Author: Bernard Bel

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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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L'intonation juste dans la théorie ancienne de l'Inde : ses applications aux musiques modale et harmonique

E. James Arnold

Revue de musi­colo­gie, JSTOR, 71e (1-2), p.11-38. Traduction : Bernard Bel.

👉  Cited on page Just into­na­tion: a gen­er­al framework

Download an English translation

Résumé

La théorie de l'intonation juste basée sur deux gammes fon­da­men­tales (grama-s), telle que la décrivent le Natya Shastra de Bharata et d'autres traités musi­cologiques anciens en san­scrit, for­malise les rela­tions internes des gammes dia­toniques avec une éton­nante pré­ci­sion. Quelques mod­i­fi­ca­tions min­imes suff­isent à l'adapter aux gammes non-diatoniques famil­ières de la musique indi­enne con­tem­po­raine. Cet arti­cle émet l'hypothèse que la théorie de Bharata pro­pose une meilleure base psy­choa­cous­tique rationnelle que les expli­ca­tions actuelles pour ce qui con­cerne les heures d'interprétation des ragas. Le mod­èle math­é­ma­tique présen­té ici, d'un sys­tème de rela­tions inter­valliques dans les gammes dia­toniques et celles qui en dérivent, est un out­il pra­tique pour étudi­er les rela­tions plus en pro­fondeur. La dis­cus­sion débouche sur une propo­si­tion d'application du sys­tème indi­en à la musique har­monique en into­na­tion juste.

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

This schol­ar­ly paper by E.J. Arnold presents a fas­ci­nat­ing explo­ration of ancient Indian music the­o­ry and its poten­tial appli­ca­tions to both modal and har­mon­ic musi­cal sys­tems. The work stands as a sig­nif­i­cant con­tri­bu­tion to com­par­a­tive musi­col­o­gy, bridg­ing Eastern and Western the­o­ret­i­cal frame­works through rig­or­ous math­e­mat­i­cal mod­el­ing and exper­i­men­tal validation.

Theoretical Framework and Methodology

Arnold's cen­tral the­sis revolves around the ancient Indian grāma-mūrcchana sys­tem, a sophis­ti­cat­ed the­o­ret­i­cal con­struct involv­ing fun­da­men­tal scales (grāma-s) and their modal trans­for­ma­tions (mūrcchana-s). The author devel­ops an inno­v­a­tive math­e­mat­i­cal mod­el using a cir­cu­lar com­pu­ta­tion­al disc that visu­al­izes the rela­tion­ships between tonal posi­tions with­in the 22-śru­ti micro­ton­al sys­tem described in Sanskrit trea­tis­es like the Nāṭyaśāstra and Dattilam.

The paper's strength lies in its method­i­cal approach, sys­tem­at­i­cal­ly exam­in­ing how this ancient sys­tem can pro­vide coher­ent expla­na­tions for har­mon­ic rela­tion­ships in both Indian clas­si­cal music and Western tonal har­mo­ny. Arnold's use of Jacques Dudon's sym­bol­ic nota­tion sys­tem for rep­re­sent­ing micro­ton­al inter­vals demon­strates schol­ar­ly rig­or and atten­tion to cross-cultural the­o­ret­i­cal precision.

Historical Context and Scholarly Significance

Arnold effec­tive­ly con­tex­tu­al­izes the research with­in broad­er musi­co­log­i­cal schol­ar­ship, acknowl­edg­ing the work of pio­neers like Sir William Jones and more recent con­tri­bu­tions from schol­ars such as Bharata com­men­ta­tors and con­tem­po­rary Indian musi­col­o­gists. The paper address­es a crit­i­cal gap in under­stand­ing how ancient the­o­ret­i­cal sys­tems might inform mod­ern musi­cal prac­tice, par­tic­u­lar­ly giv­en the his­tor­i­cal dis­rup­tion of liv­ing oral traditions.

The dis­cus­sion of the rāga system's rela­tion­ship to time cycles (sand­hiprakāśa) rep­re­sents par­tic­u­lar­ly valu­able schol­ar­ship. Arnold's analy­sis of how spe­cif­ic rāga-s cor­re­spond to par­tic­u­lar hours of the day or night, sup­port­ed by sys­tem­at­ic tab­u­la­tion of 85 rāga-s with their appro­pri­ate per­for­mance times, pro­vides empir­i­cal ground­ing for what has often remained in the realm of cul­tur­al speculation.

Mathematical Innovation and Practical Applications

The paper's most com­pelling con­tri­bu­tion lies in its math­e­mat­i­cal mod­el­ing of the śruti-swara-grāma-mūrcchana sys­tem. The cir­cu­lar disc rep­re­sen­ta­tion allows for imme­di­ate visu­al­iza­tion of har­mon­ic rela­tion­ships and demon­strates how ancient Indian the­o­ry antic­i­pat­ed many con­cepts lat­er devel­oped in Western har­mon­ic analy­sis. Arnold's exper­i­men­tal work with elec­tron­ic instru­ments, includ­ing the śru­ti har­mo­ni­um devel­oped by Bernard Bel, pro­vides cru­cial empir­i­cal val­i­da­tion of the­o­ret­i­cal predictions.

The appli­ca­tion to Western clas­si­cal har­mo­ny rep­re­sents ground­break­ing cross-cultural musi­col­o­gy. Arnold demon­strates how major and minor scales can be under­stood with­in the grāma-mūrcchana frame­work, reveal­ing pre­vi­ous­ly unrec­og­nized con­nec­tions between Eastern and Western the­o­ret­i­cal sys­tems. The analy­sis of mod­u­la­tion pro­ce­dures using the ancient Indian sys­tem offers fresh per­spec­tives on famil­iar har­mon­ic progressions.

Limitations and Areas for Development

While Arnold acknowl­edges the study's lim­i­ta­tions with­in "musi­cal geom­e­try," the paper could ben­e­fit from more exten­sive dis­cus­sion of prac­ti­cal imple­men­ta­tion chal­lenges. The the­o­ret­i­cal ele­gance of the grāma-mūrcchana sys­tem con­trasts with the prac­ti­cal dif­fi­cul­ties con­tem­po­rary musi­cians face when attempt­ing to real­ize these micro­ton­al rela­tion­ships on tra­di­tion­al instruments.

Additionally, while the paper excel­lent­ly demon­strates the­o­ret­i­cal cor­re­spon­dences between ancient Indian and Western sys­tems, it could explore more deeply the aes­thet­ic and cul­tur­al impli­ca­tions of these con­nec­tions. The rela­tion­ship between math­e­mat­i­cal pre­ci­sion and musi­cal expres­sion deserves fur­ther investigation.

