This produces a finitely sampled representation of the continuous mapping from beats to time, which can be interpolated to obtain intermediate values. For example, a performer can tap beats in real time and a computer can record the time of each tap. (Some special mathematical care must be taken to allow for music that momentarily stops, instantaneously skips ahead, or is allowed to jump backwards, but we will ignore these details.) One practical representation of the beat-to-time function is the set of times of individual beats. Ly, there is a mathematical function that maps beat numbers to time and an inverse function that maps time to beats. Thesis (MSc (Mathematical Sciences))-University of Stellenbosch, 2010. Hierdie modelle word gebruik om musiek vir twee instrumente te genereer, wat die musiek waaruit geleer is, naboots. Deur gebruik te maak van musiek wat geskryf is in ’n gegewe styl as aanleer data, word parameters vir (sigbare en onsigbare) Markov modelle (van gemengde, hoër- of eerste- orde) bereken, ten einde die musiekstyl van die data waarvan geleer is, in terme van wiskundige modelle te beskryf.
AFRIKAANSE OPSOMMING: Hierdie tesis ondersoek die toepasbaarheid van probabilitiese en outomaatteoretiese konsepte, wat uiters suksesvol toegepas word in die gebied van spraak en natuurlike taal-verwerking, op die gebied van musiekstyl nabootsing. These models are then used to imitate two instrument music in the trained style. By using music written in a certain style as training data, parameters are calculated for (visible and hidden) Markov models (of mixed, higher or first order), in order to capture the musical style of the training data in terms of mathematical models. ENGLISH ABSTRACT: We investigate the suitability of applying some of the probabilistic and automata theoretic ideas, that have been extremely successful in the areas of speech and natural language processing, to the area of musical style imitation.
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