hernandez-lanza-aschenblume.pdf

THE OM COMPOSER’SBOOK

Volume One

Collection Musique/Sciencesdirected by Jean-Michel Bardez & Moreno Andreatta

The Musique/Sciences series contributes to our understanding of the relationship betweentwo activities that have shared intimate links since ancient times: musical and scientificthought. The often-cited Quadrivium (music, astronomy, geometry, and arithmetic) re-minds us that, in an age imbued with the spirit of the Gods, it was not uncommon tothink of these two modes of thought as twins. During the twentieth century, music andscience developed new links, establishing relationships with mathematics and openingnew lines of musical research using information technology. Modeling, in its theoretical,analytical and compositional aspects, is more than ever at the center of a rich musicologi-cal debate whose philosophical implications enrich both musical and scientific knowledge.The pleasure of listening is not diminished when it is more active, more aware of certaingenerating ideas—au contraire.

Published works

Gerard Assayag, Francois Nicolas, Guerino Mazzola (dir.), Penser la musique avec lesmathematiques ?, 2006

Andre Riotte, Marcel Mesnage, Formalismes et modeles, 2 vol., 2006

Forthcoming

Moreno Andreatta, Jean-Michel Bardez, John Rahn (dir.), Autour de la Set Theory

Guerino Mazzola, La verite du beau dans la musique

Franck Jedrzejewski, Mathematical Theory of Music

THE OM COMPOSER’SBOOK

Volume One

Edited byCarlos Agon, Gerard Assayag and Jean Bresson

Preface byMiller Puckette

Collection Musique/Sciences

Editorial Board

Carlos Agon, Ircam/CNRS, ParisGerard Assayag, Ircam/CNRS, ParisMarc Chemillier, University of CaenIan Cross, University of CambridgePhilippe Depalle, McGill University, MontrealXavier Hascher, University of StrasbourgAlain Poirier, National Conservatory of Music and Dancing, ParisMiller Puckette, University of California, San DiegoHugues Vinet, Ircam/CNRS, Paris

Editorial Coordination

Claire Marquet

Page Layout

Carlos Agon and Jean Bresson

Texts translated by

Justice Olsson

Cover Design

Belleville

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ISBN 2-7521-0027-2 et 2-84426176-0

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The Genesis of Mauro Lanza’sAschenblume and the Role ofComputer Aided Composition

Software in the Formalisation ofMusical Process

- Juan Camilo Hernandez Sanchez -

Abstract. The present article will attempt to illustrate the compositional process ofMauro Lanza’s work Aschemblume for nine instruments ensemble (Fl. Cl. Perc. Pno.Vl. Vla. Vc. Cb.). The piece was a commission from the French Culture Ministry and theensemble Court-Circuit. In the first part, an introduction to the musical parameters thatunify the piece will be presented, as well as a description of the role of OpenMusic in thepre-compositional processes; in the second part the musical material will be analysed witha discussion of their construction in OpenMusic, and finally the fundamental structureof the piece will be described to show how the sections are assembled. The writing of thisarticle was made possible thanks to a close collaboration with the composer.

***

1 Introduction

Mauro Lanza’s work is characterized by the mental conception of musical ideas followedby a computer aid. The pre-compositional formalisation is a compulsory phase permittingthe composer to discern the material that could be quickly produced by the machine. Theterm musical material will be used to name each minor section possessing autonomousmusical characteristics. The composer’s intervention in the CAC process takes placewith the programming of computerised tools that respond to the needs of his musicallanguage.

Aschenblume is a German word meaning ashes settling down taking the shape of aflower. The word is taken from a poem by Paul Celan. The literal translation couldbe ”Ash flower” and its literary context strengthens the semantic connotation of eachcomponent, (the flowering through the vanishing of ashes). The process applied to theinitial material of the piece could be seen as a musical analogy of the word: the piecebegins in a rhythmic ostinato that undergoes harmonic and rhythmic disintegration andgradually becomes a sustained chord. Then the material is reiterated several times, butbearing a new musical element at each repetition. The evolution of these new elementsleads them to be progressively dissimilar from the initial material; the treatment givento their common musical principles builds up the coherence between them.

