Pattern grammars

Bernard Bel

Pattern gram­mars in for­mal rep­re­sen­ta­tions of musi­cal struc­tures. 11^th International Joint Conference on Artificial Intelligence, Workshop on AI & Music, 20 August 1989, p.113-42

Abstract

This paper intro­duces sev­er­al for­mal mod­els of pat­tern rep­re­sen­ta­tion in music. Polyvalent mul­ti­modal gram­mars describe par­tial­ly over­lap­ping sound events as found in poly­phon­ic struc­tures. Bol Processor gram­mars are char­ac­ter­i­sa­tions of sequen­tial events in terms of sub­string rep­e­ti­tions, homo­mor­phisms, etc. Parsing tech­niques, sto­chas­tic pro­duc­tion and recent devel­op­ments of BP gram­mars are briefly described.

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

Summary

This paper presents a thor­ough explo­ration of pat­tern gram­mars and their applic­a­bil­i­ty to musi­cal struc­tures, specif­i­cal­ly focus­ing on poly­phon­ic and homo­phon­ic aspects. It intro­duces Polymodal Multivalent Grammars (PMGs), demon­strates how tem­po­ral and struc­tur­al rela­tion­ships in music can be mod­eled using a lat­tice of time rela­tions, and draws par­al­lels with for­mal lan­guage the­o­ry. The dis­cus­sion also extends to Bol Processor (BP) gram­mars, offer­ing insights into pat­tern rules, mem­ber­ship tests, and sto­chas­tic pro­duc­tion for music gen­er­a­tion and analy­sis. The work’s illus­tra­tions, which delve into North Indian tabla sequences and Western musi­cal exam­ples (notably Bach), add con­crete demon­stra­tions of how these gram­mars can cap­ture and repli­cate real-world musi­cal practices.

Major Strengths

Methodological Clarity and Formal Rigor

• The paper pro­vides a clear for­mal frame­work for under­stand­ing music as an algo­rith­mic process. This is exem­pli­fied by pre­cise def­i­n­i­tions of pat­tern gram­mars, rewrit­ing rules, and homomorphisms.
• The use of math­e­mat­i­cal nota­tion (e.g., par­tial orders, lat­tices, homo­mor­phisms) lends a rig­or­ous back­ing to the arguments.

Comprehensive Treatment of Time Overlaps

• The con­cep­tu­al sep­a­ra­tion of out-time and in-time struc­tures, and the ensu­ing treat­ment of 13 dis­tinct pos­si­ble tem­po­ral rela­tions, is notable. This approach tack­les many of the com­plex­i­ties found in poly­phon­ic and par­tial­ly over­lap­ping musi­cal events.

Insightful Practical Applications

• Educating read­ers on how gram­mars can be used for music com­po­si­tion, impro­visato­ry mod­el­ing, and per­for­mance prac­tice is high­ly valuable.
• The exam­ples of North Indian tabla reper­toires and Bach’s poly­phon­ic com­po­si­tions con­crete­ly illus­trate the poten­tial breadth of these models.

Contribution to Epistemological and Analytical Discourse

• By address­ing exist­ing debates (e.g., par­al­lels with lin­guis­tic the­o­ry, eth­no­mu­si­co­log­i­cal crit­i­cisms, and gen­er­a­tive approach­es), the paper bridges a gap between tra­di­tion­al ana­lyt­i­cal meth­ods and com­pu­ta­tion­al modeling.

General Comments

This work makes a sol­id the­o­ret­i­cal con­tri­bu­tion by bring­ing togeth­er for­mal lan­guage the­o­ry and con­cise exam­ples of musi­cal struc­tures. It is equal­ly rel­e­vant to researchers in com­pu­ta­tion­al musi­col­o­gy, eth­no­mu­si­col­o­gy, and music the­o­ry. The paper may also be of broad­er inter­est to any­one study­ing the inter­sec­tion of arti­fi­cial intel­li­gence and cre­ative process­es. Overall, its strengths lie in its the­o­ret­i­cal depth, its range of illus­tra­tive appli­ca­tions, and its attempts to uni­fy diverse per­spec­tives under a sin­gle for­mal mod­el­ing frame­work for musi­cal representation.

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