Contemporary Relevance and Future Directions

Arnold's work antic­i­pates impor­tant devel­op­ments in con­tem­po­rary music the­o­ry, par­tic­u­lar­ly in the grow­ing inter­est in micro­ton­al and cross-cultural approach­es to har­mo­ny. The paper's sys­tem­at­ic approach to under­stand­ing non-equal-tempered sys­tems has impli­ca­tions for elec­tron­ic music com­po­si­tion, world music fusion, and the devel­op­ment of new the­o­ret­i­cal frame­works for glob­al musi­cal understanding.

The research also con­tributes to broad­er dis­cus­sions about the uni­ver­sal­i­ty of musi­cal prin­ci­ples ver­sus cul­tur­al speci­fici­ty, sug­gest­ing that math­e­mat­i­cal rela­tion­ships under­ly­ing musi­cal sys­tems may tran­scend cul­tur­al bound­aries while main­tain­ing dis­tinct aes­thet­ic identities.

Conclusion

This paper rep­re­sents exem­plary schol­ar­ship in com­par­a­tive musi­col­o­gy, suc­cess­ful­ly bridg­ing ancient Indian music the­o­ry and con­tem­po­rary ana­lyt­i­cal meth­ods. Arnold's math­e­mat­i­cal mod­el­ing pro­vides a robust frame­work for under­stand­ing com­plex micro­ton­al rela­tion­ships, while the prac­ti­cal appli­ca­tions demon­strate the con­tin­ued rel­e­vance of ancient the­o­ret­i­cal sys­tems. The work opens impor­tant avenues for future research in cross-cultural music the­o­ry and pro­vides valu­able tools for both schol­ars and prac­ti­tion­ers inter­est­ed in expand­ing their har­mon­ic vocab­u­lary beyond Western equal temperament.

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Raga : approches conceptuelles et expérimentales

Bernard Bel

Actes du col­loque "Structures Musicales et Assistance Informatique" (1988). Marseille.

👉  Cited on page The two-vina exper­i­ment
Download an English translation

Résumé

Les dif­fi­cultés de l'analyse acous­tique de musiques extra-européennes provi­en­nent sou­vent de caté­gori­sa­tions de phénomènes qui ne ren­dent pas compte des mod­èles explicites (ou implicites) sur lesquels s'articulent la créa­tion et la per­cep­tion de struc­tures musi­cales. Cet exposé définit la notion de mod­èle mélodique, élaborée et mod­i­fiée pen­dant neuf siè­cles en Inde pour ren­dre compte d'un phénomène mélodique par­ti­c­uli­er: le raga. Dans la deux­ième par­tie sont présen­tés les out­ils et méth­odes qui ser­vent à car­ac­téris­er l'intonation des ragas, ain­si qu'à réalis­er leur tran­scrip­tion et leur clas­si­fi­ca­tion automatiques.

Difficulties in analysing extra-European musics are often bound to cat­e­gori­sa­tions of phe­nom­e­na that do not take into account explic­it (or implic­it) mod­els on which the cre­ation and per­cep­tion of musi­cal struc­tures are based. This paper defines the con­cept of melod­ic mod­el, a con­cept elab­o­rat­ed and trans­formed for nine cen­turies in India to under­lie a par­tic­u­lar melod­ic phe­nom­e­non: raga. In the sec­ond part, tools and meth­ods are pre­sent­ed relat­ing to raga into­na­tion and their auto­mat­ic tran­scrip­tion and classification.

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

Summary

In "Rāga : approches con­ceptuelles et expéri­men­tales," the author dis­cuss­es the con­cep­tu­al his­to­ry, the­o­ret­i­cal foun­da­tions, and exper­i­men­tal inves­ti­ga­tions of the rāga sys­tem in North Indian clas­si­cal music. The first part of the paper traces the evo­lu­tion of rāga-related con­cepts from ancient Sanskrit trea­tis­es (notably the Dattilam and the Nāṭyaśāstra) to more recent per­spec­tives that empha­size melod­ic modes (mela), spe­cif­ic tonal cen­ters (toniques), and the inter­play between the­o­ry and prac­tice. The author high­lights how notions like grā­ma, mūr­c­cha­nā, and jāti have shift­ed over the cen­turies, cul­mi­nat­ing in var­i­ous attempts to clas­si­fy rāgas by scales (ṭhāṭa or mela), melod­ic phras­es (aṅga), and aspects of per­for­mance prac­tice, includ­ing the ide­al hour of rendition.

The sec­ond part of the paper presents tech­no­log­i­cal and ana­lyt­i­cal meth­ods used by the author to study raga into­na­tion and struc­ture. The author describes exper­i­men­tal devices, includ­ing custom-built pitch extrac­tors and the Melodic Movement Analyser (MMA), to cap­ture and visu­al­ize pitch con­tours (mel­o­grams), pro­duce his­tograms (tona­grams) of pitch dis­tri­b­u­tion, and explore micro­ton­al aspects of raga exe­cu­tion. Additionally, the paper delves into auto­mat­ed tran­scrip­tion meth­ods (sargam nota­tion) and pre­lim­i­nary approach­es for auto­mat­ic clas­si­fi­ca­tion of ragas, lever­ag­ing pitch-based sim­i­lar­i­ty mea­sures. By sys­tem­at­i­cal­ly com­par­ing the­o­ret­i­cal pre­dic­tions with actu­al per­for­mance data, the paper pro­pos­es a rich­er under­stand­ing of how ragas are con­cep­tu­al­ized and real­ized in practice.

Major Strengths

Comprehensive Historical Context

The author pro­vides an exten­sive overview of the key devel­op­ments and con­cep­tu­al shifts in Indian music the­o­ry, from the gråma-based sys­tem of Bharata to mod­ern ṭhāṭa and scale-based frame­works. This his­tor­i­cal arc clar­i­fies how philo­soph­i­cal, aes­thet­ic, and prac­ti­cal con­sid­er­a­tions con­verge in raga performance.

Balanced Discussion of Theory and Practice

The paper effec­tive­ly under­scores the gap between the­o­ret­i­cal ideals (e.g., 22 srutis, ancient modal struc­tures) and the real­i­ties of con­tem­po­rary per­for­mance prac­tices (e.g., stan­dard­iza­tion, par­tial tem­per­ing, the empha­sis on the bour­don). This dual approach helps illus­trate the dynam­ic nature of raga music.

Technical Innovation in Experimentation

By devis­ing hard­ware and soft­ware tools for real-time pitch extrac­tion and by automat­ing tran­scrip­tion, the author demon­strates a method­olog­i­cal frame­work that expands the pos­si­bil­i­ties for large-scale analy­sis of raga per­for­mances. The clear expla­na­tions of how these tech­nolo­gies work sup­port their applic­a­bil­i­ty and value.

