Monday, 9 May 2005
Sunday, 8 May 2005
was noted that his artistic expression came into tension with an urge to make money to survive
Module: Texts & Contexts – The Music of Anthony Braxton (MUSI3722)
Module Tutor: Dr Luke Windsor
Give a balanced and reasoned assessment of Braxton’s music.
“The limits of my language are the limits of my world”
(Wittgenstein, The Tractatus, 5.6)
Anthony Braxton is a controversial figure whose works draw on a multitude of aspects from a variety of traditions around the world. In addition to being influenced by elements from seemingly disparate musical traditions, he is considered to be a deeply introspective philosophical individual.
In his work, one perceives that mechanistically fusing the disjunct is the dominant compositional process. However, his philosophical ideology underpinning his creative output makes the model of tripartition relevant: he believes that things occur in threes – “past, present, future; mental, physical, spiritual; restructuralism, stylism, traditionalism”.[1] This invites an appraisal of discourse and theory: on which of the tripartite levels does this consideration of Braxton’s work apply to? Typically, tripartition concerns three levels concerned with the kinds of sounds present in the work, the structure and logic of the work, and any extramusical directions. These roughly correlate to the poietic, neutral and esthesic levels respectively.[2], [3] For example, it can be seen that a core component of Braxton’s processes are based around the neutral level as he adopts an approach which is as close to complete objectivity as one can get. A far better approach is to say that elements of each level are combined here, but with the neutral level featuring most prominently. The esthesic level is important too, as reception histories throughout Braxton’s compositional career suggest that, where his work seems to embrace characteristics from multiple genres, the main proponents of each of these generally chastise or altogether ignore his work.
Returning to the concept of objectivity in music performance, it may initially appear that illustration of technical procedure and proficiency takes precedence over conventional musical systems such as harmony and metre. When I say that ‘technical proficiency is valued more in a Braxtonian world than other conventional musical systems’, I do not mean that Braxton completely expunges the entire Western canon of music history. Rather, his techniques obliquely acknowledge and consolidate upon this history. This statement is re-inforced by Braxton’s view that “we have to remember the importance of fundamentals.”[4]
As Braxton himself observed, “all of the masters have demonstrated a unique way of affirming their personalities in the music.”[5] This highlights the importance of developing and maintaining his own personal voice in a way which conforms to the practices he adopts. I think this is what Braxton meant when he refers continuously to the concept of restructuralism throughout the Lock interviews. Furthermore, it should not necessarily be a reflection on Braxton’s music that it initially appears so obfuscated and convoluted. It may be argued that merely because we have a better understanding of other (non-Braxtonian) musical languages and means of artistic expression, this should not preclude the possibility of there being other systems in the musical world. If anything, perhaps it is a reflection on us that, generically speaking, we lack the capacity to commit ourselves to new means of understanding. This is extremely well illustrated by the prevalent attitudes of critics in the early Seventies: Braxton’s Four Compositions (1973) received widespread acclaim purely because of an overriding perception that he had shunned the ‘aimlessness’ of new music, and “thus maintained the formally conservative nature of pre-1960s jazz.”[6]
Braxton became active in jazz at a time when the concept of freedom was being expressed in contrasting ways. The motion towards freedom in jazz started in the Forties with figures such as Lennie Tristano, Warne Marsh, and Paul Desmond, with what was referred to as the ‘intellectual West Coast style’. This was furthered and consolidated by the jazz of the late Fifties and early Sixties on the opposite side of the USA – the ‘hard East Coast freedom’. Rather than list dates, it may be more fruitful to talk in terms of ‘waves’ of players. For instance, key figures in the ‘second wave’ of jazz developments would include Ornette Coleman, John Coltrane, Eric Dolphy, Sonny Rollins and Cecil Taylor. Coleman was of particular importance as he established a certain freedom from the rigidity of pre-defined frameworks – although it is widely acknowledged that there were precedents. By placing an emphasis on melody, Coleman rejected European approximations of Afro-American music, which can only strengthen a long-held collective belief that the rhythmic constituent of jazz is of African origin.[7] However, it is important to remember that no singular strand of musical history is responsible for influencing Braxton. By his own admission, he was also interested in the religious mysticism of contemporaries such as Sun Ra, by the instrumental manufacturing techniques of Harry Partch, and by modal extemporisation in the work of Miles Davis: “a tradition-centred synthesist, he would […] make sense of the anarchy of the past by redefining it aesthetically in the context of the mainstream.”[8]
In some respects, the theorizing of Braxton’s music is both inevitable and unavoidable, due to not only the self-inflicted intellectualisation he brings to his compositions, but also the complex terminology surrounding much of his creative output. Furthermore, it is important to remember that Braxton did not consider the world of post-war American music to be easily separable into distinct categories. Condoning such an attitude meant that “he was liberated from the conventional notions of genre, style, and value.”[9] Inferred under this liberation is the opportunity to create and develop types of musical language based on various historical constructs.
