A “Contemporary” music does not think alone!


Our musical between-times raises two questions:

-   How do we come out of musical modernity with a unilaterally subtractive orientation (a-tonal, a-thematic, a-metric) proceeding from the top-down (in an affirmative manner), not from the bottom-up (by sinking into the nihilistic “modernism” of systematic deconstruction)?

-   How do we put this musical modernity to the test of a non-musical heterogeneity if it is true that music as thought, and so as art (not as cultural function) implies, particularly today, its renewed confrontation with the non-musical?

To examine this first question, we will set out from the manner in which the poet Mallarmé, in his Coup de dés, orients his specific between-times (between the alexandrine and free verse) towards a new type of global Metre and we will sketch a musical problematic intertwining anew fresh harmonies, rhythms and Gestalts (gesture-figures).

For the second, we will set out from the manner in which the mathematician Dedekind revolutionised number theory by extending the field of the rationals by the adjunction of “cuts” and we will sketch the manner in which music can extend its space of thought by adjoining to itself other types of discourse, in particular of a linguistic nature.


To send “contemporary music” to the schools of poetry and mathematics in this way leads us to examine the manner in which our two questions - the one endogenous, the other exogenous - respond to each other and intertwine, while sketching the path of a modernity fighting simultaneously on two fronts (against nihilistic “modernism” and against academic “traditionalism”) to better affirm a contemporary musical art thinking with others according to the heterophony of composite musical works.




Towards a terza pratica extending the Music-world by the adjunction of heterophonies

(Contemporary music does not think alone !)


Musical practices – Continuities and transitions

(The Twelfth International Conference of the Department of Musicology of the Faculty of Music, University of Arts in Belgrade)

Belgrade, 25 April 2014





Version franćaise


Thank you for your invitation in this very interesting City of Belgrade.


My position in your topic "Continuities and transitions" will be very specific: I will try to present you a way of thinking that combines continuation and "revolution". My question will be: how is it possible to continue a way by a jump but without transition?

A friend of mine, the french Philosopher Alain Badiou, has written: “The rupture has for essence, not interruption, but adjunction.”

So, I want to present you how an extension by adjunction makes possible a continuation by a jump without transition.


I have modified the title of my paper to better reflect my subject. It is now: "Towards a terza pratica extending the Music-world by the adjunction of heterophonies"




« Barefoot, you wander from word to word. » Branko Miljković


Music, in particular the music that we call, in France, “contemporary”, does not think alone.

How can it think with others?

I would like to examine this problem with you by posing a more delimited question: how can we conceive today of a terza pratica?

As a quick outline of my intentions, I would like to

-       First, show the musical pertinence and urgency of a terza pratica - I will explain, of course, what I mean by that.

-       Secondly, show that such a terza pratica could find its musical principle in a heterophonic logic extending ancient polyphonic logic.

-       Thirdly, indicate by which concrete compositional processes we could envisage such a musical extension.

-       Fourthly, determine how to think this terza pratica with other types of thought: on the one hand with a mathematical thinking of adjunction and of extension, on the other with a philosophico-political thinking of justice.




Why a terza pratica?

I will employ this term in direct reference to what Monteverdi called secunda pratica. The associated musical practice is that which consists in setting words to music.

I will distance myself, in doing this, from the sense that my musicological friend, Célestin DeliŹge, gave the term in the nineties of the twentieth century[1] (Célestin DeliŹge was, I believe, a regular visitor of your musicological meetings and it is for me a joy to recall his memory here). He was inspired then by Hegel - his three stages of the work of art - rather than by the question Monteverdi posed to the vocal musical work.


To recall Monteverdi’s operation:


Monteverdi tried to give music new expressive powers by putting it to the service of the words that it welcomes and it accompanies. It is in serving the words that music masters the new expressivity that authorises the new tonal system.

The previous practice - prima pratica - was founded on modal counterpoint. This counterpoint ordered the musical composition of the voices according to a step-by-step construction, point by point (punctus contra punctum).

This element-by-element, note-by-note algebraic construction was the law of composition on which the words were arranged - ought to be arranged: at that time (the Middle Ages), music commanded the words, and the words served the music.