Interdisciplinary Relevance

The paper bridges musi­co­log­i­cal inquiry, acousti­cal analy­sis, eth­no­mu­si­co­log­i­cal con­text, and com­pu­ta­tion­al meth­ods. This inter­dis­ci­pli­nary scope sit­u­ates the work as a notable con­tri­bu­tion to schol­ar­ship on micro­ton­al music, melod­ic clas­si­fi­ca­tion, and cross-cultural cog­ni­tion of musi­cal scales.

Overall Observations

The paper offers a clear and method­i­cal­ly thor­ough account of both the the­o­ret­i­cal under­pin­nings of raga music and the exper­i­men­tal means by which such the­o­ries can be test­ed against empir­i­cal per­for­mance data. The blend­ing of his­tor­i­cal musi­col­o­gy, acoustics, and infor­mat­ics demon­strates a strong inter­dis­ci­pli­nary approach. By syn­the­siz­ing ancient trea­tis­es with mod­ern com­pu­ta­tion­al tools, the work deep­ens our under­stand­ing of how ragas con­tin­ue to thrive as vibrant, liv­ing musi­cal enti­ties while reveal­ing the com­plex­i­ty of attempts at stan­dard­iza­tion and classification.

In sum, “Raga : approches con­ceptuelles et expéri­men­tales” pro­vides valu­able tech­ni­cal insights and broad­ens our per­spec­tive on one of the most sophis­ti­cat­ed melod­ic sys­tems world­wide. Its fusion of musi­co­log­i­cal research, exper­i­men­tal data, and com­pu­ta­tion­al analy­sis stands out as a notable con­tri­bu­tion to raga stud­ies and to the broad­er field of ethnomusicology.

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Inférence de langages réguliers

Bernard Bel

Journées Françaises de l'Apprentissage (1990), Lannion, France : 5-27

Résumé

Cet exposé présente une méth­ode générale d'acquisition de con­nais­sances dans un domaine for­mal­isé à l'aide d'automates finis (lan­gages réguliers). A par­tir d'un échan­til­lon d'exemples le sys­tème con­stru­it un auto­mate "presque min­i­mal" qui n'est pas néces­saire­ment déter­min­iste. Cette con­struc­tion peut être con­trainte par des con­nais­sances sur la seg­men­ta­tion des exem­ples que le sys­tème peut acquérir en ques­tion­nant l'informateur. Dans une deux­ième phase, le sys­tème généralise l'automate à par­tir de pro­priétés con­nues du lan­gage ou(et) à par­tir d'hypothèses validées à l'aide d'oracles. Une liste non exhaus­tive d'heuristiques générales est pro­posée. La démon­stra­tion s'appuie sur un cas réel de mod­éli­sa­tion d'apprentissage de sché­mas d'improvisation musicale.

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

Summary of the Work

The paper explores a method­ol­o­gy for infer­ring reg­u­lar lan­guages (lan­gages réguliers) from exam­ples. It dis­cuss­es both the­o­ret­i­cal under­pin­nings — par­tic­u­lar­ly Gold’s the­o­rem and sub­se­quent refine­ments — along with an incre­men­tal approach to build­ing “almost min­i­mal” automa­ta. The author address­es cen­tral notions such as the canon­i­cal accep­tor, the prefix-tree accep­tor, and the impor­tance of main­tain­ing cor­rect­ness when mov­ing from a set of exam­ples to a gen­er­al­ized automa­ton. The study also show­cas­es an appli­ca­tion to musi­cal impro­vi­sa­tion schema­ta, illus­trat­ing how domain-specific rules can con­strain and refine gram­mat­i­cal inference.

Main Contributions

Incremental Learning Framework

The paper offers a struc­tured, step-by-step method: start­ing with an accep­tor built from exam­ples alone (the prefix-tree or “arbores­cent” automa­ton), merg­ing states to reduce com­plex­i­ty, and apply­ing con­straints so as not to over­gen­er­al­ize. This incre­men­tal per­spec­tive is well-motivated by real-world use cas­es where exam­ples become avail­able over time.

Formal Properties and Correctness

The author places strong empha­sis on ensur­ing the cor­rect­ness of gen­er­al­iza­tion. By ref­er­enc­ing Gold’s the­o­rem, k-reversible lan­guages, and the con­cept of learn­ing from pos­i­tive data only, the paper grounds its approach in estab­lished the­o­ret­i­cal results.

Use of Domain Constraints

A sig­nif­i­cant por­tion of the paper deals with how addi­tion­al domain knowl­edge (e.g., known seg­men­ta­tion rules for a music nota­tion sys­tem) can guide the automaton’s con­struc­tion. This intro­duces prac­ti­cal heuris­tics that make gram­mat­i­cal infer­ence more tractable in real-world scenarios.

Detailed Mathematical Rigor

The proofs, def­i­n­i­tions, and lem­mas (for instance, those on heads and tails, or min­i­mal canon­i­cal accep­tors) are stat­ed thor­ough­ly. This rig­or is help­ful both for ensur­ing cor­rect­ness and for con­vey­ing the method’s the­o­ret­i­cal reliability.

Illustrative Examples

The appli­ca­tion to musi­cal impro­vi­sa­tion, specif­i­cal­ly to Indian drum­ming tra­di­tions, serves as a con­crete illus­tra­tion. It nice­ly demon­strates the inter­play between abstract for­mal­ism (like merg­ing states) and domain-specific knowl­edge (like rhyth­mic “words” or ono­matopoe­ic syllables).

Clarity and Structure

  • The paper is log­i­cal­ly well-structured: it begins with a the­o­ret­i­cal foun­da­tion, then intro­duces incre­men­tal meth­ods for automa­ton con­struc­tion, cul­mi­nat­ing in a dis­cus­sion of domain con­straints and examples.
  • The tex­tu­al orga­ni­za­tion, with numer­ous def­i­n­i­tions in the appen­dix, is ben­e­fi­cial for ref­er­ence but can require mul­ti­ple cross-referencing steps while read­ing. A con­cise reminder of key def­i­n­i­tions in the main text can fur­ther aid comprehension.

Strengths

  • Thorough ground­ing in estab­lished the­o­ry (Gold’s the­o­rem, reversible languages).
  • A prac­ti­cal approach that bal­ances sys­tem­at­ic infer­ence with inter­ac­tive ques­tion­ing or orac­u­lar feedback.
  • Clear demon­stra­tion of how domain-specific heuris­tics reduce the search space, mak­ing learn­ing more feasible.
  • Rigor in explain­ing each step of con­struct­ing and refin­ing the automaton.
  • Engaging case study that shows the real-world poten­tial of gram­mar infer­ence out­side of pure­ly lin­guis­tic contexts.