This liberation from convention came about, in part, by the processes of social and political change which were occurring in Chicago from 1966-69. It was “an examination of all that was new [and] a time of social upheaval.”[10] This change was of vital importance if Braxton’s music was to be understood in a new context: for the first time, music created and produced by minority group in society was not automatically repudiated. Braxton had been particularly active in the AACM since its inception in 1965, and upon joining, he found it to be a major benefit, as it put him in contact with several like-minded musicians. A by-product of this was the inauguration of the Creative Construction Company, with Leo Smith and Leroy Jenkins. However, by 1969 he was beginning to seek different challenges and ultimately find other players, which culminated in him forming a group called ‘Circle’ with Chick Corea, Dave Holland and Barry Altschul. The unifying feature of the AACM was a challenge to conventions of American music which, paradoxically, was beginning to challenge itself as one of four reactionary musical currents. The AACM could be described as an ‘organisation of marginality’ if one defines marginality as
“a group who finds its desire to absorb and emulate the culture of a dominant group in an attempt to attain and enjoy the latter’s privileges and status, in tension with its urge to continue to identify with many of its own central cultural traditions.”[11]
The AACM was at the centre of the first of these musical currents, termed the ‘Chicago Black Jazz Avant-Garde’. The AEC (Art Ensemble of Chicago) would also come to prominence – Braxton himself played with musicians from the AEC, among them Joseph Jarman. One of the principal aims of the Chicago Black Jazz Avant-Garde was to consolidate and develop a stylistic assimilation of prior African and European musical characteristics; fundamentally, this meant the merging of African rhythms with European harmony. Braxton quite clearly explores this train of thought in composition 5, written for piano in 1968. In his own writings, he notes that “composition 5 was written without a formal plan or imposed structure. […] Each section was written with respect to its basic language criteria.”[12] An analysis of this composition may be found in Appendix A.
The second of these, known as the ‘European Serial Avant-Garde’, concerned itself with serialistic techniques founded on the concept of Pointillism – that is to say, the systematic scattering and fragmentation of melody in a stylistically homogenous way. Interestingly, Marilyn Crispell, the pianist in Braxton’s quartet, has been identified as performing in such a manner: “[She] plays more pointillistically.”[13] In particular, there was a focus in this avant-garde on timbre, rhythm, space, indeterminacy, layering, and a return to large-scale ideas.
The third of these was what became known as the American Experimental Tradition. Its key features were those of montage, layering, indeterminacy, use of existent materials, (particularly in a patriotic sense) and small scale repetition. This tradition, in effect, laid the groundwork for the inventions of minimalism and process music, as exploited by Glass, Reich, Cage, and Ives, amongst others. Non-musical instruments were sometimes included under this framework, as Ives’ The Unanswered Question (1908) shows, including an instruction for a pianist to use a piece of wood to form a cluster chord. The features of montage and layering can also be seen in the analysis of Composition 5. It may be argued that Braxton was as true an experimentalist as Ives in the sense that both had a profound understanding of their respective heritages, which they both utilised in their work.
The fourth of these, occurring from the mid-1960s onwards, was known as British Free Improvisation, a term associated with Derek Bailey and Evan Parker, the former of which Braxton performed with in 1974. The main concept behind this was in the shunning of pre-planned materials, and the subsequent advocacy of venturing into the musical unknown.
Broadly speaking, then, these four musical currents showed that there was a distinct move away from the confines of rigidity in traditional musical forms and structures, which occurred simultaneously on both sides of the Atlantic. However, this freedom was far from ubiquitous: it must be remembered that freedom may not necessarily be the terminus for all the aforementioned. As demonstrated above, Braxton had at least a foothold in all the major currents of the day. According to Braxton, “language is shaped by the values of its users … people tend to equate abstraction with negativity.”[14] Therefore, if he was interested in developing a language music for saxophone (a concept of abstraction most neatly subsumed under the avant-garde experimentalism and European serialistic methods) then such a language would initially have had a limited number of, one presumes, reasonably intelligent users. This is a great irony, because the number of people interested in abstract means of expression, and by extension Braxton’s creative work exploiting abstraction, would have helped preserve its original values.