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Juan Camilo Hernandez Sanchez

The musical path allows all kinds of interaction between the different bodies of musicalmaterial; the handling of their interpolation and their contrast becomes the principal axisof tension. The development of all the bearing materials is a disintegration process. Animportant feature of this process is the gradual reduction of duration of each section untilthe end of the piece where they are perceived as small fragments, keeping the essentialmusical elements that characterised them. A brutal and regular pulsation finishes thepiece in the form of a collision between the contracted elements.

2 Pre-compositional process

The formalisation of the compositional process implies a resolution of the principles thatlink the musical materials used in the piece. The main aspects are as follows:

• the development of a rhythmic hierarchical language by the polyphonic assemblingof rhythmic patterns,

• the creation of the harmonic field homogenising the sonority of the piece,

• the descending melodic shape. Each main body of material is governed by the ideaof a melodic descent,

• each section of the piece is reduced in duration.

The harmonic and rhythmic aspects are created almost entirely using OpenMusic; thecomprehension of this process is essential to the understanding of the musical material’sconstruction and its development throughout the piece. Therefore, an explanation of therhythmic and harmonic formalisation by CAC will be presented in the introduction tothe analysis of the piece.

2.1 The rhythmic hierarchical language by polyphonic assem-bling of rhythmic patterns

Rhythmic hierarchy and periodic patterns are the main rhythmic aspects developed byMauro Lanza. The hierarchy can be achieved when some specific points are emphasizedin a rhythmic sequence, creating varying levels of importance. The accented pointsconstitute an original rhythmic pattern that arithmetically generates all of the minorrhythmic structures. In Aschenblume, as in other Lanza works, there is a polyphonictreatment of the rhythmic hierarchies, the original rhythmic pattern is highlighted in thepoints where all voices are assembled; each voice has its own duration and is repeatedthroughout the whole length of the original pattern. The rhythmic sub patterns of eachvoice are obtained from a modulo division of the original pattern, that allows sub patternsto be generated, and that coincide with the original pattern onsets.

The onsets of the original pattern are expressed in ratios, which are note valuesmeasured in relation to the beginning of the pattern that is the point zero. The divisorindicates the division unity and the numerator the position of each onset. For example,in a 21 sixteenths note pattern that has onset the 5th , 13th , 15th and 2st sixteenth notewill be represented as follows:

0 5/16 13/16 15/16 21/16

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The Genesis of Mauro Lanza’s Aschenblume...

The possible duration of the derived pattern is expressed also as a ratio and it issaid to be a modulo. The numerators of the original pattern onsets are divided by thenumerator of the modulo; The remainders of each division are the onsets’ values thatdetermine the derived pattern, if there are repeated remainders this value has to be takenjust once. With a pattern that lasts 8 sixteenth notes the operation will as follows:

Original pattern onsets 0 5 13 15 21/8 Sub pattern durationRemainders 0 5 5 7 5Sub pattern onsets 0 5 7

Figure 1. Rhythmic pattern with two sub-patterns periodicities

The composer creates an initial CAC tool in order to accelerate this process. The toolis an OM function called Subpatterns that generates the sub patterns with any moduloand any division unity.

The rhythmic density depends on the number of notes in the modulo of a sub pattern,and can also be controlled with another function created by the composer. The functioncreates some restrictive constraints so as to choose the less dense patterns. In orderto solve the constraints the search-engine Pmc-engine (from Mikael Laurson’s PWCon-straints library) is used. This search-engine yields solutions found in a search domaingiving preference to the solutions that respond to the constraints. The constraints arerules and heuristic rules; the rules take the sub pattern solutions responding to a simpletrue or false question, the heuristic rules select the sub patterns according to the desireddensity value. Then the composer can find patterns determining the minimum valueallowed in a voice and control the number of notes of each sub pattern depending of itsdensity.

In some sections of the piece the pitch is also formalised in order to create melodicpatterns corresponding with the periodicity of the sub patterns, while the pitch reinforcesthe original pattern creating a heterophony. Each note of the chosen melody is allocatedto each onset of the original pattern, the same notes are then allocated to the remindersof the division. When there are equal values as reminders of different divisions and theallocated note is different, this value appears in the sub pattern taking only one notefrom the allocated notes at each repetition.

