Chaos In Aperiodicity Of Musical Oscillators

Abstract

The aperiodicity characteristic of many self-sustained musical instruments like bowed strings, voice, woodwinds or brass, reveals certain chaotic structures when observed over many periods. Short-lived subharmonics are often detectable and these are thought to be the result of at least four general properties of the iinstruments: complex resonance paths, limit-cycles and phase transition boundaries in the feeback mechanism and pulsed noise in the excitation mechxnism. Examples from real data and simulations isolating these phenomena in physical models simulations will be compared. The conclusions point to principles that can be applied to music synthesis methods. Phase portraits of recorded instrument tones can be animated in time to display the characteristics of aperidocity in a meaningful way. It is seen that certain portions of the waveform are more variable from period-toperiod than other portions. Through time, the variation exhibits a degree of repetitive structure that gives rise to perceptible noisy subharmonics. One method for portraying subharmonic activity is to display succesive periods as raster lines in an oblong plot of phase vs. period. Gray-level is used to display the variations observed in phase portraits. The best sensitivity to this variation has been acheived by plotting period-to-period vector length differences where the vector is the distance between two samples in the phase portrait. Subharmonics arise from several possible mechanisms. Trombone tones have been analyzed with the method and show a correlation between overblown harmonic number and subharmonic number. For example, a fourth harmonic shows distinct fourth subharmonics in its raster plot. The explanation is that the fundamental round-trip still contributes to the system even