Another major Western development was that of the tempered scale. A key exponent of this was Harry Partch. ‘Temperament’, according to Partch, is defined as “a system which robs its intervals of their purity.”[15] These developments were at the detriment of the temporary advances in improvisation. Braxton is acknowledged as being influential in its subsequent re-introduction.
For Braxton, the musical world was not about clear, distinct delineation but a continual evolution of several assimilated styles, none of which were in stasis. This may well be something that he had in common with his fellow countrymen: “The young black composers who emerged during the mid-century years were more eclectic … [they] drew freely upon widely divergent styles.”[16] To use Braxton’s own terminology, such an evolution could be labelled re-structuralist. He defines this as “the phenomenon of change in the structural properties of an information continuum.”[17] His own personal listening is a reflection on this inclusive attitude, which in turn is showed in his compositions. There are two implicit dangers in the theorising of Braxton’s work: in his book, Lock attempts to place a rigid framework upon the types of feeder material evident in Braxton’s compositional processes. If Braxton claims, as he does, that his core materials are in a continual state of evolution, it suggests that there must be a finite limit to the use and relevance of fixed paradigms and diagrammatic sketches. The other danger is that music historians will in time showcase Braxton as a founder (if not the apotheosis) of black experimentalism whose work was foregrounded in the industrialised West. Rather than uncover similar musicians equally deserving yet devoid of recognition, history seems set to apply a certain commodificatory process to Braxton and his body of work, permanently making him an iconoclast: “As soon as original innovations which signify subculture are translated to commodities and made generally available, they are frozen.”[18]
According to Heffley, a completely objective approach to Braxton’s quartet music is appropriated by means of an understanding of the spiritual and anthropological functions underpinning his compositional processes: “It [the quartet instrumentation] covers both African and Western and masculine and feminine poles of the American middle ground as voiced by the instruments.”[19] Undoubtedly, Braxton considered the percussion and bass to be representative of African poles whilst the saxophone and guitar were representative of Western poles. This is important because Braxton is attempting to reconcile more than just musical parameters within his work: he is also attempting, along with his many contemporaries, to re-introduce a spiritual aspect of music. This is one of the single biggest criticisms of twentieth (and indeed twenty first) century music - that it is created and produced to satiate material requirement, as opposed to fulfillance of broader functions in society, which might include dirge songs, laments, or politically-oriented songs. Yet Braxton is more than just an experimentalist: he is attempting to counter a widespread perception of inconsequentiality in modern music by redefining it in terms of existent works. As an approach, this has striking similarities to a disquisitional method outlined by a musicologist called Tagg twenty five years later. Tagg was the chief advocate of what became known as the ‘hermeneutic/semiological’ method – that is to say, popular music could be analysed by means of ‘surrogate songs’ functioning as meta-analytical objects. By combining the initial objection with extramusical fields of association (something also concerned with the esthesic level in the theoretical model of tripartition) one can analyse the extent of ‘inter-objective comparison.’[20]
In South America, slaves working in the plantations came from a variety of African countries. It naturally followed that the slaves possessed a difference in culture and thus no shared language, possibly even no shared religion. Anthropological evidence suggests that, where possible, the slaves practised funeral dances, ring shouts, and other traditional forms of music making. Since the days of religious persecution circa 1890, a raised influx of slaves into South America in the intervening decades meant that “slaves and free Negroes had contact under circumstances of camaraderie that promoted a lowering of barriers.”[21] It follows that the slaves were exposed to British and American folk songs and hymns, in which a certain codificatory process – one of encoding – was applied by the slaves and integrated into the songs which they knew. Christianity, in the world of the slaves, took on something of a double entendre as a means of salvation and respite. Yet for all the hardship endured by the slaves, it seems that “the religious music […] is … pervaded by a sense of change, transcendence, ultimate justice, and personal worth.”[22] The early twentieth century provided a reason for slave labour acquisition, fuelling notions that those of dark skin were somehow socially and morally beneath their owners. Evidence shows a mass migration of blacks from South to North America, in the hope of finding new opportunities. This effectively signalled a growing sense of impatience and distrust at their collective poor treatment, brought about by “a conformative mode [of black artists] that would last until the 1960s.”[23] This dissent culminated in the civil rights movement championed by Martin Luther King. As of 1963, Congress passed amendments and laws which prohibited any form of discrimination. In a social and political context, the timing could hardly have been better for Braxton, as an aspiring musician. This strand of history encouraged liberalism and diversity in a way that was previously unthinkable in American history, and consequently made audiences more receptive to a wider source pool of musics.