Monteverdi wants to reverse this rapport: he revives the ancient hierarchy of Gregorian monody where the Latin prosody commanded the expressivity of the musical neumes.

In following this attitude, Monteverdi will reinvent melody in the new harmonic context that authorises tonality: this melody can no longer arise, like the voices of counterpoint, from a note-by-note algebraic construction - we know elsewhere the difficulties there will be in conceiving of treatises of melody as though they were treatises of counterpoint, of orchestration or even of composition -. A melody is a musical topology subtly and globally espousing an autonomous prosody.

This resurrection of melody, subtly weaving itself around a prosody of an lingual order, comes to modify the musical category of the voice.


In the prima pratica, a musical voice had for its partner another musical voice - such is the very principal of counterpoint. Polyphony then resulted from weaving the voices between themselves, stitch by stitch, and constituted in this way a homogenous plurality. Certainly, the possible Cantus Firmus singularly served as a matrix, but it was itself algebraically framed without being melodically ornamented. In this way, the Cantus Firmus reinforced the skeletal logic of the voices of counterpoint, of polyphonic counterpoint. In total, it fixed the common law for a collectivity of voices that one can declare to be of a fraternal type.


This notion of voice, with its principle of modal and contrapuntal polyphony, will be found relativised in the secunda pratica.

Understand well: Monteverdi does not try to disqualify prima pratica, he does not try to delete the polyphony of the Middle Ages and the Renaissance, he does not try to reject contrapuntal logic; he tries to extend the notion of the voice by adding a new expectation of expressivity to music.

In secunda pratica, the voice once more becomes melody (as it was in Gregorian monody), but this time it is a new type of melody, because it is a tonal melody. In so doing, the melodic voice will have for partner no longer another voice, as in contrapuntal polyphony, but the functional harmony that the tonal system has just invented - think, for example, of the compositional practice that Monteverdi will draw from the simple tonic-dominant relationship at the beginning of his madrigal[2] Hor ch’el Ciel e la Terra. A new system of melody (already harmonised and harmonically accompanied) begins here, and we are familiar with the eminently fecund destiny of it in the centuries that follow until today.

On this point, a new musical power is inaugurated that comes to split the notion of the musical voice into two types:

-       the new melodic type;

-       the old contrapuntal type, which will internally weave functional harmony (one knows the choral destiny of the four voices harmonically superimposed).

It is worth noting in passing that this process liberates the melodic voice from properly thematic functions - those that appeared in contrapuntal polyphony starting with Guillaume Dufay and which agreed with the algebra of notes (pitches and durations).

As such, in this new polyphonic system,

-       the melodic voice is not a thematic voice (as the voice of the Cantus Firmus could be);

-       the thematic voice is not one of the four voices of harmony;

-       the four voices - implicit or explicit - of tonal harmony, those that put into movement tonal harmonic functions, are not melodic.

We grasp the considerable polyphonic possibilities that this secunda pratica offers. Polyphony is organised from then on around a sort of musical division of labour:

-   on the one side, the melodic expressivity that exhausts the sung text and its prosody;

-   on the other side, the dynamic of tonal harmony, materialised by a completely new combinatory of voices obeying the old contrapuntal rules;

-   on a last side, some more properly thematic functions brought to bear by such or such local configuration of this system.


The polyphony that proceeds from this intrinsic diversity of voices no longer has fraternity as a paradigm. On the one side, the melody is a voice that demands its individuality; on the other, the theme affirms a musical consciousness of self. The harmonic plurality finally materialises a body in movement. All this turns around a voice that preserves its irreducible specificity: by speaking at the same time that it sings. In sum, a sister voice rather than a brother, and a paradigm that recalls love between two sexes rather than the asexual fraternity of counterpoint - we are familiar with the manner in which this harmonised melody will be able to celebrate the nuptials of love.


These new resources, patiently composed around an initial adjunction - the adjunction of a melody in service of a prosody - will give music a new discursive power: it is in fact here that baroque music, as a musical discourse of an entirely new type, is born.

