Browsing by Author "Conklin, Darrell"

Now showing 1 - 7 of 7
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    COMPARING HUMAN AND COMPUTATIONAL MODELS OF MUSIC PREDICTION
    (1992-05-01) Witten, Ian H.; Manzara, Leonard C.; Conklin, Darrell
    The information content of each successive note in a piece of music is not an intrinsic musical property but depends on the listener's own model of a genre of music. Human listeners' models can be elicited by having them guess successive notes and assign probabilities to their guesses by gambling. Computational models can be constructed by developing a structural framework for prediction, and "training" the system by having it assimilate a corpus of sample compositions and adjust its internal probability estimates accordingly. These two modeling techniques turn out to yield remarkably similar values for the information content, or "entropy," of the Bach chorale melodies. While previous research has concentrated on the overall information content of whole pieces of music, the present study evaluates and compares the two kinds of model in fine detail. Their predictions for two particular chorale melodies are analyzed on a note-by-note basis, and the smoothed information profiles of the chorales are examined and compared. Apart from the intrinsic interest of comparing human with computational models of music, several conclusions are drawn for the improvement of computational models.
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    COMPLEXITY-BASED INDUCTION
    (1991-07-01) Witten, Ian H.; Conklin, Darrell
    A central problem in machine learning research is the evaluation of proposed theories from a hypothesis space. Without some sort of preference criterion, any two theories that "explain" a set of examples are equally acceptable. This paper presents \fIcomplexity-based induction\fR, a well-founded objective preference criterion. Complexity measures are described in two inductive inference settings: logical, where the observable statements entailed by a theory form a set; and probabilistic, where this set is governed by a probability distribution. With complexity-based induction, the goals of logical and probabilistic induction can be expressed identically--to extract maximal redundency from the world, in other words, to produce strings that are random. A major strength of the method is its application to domains where negative examples of concepts are scarce or an oracle unavailable. Examples of logic program induction are given to illustrate the technique.
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    MODELLING AND GENERATING MUSIC USING MULTIPLE VIEWPOINTS
    (1988-07-01) Conklin, Darrell; Cleary, John G.
    A technique for modelling tonal music using multiple viewpoints is described. Markov models are used with a different model for each of a number of different viewpoints: for example, the durations of notes or their relative intervals. The models are extracted from existing pieces, or can be constructed by hand. The technique is evaluated by using models to generate new pieces. Examples are given of pieces generated using models of monodic Gregorian chant and two voice polyphony.
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    MODELLING MUSIC: SYSTEMS, STRUCTURE, AND PREDICTION
    (1989-05-01) Conklin, Darrell; Witten, Ian H.
    This note opens with a commentary on the Georgescus' visionary paper entitled "A systems approach to music," which established an ambitious framework that encompasses a wide range of musical phenomena. Attention is concentrated on the higher-level aspects; in particular, the notion that the evolution of musical genres may exhibit structural instability by shifting to new musical paradigms, and the radical extension of this notion to the identification of morphogenesis in individual works. It is argued that structural discontinuities relate to creative processes rather than to artistic works per se, because they correspond to a breakdown of the listener's predictive model of the music. This focuses attention on the problem of deriving predictive models for particular musical pieces and genres--the subject of our own research. We equate predictive power with the ability of a model to compress the musical surface (roughly, text) of unseen works. Following a brief examination of theories for analyzing and generating music, the methodology of adaptive modeling and compression is set out, and extended from its conventional domain of strictly sequential natural language text to the much richer musical surface through the use of multiple viewpoints--specialized knowledge sources that deal with particular aspects of music. Finally, we discuss how the performance of models formed adaptively might be compared with that of live musicians, and outline an experiment currently in progress to establish how well human subjects can predict the musical surface of Bach Chorales.
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    Prediction and entropy of music
    (1990) Conklin, Darrell; Witten, Ian H.
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    PREDICTION AND ENTROPY OF MUSIC
    (1991-12-01) Witten, Ian H.; Conklin, Darrell
    The topic of music theory evaluation has recently aroused heated debate within the music theory community (Journal of Music Theory, 33(1), 1989). This paper develops a class of theories called \fImultiple viewpoint systems\fR. A multiple viewpoint theory of music is a collection of independent views on the musical surface, each modelling and predicting specific types of musical phenomena. When and why is one theory of music to be preferred over another? Some researchers believe that the notion of preference can be formalized, and others that it is subjective and based on esthetic criteria. This paper attempts a conciliation of these two views. On one hand, we believe that the best theory of a musical concept generates creative, esthetically more pleasing instances of the concept, and that this part of music theory evaluation cannot be truly objective. However, we conjecture that predictive power is a sufficient condition for esthetic quality. Predictive power is measured by performing inductive inference over a sample, and estimating the entropy, or complexity of the concept by applying rigorous tests to the theory. Musical concepts are not static; although some broad generalizations can apply, other generalizations are forced to change from piece to piece. To model this effect, we use a \fIlong-term\fR model which represents the general musical concept, and a \fIshort-term\fR model which adapts to a particular piece. The methods outlined in this paper are applied to the musical concept of "next event in a Bach chorale melody". Short and long-term multiple viewpoint systems are induced from a sample, and applications of the preference evaluation are given.
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    PREDICTION AND ENTROPY OF MUSIC
    (1990-04-01) Conklin, Darrell
    This thesis develops and evaluates predictive theories of music. Good theories should model a particular class of music and predict new pieces in the class with high probability. Attention is restricted to melody alone--harmony and polyphony are not considered. Theories are constructed using an empirical learning approach, and to construct and evaluate them, one hundred Bach chorale melodies are analyzed. Theories are evaluated by a data compression measure, which is a strong indicator of their predictive power. The entropy of the chorales is estimated by averaging the amount of compression given to a test set using a theory learned from a training set. The central hypothesis is that the chorales are quite redundant in the information theoretic sense. A novel approach to the induction of sequence generating rules, called multiple viewpoints, is created. This method is based on the variable-order Markov model, with extensions to incorporate timescales and parallel streams of description. A multiple viewpoint system comprises two parts: a long-term theory which adapts to a class of sequences, and a short-term theory which adapts to a particular instance of the class. Predictions from both are combined into an overall prediction. The performance of several different multiple viewpoint systems is assessed on the chorale data. The redundancy of the chorales is thereby estimated to be 55%. This thesis concludes that the estimate must be compared with human performance at the same predictive task. The theory should also be evaluated in terms of the quality of the new chorales it generates, and by its ability to discriminate chorales from non-chorales.