Braxton was in many ways the antithesis to the Western concert tradition. First and foremost, he encouraged improvisation, something that would never concur with the ideology of those in art music unless it had been fully conceptualized beforehand.[24] Second, in marked contrast to group improvisation seen in Braxton’s works, art music very much espoused the soloistic improvisation. Third, he advocated a form of experimentalism which was totally at odds with the sterile absoluteness of the Western art music environment, a kind of clinicism which prized almost above anything else the dedication of the performers in realising the classical masterwork to an unflinching degree of accuracy.
Analysing composition 5, (excerpts of which are included on the CD) it is clear that a balance has been struck between improvisation and Braxton’s own notation. For example, the way in which Braxton assigns virtually every note its own dynamic suggests that there is a kind of parametrical hierarchy at work here, in much the same way as serial music specifies a certain set of musical parameters throughout a work. This may mean that there are aspects of serial music influencing Braxton’s compositional processes, but this is something he denies outright in his composition notes. The way in which Braxton has constructed melodic material here is extremely reminiscent of Webern’s approach to his Three Little Pieces for Violoncelle and Piano. (op. 11) By referencing the serial composer, attention is draw to the disjunct, fragmentary nature of composition 5. The performer is informed that he/she has a certain degree of freedom and responsibility. The only major difference is that the latter shows a bi-symmetry of melodic contour whilst the former is a series of linear constructs.[25]
In a broader sense, it can be seen that Braxton reconciles the improvisatory aspect of his native Afro-American heritage with that of the newer European musical avant-gardes, as demonstrated in the relative freedom entrusted to the performer. Braxton elucidates as much: “I have chosen this approach […] to capture the elasticity of the creative improvising musician.”[26] This is why traditional barriers of mediation between composer and performer are torn down here, and possibly why those in the art music establishment have never been truly comfortable with his work – in the latter there exists a clearly defined separation between the composer, performer, and audience. Consider:
The more we behave as musical consumers, treating music as some kind of electronically mediated commodity, or lifestyle accessory, the less compatible our behaviour becomes with nineteenth-century conceptions of the composer’s authority.[27]
Another way in which this composition varies from classical pieces is the methods used in preparation of impending sections. Braxton conceived of this piece as having several juxtaposed sections exploiting various language types, but there is virtually no preparation here. This lies in contrast to a classical piece which carefully sets up key changes.
The term ‘sound world’ is of relevance here. In abstract terms, a musical work can be viewed as an entity which is foregrounded at a concert. What this composition aims to do is to provide some semblance of a pointillist backdrop; that is, to invoke a sense of spatiality in which new heuristics can be explored. Moreover, this kind of fragmentation and ‘continuous discontinuity’ functions as a form of loose homogenous texture. Although the inherent nature of Braxton’s material in this composition is heterogenous, the processes - which transform it and shape it into a composition in its own right - change its classification. Then there are the obvious metaphysical and cosmological aspects of this work, when one considers the interconnections between spatial states.
When Braxton talks about pulse dynamics and pulse structures, I think that he is referring back to the rudiments of music theory: that is to say, “musical sounds are derived from vibrations striking with regularity and rapidity upon the atmosphere.”[28] In a tempered scale, naturally occurring differentials in vibrations offset pulsations. The differentials in pulsations give rise to the fundamental principle underpinning tempered scales: that is, a geometrically progressing series, each of which is defined and functionalized by an iterative sequence. Pulse dynamics, which can generate larger structural shapes, are therefore one of many variables in a parametrical hierarchy. Although this composition does not make use of serial procedures, it is undeniable that the exponents of this technique deeply influenced him, along with other experimentalists. When Pierre Boulez opened the IRCAM institute in Paris, Braxton attempted to gain access but was refused, while a contemporary – George Lewis – was permitted entry.
The conclusions to be drawn here are many.
Firstly, Braxton did not gain the same kind of widespread recognition and fame as some of his contemporaries. Whilst some musicologists argue that this diminishes the power of his message, I think this makes his work an even more potent opposing force. This argument can be equally applied to genres, for broadly speaking the West is typically preoccupied with rock n roll, with jazz simultaneously being a misunderstood force and an outlet for anti-conformity.
