Tone colour in music and bifurcation control

An intrinsic characteristic of musical sounds is the qualitative evolution their timbre (tone colour). In this paper, we interpret each change by a bifurcation. We employ spectral and temporal envelopes as two most salient features tone colour. Fourier analysis note generates its n-leading harmonic partials an amplitude n-vector A for n?2. introduce manifolds associated with vectors. This to accommodate note. Then, are modelled solutions radial coupling n-tuple parametric Hopf oscillators. use one bifurcation parameter interpolate envelope over set consecutive time-intervals via control. Bifurcation scenarios involve asymptotic sets time-asymptotic limits partials. Each homeomorphic k-tori, where k?n number contributing classification colour then drawn up encoding geometry acoustic signals into sets. For instance, treat audio C?4 files obtained from piano violin. Different distinguish bifurcations these sounds. complete hysteresis cycle observed within played