Time-Varying Spectra of Violin Tones
James W. Beauchamp · The Journal of the Acoustical Society of America · 1969
Harmonic analyses of several violin tones have been performed by computer. Each sound is represented by a finite series of harmonic-amplitude and phase-spectrum components varying with time. Graphical representations of spectra being explored are: (1) individual plots of fundamental-frequency harmonic amplitudes (both linear and dB), and relative phases as functions of time; (2) line-spectra movies with harmonic amplitude changes slowed 20:1; (3) spectrograms with vertical frequency scale, horizontal time scale, and darkness indicating amplitude. Spectrum analysis can be performed synchronously with the fundamental or asynchronously at a base frequency much lower than the fundamental, with advantages for each method. Completeness of harmonic analysis is demonstrated by examples of tones resynthesized using smoothed versions of harmonic-amplitude and pitch curves. For storage purposes, synthetic tones typically require 500 to 800 parameter-time coordinates per 1 sec of sound. Over all, the violin tones analyzed are characterized by strong resonances in regions 500–700 Hz and 1800–2500 Hz, a strong antiresonance at 1100–1500 Hz, and many peaks and valleys above 2000 Hz. Features of attack, steady-state, and decay will be discussed in terms of spectrum graphs.