Thesis (MPhil)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: Tonality cognition incorporates a number of diverse and multidisciplinary aspects, including music
cognition, acoustics, culture, computer-aided modelling, music theory and brain science. Current
research shows growing emphasis on the use of computational models implemented on digital
computers for music analysis, particularly with reference to the analysis of statistical properties,
form and tonal properties. The applications of these analytical techniques are numerous, including
the classification of genre and style, Music Information Retrieval (MIR), data mining and
algorithmic composition.
The research described in this document focuses on three aspects of tonality analysis, namely music
cognition, computational modelling and music theory, particularly from the perspectives of
statistical analysis and key-finding. Mathematical formulations are presented for a number of
computational algorithms for analysing the statistical and tonal properties of music encoded in
symbolic 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 tonal
analysis. The implementation and validation of these computational algorithms on the Matlab
software platform are subsequently discussed.
The software application is used to determine whether a more optimal combination of pitch class
weighing model and key profile template for the template-based key-finding algorithm can be
derived, using the 24 preludes from Bach’s Well-tempered Clavier Book I, the Courante from
Bach's Cello Suite in C major and the Gavotte from Bach's French Suite No. 5 in G major (BWV
816) as test material. Four pitch class weighing models, namely histogram weighing, flat weighing,
linear durational weighing and durational accent weighing, are investigated. Two prominent key
profile templates proposed in literature are considered, namely a key profile derived from tonality
cognition experiments and a key profile based on classical music theory principles. The results
show that the key-finding performances of all the combinations of the pitch class weighing models
and existing key profile templates depend on the nature of the test material and that none of the
combinations perform optimally for all test material.
The software application is subsequently used to determine whether a more optimal key profile
template can be derived using a pattern search parameter estimation algorithm. This investigation
was conducted for diverse sets of search conditions, including unconstrained and constrained key
profile coefficients, different pitch class weighing models, various key resolutions and different
search 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 be
derived. In comparing the average key-finding scores for all of the test material, the optimised
profiles outperform the existing profiles substantially. The optimised key profiles introduce new
pitch class hierarchies where the supertonic and the subdominant rate higher at the expense of the
mediant in the major profile to improve the tracking of key modulations. / AFRIKAANSE OPSOMMING: Kognitiewe tonaliteit behels 'n aantal uiteenlopende en multidissiplinêre aspekte, insluitende
musiek, akoestiek, kultuur, rekenaargesteunde modelering, musiekteorie en breinwetenskap.
Huidige navorsing toon toenemende klem op die gebruik van berekenende modelering wat op
digitale rekenaars geimplimenteer is vir musiekanalise, veral met verwysing na die analise van
statistiese eienskappe, vorm en tonale eienskappe. Die aanwending van hierdie analitiese tegnieke
is veelvoudig, insluitende die klassifikasie van genre of styl, onttrekking van musiekinformasie,
dataversameling en algoritmiese komposisie.
Die navorsing wat in hierdie dokument beskryf word fokus op drie aspekte van tonaliteit analise,
naamlik musiekkognisie, berekenende modelering en musiekteorie, veral vanuit die perspektiewe
van statistiese analise and toonsoortsoek. Wiskundige formulerings word aangebied vir 'n aantal
berekeningalgoritmes vir die analise van die statistiese en tonale eienskappe van musiek wat in
simboliese formaat ge-enkodeer is. Hierdie sluit algoritmes in vir die bepaling van die
verspreidings van nootlengtes, toonintervalle en toonklasse vir statistiese analise en vir templaatgebaseerde
toonsoortsoek vir tonale analise. Die implementering en validering van hierdie
berekeningalgoritmes op die Matlab programmatuur platvorm word vervolgens bespreek.
Die programmatuur toepassing word vervolgens gebruik om te bepaal of 'n meer optimale
kombinasie van toonklas weegmodel en toonsoortprofiel templaat vir die templaat-gebaseerde
toonsoortsoek algoritme afgelei kan word, deur gebruik te maak van Bach se Well-tempered Clavier
Book I, die Courante van Bach se Cello Suite in C major en die Gavotte van Bach se French Suite
No. 5 in G major (BWV 816) as toetsmateriaal. Vier toonklas weegmodelle, naamlik histogram
weging, plat weging, lineêre duurtyd weging en duurtyd aksent weging, word ondersoek. Twee
prominente toonsoortprofiel template uit die literatuur word oorweeg, naamlik 'n toonsoortprofiel
wat van tonaliteit kognisie eksperimente afgelei is en 'n toonsoortprofiel gebaseer op klassieke
musiekteoretiese beginsels. Die resultate wys dat die toonsoortsoek prestasies van al die
kombinasies van die toonklas weegmodelle en bestaande toonsoortprofiel template afhang van die
aard van die toetsmateriaal en dat geen van die kombinasies optimaal presteer vir alle toetsmateriaal
nie.
Die programmatuur toepassing word vervolgens aangewend om vas te stel of 'n meer optimale
toonsoortprofiel afgelei kan word deur gebruik te maak van 'n patroonsoek parameterestimasie
algoritme. Hierdie ondersoek is uitgevoer vir uiteenlopende stelle soektoestande, insluitende
onbeperkte en beperkte toonsoortprofiel koëffisiënte, verskillende toonklas weegmodelle, 'n
verskeidenheid toonsoort resolusies en verskillende soekalgoritme parameters. Deur gebruik te
maak van dieselfde toetsmateriaal as vir die toonsoortsoek evaluerings, toon die ondersoek dat 'n
meer optimale toonsoortprofiel, in vergelyking met bestaande profiele, afgegelei kan word. In 'n
vergelyking van die gemiddelde toonsoortsoek prestasie vir al die toetsmateriaal, presteer die geoptimeerde
profiele aansienlik beter as die bestaande profiele. The ge-optimeerde toonsoortprofiele
lei tot nuwe toonklas hiërargiee waar die supertonikum en die subdominant hoër rangposissies
beklee ten koste van die mediant in die majeur profiel, ten einde die navolg van toonsoort
modulasies te verbeter.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/71852 |
| Date | 12 1900 |
| Creators | Vermeulen, Hendrik Johannes |
| Contributors | Herbst, Theo, Stellenbosch University. Faculty of Arts and Social Sciences. Dept. of Music. |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | English |
| Type | Thesis |
| Format | 213 p. |
| Rights | Stellenbosch University |
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