Acquisition et représentation de connaissances en musique

Bernard Bel

Knowledge acquisition and representation in music

Thèse de doc­tor­at en sci­ences. Université de droit, d'économie et des sci­ences - Aix-Marseille III
https://theses.hal.science/tel-00009692

Résumé

Cette étude traite de la représen­ta­tion infor­ma­tique de con­nais­sances en musique, abor­dée à par­tir de deux expéri­ences en grandeur réelle. La pre­mière est une méth­ode d'acquisition de con­nais­sances en ethno­gra­phie met­tant en inter­ac­tion un expert (le musi­cien), un ana­lyste (le musi­co­logue) et une machine dans une sit­u­a­tion d'apprentissage. Les sché­mas d'improvisation des musi­ciens sont iden­ti­fiés et exprimés à l'aide de règles de pro­duc­tion dans un for­mal­isme dérivé des gram­maires généra­tives et des lan­gages de formes. Un algo­rithme déter­min­iste de test d'appartenance de chaînes arbi­traires au lan­gage défi­ni par une gram­maire (sen­si­ble au con­texte) est présen­té, ain­si qu'une tech­nique d'inférence induc­tive de lan­gages réguliers per­me­t­tant l'acquisition automa­tique de con­nais­sances lex­i­cales et syn­tax­iques. La sec­onde expéri­ence s'insère dans l'élaboration d'un envi­ron­nement de com­po­si­tion musi­cale assistée par ordi­na­teur. Le prob­lème est ici la représen­ta­tion du temps dans une struc­ture dis­crète d'“objets tem­porels”, et plus générale­ment la syn­chro­ni­sa­tion de proces­sus par­al­lèles. Une méth­ode est pro­posée pour la déter­mi­na­tion d'une struc­ture à par­tir de don­nées incom­plètes sur la syn­chro­ni­sa­tion des objets. La notion d'“objet sonore” est ensuite explic­itée formelle­ment. Un algo­rithme effi­cace per­met l'instanciation des objets sonores affec­tés à une struc­ture en ten­ant compte des con­traintes liées à leurs pro­priétés métriques et topologiques.

Excerpts of an AI review of this paper (Claude AI, June 2025)

Summary

This 1990 doc­tor­al the­sis presents an inno­v­a­tive approach to com­put­er rep­re­sen­ta­tion of musi­cal knowl­edge through two major exper­i­men­tal frame­works. The work bridges arti­fi­cial intel­li­gence, for­mal lan­guage the­o­ry, and musi­col­o­gy, address­ing fun­da­men­tal prob­lems in knowl­edge acqui­si­tion and time rep­re­sen­ta­tion in musi­cal structures.

First Experiment: Knowledge Acquisition in Ethnography

The first part intro­duces a nov­el method­ol­o­gy for acquir­ing musi­cal knowl­edge through a "dialec­ti­cal anthro­pol­o­gy" approach involv­ing three actors: an expert musi­cian, a musicologist-analyst, and a com­put­er sys­tem. This method­ol­o­gy was applied to study­ing impro­vi­sa­tion pat­terns (qa'ida) of North Indian tabla per­cus­sion music.

Key Contributions

• Development of BP (Bol Processor) gram­mars, an exten­sion of for­mal gram­mars capa­ble of rep­re­sent­ing rep­e­ti­tion pat­terns and homo­mor­phic transformations
• A deter­min­is­tic mem­ber­ship test algo­rithm for a sub­class of context-sensitive grammars
• An induc­tive infer­ence tech­nique for reg­u­lar lan­guages that simul­ta­ne­ous­ly acquires lex­i­cal and syn­tac­tic knowledge
• Introduction of neg­a­tive con­text rules and sto­chas­tic con­trol mechanisms

The sys­tem enables musi­cians to val­i­date machine-generated musi­cal phras­es, cre­at­ing a feed­back loop that refines gram­mat­i­cal mod­els of impro­vi­sa­tion schemas. The approach moves beyond tra­di­tion­al ethno­graph­ic col­lec­tion by mak­ing the com­put­er an active part­ner in knowl­edge acquisition.

Second Experiment: Computer-Assisted Musical Composition

The sec­ond part address­es time rep­re­sen­ta­tion and syn­chro­niza­tion in dis­crete musi­cal struc­tures, devel­op­ing the BP2 envi­ron­ment for musi­cal composition.