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Original pattern onsets 0 5 13 15 21/8 Sub pattern durationRemainders 0 5 5 7 5Notes C D E F G

Sub-pattern modulo 8 7Onsets 0 5 7 0 1 5 6Note C D E G F C G F D E

Figure 2. Heterophony over the rhythmic pattern appeared in the figure 1

3 Creation of a harmonic field

The Aschenblume’s harmony is obtained completely from two ”bell-like” spectra createdby physical modelling synthesis1. The two instruments employed are a free and a clampedcircular plate; their spectra are inharmonic with a huge quantity of non-temperate par-tials. In order to be used, the partials are approximated into quartertones and the clarinetis tuned a quartertone lower. Tempered instruments such as the piano and some pitchedpercussion instruments mostly play tempered notes; in the sections where more notes areneeded the harmonies are approximated into semitones.

Figure 3. Free circular plate spectra

1This kind of synthesis permits the creation of ”virtual” instruments starting from their dimensionsand the physical properties of their material. The procedure is made possible by the Modalys software,realized at the IRCAM. The composer Mauro Lanza created an interface to control the synthesis frominside OpenMusic.

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Figure 4. Clamped circular plate spectra

The harmonic field obtained is not intended as a musical representation of an acousticmodel in the spectral music manner, but to give a homogeneous sonority to the wholepiece. Therefore, the spectra becomes the ensemble of notes used in the piece and itscoherence of form is due to the organisation of sub-ensembles of partials. Some partialshave higher amplitudes depending on which part of the instrument’s register is sampled.In order to create the partial sub-ensembles, a constraint tool is used to search theinstruments’ points at which there are fewer simultaneously sounding partials. Each oneof the points becomes the harmony of a section, and they are played either as chordswith their corresponding amplitudes or melodically as a scale for each instrument.

The points with common partials are used as the harmony of the related sections ofthe piece, which gives them harmonic homogeneity.

Figure 5. Enumeration of chords obtained from the partials of different points of the instru-ments

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4 Aschenblume musical materials

As we explained in the introduction, new material appears constantly throughout thepiece. A description of each section is necessary if the reader is to understand theirformal structure.

4.1 Material A

The piano presents a homo-rhythm in sixteenth notes accentuating points that shape amelodic descent. The homo-rhythm accelerates while the accents decelerate, because theperiods between them are enlarged. This process creates a temporal paradox that willbe resolved as a sustained chord. All the other instruments underline the piano accentsin triplet subdivision, generating a small gap between each. However, the percussionfollows the same pattern as the piano accents. The melodic descent movement is appliedto the other instruments in different periodicities from that of the piano.

To create this material the composer developed a CAC tool, a patch that appliesthe following process: the harmonic field is approximated into semitones and filtered byan intervallic structure transposing in chromatic downward steps. Each transposition isarpeggiated downwards avoiding the notes from of the harmonic field, thus creating anirregular descent. There are two note chords accentuating points of a melodic descent.The filtering process is carried out in the OM patch as well as upon the acceleration of thehomo-rhythm. Placing of accents is done manually by the composer. The following stepis the extraction of the onsets of the accentuated notes, in order to generate the rhythmfor the other instruments. A patch takes these onsets and approximates them into atriplet subdivision, the resulting rhythm being allocated to the flute, clarinet, violin andalto. The percussion accentuates in the same subdivision as the piano, approximatelyfollowing its melodic descent shape with bongos and congas.

Figure 6. Material A (Meas. 1)

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The melodic descent for the other instruments is chosen by the composer from theharmonic field assigning different registers to each instrument and allowing them to havecommon notes. The number of notes of this descent is progressively reduced until eachinstrument only has one sustained note, and this procedure leads to the incoming chord.The melodic descent is orchestrated in such a way as to have three periodicity levels. Theviolin and flute are always have a similarly patterned descent, and notes reduction. Thealto and clarinet play the descent in a periodicity that is different from the violin andflute. Finally, the heterophony principle is used to allocate some pianissimo descendingnotes in different periodicities for the flute and clarinet.

Figure 7. Melodic descents periodicities for Flute, Clarinet, Violin and Viola (meas. 1)

Throughout the piece the piano harmony evolves, changing the intervallic structurethat is transposed, while the other instruments remain harmonically similar to their firstappearance. The sustained arriving chord undergoes a harmonic enhancing metamor-phosis; its dynamics and orchestration also evolve, using the amplitudes of the chordsextracted from the spectra as a model.