Overall Assessment

The paper pro­vides a sol­id com­bi­na­tion of the­o­ry and prac­tice in gram­mat­i­cal infer­ence for reg­u­lar lan­guages. By care­ful­ly detail­ing each step — build­ing ini­tial automa­ta, con­strain­ing merges using domain knowl­edge, and ver­i­fy­ing new gen­er­al­iza­tions through queries — the approach is shown to be sys­tem­at­ic and adapt­able. Readers inter­est­ed in inter­ac­tive or incre­men­tal lan­guage learn­ing, par­tic­u­lar­ly those with domain-specific con­straints, will like­ly find this dis­cus­sion instruc­tive and thorough.

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Migrating Musical Concepts - an overview of the Bol Processor

Bernard Bel

Computer Music Journal (1998), Vol. 22, 2: 56-64

Abstract

The Bol Processor is the out­come of a migra­to­ry process, its design hav­ing been car­ried over in three phas­es and places: in col­lab­o­ra­tion with tra­di­tion­al North Indian musi­cians (1980-85), Western musi­cians in Europe (1985-93) and back in India with Carnatic musi­cians (1995-97).The the­o­ret­i­cal frame­work of the under­ly­ing research project also evolved in three stages, tak­ing inspi­ra­tion from expert sys­tems in the ear­ly 1980s, symbolic-numeric machine-learning in the end of the decade, and com­po­si­tion the­o­ry in the 1990s.Throughout this process, the design­er has been faced with the chal­lenge of blend­ing soft­ware with "mind­ware", here tak­en to mean musi­cians' striv­ing for "[…] tools enabling them to manip­u­late objects so as to imbue them with 'soul' or expe­ri­en­tial val­ue […]" (Laske 1996). In a cross-cultural approach this led to mod­el­ling descrip­tions of music and com­po­si­tion­al process­es at a lev­el of abstrac­tion suf­fi­cient­ly high to encom­pass "local" musi­cal con­cepts with­out get­ting too abstruse.

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

Summary

Bernard Bel’s man­u­script pro­vides an exten­sive overview of the Bol Processor (BP), a music soft­ware envi­ron­ment that evolved through col­lab­o­ra­tions with Indian and Western musi­cians. The soft­ware address­es rhyth­mic, melod­ic, and com­po­si­tion­al tasks using a grammars-based approach, sym­bol­ic time nota­tion, and sophis­ti­cat­ed algo­rithms (e.g., poly­met­ric expan­sion, quan­ti­za­tion). The review traces the his­to­ry and the­o­ret­i­cal under­pin­nings of this sys­tem, mov­ing through the project’s three phas­es of devel­op­ment and cul­mi­nat­ing in a flex­i­ble inter­face link­ing BP to Csound. By empha­siz­ing text-based data rep­re­sen­ta­tions, BP aims to fos­ter deep­er think­ing about music struc­ture and com­po­si­tion­al process­es, accom­mo­dat­ing con­texts that fall out­side pure­ly Western traditions.

Strengths

Historical and Contextual Depth: The author clear­ly artic­u­lates how the project emerged from eth­no­mu­si­co­log­i­cal research in Indian music, then expand­ed to address Western com­po­si­tion­al tech­niques. This his­tor­i­cal fram­ing high­lights how the soft­ware bridges cul­tur­al con­texts while retain­ing a con­sis­tent­ly pow­er­ful grammar-based approach.

Clear Explanations of Core Algorithms: The detailed descrip­tions of poly­met­ric expan­sion, time-stretching, quan­ti­za­tion, and grammar-based trans­for­ma­tions are a valu­able tech­ni­cal resource. The author pro­vides exam­ples, dia­grams, and ref­er­ences that elu­ci­date these con­cepts for read­ers unfa­mil­iar with for­mal lan­guage meth­ods applied to music.

Innovative Methodology: The soft­ware design seam­less­ly inte­grates sym­bol­ic approach­es (for­mal gram­mars, integer-based time units, con­straint sat­is­fac­tion) with phys­i­cal exe­cu­tion in MIDI and Csound domains. This dual­i­ty allows com­posers and researchers to treat time both dis­crete­ly and con­tin­u­ous­ly as required.

Attention to Cross-Cultural Music Needs: BP’s adapt­abil­i­ty to var­i­ous musi­cal nota­tions, includ­ing Indian and Western pitch/note rep­re­sen­ta­tions, is a strong sig­na­ture of this work, reflect­ing deep respect for non-Western musi­cal con­cepts and per­for­mance practices.

Comprehensive References and Examples: The sup­port­ing ref­er­ences shed light on relat­ed research in com­po­si­tion the­o­ry, music cog­ni­tion, and com­pu­ta­tion­al mod­els. Numerous code-like illus­tra­tions and fig­ures demon­strate how actu­al musi­cal tasks are imple­ment­ed, assist­ing prac­ti­tion­ers who might want to repli­cate or mod­i­fy these ideas.

Overall Impressions

The man­u­script pro­vides an in-depth look at a unique­ly ver­sa­tile sys­tem for musi­cal analy­sis and com­po­si­tion. The author’s com­mit­ment to text-based inter­ac­tion, cou­pled with robust sup­port for real-time oper­a­tions and cross-cultural music con­cepts, stands out as a mature, flex­i­ble frame­work. The paper offers a thought­ful pre­sen­ta­tion of both under­ly­ing the­o­ret­i­cal foun­da­tions and prac­ti­cal imple­men­ta­tions, mak­ing it rel­e­vant for those inter­est­ed in computer-aided com­po­si­tion, musi­co­log­i­cal research, and inter­dis­ci­pli­nary approach­es bridg­ing Indian and Western musi­cal forms.

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Can a computer help resolve the problem of ethnographic description?

James Kippen & Bernard Bel

Anthropological Quarterly (1989), 62, 3: 131-144

Abstract

A major prob­lem in ethno­graph­ic descrip­tion may be summed up as the search for ways to dis­en­tan­gle folk from ana­lyt­i­cal mod­els. Knowledge-based sys­tems have con­tributed to the devel­op­ment of for­mal struc­tures for the manip­u­la­tion of sym­bols asso­ci­at­ed with par­tic­u­lar phys­i­cal and con­cep­tu­al phe­nom­e­na. Importantly, their out­put can be inter­pret­ed by experts in the domain. This pro­vides eval­u­a­tion pro­ce­dures for mod­els elab­o­rat­ed joint­ly by ana­lysts and infor­mants. This paper describes an inter­ac­tive sys­tem in which knowl­edge is rep­re­sent­ed as pro­duc­tion rules in a for­mat derived from the the­o­ry of for­mal lan­guages. Modus ponens and modus tol­lens are explained and com­pared to deriva­tion schema­ta in first-order pred­i­cate log­ic. The results of an appli­ca­tion to the study of North Indian tabla drum­ming are assessed. We con­clude that (1) knowl­edge rep­re­sent­ed at a low the­o­ret­i­cal lev­el fails to descrim­i­nate between the input from infor­mants and the intu­itive assump­tions of ana­lysts, (2) exper­i­men­tal pro­ce­dures can be improved con­sid­er­ably if the sys­tem is designed to per­form auto­mat­ed knowl­edge acqui­si­tion (using prob­a­bilis­tic gram­mars and induc­tive learning).

