A Computational Model of the Cognition of Tonality

Milne, Andrew J. (2013). A Computational Model of the Cognition of Tonality. PhD thesis The Open University.

DOI: https://doi.org/10.21954/ou.ro.00009783


Tonality is the organization of pitches, both simultaneously and across time, so that certain pitches and chords are heard as attracted, in varying degrees, to other pitches and chords. Most art music from the seventeenth to the nineteenth centuries, and popular music to the present day, is heavily steeped in a musical language that makes use of tonality to define a ‘central’ most attractive pitch or chord called the tonic. It is widely thought that the feelings of expectancy and resolution induced by movements towards and away from the tonic allow composers to imbue tonal music with meaning and emotion.

In this dissertation, I identify and model some of the innate processes by which feelings of tension, resolution, stability, and so forth, are induced by successions of pitches and chords, irrespective of their harmonic consonance. By innate, I mean processes that do not require the learning of a musical corpus—such processes are important because they provide explanations for why tonal music, and our cognition of it, take the specific forms they do.

To do this, I introduce a novel family of mathematical methods—metrics applied to expectation tensors—for calculating the similarity of pitch collections. Importantly, such tensors can represent not just the notated pitches of tones, but also their spectral pitches (their harmonics). I then demonstrate how these techniques can be used to model participants’ ratings of the fits of tones in microtonal melodies, and the fits of all twelve chromatic pitches to an established key centre (Krumhansl’s probe tone data). The techniques can also be generalized to predict the tonics of any arbitrarily chosen scale—even scales with unfamiliar tunings.

In summary, I demonstrate that psychoacoustic processes, which are innate and universal, play an important role in our cognition of tonality.

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