4.2 Material B

It is a rhythmic pattern built up with the original pattern and four sub-patterns, eachone in a different subdivision unity. The double bass and the vibraphone play the originalpattern in a regular pulse of 9 sixteenth notes. The piano has a second sub-pattern thatuses the same periodicity with an internal division, it doubles the vibraphone at eachassembling with the original pattern. The viola and the violin use a triplet sub-divisionhaving a periodicity of 10 triplet eighth notes. The clarinet plays a sub-pattern lasting 3quarter notes and its sub-division unity is the triplet. The flute and the violoncello havea quintuplet sub-division and their periodicity is equal to one half note.

The harmony of this section is an orchestration of the 8th chord from the nodesobtained in the spectra. The original rhythmic pattern is characterised by having thefundamental (C[), the 3rd, and the 7th partials (Pno., Vbr.). The rest of the partialsare distributed among the other instruments, the voices, rhythmically assembled, use thesame notes. Therefore we may conclude that the original pattern is harmonically stablewhile the sub-patterns are changing, a process that generates an internal evolution of thematerial very important to its interpolation with the other bodies of material.

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Figure 8. Material B (meas. 51)

4.3 Material C

It often appears as a transition element, characterised by the rhythmic assembling ofall the voices, and the polarisation over the medium and high registers. It has a sextu-plet melodic ascending figure built up in a scale whose intervallic structure is identicalthroughout all octaves. As a result, it is the only section constructed using a harmonyout of the spectra.

All the voices begin in a different sixteenth note of the sextuplet, in order to createpolyphony, in which each sixteenth note should have the maximum possible number ofsimultaneous notes from the scale.

The appearance of this material articulates the formal structure of the piece becauseof how it it differs from the other bodies of material, especially with regard to its homo-rhythmic polyphony and its ascending character.

4.4 Material D

Perceptually, this section is a reminder of the material A, the piano plays a similar homo-rhythm accentuating the descending notes. The main differences lie in the polyphonicand rhythmic treatment given to the other voices: polyphonically the differences lie inthe instruments playing in canon with the piano; rhythmically they arise from a commonsixteenth note unit division throughout all the voices.

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Figure 9. Material C (meas. 125)

The computer tools initially apply the filter to the harmonic field polarising aroundthe two highest notes of the chord 2. The composer manually chooses the accents that inthis case accelerate until they become constant eighth notes, whereas the homo-rhythmremains in sixteenth notes throughout the section.

The appearance of the instruments follows an asymmetrical four voice canon playedsimultaneously by the violin and the viola, twelve quarter notes after by the flute andthe glockenspiel, the violoncello joins twenty-three quarter notes after the piano entry.The rhythm is obtained from the piano accents that are taken as onsets and augmentedin different proportions for each instrument. The used proportions are irregular and areapproximated into sixteenth notes, which are applied as subdivision unit. The melodicdescent is also used in instruments that are perceived as an irregular echo of the pianoaccents. In order to polarise the harmony completing Chord 2, it is formed by the gradualreduction of the descending melody until each voice has just two notes.

Figure 10. Rhythmic structure of Material D canon

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The final part is the most developed element of this section; in the rest of the pieceit evolves becoming a constant sixteenth note pattern where the two highest notes arealternated. Each note is harmonised with the chord notes played by each instrument withits respective register in such a way that the highest notes of each voice are simultaneous.The same is applied to the lowest notes. This fast alternation of high and low registermostly emerges at the end of the piece, sometimes transposed or harmonically enriched.In the formal scheme it is named D’.

Figure 11. Polarisation over Chord 2 in the Material D (Meas. 91)

4.5 Material E

Constructed with the rhythmic pattern tool, this section appears usually as a transitionbetween two sections. Using the chord 27 as its harmony, its principal characteristic isthe flute and the double bass sustaining the outer notes while the rest of the ensembleplays the rhythmic pattern and sub-patterns.

