A Computational Model of Tonality Cognition Based on Prime Factor Representation of Frequency Ratios and Its Application

Publication Type:

Conference Paper


The 12th Sound and Music Computing Conference, Music Technology Research Group, Dept. of Computer Science, Maynooth University, Maynooth, Co. Kildare, Ireland (2015)






ice-breaker activity, PFG Tonnetz, pitch contour, prime factor representation, tonality


We present a computational model of tonality cognition derived from physical and cognitive principles on the frequency ratios of consonant intervals.
The proposed model, which we call the Prime Factor-based Generalized Tonnetz (PFG Tonnetz), is based on the Prime Factor Representation of frequency ratios and can be regarded as a generalization of the Tonnetz.
Our assumed application of the PFG Tonnetz is a system for supporting spontaneous and improvisational participation of inexpert citizens in music performance for regional promotion.
For this application, the system needs to determine the pitch satisfying constraints on tonality against surrounding polyphonic music because inexpert users frequently lack music skills related to tonality.
We also explore a working hypothesis on the robustness of the PFG Tonnetz against recognition errors on harmonic overtones in polyphonic audio signals.
On the basis of this hypothesis, the PFG Tonnetz has a good potential as a representation of the tonality constraints of surrounding polyphonic music.

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