p a p e r s
p u b l i c a t i o n s
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.
[extended summary] -
[full copy (.pdf,~6Mb)] -
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.
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.
study crosses disciplinary boundaries and improves the understanding of AF by
examining musical practices worldwide. Further study should include cross-cultural empirical investigations.