The Calculation of Vowel Resonances, and an Electrical Vocal Tract

Abstract

By treating the vocal tract as a series of cylindrical sections, or acoustic lines, it is possible to use transmission line theory in finding the resonances. With constants uniformly distributed along each section, resonances appear as modes of vibration of the tract taken as a whole. Thus, the fundamental mode of the smaller cavity may be affected considerably by a higher mode of the larger; and in addition, higher resonances are found without postulating additional cavities. This is an advantage over the lumped constant treatment, where it is necessary to postulate a different cavity for each resonance, and where the interaction terms in the equation do not include the higher modes of vibration. Under the distributed treatment, dimensions for each vowel may be taken from x-ray photographs of the vocal tract. The calculations then yield at least three resonances which lie in the frequency regions known for the vowel, from analyses of normal speech. Dependence of the different resonances upon the different cavities is discussed in some detail in the paper. An electrical circuit based on the transmission line analogy has been made to produce acceptable vowel sounds. This circuit is useful in confirming the general theory and in research on the phonetic effects of articulator movements. The possibility of using such a circuit as a phonetic standard for vowel sounds is discussed.

An Acoustic Study of the Tongue Root Contrast in Degema Vowels

“…Earlier discussion has addressed the fact that formant bandwidth is directly related to damping in the acoustic system; the greater the bandwidth, the more the damping. By modeling the vocal tract configuration of the vowel /i/ as a series of connected acoustic cylinders, and performing calculations on an electrical analog developed by Dunn [1950], van den Berg [1955] was able to distinguish three different contributions to the resistance (damping) of the supraglottal vocal tract. These are: (1) Radiation resistance, due to the coupling of the mouth opening with the air outside which affects primarily the formants above 2,000 Hz.…”

Some Spectral Characteristics of Airflow Signals Associated with Oral Reading

“…Calculations were initially made for the vowel /i/ and /u/ configuration with out the face mask-pneumotachograph. These vowels were selected because the dimen sional data of the vocal tract configuration and the resulting resonance data were avail able in the literature [Dunn, 1950] and be cause these two vowels have low first reson ance frequencies and are most likely to in fluence the 40-to 50-Hz airflow components. The vocal tract configurations of these vow els were then extended to include the config uration of the face mask-pneumotachograph.…”

Some experiments with computer synthesized speech

“…The tube is simulated as a sequence of short, uniform cylindrical tubes where the cross-sectional area of each section is adjusted to represent the area of vocal tract at different points along its length. In earlier tube analogs (Dunn, 1950), the cylindrical sections were simulated by electrical networks. Others (Kelly & Lochbaum, 1962;Mermelstein, 1969) calculated the progression of the sound pulses from section to section all the way from vocal cords to lips, taking into account reflections and transmissions at the area discontinuities at section boundaries.…”