Wolfram Computation Meets Knowledge

Wolfram Summer School


Timothy Walker

Summer School

Class of 2009


Timothy (Bim) Walker is a faculty member at Ohio Dominican University in Columbus, Ohio. He majored in physics and psychology at Carnegie Mellon University and received his PhD in cognitive psychology from The Ohio State University, studying music cognition. His research interests include music performance, computational modeling, and neural networks. He enjoys playing guitar, riding motorcycles, playing basketball, and other ways of getting away from computer monitors.

Project: Musical Scale Analysis

This Summer School project consists of developing tools for the analysis of music files, with data obtained both from the web and from the WolframTones log files. For MIDI files obtained from the web, an attempt will be made to determine the musical scale of the piece. This can be a difficult problem to solve algorithmically, and there is considerable disagreement among music theorists about how to proceed. This project will use several different approaches and look at the correspondence among them. The first step is to extract the MIDI note value, which is a 7-bit number in which middle C = 60. As standard tuning uses a 12-step, equal-tempered scale, this means that the note values can be divided mod 12 to collapse all notes into pitch classes (also referred to as “chroma”). The resulting distribution of chroma can potentially be used to identify the key of the piece.

The difficulty, however, lies in the fact that a distribution of pitches is a static set, ignoring the temporal patterning in music that induces a sense of expectancy and resolution (or not) to a tonic. Two different analogs of tempo will be calculated by finding the average of inter-onset interval (IOI; the length of time between a note and the subsequent note) and the average duration of each note. Several metrics will then be determined for each piece:

  • The first note
  • The last note
  • The most frequently occurring note
  • When the first and second most frequently occurring notes are separated by a perfect fifth (7 semitones)
  • The most frequently occurring note when notes are weighted by IOI percentage
  • The most frequently occurring note when notes are weighted by duration percentage
  • The lower of perfect-fifth pairs when notes are weighted by IOI percentage
  • The lower of perfect-fifth pairs when notes are weighted by duration percentage

It is not likely that these metrics will all choose same chroma, but a relative correspondence across metrics will be a good indication of the overall tonic.

For many of the pieces, the key will already be known, so these pieces can serve as test cases for the validity of the metrics. The same metrics can then be applied to the WolframTones files, and data from the log files (e.g. geographic location from IP addresses) can be analyzed for patterns of preferences.

Favorite Three-Color Cellular Automaton

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