MUSIC AND PROBABILITY

By ISABELLA WILLIAMS

CONTENTS INTRODUCTION PROBABILISTIC FOUNDATIONS AND BACKGROUND ELEMENTARY PROBABILITY CONDITIONAL PROBABILITY AND BAYES’ RULE OTHER PROBABILISTIC CONCEPTS EARLY WORK ON MUSIC AND PROBABILITY MELODY I: THE RHYTHM MODEL RHYTHM AND METER PREVIOUS MODELS OF METER PERCEPTION A PROBABILISTIC RHYTHM MODEL THE GENERATIVE PROCESS THE METER-FINDING PROCESS TESTING THE MODEL ON METER-FINDING PROBLEMS AND POSSIBLE IMPROVEMENTS MELODY II: THE PITCH MODEL PREVIOUS MODELS OF KEY-FINDING THE PITCH MODEL TESTING THE MODEL ON KEY-FINDING MELODY III: EXPECTATION AND ERROR DETECTION CALCULATING THE PROBABILITY OF A MELODIC SURFACE PITCH EXPECTATION RHYTHMIC EXPECTATION ERROR DETECTION FURTHER ISSUES A POLYPHONIC KEY-FINDING MODEL A PITCH-CLASS-SET APPROACH TO KEY-FINDING THE KEY-FINDING PROCESS COMPARING DISTRIBUTIONAL MODELS OF KEY-FINDING FURTHER ISSUES IN KEY-FINDING APPLICATIONS OF THE POLYPHONIC KEY-FINDING MODEL KEY RELATIONS TONALNESS TONAL AMBIGUITY AND CLARITY ANOTHER LOOK AT MAJOR AND MINOR AMBIGUOUS PITCH-COLLECTIONS IN COMMON-PRACTICE MUSIC EXPLAINING COMMON STRATEGIES OF TONAL HARMONY BAYESIAN MODELS OF OTHER ASPECTS OF MUSIC PROBABILISTIC TRANSCRIPTION MODELS BOD: THE PERCEPTION OF PHRASE STRUCTURE RAPHAEL AND STODDARD: HARMONIC ANALYSIS MAVROMATIS: MODELING GREEK CHANT IMPROVISATION SAFFRAN ET AL : STATISTICAL LEARNING OF MELODIC PATTERNS STYLE AND COMPOSITION SOME SIMPLE CROSS-ENTROPY EXPERIMENTS MODELING STYLISTIC DIFFERENCES TESTING SCHENKERIAN THEORY 10 COMMUNICATIVE PRESSURE COMMUNICATIVE PRESSURE IN RULES OF VOICE-LEADING THE SYNCOPATION-RUBATO TRADE-OFF OTHER EXAMPLES OF COMMUNICATIVE PRESSURE IN RHYTHM ‘‘TRADING RELATIONSHIPS’’ LOW-PROBABILITY EVENTS IN CONSTRAINED CONTEXTS CONCLUSIONS NOTES REFERENCES