concerns. It is based on the traditional jazz standard Indiana. While it was common practice for be-bop era musicians to compose new melodies on existing chord changes (Gershwin’s I Got Rhythm being adapted by Parker to form Anthropology, for example), Tristano’s realisation of this chord progression is improvisatory. Tristano creates rhythmic tension mainly via displacement; effectively he conceals the traditional points of emphasis (the start of the bar, major points in the form) for extended periods. My performance, Rumination, places the same harmonic form in the time-signature 7/4, and draws upon the local polyrhythmic language of Carter to create oblique gestures over the form.

* * * * *

“The musical universe, not signifying any particular meaning, is first of all the antipode to any coherent system. The philosopher who reflects upon the world aspires at the very least to coherence in attempting to resolve contradictions, reduce the irreducible, to integrate the necessary evils of duality and plurality. Music ignores such concerns since it does not have ideas to line up logically with one another. Harmony itself is less the rational synthesis of opposites than the irrational symbiosis of the heterogeneous. Is it not harmony that, in Plato, causes contradictory virtues to reconcile and agree among themselves? The experienced simultaneity of opposites is the daily regime, incomprehensible as it might be, of a life full of music.”[16]

The notion of contrast in music is not a new one. Although Plato saw music as a danger to the level-mindedness of man, it harkens back to his notion of an object/body split[17]. It’s realisations in music are well known: melody/harmony, content/form and text/music, to name a few. Jankelevitch, however, sees this notion of contrast as the very thing that gives music its charm. It is the thing that results in the ineffability of music; music reconciles elements that would seem irreconcilable. Jankelevitch gives the example of polyphony as the only instance where multiple melodies can he heard simultaneously, on more or less equal footing. This notion of polyphony, then, brings us back to Carter, and in the case of my program, the notion of interplay between the contrasting elements of structure and improvisation. While this is a commonly excepted paradigm in the musical world, these two terms are not mutually exclusive, especially for someone, like myself, who pursuing developing a language for improvisation through structured concepts like those in Carter’s music.

My process of coming to terms with a new (for me) language for improvisation that is based on Carter’s rhythmic language has been via a gradual building up, in complexity, of rhythmic vocabulary. Starting with the very basic ideas of primary pulsation, primary pulsation division and grouping, and utilising a strict methodology involving the exploration any number of combinations of these factors, I have gained an intuitional aural understanding of enough of Carter’s rhythmic language to improvise using it as a basis. The challenge has then become to maintain this language while also adding a ‘higher’ level of rhythmic structure, so that the improvisation may still develop organically (from the creators point of view) whilst also having some reference (Carter’s scores were used in this regard) to the overarching, form-giving rhythmic structures. This method of mixing the improvised with the structured, or, as is becoming more apparent in these notes, the mixing of various kinds of structure, is exemplified not only in this recital, but is currently my mode of considering all of the performing I do, no matter what the points of reference are (Jazz, Carter, etc.). This technique of building from the ‘bottom, up’ is in stark contrast to the musicological way of analysing Carter’s large scale rhythmic structures, which, citing the idea that the meaning of music is not contained in it’s details, takes the largest structures first (in the case of Carter, structural polyrhythm and the length, in time, of the work), and, using mathematical calculations, derives the notation for the smaller structures. This method, although a valid method for analysis, is practically useless for anyone wishing to adopt Carter’s rhythmic language to use in a creative way. As Hofstadter demonstrates in his investigation into intelligence and creativity in ‘Gödel, Escher, Bach’[18], building a complex model up from smaller, cellular ideas is not only an effective methodology in teaching and learning, but also mirrors the model we have of intelligence itself.

My notion of interplay between structure and improvisation, therefore, is one that is not only natural and engaging in the realm of music (Jankelevitch may even say that this is how I might give meaning to my music), but is also in line with a greater notion of what intelligence is.

In conclusion, I am not under the impression that any of this information in my notes conveys the meaning of any of the music contained in my program. Jankelevitch states in his book that it is impossible for the performer to convey any particular meaning to his audience, but that it may mean anything to anyone. It is an open system, “not signifying any particular meaning ”[19] and therefore, according to Jankelevitch, ineffable. Similarly, I believe, Carter is saying something similar when he talks of the composer: "What he is aiming at, after all, is a whole in which all the technical workings are interdependent and combine to produce the kind of artistic experience that gives a work its validity and in so doing makes all its procedures relevant."[20] While I am concerned with details in the sense of using them to develop a language, in the end, the ‘meaning’ or any piece of music can only be determined on an individual basis.

