Spectrum modelling approaches from additive to analysis-resynthesis and formant

Until recently, the supremacy of pitch over other sound attributes prevailed in Western music theory. Time and timbre, for example, were considered to be of secondary importance. Today, however, this ideology is changing, and the tendency is now to consider that attributes such as pitch, time and timbre are all descriptors for the same phenomenon, but from different perspectives. For example, pitch may be considered as one aspect of the perception of timbre and timbre as one aspect of the perception of time. Pitch may, in turn, be considered as a quantifier to measure time. The music and theoretical work of composers such as Karlheinz Stockhausen, Pierre Schaeffer, Iannis Xenakis, Jean-Claude Risset, Horacio Vaggione, Trevor Wishart and Joi e Antunes have helped to emancipate the role of time and timbre in Western music (Stockhausen, 1959 Schaeffer, 1966 Xenakis, 1971 Risset, 1992 Vaggione, 1993 Wishart, 1985, 1994 Antunes, 1995). 

Spectral modelling techniques are the legacy of the Fourier analysis theory. Originally developed in the nineteenth century, Fourier analysis considers that a pitched sound is made up of various sinusoidal components, where the frequencies of higher components are integral multiples of the frequency of the lowest component. The pitch of a musical note is then assumed to be determined by the lowest component, normally referred to as the fundamental frequency. In this case, timbre is the result of the presence of specific components and their relative amplitudes, as if it were the result of a chord over a prominently loud fundamental with notes played at different volumes. Despite the fact that not all interesting musical sounds have a clear pitch and the pitch of a sound may not necessarily correspond to the lower component of its spectrum, Fourier analysis still constitutes one of the pillars of acoustics and music. 

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Spectrum modelling approaches from additive to analysis-resynthesis and formant... 

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