The original pattern appears in the cowbells over the fundamental of the chord, it hasa regular periodicity of 7 sixteenth notes. The sub patterns are individual for each instru-ment, which means that they are not doubled. The violin and the viola are sub-dividedin half note quintuplets, with a 9 and 8 quintuplet eighth note periodicity respectively.The violoncello and the clarinet are subdivided in triplets and their periodicities are 11and 12 triplet eighth notes. The piano does not have a regular periodicity; its role is to

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provide a link to the previous section.

Figure 12. Material E (Meas. 137)

4.6 Material F

A contrasting element appears with this material, which consists of a rhythmic unifica-tion of the entire ensemble undergoing a deceleration. This is a very short section thatintroduces a new element, by way of dynamical and orchestration contrast. Therefore, ithas great importance in the formal articulation.

The tool develops this material by expanding a spectrum that is contracted in thelower part of all registers; the computer contracts the given chord in the lower register,subsequently, the chord is gradually transposed towards its original register. The rhyth-mic deceleration is a simple interpolation between two rhythmic values, always beginingwith sixteenth notes, and the final value depending on the following section. The result-ing rhythm has a regular pulsation gradually transformed into syncopations, creating aspecial tension and introducing a new element.

4.7 Material G

It is similar to Material C in many aspects: it has a homo-rhythmic quintuplet subdivisionunit for all the playing instruments; each instrument begins at a different note of thequintuplet, creating the same polyphonic effect that appeared in Material C.

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Figure 13. Material F (Meas. 163 )

The main difference is harmony. In this case the ascending movement occurs overa B[ arpeggio, the clarinet part distorts the harmony with microtonal neighbour notesthat are gradually eliminated to reach a sustained B[ unison in all instruments. It is alsoa reminder of the disintegration that occurred in Material A.

Figure 14. Material G (Measure 167)

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The treatment of timbre is unique to this material because of the absence of piano andpitched percussion, as well as the use of string harmonics amalgamated with woodwindsin the high register.

4.8 Material H

This section is characterized by a rhythmic pattern. The double bass rasps out the lowestnote of the spectra and the flute plays the highest note in this section, accentuating theoriginal pattern, which has a periodicity of 8 quintuplet eighth notes. The violoncelloplays a sub-pattern with the same periodicity as the original, whereas the melodic treat-ment generates an internal subdivision. The viola also accentuates the original patternin sixteenth notes creating a little gap.

The triplet subdivision is applied to the violin, clarinet and piano, the latter beingdoubled by a glockenspiel. Each instrument has a different periodicity: 5 eighth tripletnotes for the violin, 21 eighth triplet notes for the piano, clarinet and glockenspiel.

Chord 30, obtained from the clamped circular plate, is used in this section with astrong emphasise on E. The highest notes are placed just after the original pattern accent.As a consequence, iambic polyphony is created with the short note in the low registerand the long one in the high register. This idea is used as a principle to engender anddevelop new materials such as D’ and J.

Figure 15. Material H (182)

Two minor materials appear as a variation of Material H. The first one (H’) presentsan acceleration the original pattern of Material H and a change of its subdivision unityinto sixteenth notes, the main similarity being the continuous gathering of the double

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bass and the flute, even if the raspy E note played by the double bass subtly becomes aharmonic two octaves higher, recalling Material B. The second one (H”) seems to forma hybrid with Material E, because of the appearance of an accentuated C sharp note incowbells, double bass and piano. However, the harmonic in the double bass and iambiccharacter link it with Material H.

4.9 Material I

In this material the heterophony is much more flagrant, played over a descending melody.Not all the instruments play it in unison but in microtonal approximations, yielding aricher sonority. Only the double bass and the cowbells play the structural melody overthe original pattern, the periodicity of each instrument is independent and is constantlychanged at each appearance of the material.

Figure 16. Heterophony in Material I (272)

4.10 Material J

Using a lot of notes from the free circular plate spectra, the lower partials are grouped asa sort of cluster strongly attacked by the piano and lower strings with a Bartok pizzicato.Immediately after this, a longer high chord ensues and develops the iambic idea set forth

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in Material H. The high notes will gradually be extended in a melodic descent or inoverblown descending notes. Normally attributed to the flute, here they are played asa strings glissando. This procedure is often applied to create interpolation with othermaterial.