Key Innovations

• Introduction of "sym­bol­ic time" as dis­tinct from phys­i­cal time
• Development of poly­met­ric for­mu­las for rep­re­sent­ing par­al­lel musi­cal sequences
• Formal treat­ment of "time objects" and "out-time objects" (tem­po­ral vs. atemporal)
• An effi­cient algo­rithm for syn­chro­niz­ing sequences with incom­plete tem­po­ral information
• A con­straint sat­is­fac­tion approach to "sound object" instan­ti­a­tion con­sid­er­ing met­ric and topo­log­i­cal properties

Theoretical Framework

The work estab­lish­es con­nec­tions between musi­cal struc­tures and for­mal lan­guage the­o­ry, intro­duc­ing con­cepts such as:

• Pattern gram­mars and restrict­ed pat­tern lan­guages (RPL)
• Transformational gram­mars adapt­ed to musi­cal contexts
• Event uni­vers­es struc­tured by simul­tane­ity, prece­dence, and sequen­tial­i­ty relations
• Trace the­o­ry appli­ca­tions to poly­met­ric structures

Strengths

• Methodological Innovation: The dialec­ti­cal anthro­pol­o­gy approach rep­re­sents a sig­nif­i­cant advance­ment in eth­no­mu­si­co­log­i­cal method­ol­o­gy. By plac­ing the com­put­er as an active par­tic­i­pant rather than a pas­sive tool, Bel cre­ates a gen­uine­ly inter­ac­tive knowl­edge acqui­si­tion sys­tem that respects both the exper­tise of tra­di­tion­al musi­cians and the rig­or of for­mal methods.
• Theoretical Rigor: The math­e­mat­i­cal for­mal­iza­tion is sophis­ti­cat­ed yet prac­ti­cal. The exten­sion of for­mal gram­mars to han­dle musi­cal rep­e­ti­tion pat­terns and homo­mor­phic trans­for­ma­tions address­es real needs in musi­cal rep­re­sen­ta­tion that exist­ing com­pu­ta­tion­al lin­guis­tics tools couldn't meet.
• Cross-Cultural Sensitivity: The work demon­strates gen­uine respect for non-Western musi­cal tra­di­tions while avoid­ing eth­no­cen­tric bias­es com­mon in com­pu­ta­tion­al musi­col­o­gy. The choice to work with North Indian tabla music, with its oral trans­mis­sion tra­di­tion, was par­tic­u­lar­ly appro­pri­ate for test­ing knowl­edge acqui­si­tion methodologies.
• Practical Implementation: Both BP1 and BP2 sys­tems were actu­al­ly imple­ment­ed and test­ed, demon­strat­ing the fea­si­bil­i­ty of the the­o­ret­i­cal pro­pos­als. The com­plex­i­ty analy­sis (show­ing polynomial-time algo­rithms) indi­cates prac­ti­cal applicability.
• Time Representation Innovation: The dis­tinc­tion between sym­bol­ic and phys­i­cal time, along with the con­cept of "time struc­ture," pro­vides a flex­i­ble frame­work that can accom­mo­date dif­fer­ent musi­cal tem­po­ral­i­ties beyond Western metro­nom­ic time.

Significance and Impact

This work was pio­neer­ing in sev­er­al respects:

• Methodology: The inter­ac­tive, computer-mediated approach to ethno­graph­ic knowl­edge acqui­si­tion antic­i­pat­ed lat­er devel­op­ments in dig­i­tal human­i­ties and com­pu­ta­tion­al ethnomusicology.
• Formal Methods: The exten­sion of for­mal lan­guage the­o­ry to musi­cal appli­ca­tions pro­vid­ed tools that were lat­er adopt­ed and extend­ed by oth­er researchers in com­pu­ta­tion­al musicology.
• Cultural Perspective: The work demon­strat­ed how com­pu­ta­tion­al meth­ods could be applied respect­ful­ly to non-Western musi­cal tra­di­tions, open­ing paths for more inclu­sive com­pu­ta­tion­al musicology.
• Temporal Modeling: The sophis­ti­cat­ed treat­ment of musi­cal time influ­enced sub­se­quent work in com­put­er music and musi­cal infor­ma­tion retrieval.

Contemporary Relevance

Thirty years lat­er, this work remains rel­e­vant to sev­er­al cur­rent research areas:

• Machine learn­ing appli­ca­tions to music (the induc­tive infer­ence tech­niques antic­i­pate mod­ern approaches)
• Digital human­i­ties methodologies
• Music infor­ma­tion retrieval systems
• Computer-assisted com­po­si­tion environments
• Cross-cultural com­pu­ta­tion­al musicology

The empha­sis on expert-machine col­lab­o­ra­tion pre­fig­ures cur­rent inter­est in human-AI col­lab­o­ra­tion in cre­ative domains.

Conclusion

Bel's the­sis rep­re­sents a sig­nif­i­cant con­tri­bu­tion to com­pu­ta­tion­al musi­col­o­gy, com­bin­ing the­o­ret­i­cal inno­va­tion with prac­ti­cal imple­men­ta­tion and cul­tur­al sen­si­tiv­i­ty. While some lim­i­ta­tions exist, par­tic­u­lar­ly regard­ing scope and eval­u­a­tion, the work estab­lished impor­tant foun­da­tions for computer-mediated musi­cal knowl­edge rep­re­sen­ta­tion. The dialec­ti­cal method­ol­o­gy for knowl­edge acqui­si­tion and the sophis­ti­cat­ed treat­ment of musi­cal time remain valu­able con­tri­bu­tions to the field. The work demon­strates how for­mal com­pu­ta­tion­al meth­ods can be applied to musi­cal knowl­edge while respect­ing the com­plex­i­ty and cul­tur­al speci­fici­ty of musi­cal traditions.

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