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

Summary of the Work

The arti­cle focus­es on the use of com­pu­ta­tion­al approach­es — par­tic­u­lar­ly knowledge-based sys­tems — to address the chal­lenge of pro­duc­ing con­sis­tent and sys­tem­at­ic ethno­graph­ic descrip­tions. The authors draw on their research with the Bol Processor (BP), a for­mal language-based sys­tem orig­i­nal­ly devel­oped to rep­re­sent and gen­er­ate sequences of ver­bal drum syl­la­bles (bols) in North Indian tabla per­for­mance. They describe how the BP’s gram­mar for­mal­ism, infer­ence engine, and mem­ber­ship tests facil­i­tate iter­a­tive inter­ac­tion between an ana­lyst and infor­mants (expert musi­cians). By demon­strat­ing the system’s abil­i­ty to pro­duce, rec­og­nize, and eval­u­ate per­mis­si­ble melod­ic or rhyth­mic vari­a­tions, the authors aim to illu­mi­nate how com­put­ers can be more deeply inte­grat­ed into anthro­po­log­i­cal and eth­no­mu­si­co­log­i­cal research.

Key Contributions

Formal Grammar and Pattern Representation: The paper offers a clear expla­na­tion of how context-free and context-sensitive gram­mars can be used to spec­i­fy cul­tur­al­ly valid musi­cal struc­tures. In par­tic­u­lar, the authors high­light the impor­tance of rep­re­sent­ing pat­terns and con­straints on musi­cal impro­vi­sa­tion in a gen­er­a­tive format.

Interactive Methodology: A cen­tral point is the iter­a­tive feed­back loop that allows infor­mants to assess computer-generated sequences and pro­vide cor­rec­tions. This “apprentice-like” inter­ac­tion under­scores how com­pu­ta­tion­al tools can help researchers refine the­o­ret­i­cal mod­els of cul­tur­al knowl­edge in near-real-time.

Probabilistic Grammars: The authors incor­po­rate a weight­ing sys­tem for pro­duc­tion rules, there­by account­ing for the rel­a­tive like­li­hood of dif­fer­ent musi­cal deriva­tions. This approach not only adds real­ism to the gen­er­a­tive process but also tack­les com­mon issues with pure­ly enu­mer­a­tive or ran­dom output.

Membership Testing: The mem­ber­ship test, which decides whether a new­ly pro­posed sequence belongs to a giv­en gram­mar, is described as an effi­cient, deter­min­is­tic bottom-up pars­er. This fea­ture is sig­nif­i­cant because it allows infor­mants to offer nov­el vari­a­tions while enabling the sys­tem to quick­ly judge their adher­ence to the emer­gent rule set.

Reflections on Folk vs. Analytical Models: The arti­cle rais­es impor­tant anthro­po­log­i­cal ques­tions about the bound­ary between infor­mants’ inter­nal­ized (folk) knowl­edge and the analyst’s for­mal (re)construction. The authors’ frank dis­cus­sion of the chal­lenges involved, such as the risk of over­for­mal­iz­ing or “antic­i­pat­ing” infor­mant knowl­edge, is method­olog­i­cal­ly relevant.

Strengths

  • The paper empha­sizes the val­ue of com­bin­ing field­work with com­pu­ta­tion­al exper­i­men­ta­tion. This dual approach—grounded in real ethno­graph­ic and musi­cal practice—provides a com­pelling demon­stra­tion of how arti­fi­cial intel­li­gence tech­niques can advance the study of music and culture.
  • Clear exam­ples illus­trate code struc­tures, pars­ing mechan­ics, and the gram­mar design. These con­crete details will help oth­er researchers adapt or repli­cate the Bol Processor approach in dif­fer­ent cul­tur­al or musi­cal contexts.
  • The account of iter­a­tive knowl­edge acqui­si­tion high­lights a col­lab­o­ra­tive research dynam­ic, show­ing how insight flows back and forth between infor­mants and com­pu­ta­tion­al mod­els, rather than being a uni­di­rec­tion­al exer­cise of extract­ing information.

Conclusion

This study offers a thought­ful and inno­v­a­tive approach to bridg­ing ethno­graph­ic inquiry with com­pu­ta­tion­al mod­els. By show­ing how arrange­ments of sym­bol­ic musi­cal data can be sys­tem­at­i­cal­ly gen­er­at­ed, test­ed, and refined in con­junc­tion with human experts, the authors illus­trate a nov­el and promis­ing method for ethno­graph­ic descrip­tion. The paper encour­ages a nuanced under­stand­ing of both the poten­tial and lim­i­ta­tions of using expert sys­tems to cap­ture the com­plex­i­ty of cul­tur­al knowledge.

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Modelling improvisatory and compositional processes

James Kippen & Bernard Bel

In Denise Penrose & Ray Lauzanna (eds.) Languages of Design, 1 (1992). Elsevier Science Publishers, Amsterdam: 11-26.

Abstract

An appli­ca­tion of for­mal lan­guages to the rep­re­sen­ta­tion of musi­cal process­es is intro­duced. Initial inter­est was the struc­ture of impro­vi­sa­tion in North Indian tabla drum music, for which exper­i­ments have been con­duct­ed in the field as far back as 1983 with an expert sys­tem called the Bol Processor, BP1. The com­put­er was used to gen­er­ate and ana­lyze drum­ming pat­terns rep­re­sent­ed as strings of ono­matope­ic syl­la­bles, bols, by manip­u­lat­ing for­mal gram­mars. Material was then sub­mit­ted to musi­cians who assessed its accu­ra­cy and increas­ing­ly more elab­o­rate and sophis­ti­cat­ed rule bases emerged to rep­re­sent the musi­cal idiom.

Since sev­er­al method­olog­i­cal pit­falls were encoun­tered in trans­fer­ring knowl­edge from musi­cian to machine, a new device, named QAVAID, was designed with the capa­bil­i­ty of learn­ing from a sam­ple set of impro­vised vari­a­tions sup­plied by a musi­cian. A new ver­sion of Bol Processor, BP2, has been imple­ment­ed in a MIDI stu­dio envi­ron­ment to serve as a aid to rule-based com­po­si­tion in con­tem­po­rary music. Extensions of the syn­tac­tic mod­el, such as sub­sti­tu­tions, metavari­ables, and remote con­texts, are briefly introduced.