[1] Vladimir Jankelevitch, Music and the Ineffable (New Jersey: Princeton University Press, 2003), 28-29.

[2] Elliott Carter, 90+ (New York: Hendon Music, Inc., Boosey and Hawkes, 1994).

[3] ———, Two Diversions for Solo Piano (New York: Hendon Music, Inc., Boosey and Hawkes, 2005).

[4] ———, Night Fantasies (Associated Music Publishers Inc., 1980), program notes.

[5] David Schiff, The Music of Elliott Carter, Second ed. (Ithaca, New York: Cornell University Press, 1998), 213.

[6] John Roeder, "Interacting Pulse Streams in Schoenberg's Atonal Polyphony," Music Theory Spectrum 16, no. 2 (1994).

[7] Ibid.: 232-33.

[8] Ibid.: 233.

[9] Ibid.

[10] Simha Arom, African Polyphony and Polyrhythm, First ed. (Cambridge: Press Syndicate of the University of Cambridge, 1991), 173.

[11] Carter, Two Diversions for Solo Piano.

[12] Elliott Carter, Collected Essays and Lectures, 1937-1995, ed. W. Jonathan Bernard (Rochester, New York: University of Rochester Press, 1997), 63.

[13] Ibid., 66.

[14] Ibid., 70.

[15] Lennie Tristano, The New Tristano (Atlantic/Wea, 1956).

[16] Jankelevitch, Music and the Ineffable, 18.

[17] Richard Kraut, "Plato," in The Stanford Encyclopedia of Philosophy (The Metaphysics Research Lab, Center for the Study of Language and Information, Stanford University 2009).

[18] Douglas R Hofstadter, Gödel, Escher, Bach: An Eternal Golden Braid (Basic Books, 1999).

[19] Jankelevitch, Music and the Ineffable, 18.

[20] Carter, Collected Essays and Lectures, 1937-1995, 214.


Arom, Simha. African Polyphony and Polyrhythm. First ed. Cambridge: Press Syndicate of the University of Cambridge, 1991.

Carter, Elliott. 90+. New York: Hendon Music, Inc., Boosey and Hawkes, 1994.

———. Collected Essays and Lectures, 1937-1995. Edited by W. Jonathan Bernard. Rochester, New York: University of Rochester Press, 1997.

———. Night Fantasies: Associated Music Publishers Inc., 1980.

———. Two Diversions for Solo Piano. New York: Hendon Music, Inc., Boosey and Hawkes, 2005.

Hofstadter, Douglas R. Gödel, Escher, Bach: An Eternal Golden Braid: Basic Books, 1999.

Jankelevitch, Vladimir. Music and the Ineffable. New Jersey: Princeton University Press, 2003.

Kraut, Richard. "Plato." In The Stanford Encyclopedia of Philosophy: The Metaphysics Research Lab, Center for the Study of Language and Information, Stanford University 2009.

Roeder, John. "Interacting Pulse Streams in Schoenberg's Atonal Polyphony." Music Theory Spectrum 16, no. 2 (1994): 231-49.

Schiff, David. The Music of Elliott Carter. Second ed. Ithaca, New York: Cornell University Press, 1998.

Tristano, Lennie. The New Tristano: Atlantic/Wea, 1956.


  1. Hi Mark,
    A very interesting essay and insight into your musical endeavours/passions. I have a quick question to better understand this. What do the words "univocal" and "modelised" mean? I'm assuming modelised is a term created to fit Carter's own musical definitions/constructs? Could you give me an exact definition?
    It's near [10]. Thanks for sharing this.
    PS: I'm keen to read the Gödel, Escher, Bach book now too.

  2. Thanks for your interest, Heather.
    My dictionary defines univocal as:

    "adjective Philosophy & Linguistics
    (of a word or term) having only one possible meaning; unambiguous : a univocal set of instructions."

    Modelised is explained by Arom (which I quote). How I've related it to my work with Carter is also in this passage.