Computation and simulation of frequency variations in musical instrument sounds

Abstract

Frequency variations of musical instrument sounds were measured using phase-derivative and frequency-tracking methods based on the short-time Fourier transform. Frequency variations are important features of instrument sounds and are very useful for musical expression. Three categories of variation are: vibrato, portamento, and microvariation. Microvariations exist even when a tone is played at a constant pitch, and they can be approximated as small frequency-deviation low-frequency noise signals. Portamento is a purposeful pitch glide embellishment that can occur during attacks, between notes, or, less often, at the ends of notes. Vibrato can be characterized as an approximately sinusoidal frequency variation, and usually its amplitude is sufficient to interact with instrument resonances and cause significant harmonic amplitude modulations. Deviation amplitudes and frequencies of acoustic instrument vibratos are not perfectly steady, but rather vary over the durations of instrument tones. Measurements of vibrato characteristics of the harmonic frequencies and amplitudes as well as the frequency and amplitude microvariations of various instruments and voice indicate that a variety of parameters are required for effective instrument synthesis. The challenge in synthesis is to avoid a “mechanical sound.”