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

Summary of the Work

The man­u­script presents a for­mal language-based approach to mod­el­ing impro­visato­ry and com­po­si­tion­al process­es in music — par­tic­u­lar­ly North Indian tabla drum­ming — and high­lights the devel­op­ment of the Bol Processor soft­ware. The arti­cle effec­tive­ly demon­strates how gen­er­a­tive gram­mars, pat­tern lan­guages, and relat­ed exten­sions (e.g., pat­tern rules, homo­mor­phisms, neg­a­tive con­texts, and remote con­texts) can cap­ture the com­plex­i­ty and flex­i­bil­i­ty of musi­cal form, espe­cial­ly with regard to impro­vi­sa­tion. The authors also illus­trate the tran­si­tion from an ini­tial musi­co­log­i­cal focus in the ear­li­er Bol Processor (BP1) to the more gen­er­al­ized and com­po­si­tion­al ori­en­ta­tion of BP2, high­light­ing the system’s role in computer-assisted com­po­si­tion. Throughout, there is a strong empha­sis on inte­grat­ing eth­no­mu­si­co­log­i­cal insights, com­pu­ta­tion­al meth­ods, and prac­ti­cal soft­ware design.

Strengths

Comprehensive Description of Formal Methods

The paper pro­vides a thor­ough expla­na­tion of how dif­fer­ent gram­mar types — finite-state automa­ta, context-free gram­mars, type-0 gram­mars — are rel­e­vant for describ­ing musi­cal forms. This is com­ple­ment­ed by exam­ples that clar­i­fy the the­o­ret­i­cal con­cepts (e.g., the use of pat­tern rules to han­dle repeat­ed sec­tions or “voiced/unvoiced” trans­for­ma­tions). These sec­tions effec­tive­ly detail both tra­di­tion­al and inno­v­a­tive mod­el expansions.

Contextual Application in Ethnomusicology

By apply­ing gen­er­a­tive mod­els to North Indian tabla’s “theme-and-variations” struc­tures (qa‘idas), the paper demon­strates how such com­pu­ta­tion­al approach­es can illu­mi­nate facets of an oral­ly trans­mit­ted musi­cal tra­di­tion. The depth of col­lab­o­ra­tion with expert musi­cians and the iter­a­tive process of eval­u­a­tion is indica­tive of a con­sci­en­tious ethno­graph­ic methodology.

Transition to a Generalized Composition Environment

BP2 goes beyond tra­di­tion­al eth­no­mu­si­co­log­i­cal appli­ca­tions and can be employed as a computer-aided com­po­si­tion tool for broad­er musi­cal con­texts. The con­cept of “sound-objects” and flex­i­ble time-handling approach­es (stri­at­ed vs. smooth time, time piv­ots, con­straint sat­is­fac­tion, etc.) make the work­flow appeal­ing to com­posers and researchers inter­est­ed in gen­er­a­tive music systems.

Balanced Presentation of Achievements and Challenges

The paper address­es prob­lems of knowl­edge trans­fer, data rep­re­sen­ta­tion, and the com­plex­i­ty of rule-based sys­tems, pro­vid­ing valu­able lessons for future com­pu­ta­tion­al musi­col­o­gy projects. It also describes how the QAVAID sub­sys­tem attempts to auto­mate knowl­edge acqui­si­tion and infer­ence, there­by remov­ing some of the bot­tle­necks encoun­tered when man­u­al­ly con­struct­ing grammars.

Extensive Reference to Prior Research

A sub­stan­tial and well-organized ref­er­ence sec­tion places the work in con­ver­sa­tion with rel­e­vant lit­er­a­ture from for­mal lan­guage the­o­ry, musi­co­log­i­cal stud­ies, and AI-based com­po­si­tion sys­tems. The inclu­sion of the­o­ret­i­cal sources (e.g., cita­tions to Chomsky’s hier­ar­chy) and prac­ti­cal ref­er­ences (e.g., man­u­al or share­ware avail­abil­i­ty) under­scores the paper’s aca­d­e­m­ic depth and real-world applicability.

Overall Appraisal

This study offers a detailed and inno­v­a­tive account of how for­mal gen­er­a­tive tools can be har­nessed to describe, ana­lyze, and pro­duce com­plex musi­cal struc­tures. By bridg­ing the­o­ret­i­cal com­put­er sci­ence, eth­no­mu­si­co­log­i­cal field­work, and com­po­si­tion­al prac­tice, the man­u­script opens pos­si­bil­i­ties for deep­er explo­ration of music’s syn­tac­tic fea­tures and cre­ative appli­ca­tions in con­tem­po­rary com­po­si­tion. Its empha­sis on prac­ti­cal soft­ware devel­op­ment, eval­u­at­ed in tan­dem with expert cri­tiques, posi­tions it as a note­wor­thy resource for researchers and prac­ti­tion­ers at the inter­sec­tion of musi­col­o­gy, AI, and dig­i­tal arts.

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Bol Processor grammars

James Kippen & Bernard Bel

In Mira Balaban, Otto Laske et Kemal Ebcioglu (eds.) Understanding Music with AI, American Association for Artificial Intelligence Press, Menlo Park CA (1992): 366-400.

Abstract

Bol Processor gram­mars are an exten­sion of unre­strict­ed gen­er­a­tive gram­mars allow­ing a sim­ple rep­re­sen­ta­tion of string "pat­terns", here tak­en to mean rep­e­ti­tions and homo­mor­phic trans­for­ma­tions. These have been suc­cess­ful­ly applied to the sim­u­la­tion of impro­visato­ry tech­niques in tra­di­tion­al drum music, using a production-rule sys­tem called "Bol Processor BP1". The basic con­cepts and pars­ing tech­niques of BP1 are presented.

A new ver­sion of Bol Processor, name­ly "BP2", has been designed to serve as a aid to rule-based com­po­si­tion in con­tem­po­rary music. Extensions of the syn­tac­tic mod­el, such as metavari­ables, remote con­texts, sub­sti­tu­tions and pro­grammed gram­mars, are briefly introduced.

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

Overview and Summary

The authors pro­pose a for­mal­ism, called "Bol Processor gram­mars," designed to cap­ture and sim­u­late per­for­mance and impro­visato­ry behav­iors in tra­di­tion­al drum music—particularly North Indian tabla. This work presents a detailed account of how their pro­posed grammar-based sys­tem (BP1 and sub­se­quent­ly BP2) man­ages musi­cal ele­ments such as gen­er­a­tive rules, pars­ing pro­ce­dures, and higher-order trans­for­ma­tions. The authors draw on con­cepts from for­mal lan­guage the­o­ry, specif­i­cal­ly incor­po­rat­ing string rewrit­ing, gen­er­a­tive gram­mars of vary­ing types (from context-free to unre­strict­ed), and pat­tern languages.