This new discursivity of music will authorise it to enter into closer relationships with the discursivity of the language that it sings: music will hierarchise and segment its discursive flux according to properly musical - and no longer lingual - laws. It will in this way be endowed with a sort of power of nomination over the words that it sings: musical discourse phrases its discourse, articulates the phrases produced into different segments, detailing these segments as smaller entities so that it can double the linguistic syntax of the words with an ersatz musical syntax. This doubling will give music the impression that it comments on language.

As such, music is endowed with a para-signifying capacity: not a signifying capacity like that of a language - music does not signify, music is not a language - but a capacity to declare that it, music, knows well what language signifies, that it knows well that the words put to music are, for their part, signifiers.


Music is endowed in this way with a sort of signifying aura, with a significance that is not a signification, and it is endowed with it precisely by serving a linguistic signification that remains fundamentally heterogeneous and inaccessible to it.





We will formalise this process engaged by the secunda pratica by passing over the mathematical models of adjunction and of extension.

I will not detail these models here. They are of three types:

-       the “cuts” of Dedekind, then of Conway, that enable the construction of the real numbers from the rational numbers, then the surreal numbers from the real numbers;

-       the algebraic extensions of fields that enable the construction of the field of algebraic numbers from that of the rational numbers, then the field of complex (numbers) from that of the real numbers;

-       the generic extensions by forcing of Paul Cohen.

It is worth noting that, in the two first cases, the analogy with our three pratiche [comme pratiké]:

-       the cuts first of all pass from a numerical prima pratica - that of the rationals - to a secunda pratica - that of the reals - then from this secunda to a terza - that of the surreals;

-       the extensions of fields first of all pass from a prima pratica - the field of rational numbers - to a secunda - the field of algebraic numbers - then from this secunda to a terza - the field of the complex (numbers).

Take from this the following principal idea: one can pass from a secunda pratica to a terza pratica in the same way as one has already passed from a prima pratica to a secunda pratica!


For each of these three mathematical models (take my word for it!), the process properly called adjunction consists of three successive and cumulative stages:

1.     first of all the construction of words, or specific objects composing a lexicon;

2.     then the transformation of these words into names (apt to designate and signify) by bestowing the previously constructed words with a properly signifying face;

3.     finally the construction of statements from these names in order to control, from the inside of the original situation, the expected results in the future extended situation.

Once this adjunction is effectuated (with words becoming names incorporated into statements), the process of extension consists in making the new adjunct object interact with the original situation. The point is not only to graph, to stick, or to add together, but to engender a recomposition of the entire original situation. The idea is to generate a new extended situation in which the original situation remains a single delimited region, a particular case of what is from then on generalised. One will say that, in this phase of extension, one passes from a simple cut-and-paste to the production of an ensemble, that one transforms a sum into a product, the product of a global interaction.


Remember that to add is to construct a system with words becoming names able to produce statements and that to extend is to mobilise these statements to control (from the very interior of the original situation - this is the genius of the operation) the global interaction able to generate a situation of a completely different species: an extended situation.




We will see how secunda pratica answers to these formal characteristics of an adjunction and an extension before coming to our terza pratica.

-       First of all, the hierarchised segmentation of the tonal phrase forms the fundamental entities which will take the place of words in the new musical discursivity: a musical word is here an elementary melodico-harmonic motif, perceptible and identifiable by ear.

-       Then, these musical “words” see themselves correlated to ordinary words (those that are pronounced by the text set to music) in order to musically “name” the words said by the voice: the musical motifs become in this way musical names, able to name the joy or sadness, love or hate, anger or tenderness evoked by the sung text (think about the leitmotifs of Wagner but also, more generally, baroque rhetoric… ).

-       Finally, these musical names will interact to compose musical phrases constituting a more global musical discourse, a discourse which will espouse and musically “express” the affects and actions designated by prosodised language.

In this way, musical words, names and statements come to add to music a new type of melody (in comparison to “contrapuntal” melody). This melody is endowed with the para-signifying capacity of which I have spoken.

