Synthesis of Voiced Sounds From a Two-Mass Model of the Vocal Chords

Vol. 51, No. 6, July-August, 1972 Printed in U.S.A. Synthesis of Voiced Sounds From a Two-Mass Model of the Vocal Cords By K. ISHIZAKA and J. L. FLANAGAN ( M a n u s c r i p t received J a n u a r y 13, 1972) A model of voiced-sound generation is derived in which the detailed acoustic behavior of the human vocal cords and the vocal tract is computed. The vocal cords are approximated by a self-oscillating source composed of two stiffness-coupled masses. The vocal tract is represented as a bilateral transmission line. One-dimensional Bernoulli flow through the vocal cords and plane-wave propagation in the tract are used to establish acoustic factors dominant in the generation of voiced speech. A difference-equation description of the continuous system is derived, and the cord-tract system is programmed for interactive study on a DDP-516 computer. Sampled waveforms are calculated for: acoustic volume velocity through the cord opening (glottis)] glottal area; and mouth-output sound pressure. Functional relations between fundamental voice frequency, subglottal (lung) pressure, cord tension, glottal area, and duty ratio of cord vibration are also determined. Results show that the two-mass model duplicates principal features of cord behavior in the human. The variation of fundamental frequency with subglottal pressure is found to be 2 to 3 Hz/cm H20, and is essentially independent of vowel configuration in the programmed tract. Acoustic interaction between tract eigenfrequencies and glottal volume flow is strong.