Secondly, it may initially appear that in an effort to make completely original music, Braxton shuns the entire Western canon of music history. However, his techniques obliquely acknowledge and consolidate upon art music history – Braxton concurs as much.
Thirdly, an increasingly sound knowledge and understanding of other non-Braxtonian musical languages and means of artistic expression should not automatically preclude the possibility of there being other systems in the musical world. Critical acclaim for Braxton in the Seventies stemmed from the fact that he was widely perceived to have shunned the so-called ‘aimlessness’ of new music in favour of more formal roots, when in fact Braxton was merely demonstrating and consolidating upon a pre-existent technique and style of playing.
A fourth conclusion to draw is that there were a variety of new musical currents beginning to take shape. Broadly speaking, rigidity in musical structure was a general cause for rejection by performing artists. By having at least a foothold in the major currents of his day, Braxton was of a disposition to make well-informed music.
A fifth conclusion is that there is potentially a limit to the relevance of fixed paradigms as advocated by Lock, particularly if Braxton suggests that his work is in a continual state of evolution. There is also a danger of music historians showcasing Braxton as a founder of black experimentalism when others are equally deserving of recognition.
The sixth conclusion is that Braxton operated in an environment which was radically different to the Western art music scene. Where the concert tradition espoused conceptualized solo improvisation, Braxton attempted to explore group improvisation.
Finally, if a musical work such as composition 5 is viewed as a single entity containing several disjunct constructs, it can be seen that the systematic imposition of continuity upon the discontinuous can function as a homogenous texture in its own right. I think that this is one of several latent features of the composition.
Word Count: 3,860
Bibliography
Berendt, Joachim E. (rev. Huesmann, Günther) (trans. Bredigkeit, B., Bredigkeit, H., Morgenstern, D., Nevill, T.) From Ragtime to Fusion and Beyond: Sixth Edition (Brooklyn, Lawrence Hill, 1992)
Braxton, Anthony. Composition Notes Book A (California, Synthesis Music, 1988)
Cook, Nicholas. Music: A Very Short Introduction (
Floyd Jr., Samuel A. The Power of Black Music (Oxford, Oxford University Press, 1995)
Gabbard, Krin. (ed.) Jazz Among the Discourses (London, Duke University Press, 1995)
Hebdige, Dick. Subculture: The Meaning of Style (London, Routledge, 1987)
Heffley, Mike. The Music of Anthony Braxton (New York, Excelsior Music Publishing Co., 1996)
Levine, Lawrence W. Black Culture and Black Consciousness: Afro-American Folk Thought from Slavery to Freedom (New York, Oxford University Press, 1977)
Lock, Graham. Forces in Motion: The Music and Thoughts of Anthony Braxton (New York, Da Capo Press, 1988)
Molino, Jean. Introduction à l’analyse linguistique de la poésie [Introduction to a Linguistic Analysis of Poetry] (Paris, Presses Universitaires de France, 1982)
Nattiez, Jean-Jacques. (trans. Abbate, Carolyn) Music and Discourse: Towards a Semiology of Music (New Jersey, Princeton, 1991)
Partch, Harry. Genesis of a Music: Second Edition (New York, Da Capo Press, 1979)
Radano, Ronald M. New Musical Figurations: Anthony Braxton’s Cultural Critique (Chicago, University of Chicago Press, 1993)
Small, Christopher. Music of the Common Tongue (London, Calder, 1987)
Southern, Eileen. The Music of Black Americans: A History (2nd Edition) (London, W.W. Norton, 1983)
Spain, Henry A. Equal Temperament in Theory and Practice (London, Novello, n.d.)
Stuckey, Sterling. Slave Culture: Nationalist Theory and the Foundations of Black America (Oxford, Oxford University Press, 1987)
Tagg, Philip in Middleton, Richard. Reading Pop (
Wilmer, Valerie. As Serious As Your Life: The Story of the New Jazz (London, Pluto Press, 1987)
Wittgenstein, Ludwig. Tractatus Logico Philosophicus (London, Routledge, 2001)
Discography
Braxton, Anthony. Willisau (Quartet) 1991 (Anthony Braxton, Marilyn Crispell, Mark Dresser, Gerry Hemingway) (Hat Hut Records, Switzerland, 1991)
Web Links
Smith, Tim and Clifford, Robert. ‘Binary Principle: System of Melodic Contour in the Webern Op. 11 No. 1’, Bach, the Baroque, and Beyond, no date. (Accessed 30th April 2005), <http://jan.ucc.nau.edu/~tas3/webern.html>
Appendix B
Track listing for the accompanying CD:
1. Excerpts from Composition 5 (2:40)
Appendix C
This table shows the geometrical progression of pulsations in terms of oscillatory air movements.[29] This means that any tempered scale can be expressed and functionalized by means of iterative sequences.