The extension (to which this adjunction leads) holds to the musical generalisation of these new expressive capacities proven around harmonised melody. Secunda pratica is not only an old instrumental music to which could be added a new type of melodic voice: it is a complete revision that systematically shattered what voice, polyphony, monody, melody, harmony and choir meant until then.

In total, this secunda pratica revolutionises prima pratica not just by destroying it, not by undermining its foundations to better delete or dissolve it; it revolutionises it from the top down: by enlarging the space of thought and relativising prima pratica, which appears like a particular case, like a circumscribed region of the new extended situation.




If you have followed me up until now, I ask you then: can one engage the twenty-first musical century with a terza pratica which could be to the secunda pratica what the latter was to prima pratica?

Such is the hypothesis at work in my compositional labour, that which guided the choral study entitled Dido and Aeneas, which had its premiŹre on Wednesday evening.

We will examine more closely this hypothesis of a terza pratica.




There is, first of all, the idea that we intend to extend the properly artistic power of music by banking anew on a musically delimited pratica: that which sets words to music.

As Adorno suggested, [3] music has need of the heterogeneous to remain an art, an autonomous form of thought, in order not to fade into the exercise of simple cultural and religious functions (to amuse, to accompany dance, to accompany images, to illustrate films, to contribute to the sociological identifications of the youth, to participate in the sportive cults of vast stadiums, etc.).


The heterogeneity - which I propose to privilege for my music - will remain that of language.


It will consist then - and this will be my first axiom - in re-examining anew what “set words to music” can mean today.

In terms of words set to music, we shall determine two principal essential points:

1.     These words must say something about this time, this time precisely in which music wants to be contemporary; the words set to music cannot just be vocalises, mumbling, glossolalia, scat and other language games; they cannot be limited moreover to quotidian babble, to the commerce of opinion; the words set to music ought to signify a contemporary “who goes there?” of thought; they ought to engage with the emancipatory aspects of this time (against the general dumbing-down extolled by globalised capitalism – a lateral thesis could be that globalisation is only the supreme - financial and imperialist - stage of capitalism, and there is nothing insurmountable there!)

Our first principle will then be: Terza pratica should carefully choose the words that it wants to set to music.

2.     The second principle, the corollary of the preceding one: the setting to music of these words, carefully chosen, should not efface what they say! The words set to music should remain globally comprehensible to the ear. To set to music should not mean to undo linguistic prosody, to take the syntagms apart, to deconstruct the words to reduce the linguistic discourse to a pure acoustic game of unsignifying phonemes.

Our second principle will then be: terza pratica should globally respect the phrasing and the prosody of the language mobilised so that the words set to music remain comprehensible - the heterogeneity to which music has recourse should remain heterogeneous and not be musically dissolved, assimilated or denatured: when a host invites a stranger to his home, he does not force him to dress and speak like the natives!


There is then the following principal idea: terza pratica should enable the extension of different types of musical polyphony to true heterophonies.

I repeat: the goal of all this is to extend music. The goal is not to musically welcome the heterogeneous, as though the point was for music to make propaganda for this heterogeneity (by mobilising the existing repertoire of conventional musical effects): to welcome the heterogeneous, to set a contemporary discourse to music, this should be for music the occasion to invent new properly musical alterities for itself: in order for the global heterophony between the two types of discourse - musical and lingual - to be a true heterophony, not a simple superimposition or a pure collage, it is in fact necessary that this bringing together also mobilises a heterophony intrinsic to each discourse.


As one doubts, this extension (of polyphony towards heterophony) will correspond to a profound modification of the notion of voice: it will not be completely the same “voice” that can make music heterophonic; one will not play with alterity as one played with alliances (counterpoint) or (melodico-harmonic) complementation.


The voice susceptible to compose a heterophony will not be a voice susceptible to be repeated and varied as in contrapuntal polyphony - we will say: this will not be the singular of a plural. It will not be moreover an indivisible and unrepeatable entity as is the melody of secunda pratica - this will not be an individual voice. The voice of heterophony will be itself composite, that is to say interiorly marked with intrinsic alterity: this is the endogenous condition that allows this voice to participate, in a non-accidental manner, in a more global heterogeneity - this will be an dividual voice (that is to say interiorly multiple, without prerequisite or guaranteed unity).

