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Vassilakis, P.N. (2001).  Perceptual and Physical Properties of Amplitude Fluctuation and their Musical Significance.  Doctoral Dissertation.  University of California, Los Angeles.  Advisor: R.A. Kendall.  Committee: P.M. Narins, A.J. Racy,  R.W.H. Savage, G.A. Williams. 

Abstract   [extended summary]  -  [full copy (.pdf,~6Mb)]  -  [ProQuest]
Amplitude fluctuation (AF) is a manifestation of wave interference and a significant expressive tool in the production of musical sound. Musicians worldwide manipulate the AF parameters to exploit the sensations of beating and roughness, creating desired sonic effects. The history of the understanding of amplitude fluctuation is reviewed, revealing conflicting opinions regarding its physical properties and inconsistencies in its graphical representation. It is shown that degree of amplitude fluctuation (AF-degree) and amplitude modulation depth (AM-depth) are conceptually and quantitatively different. Thus, previous studies manipulating AF-degree through implementation of AM-depth must be revised.

AFs satisfy all criteria defining a wave, including transfer of energy at the fluctuation rate. Theoretical values for the frequency and amplitude of the fluctuation component are compared to values obtained through Hilbert demodulation and frequency analysis, confirming the energy content of AF.  However, the results are quantitatively inconclusive, warranting further study.

An alternative signal representation is proposed based on the complex equation of vibration, resulting in spiral sine signals and twisted-spiral complex signals. Three-dimensional spiral signals solve numerous problems associated with traditional signals and represent the energy content of AF.

The fact that AFs carry energy is challenged by previous experiments where sound interference products appear to arise at a neural level.  New dichotic experiments illustrate that the perception of interference does not arise unless waves interact physically. The observed dichotic wave interaction matches results from sound localization studies.

Musical instrument construction and performance practice indicates that sound variations involving the sensation of roughness are found in most musical traditions. A new roughness estimation model is proposed demonstrating better agreement between estimated and observed roughness than earlier models. A hypothesis linking dissonance and roughness ratings of harmonic intervals within the chromatic scale is tested. Clear presence/absence of roughness appears to dominate dissonance ratings.  In other cases, dissonance decisions ignore roughness and are culturally/historically mediated. The results suggest that the consonance hierarchy of harmonic intervals in the Western musical tradition corresponds to variations in roughness degrees.

The study crosses disciplinary boundaries and improves the understanding of AF by examining musical practices worldwide. Further study should include cross-cultural empirical investigations.