Figure 17. Material J (291)

4.11 Interpolation

Interpolation is a transition between two musical situations. In this piece it becomes avery important bridge between bodies of material. Elements from the incoming sectionare mixed in with elements from the outgoing section. This gathering process is gradualand leads to the complete transformation of the outgoing section into the incoming one.A different kind of interpolation occurs, depending on the characteristics of the sections.Some specific examples are presented below to explain how the material is assembled.

In Measure 121, interpolation occurs between Material A and Material C. The proce-dure starts when the accentuated notes of Material A are followed by sextuplet ascendingnotes. It begins by adding the first sextuplet note to Material A, then grows note bynote into a complete ascending scale of Material C in each instrument.

Another striking example appears in Measure 286, in an interpolation between Mate-rial C and J. One note is subtracted from the ascending scale of Material C to only keeptwo notes, one lower than the other. The orchestration is reduced to three instruments:

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Figure 18. Interpolation between Material A and Material C (121)

a violin, clarinet and viola. Each begins at a different beat of the sextuplet, the rhythmdecelerates and the lower notes gradually assemble at the same point of beat and thehigher ones at the subsequent point of beat. Simultaneously, the interval between the twonotes grows in a contrary motion, while the rest of the ensemble appears and reinforcesthe process rhythmically and melodically up to the arrival of material J.

Yet another interpolation type is to be found in Measure 232 between Materials Jand D. In this case, after the attack over the high notes of Material J, the descendingintervallic structure of the piano in Material D gradually lengthens, as do the flute andstring canons.

5 General structure of the piece

The original project of the piece is to gradually reduce the length of the materials. Thisprocess is not always regular because the composer has the subjective time perceptionof each sub-section in mind. The length of each sub-section depends on the quantity ofmaterial played in them, as well as how they are connected.

The structure of the piece possesses a special unity. It also has a formal hierarchybuilt in three different levels of segmentation. Firstly, the form of the piece is segmentedinto three, each segment being characterised by specific material and processes. Secondly,there are sub-sections that bring together elements of material that do not contrast witheach other, either because there of a succession of similar material, or because there isinterpolation among the elements. Finally, a local level is marked out by the incomingmaterial, previously described in Aschenblume Musical Materials.

The formal schemas presented below show the three levels of segmentation. The mainsection is divided in sub-sections. The measures at which they occur and their duration

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Figure 19. Interpolation between Material C and Material J (286)

Figure 20. Interpolation between Materiel J and Materiel D (232)

in ratios are specified underneath. The third level shows the materials of each sub-sectionwith arrows between those that are interpolated. Here is an example of their schematicrepresentation.

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SectionMeasures

Sub-sectionsMeasures

Duration in ratiosMaterials

Table 1. Formal scheme of the piece

1st SECTION 1-1621 2 3 4 5

1-19 20-41 42-67 68-77 78-9374/4 83/4 + 1/8 102/4 40/4 763/4 + 1/8

A →→→ A’ A →→→ A’ A → B → A’ A → C D

1st SECTION 1-1626 7 8 9

94-110 111-119 120-129 130-13767/4 + 1/8 36/4 40/4 32/4

D →→ A →→ A’ A →→→ B A →→→ C D →→→ B

1st SECTION 1-16210 11

138-153 154-16264/4 35/4

E →→→ A’ A →→→ E

Table 2. Formal scheme of the first section

5.1 1st Section (1-181)

It shows the first disintegration process undergone by Material A, which is repeated oncewithout any modifications. At its third appearance the materials B, C, D and E aregradually introduced by interpolation inside the process. This first section is dividedin 11 sub-sections, each of them having interpolation between two or three bodies ofmaterial.

The initial disintegration process of A can be time stretched, from the 3rd sub-sectionwhere B is introduced, then the process occurs from the 4th to the 6th sub-sections andfinally from the 7th to the 10th. The time reduction of sub-sections is irregular, due tothe introduction of new materials within. Nevertheless, there is more material in lesstime, which means that they are gradually undergoing a time reduction.

