Analysis of local and global timing and pitch change in or- dinary melodies

This paper describes a set of statistical relationships between pitch change structure and timing structures in ordinary melodies. We obtained over 5000 MIDI files for ordinary western melodies, each with a prescribed tempo, so that note timings could be given in seconds. 1): We find that the frequencies of occurrence of different pitch change sizes are stationary: they do not vary during the time-course of a melody, apart from during the first 1 second and the final 1 second. 2): There is an inverse relationship between the mean (absolute) pitch change size in a melody and the mean time interval between successive note onsets: melodies with larger pitch changes tend to be faster.3): The time intervals between successive occurrences of the same pitch change size reflect an active process. 4): For each melody, we construct a function showing the temporal rise and fall in the likelihood of the melody as given by the log of the reciprocal of the frequency of the most recent pitch change. Fourier analysis of these functions shows a regular pattern of coherent variability with a period of between 2 and 6 seconds. Low likelihood portions of a melody are balanced by higher likelihood ones over a time scale of a few seconds.