The mono­graph not only dis­cuss­es the­o­ret­i­cal frame­works but also pro­vides imple­men­ta­tions and exam­ples rel­e­vant to com­po­si­tion, impro­vi­sa­tion, and eth­no­mu­si­co­log­i­cal analy­sis. By com­bin­ing stan­dard gram­mars with addi­tion­al fea­tures (e.g., pat­tern rules, neg­a­tive con­texts, remote con­texts, sub­sti­tu­tions, homo­mor­phisms, and a sophis­ti­cat­ed weight­ing mech­a­nism), the Bol Processor aims to mod­el cre­ative aspects of impro­visato­ry traditions.

Contribution and Significance

  • The paper bridges the­o­ret­i­cal com­put­er sci­ence (rewrit­ing sys­tems, gen­er­a­tive gram­mars) with eth­no­mu­si­co­log­i­cal inquiry. This inter­dis­ci­pli­nary approach shows how lan­guage mod­els can adapt to musi­cal per­for­mance tra­di­tions, espe­cial­ly where oral trans­mis­sion prevails.
  • The authors intro­duce exten­sions to clas­si­cal Chomsky hier­ar­chies by incor­po­rat­ing string pat­tern lan­guages and homo­mor­phisms specif­i­cal­ly tai­lored for music com­po­si­tion and analy­sis. This advance­ment is espe­cial­ly valu­able to those research­ing com­pu­ta­tion­al musi­col­o­gy or algo­rith­mic composition.
  • By pro­vid­ing prac­ti­cal imple­men­ta­tion details and guide­lines (e.g., sub­gram­mars, weight­ing rules, context-sensitive sub­sti­tu­tions), the study con­veys a clear path for oth­ers look­ing to mod­el or sim­u­late impro­vi­sa­tion­al processes.

Strengths

  • Clarity of Theoretical Underpinnings: The text care­ful­ly explains the fun­da­men­tals of gen­er­a­tive gram­mars and pat­tern lan­guages, ensur­ing that read­ers unfa­mil­iar with for­mal lan­guage the­o­ry can still fol­low the ratio­nale behind the Bol Processor model.
  • Comprehensive Examples: The inclu­sion of worked-through gram­mar list­ings, detailed pars­ing traces, and real-world musi­cal seg­ments high­lights an applied per­spec­tive. Readers can see exact­ly how the rules oper­ate on con­crete musi­cal materials.
  • Interdisciplinary Integration: The man­u­script thought­ful­ly weaves togeth­er com­pu­ta­tion­al lin­guis­tics, eth­no­mu­si­col­o­gy, and com­po­si­tion, offer­ing a unique per­spec­tive to each discipline.
  • Generative and Analytical Capacities: Emphasizing both the gen­er­a­tion of new musi­cal vari­a­tions and the pars­ing of exist­ing per­for­mances demon­strates the system’s two-fold util­i­ty: it sup­ports cre­ative com­po­si­tion while pro­vid­ing a frame­work for empir­i­cal analysis.

Areas for Further Development

  • Handling of Larger-Scale Form: While the paper address­es theme-variation struc­tures, the method­ol­o­gy could be extend­ed to more exten­sive glob­al forms or multi-sectional pieces. More elab­o­ra­tion on how the gram­mar might man­age nest­ed forms or very long struc­tures would strength­en the approach.
  • Quantitative Evaluation: The text pro­vides evi­dence of suc­cess­ful mod­el­ing but could ben­e­fit from addi­tion­al dis­cus­sion of how cor­rect­ness or “musi­cal plau­si­bil­i­ty” is sys­tem­at­i­cal­ly test­ed, beyond anec­do­tal or inter­ac­tive ses­sions with experts.
  • Comparisons with Other Systems: A more in-depth com­par­i­son with exist­ing com­pu­ta­tion­al music sys­tems that also employ gen­er­a­tive gram­mars (e.g., pure­ly context-free or Markov-based approach­es) might deep­en an under­stand­ing of the Bol Processor’s unique contributions.

Readability and Presentation

  • The writ­ing is clear and con­sis­tent­ly struc­tured, espe­cial­ly around the dis­crete sec­tions (intro­duc­tion, pat­tern rules, pars­ing, and advanced fea­tures in BP2). Diagrams and gram­mar list­ings are help­ful, though fur­ther clar­i­fy­ing anno­ta­tions in some fig­ures could assist read­ers less famil­iar with for­mal notation.
  • The appen­dices excel in pre­sent­ing extend­ed exam­ples and step-by-step pars­es, adding trans­paren­cy to the meth­ods. This style of pre­sen­ta­tion ensures repro­ducibil­i­ty and offers insights into how to adapt or mod­i­fy the sys­tem for oth­er musi­cal styles.

Potential Impact on the Field

The sys­tem has appar­ent impli­ca­tions not just for tabla and oth­er per­cus­sion tra­di­tions but for any domain where com­plex vari­a­tions can be expressed in a rule-based man­ner. Likewise, com­posers work­ing with algo­rith­mic or computer-aided com­po­si­tion may dis­cov­er a robust set of tech­niques for shap­ing vari­a­tion, tex­ture, and form. Researchers in eth­no­mu­si­col­o­gy might find new ana­lyt­i­cal tools for uncov­er­ing sys­tem­at­ic ele­ments in impro­vi­sa­tion­al practices.

Overall, the work stands as a thor­ough explo­ration of gen­er­a­tive and pars­ing approach­es tai­lored to music, illus­trat­ing how com­pu­ta­tion­al mod­els can deep­en under­stand­ing of both fixed and impro­vised musi­cal structures.

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The identification and modelling of a percussion ‘language’

James Kippen & Bernard Bel

Computers and the Humanities (1989), 23, 3: 119-214

Abstract

In exper­i­men­tal research into per­cus­sion ‘lan­guages', an inter­ac­tive com­put­er sys­tem, the Bol Processor, has been devel­oped by the authors to analyse the per­for­mances of expert musi­cians and gen­er­ate its own musi­cal items that were assessed for qual­i­ty and accu­ra­cy by the infor­mants. The prob­lem of trans­fer­ring knowl­edge from a human expert to a machine in this con­text is the focus of this paper. A pro­to­typ­i­cal gram­mat­i­cal infer­encer named QAVAID (Question Answer Validated Analytical Inference Device, an acronym also mean­ing ‘gram­mar' in Arabic/Urdu) is described and its oper­a­tion in a real exper­i­men­tal sit­u­a­tion is demon­strat­ed. The paper con­cludes on the nature of the knowl­edge acquired and the scope and lim­i­ta­tions of a cognitive-computational approach to music.