With this condition, heterophony will be something other than the new disparate and arbitrary assemblage of ancient polyphonic voices.

Our first compositional principle will then be: a heterophony will incorporate intrinsically composite, dividual musical voices (but this, certainly, does not prohibit some secondary incorporation of such or such voice of a more classical type).


Our second compositional principle will be: in the setting to music of words remaining words, in the disjunctive duality between music and language, we need a third element. This third element will not come to synthesise disjunction from the top down; it will not moreover mediate it from the bottom up; it will rather create the conditions of a participation between disjunct orders (think of the manner in which Plato speaks about a participation between intelligible and sensible). The third element will favour the constitution of a resonance between musical and lingual voices.

This third term will be a chorus. I suggest then - the second principle will guide me here - that we need a heterophony of two distinct choruses, susceptible however to share the common characteristic of being a choir. We need then an instrumental and a vocal choir.

The addition of this term, chorus, involves already a nominal displacement: one passes from the primitive duality of the musical and of the lingual (that of our pratica consisting of setting words to music) to the choral duality of the instrumental and of the vocal. We have in this way begun to make immanent an exogenous contradiction in the music. Certainly, one is not yet finished with the level of lexicon and of names, but we will return to the importance of these instances in the process of adjunction.

So then, two choirs.

1.     We will have, on the one hand, an instrumental choir: we must then treat the orchestra (or any other more restricted instrumental formation) like a choir made of composite voices. One senses that this will imply diagonalising the traditional instrumental families (woodwinds and brass; bowed, plucked or struck strings; skins with or without defined pitches; etc.). One will orient oneself instead towards an extended formula of chamber music (think of Farben) where each instrument configures by itself its own little chamber music, interiorises a specific form of heterogeneity. In such an instrumental choir, with a heterophonic vocation, it will then be difficult to tell exactly the number of voices!

2.     On the other hand, that of the vocal, we will have what I propose to call a Babelian choir, that is to say a choir simultaneously speaking different languages. They will not say the same thing under different simultaneous translations, but synchronically state different ideas. The difficulty will be in ensuring that this heterophony does not degenerate into cacophony (we could say into chaos-phony /  chaophony). The stake of the vocal composition will rest on this point: how do we simultaneously set different properties of different languages to music? To do this, the idea will be to play with proto-musical properties of each language: what is the rhythm of its syllables (long/short, accentuated/non-accentuated, agglomerated or equally distributed?), what is the prosody of its accents (syntactic/semantic, word for word or by syntagm?)? The idea will be that a Babelian chorus, musically prestructured according to these different types, will be able to more spontaneously interact with an instrumental choir.

In my own music, I expect to work with six languages (French, Latin, Arabic, German, Russian and English) regrouped into four categories according to which the prosody is syllabic or not, according to the pre-eminence or not of a lexical mode of accentuation - see the following diagram. My Dido and Aeneas began with only three of them.



Does such a Babelian chorus sustain a discourse? No, without doubt.

Take the example of spontaneous political gatherings that constitute themselves as the principal sites of affirmative, emancipatory politics. Such were the recent gatherings in Kasbah (Tunis), Tahrir (Cairo), and Puerta del Sol Squares (Madrid), in Zuccotti Park (New York), Taksim Square (Istanbul) until - why not - Maēdan Square (Kiev). Each gathering declares without exactly discoursing. They declare for example “Down with Ben Ali/Mubarak!” or “We are the 99%” but the sum of the discourses effectively held on each square at the same instant could not constitute by itself a discourse (in this way, the gathering distinguishes itself from the protest that, even spontaneously, is unified around some common words that tend to add up diachronically to a continuous discourse).

One will pose then – provisionally - that heterophony declares without exactly forming a discourse.

But we will return to our musical focus.


In total, the system envisaged will place in global, heterophonic resonance on the one hand an instrumental choir made of composite voices, on the other a vocal choir of a Babelian type.

