Key profile optimisation for the computational modelling of tonal centre

[摘要] ENGLISH ABSTRACT:Tonality cognition incorporates a number of diverse and multidisciplinary aspects, including musiccognition, acoustics, culture, computer-aided modelling, music theory and brain science. Currentresearch shows growing emphasis on the use of computational models implemented on digitalcomputers for music analysis, particularly with reference to the analysis of statistical properties,form and tonal properties. The applications of these analytical techniques are numerous, includingthe classification of genre and style, Music Information Retrieval (MIR), data mining andalgorithmic composition.The research described in this document focuses on three aspects of tonality analysis, namely musiccognition, computational modelling and music theory, particularly from the perspectives ofstatistical analysis and key-finding. Mathematical formulations are presented for a number ofcomputational algorithms for analysing the statistical and tonal properties of music encoded insymbolic format. These include algorithms for determining the distributions of note durations,pitch intervals and pitch classes for statistical analysis and for template-based key-finding for tonalanalysis. The implementation and validation of these computational algorithms on the Matlabsoftware platform are subsequently discussed.The software application is used to determine whether a more optimal combination of pitch classweighing model and key profile template for the template-based key-finding algorithm can bederived, using the 24 preludes from Bach's Well-tempered Clavier Book I, the Courante fromBach's Cello Suite in C major and the Gavotte from Bach's French Suite No. 5 in G major (BWV816) as test material. Four pitch class weighing models, namely histogram weighing, flat weighing,linear durational weighing and durational accent weighing, are investigated. Two prominent keyprofile templates proposed in literature are considered, namely a key profile derived from tonalitycognition experiments and a key profile based on classical music theory principles. The resultsshow that the key-finding performances of all the combinations of the pitch class weighing modelsand existing key profile templates depend on the nature of the test material and that none of thecombinations perform optimally for all test material.The software application is subsequently used to determine whether a more optimal key profiletemplate can be derived using a pattern search parameter estimation algorithm. This investigationwas conducted for diverse sets of search conditions, including unconstrained and constrained keyprofile coefficients, different pitch class weighing models, various key resolutions and differentsearch algorithm parameters. Using the same sample material as for the key-finding evaluations,the investigation showed that a more optimal key profile, compared to existing profiles, can bederived. In comparing the average key-finding scores for all of the test material, the optimisedprofiles outperform the existing profiles substantially. The optimised key profiles introduce newpitch class hierarchies where the supertonic and the subdominant rate higher at the expense of themediant in the major profile to improve the tracking of key modulations.

[发布机构] Stellenbosch University