5.2 2nd Section

The presentation of Material F articulates the piece. After it appears, the process changesand the material made up by rhythmic patterns such as B, E, I, H occur frequently. They

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2st SECTION 163-31412 13 14 15 16

163-169 170-181 182-184 185-191 191-192F → → → G D → → → C H B → C H H’ → A’

2st SECTION 163-31417 18 19 20

203-207 208-212 213-238 239-258A →→→ I B →→→ C F → C → J-D F D → C → J

2st SECTION 163-31421 22 23 24 25

259-263 264-271 271-275 275-281 282-292H’ E K → → I B →→→ I B I D F → C → J

2st SECTION 163-31426 27

293-300 301-314F →→ A J F H H’ K →→ J →→ J’

Table 3. Formal scheme of the second section

are generally bridged by short appearances of the material elements developed in the firstsection.

The sub-sections become gradually shorter and the quantity of materials interpolatedinside them increases. This means that the materials undergo a noticeable reduction inlength. The main process after Material F is the assembling of materials that possessspecial tension, released over louder materials such as H or J at the end. Between sub-sections 12 and 15, it finally achieves a total release over material A’. Its duration isreduced gradually throughout its appearance inside the sub-sections 19, 20, 25, 26 and27.

Between sub-sections 21 to 24, the materials with rhythmic patterns quickly succeedeach other, and finally arrive at material I, which generates a sort of rhythmic and melodicunification of the ensemble by its hetereophonic character. This unification is perceivedas a point of release for the entire piece.

5.3 3rd Section

The length of the material is reduced so as to complete contract the material and bringit together in a single entity that possesses characteristics from all. The piece finisheswith a strong and regular pulsing beat, the result of the total contraction of all elements.

The sub-sections are no longer than 31 quarter notes, which are quickly reduced toan average of 4. When this happens, there is only one body of material left in each sub-section, strongly contrasted with the others. Consequently this section is divided intoseveral smaller sub-sections that are juxtaposed until maximum reduction is achieved.Finally in measure 417 a new body of material arises out of this contraction process. It

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possesses a rhythmic pattern, and all the instruments have the same subdivision unit. Theconstant pulsation is progressively announced by piano clusters and a Bartok pizzicato,both recalling Material J. It finally arrives in measure 427 and creates a tension that issuddenly stopped.

6 Conclusions

As mentioned in the introduction, the purpose of this article is not the detailed descriptionof technical procedures used when programming OpenMusic tools. Rather, this articleemphasizes the remarkable advances in algorithmic procedures, in obtaining expressiveand artistic results. Composers generally employ constraints as a tool for composition,however in Lanza’s piece the use of the computer accelerates the compositional process.The generation of hierarchical rhythmic structures is a new development in the subjectof Computer-Assisted Composition. The composer has managed to open a new avenue ofexploration through the control of a rhythmic generator using melodic constraints, andhas achieved significant results.

The value of this piece may also lay in the fact that the formalisation principles areperceived as homogeneous and musical, in turn shedding light upon the global formalstructure. The present article has described these principles and the ways in whichthey are applied with each body of material. The purpose is to point out CAC theforethought that was applied when developing a model for programming tools. Themodel then became part of the musical language that the composer has used for morerecent pieces. It is fair to say that CAC procedures are developed as an extension of thecomposer’s musical language.

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Born in Bogota, Colombia in 1982. He began by playing tra-ditional Colombian music, moving to jazz, rock and classicalmusic. He studied composition for two years at JaverianaUniversity with Harold Vasquez C. and Marco Suarez. Hewon the Colombian Cultural Ministry National Competi-tion which allowed him to come to France to continue hisstudies. In France he has studied with Jean Luc Herve atNanterre Conservatoire and Evry University where he wasawarded a ”Maitrise” for his paper Formalization In TheCompositional Process. In 2003 he studied at the CCMIX(Ianis Xenakis Music Creation Centre) with Gerard Pape,

Bruno Bossis, Jean-Claude Risset, Curtis Roads, Agostino di Scipio among others(composers as well as software developers). He has also studied with Brien Ferney-hough, Luca Francesconi and Philippe Leroux at Royaumont Foundation where thepiece Aneantir was premiered. Since 2004 he has studied composition with PhilippeLeroux at Blancmesnil National School.

His pieces have been played mostly in the Forum De La Jeune Creation organized bythe New Music International Society, 2002 Sin Aliento, 2003 Vestiges du reve, 2004Eblouir, as well as at the CCMIX in the Rencontres DıAutomne Transmutacioncinematica.

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