[1] Lock, Graham. Forces in Motion: The Music and Thoughts of Anthony Braxton (New York, Da Capo Press, 1988), p. 162
[2] Molino, Jean. Introduction à l’analyse linguistique de la poésie [Introduction to a Linguistic Analysis of Poetry] (Paris, Presses Universitaires de France, 1982), p. 24-28
[3] Nattiez, Jean-Jacques. (trans. Abbate, Carolyn) Music and Discourse: Towards a Semiology of Music (New Jersey, Princeton, 1991), p. 11f
[4] Lock, Graham. Forces in Motion: The Music and Thoughts of Anthony Braxton (New York, Da Capo Press, 1988), p. 158
[5] Ibid., p. 151
[6] Radano, Ronald M. ‘Critical Alchemy: Anthony Braxton’ in Gabbard, Krin. (ed.) Jazz Among the Discourses (London, Duke University Press, 1995), p. 196
[7] Wilmer, Valerie. As Serious As Your Life: The Story of the New Jazz (London, Pluto Press, 1987), p. 60
[8] Radano, Ronald M. ‘Critical Alchemy: Anthony Braxton’ in Gabbard, Krin. (ed.) Jazz Among the Discourses (London, Duke University Press, 1995), p. 190
[9] Radano, Ronald M. New Musical Figurations: Anthony Braxton’s Cultural Critique (Chicago, University of Chicago Press, 1993), p. 28
[10] Ibid., p. 48
[11] Levine, Lawrence W. Black Culture and Black Consciousness: Afro-American Folk Thought from Slavery to Freedom (New York, Oxford University Press, 1977), p. 138
[12] Braxton, Anthony. Composition Notes Book A (California, Synthesis Music, 1988), p. 38
[13] Berendt, Joachim E. (rev. Huesmann, Günther) (trans. Bredigkeit, B., Bredigkeit, H., Morgenstern, D., Nevill, T.) From Ragtime to Fusion and Beyond: Sixth Edition (Brooklyn, Lawrence Hill, 1992), p. 286
[14] Lock, Graham. Forces in Motion: The Music and Thoughts of Anthony Braxton (New York, Da Capo Press, 1988), p. 186f
[15] Partch, Harry. Genesis of a Music: Second Edition (New York, Da Capo Press, 1979), p. 74
[16] Southern, Eileen. The Music of Black Americans: A History (2nd Edition) (London, W.W. Norton, 1983), p. 518
[17] Lock, Graham. Forces in Motion: The Music and Thoughts of Anthony Braxton (New York, Da Capo Press, 1988), p. 162f
[18] Hebdige, Dick. Subculture: The Meaning of Style (London, Routledge, 1987), p. 96
[19] Heffley, Mike. The Music of Anthony Braxton (New York, Excelsior Music Publishing Co., 1996), p. 339
[20] Tagg, Philip in Middleton, Richard. Reading Pop (
[21] Walker, David. ‘In Defence of African Rights and Liberty’ in Stuckey, Sterling. Slave Culture: Nationalist Theory and the Foundations of Black America (Oxford, Oxford University Press, 1987), p. 104
[22] Levine, Lawrence W. Black Culture and Black Consciousness: Afro-American Folk Thought from Slavery to Freedom (New York, Oxford University Press, 1977), p. 39
[23] Floyd Jr., Samuel A. The Power of Black Music (Oxford, Oxford University Press, 1995), p. 161
[24] Small, Christopher. Music of the Common Tongue (London, Calder, 1987), p. 282
[25] Smith, Tim and Clifford, Robert. ‘Binary Principle: System of Melodic Contour in the Webern Op. 11 No. 1’, Bach, the Baroque, and Beyond, no date. (Accessed 30th April 2005), <http://jan.ucc.nau.edu/~tas3/webern.html>
[26] Braxton, Anthony. Composition Notes Book A (California, Synthesis Music, 1988), p. 37
[27] Cook, Nicholas. Music: A Very Short Introduction (
[28] Spain, Henry A. Equal Temperament in Theory and Practice (London, Novello, n.d.), p. 24
[29] Ibid., p. 13