The spiral array is a geometric representation of tonality. It was the result of my MIT PhD thesis, Toward a Mathematical Model of Tonality, supervised by Professor Jeanne Bamberger (Music & Theater Arts) with thesis advisor Professor Georgia Perakis (Operations Research Center).
Springer Book
The model and its associated algorithms for key finding, chord tracking, pitch spelling, tonal segmentation, and real-time visualisation are described in a Springer book in the ORMS series: Mathematical and Computational Modeling of Tonality (sample chapter).
Chew, E. (2014, available Dec 2013) Mathematical and Computational Modeling of Tonality: Theory and Applications. International Series on Operations Research and Management Science, Vol. 204, New York, NY: Springer. isbn: 978-1-4614-9474-4
Real-time Analysis and Visualisation
Collaboration with Alexandre François
The algorithms have been implemented and adapted for real-time visualisation in the musa_rt (music on the spiral array . real-time) software. The latest musa_rt supports augmented reality and MIDI or audio input. Download the musa_rt app from the app store.
Musa_rt was featured in the Los Angeles Philharmonic Inside the Music pre-concert video series.
A brief description of how to view the tonal entities represented in musa_rt (main parts in 1:27 to 3:32).
Harmonic Tension and Music Generation
Collaboration with Dorien Herremans
An extension of the spiral array to model harmonic tension was created In the MSCA project MorpheuS : Hybrid Machine Learning – Optimization techniques To Generate Structured Music Through Morphing And Fusion. Download Python/Java code for the MorpheuS tension visualiser.
The tension model is embedded in the MorpheuS automatic music score generation software to constrain harmonic tension based on template or user-designed profiles. MorpheuS generated pieces based on templates by Stravinsky, Beethoven, Bach, and Kabalevsky have been performed internationally.
Herremans, D, Chew, E. 2017. MorpheuS: generating structured music with constrained patterns and tension. IEEE Transactions on Affective Computing, 10(4): 510-523. doi: 10.1109/TAFFC.2017.2737984