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

Summary

This paper explores a nov­el approach to mod­el­ing North Indian tabla drum­ming as a “per­cus­sion lan­guage” by apply­ing for­mal lan­guage the­o­ry, machine learn­ing, and inter­ac­tive generative/analytic com­put­er meth­ods. The authors dis­cuss two sys­tems— Bol Processor and QAVAID — that each plays a dis­tinct role in ana­lyz­ing and gen­er­at­ing rhyth­mic pat­terns (termed “sen­tences”) under the guid­ance of expert infor­mants. They exam­ine how knowl­edge is incre­men­tal­ly acquired and for­mal­ized as a gram­mar, how alter­na­tive seg­men­ta­tions can be eval­u­at­ed, and how prob­a­bilis­tic mod­el­ing may be employed to gen­er­ate orig­i­nal musi­cal sen­tences for expert eval­u­a­tion. The work’s eth­no­mu­si­co­log­i­cal per­spec­tive unites com­pu­ta­tion­al for­mal­iza­tion with the real-world prac­tice of tabla impro­vi­sa­tion and teach­ing, rais­ing broad­er ques­tions about the nature of knowl­edge trans­fer between human expert, machine learn­er, and cul­tur­al context.

Contribution and Strengths

Interdisciplinary Framework

The paper posi­tions itself at the inter­sec­tion of musi­col­o­gy, cog­ni­tive sci­ence, com­pu­ta­tion­al lin­guis­tics, and ethnog­ra­phy. This breadth under­scores the com­plex­i­ty of “music as lan­guage” and effec­tive­ly high­lights the idea that music may be for­mal­ly scru­ti­nized with meth­ods akin to those in com­put­er science.

Formal Language Techniques

By ground­ing the analy­sis in the Chomskian hier­ar­chy (reg­u­lar and context-free gram­mars) and ref­er­enc­ing Gold’s con­cept of “iden­ti­fi­ca­tion in the lim­it,” the authors tie their eth­no­mu­si­co­log­i­cal obser­va­tions to well-established the­o­ret­i­cal under­pin­nings. These con­nec­tions help clar­i­fy why a sys­tem­at­ic, incre­men­tal approach to gram­mar infer­ence is suit­able for mod­el­ing the impro­vi­sa­tion­al com­po­nents of North Indian tabla drumming.

Attention to Vocabulary and Segmentation

The dis­cus­sion on how the sys­tem learns seg­men­ta­tion and defines “words” in the drum­ming lex­i­con is illu­mi­nat­ing. Though seg­ment­ing tabla phras­es is not anal­o­gous to seg­ment­ing words in spo­ken lan­guages, the authors show how incre­men­tal analy­sis can pro­pose, refine, or dis­card poten­tial lex­i­cal bound­aries in a prin­ci­pled manner.

Interactive and Incremental Learning

A sig­nif­i­cant fea­ture is the inter­ac­tive mod­el: the sys­tem gen­er­ates out­put strings that are val­i­dat­ed or reject­ed by the human infor­mant, there­by trig­ger­ing incre­men­tal adjust­ments to the gram­mar. This mim­ics student-teacher inter­ac­tions and demon­strates a strong attempt to reflect authen­tic learn­ing and teach­ing processes.

Probabilistic Aspect

Introducing sto­chas­tic­i­ty in syn­the­sis breaks from pure­ly deter­min­is­tic meth­ods. It points to a more real­is­tic reflec­tion of the ways in which live per­for­mance might involve cre­ative, non-deterministic choic­es, while main­tain­ing con­straints guid­ed by the learned grammar.

Methodological Observations

Data Representation

The authors clear­ly define the sym­bol inven­to­ry (bols like dha, ge, ti, etc.) and acknowl­edge the com­plex­i­ty of how these sym­bols relate to son­ic events. By lim­it­ing the approach to frequency-based seg­men­ta­tion and gram­mar infer­ence, the sys­tem oper­at­ing with­in a “text pre­sen­ta­tion pro­to­col” remains suit­ably rigorous.

User–System Dialogue

Illustrations of the QAVAID question–answer mech­a­nism high­light prac­ti­cal aspects of gram­mar con­struc­tion. This is valu­able for explain­ing how the sys­tem backs up, mod­i­fies rules, or infers new chunks based on par­tial dis­agree­ments from the expert and how it tests repeat­ed merges or seg­men­ta­tions for consistency.

Scalability Considerations

The exper­i­ments pre­sent­ed involve a lim­it­ed num­ber of exam­ples. The authors note com­pu­ta­tion­al con­straints and care­ful­ly frame how repeat­ed merges, lex­i­cal expan­sions, and neg­a­tive exam­ples (machine out­puts the user rejects) unfold in real­is­tic time on a micro­com­put­er. This trans­paren­cy about per­for­mance con­sid­er­a­tions is commendable.

Comparison to Existing Tools

While the authors ref­er­ence for­mal lan­guage the­o­ry, it could be help­ful to sit­u­ate the QAVAID approach more explic­it­ly along­side oth­er grammar-inference sys­tems (or music cog­ni­tion mod­els) in terms of effi­cien­cy and suc­cess rates. This might pro­vide addi­tion­al con­text about how QAVAID’s tight-fit method­ol­o­gy dif­fers from exist­ing machine-learning strate­gies in music.

Suggestions for Future Work

Integration of Connectionist Approaches

A deep­er inves­ti­ga­tion into how sub-symbolic learn­ing algo­rithms (e.g., neur­al net­works) might coex­ist or com­ple­ment a sym­bol­ic grammar-inference approach could shed light on whether deep­er hier­ar­chi­cal or pattern-based musi­cal struc­tures can be dis­cov­ered automatically.

Temporal and Metric Awareness

Incorporating real-time con­straints, includ­ing an explic­it mod­el of cycle bound­aries and tem­po vari­a­tions, might enable QAVAID or a suc­ces­sor sys­tem to han­dle per­for­mances that devi­ate sub­tly from rig­or­ous­ly mea­sured durations.

Generative Evaluation

Extending the sys­tem to pro­duce longer per­for­mance sequences and eval­u­at­ing how coher­ent or context-appropriate they sound in extend­ed impro­vi­sa­tion might reveal new facets of pat­tern syn­er­gy that short exam­ples do not expose.

Cross-Cultural Applicability

The strate­gies deployed here for tabla might prove adapt­able to oth­er deeply mnemon­ic or impro­visato­ry musi­cal tra­di­tions (e.g., West African drum­ming, Middle Eastern per­cus­sion). Investigating how the mod­el gen­er­al­izes across cul­tures could under­score the method’s ver­sa­til­i­ty and reveal new limitations.

Conclusion

By merg­ing for­mal lan­guage the­o­ry with eth­no­mu­si­co­log­i­cal field­work and machine learn­ing, the authors pro­pose a pow­er­ful mod­el for cap­tur­ing core aspects of tabla impro­vi­sa­tion. The frame­work encour­ages close human–computer col­lab­o­ra­tion through dynam­ic ques­tion­ing and incre­men­tal gram­mar build­ing. This approach not only advances a cognitive-computational per­spec­tive on music but also opens a path­way for fur­ther inquiries into cross-cultural appli­ca­tions, time-sensitive per­for­mance mod­el­ing, and cre­ative com­po­si­tion with­in implic­it musi­cal grammars.

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