I will not detail here a point that merits a more detailed exposé: the most pertinent mode of composition for such a global heterophony arises perhaps from the category of montage [4]. The stake could then be to constitute a specifically musical version of this category, which could distinguish it from its native cinematographic usage: how to compose a properly musical montage?


Such could be a possible horizon for the terza pratica that I have in mind.


The difficulty is that we are speaking of a horizon, that of an extended musical world: it remains to be seen through which type of adjunction, here and now, it will be possible for us to prefigure it.

To return to the proposed formalisation, with which new types of properly musical words, names and statements will we be able to construct, patiently, step by step, the adjunction able to extend our Music-world? [5]

This point opens other compositional problems that concern not so much the intended heterophonic expressivity than the musical system susceptible to produce the new objects that will serve us for words, names and statements.

To recap: secunda pratica enlarged prima pratica through its new conception of voices, but it was able to do this because it subsumed the old modality in the new tonality. In its turn, a terza pratica can enlarge the secunda pratica only by associating its new heterophonic orientation with a new type of musical system, extending the old musical systems (modal and tonal, serial and spectral).


To detail this new group of compositional tasks could be the sole object of an entirely different lecture. I will content myself to indicate here the manner in which, for my part, I envisage these more technical tasks.


It is first of all clear that it could not be done by the simple enlargement of serialism: the serial path was necessary and fecund; it is today saturated as is the tonal and, a fortiori, modal paths. Spectralism, even more so, could not show the way.

For me, I try to implement a system that articulates the following dimensions.

-       In the first place, it tries to reconfigure a functional harmony around vast structures of pitches that I call rainbow chords.

-       In the second place, I try to globally frame each work around a vast polyrhythmic Metre, and it is around this point that the experience of Mallarmé in his Coup de dés (such as has been recently laid bare by Quentin Meillassoux) interests me.[6]

-       In third place, I start from there to frame the development of the work through a global Matrix (obtained by blending the rainbow harmonies and rhythmic grids that follow from the two preceding points).

-       Finally, I animate this vast matrix from the inside through a network of gestural figures - of local Gestalts - which come to enlarge the older leitmotivic system.

In total, I try then to exceed the triple subtraction at the foundation of the twentieth century - “no tone, no metre, no theme!” - without, for all that, returning, full of remorse, with my head hung low and with a downcast gaze, to the old system of tonality, metre and thematism.




What we understand well - and this will be my last point - is that the passage to a terza pratica can be today only a fight on two fronts (and no longer on just one, as at the time of secunda pratica): against a certain modernism (which advocates fleeing before an indefinitely renewed electro-acoustic technology) and against a certain traditionalism (which advocates a pure and simple return to the naturalist identities of the good old recipes: those of the acoustic tone, of the dancing metre and of the psychologically identifiable theme). So we have, on the one hand, an active nihilism (“we want perpetually-updated technique at the fault of wanting new ideas!”) and, on the other hand, passive nihilism (“all desire entails risks; so we should content ourselves with managing the long-proven natural!”).

Against these two figures of the same nihilism, the music that wants to continue to be a contemporary form of thought can prolong its old pratica under the form of a terza pratica that seeks the creation of choral heterophonies by assuring the musical composition of its new voices with new harmonic, rhythmic and gestaltic systems.


If prima pratica promised contrapuntal fraternity, if secunda pratica magnified the figure of love between dissimilar individualities, terza pratica could contribute to implementing, at the heart of the new century and within its unique world, a justice here and now. Music could then be the carrier not of hope in the future, but of the hope that justice is already here, in such a withdrawn and circumscribed place, and that it counts then already, universally, for all!


I thank you for your attention.

[1] Célestin DeliŹge : Le duel de l’image et du concept. Essai sur la modernité musicale (1994) in Invention musicale et idéologies 2 (Mardaga, 2007 ; pp. 219-254)

[2] Madrigali guerrieri e amorosi (1638)

[3] “Kunst bedarf eines ihr Heterogenen, um es zu werden“. (1966).

[4] film editing

[5] Franćois Nicolas: Le monde-Musique (Aedam musicĺ; Paris; 2014).

[6] Quentin Meillassoux: Le Nombre et la SirŹne (Fayard)