An Application of Calculated Consonance in Computer-Assisted Microtonal Music
Date
2013-12-23
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Abstract
Harmony (the audible result of varied combinations of simultaneously sounding tones) ought to, for the most part, sound pleasing to the ear. The result depends, among other factors, on a proper choice of the pitches for the tones that form harmonious chords, and on their correct intonation during musical performance.
This thesis proposes a computational method for calculation of relative consonance among groups of tones, and its possible practical applications in machine-assisted arrangement of tones, namely the choice of tone pitches and their microtonal adjustment. The consonance of tone groups is calculated using a model that is based on the physiological theory of tone consonance that was published by Hermann Helmholtz in the middle of the 19th century.
Given a group of tones that have fixed pitches, changes in the aggregate dissonance caused by adding another “probe” tone of a variable pitch can be represented as a “dissonance landscape”. Local minima in the “height” of the landscape correspond to local minima of the aggregate dissonance as a function of the pitch of the probe tone. Finding a local dissonance minimum simulates the actions of a musician who is “tuning by ear”. The set of all local minima within a given pitch range is a collection of potentially good pitch choices from which a composer (a human, or an algorithmic process) can fashion melodies that sound in harmony with the fixed tones.
Several practical examples, realized in an experimental software, demonstrate applications of the method for: 1) computer-assisted microtonal tone arrangement (music composition), 2) algorithmic (machine-generated) music, and 3) musical interplay between a human and a machine.
The just intonation aspect of the tuning method naturally leads to more than twelve, potentially to many, pitches in an octave. Without some restrictions that limit the complexity of the process, handling of so many possibilities by a human composer and their precise rendition as sound by a performing musician would be very difficult. Restricting the continuum of possible pitches to the discrete 53-division of the octave, and employing machine-assistance in their arrangement and in sound synthesis make applications of the method feasible.
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Music, Acoustics, Computer Science
Citation
Burleigh, I. G. (2013). An Application of Calculated Consonance in Computer-Assisted Microtonal Music (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/24833