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Supplementary information

This document describes sound files, spectra and acoustical impedance measurements from experiments in which the acoustic impedance spectrum of the player's vocal tract was measured, during performance, just inside the player's lips. (The acoustic impedance Z is the ratio of acoustic pressure to acoustic flow.)

The paper explains the production of strong formants in the sound of the instrument. The associated Supplementary sound file consists of a sample of the "high tongue" sound, followed by a sample of the "low tongue" sound. This pair of samples is repeated three times. Spectra of the two sounds are shown below.

Fig 1. The relative sound pressure level (thin line, left ordinate) of the frequency components of the high drone sound. The acoustical impedance spectrum (solid line, right ordinate) is shown on the same graph. / To produce the "high tongue" or high drone sound, the tongue is held close to the hard palate to make a narrow constriction. Consequently, the acoustic impedance has high values at the resonances, as shown in Fig 1. The frequencies at which the impedance is high correspond to resonances that have pressure antinodes and velocity nodes near the lips. Consequently, there is very little acoustic flow into the instrument at these frequencies, and so a minimum in the spectral envelope (Fig 1). Between these minima, the flow is not impeded so much, and so there are formants, or peaks in the spectral envelope, at frequencies at which the impedance is low.
Fig 2. The relative sound pressure level (thin line) of the frequency components of a sound produced with the tongue low in the mouth. The acoustical impedance spectrum (solid line) is shown on the same graph. / To produce the "low tongue" sound, the tongue lies low in the mouth (Fig 2). Even at the resonant frequencies, the acoustic impedance is lower, because of the larger aperture. Consequently, the acoustical flow at these frequencies is not inhibited substantially and there are no strong formants. The absence of the strong formant is also clear in the sound file, as well as in both the spectrum.
Note that, in the sound files, the pitch as well as the timbre is changed by the tongue position.

The curves are typical. In the high tongue configuration (like those in Fig 1), maxima in the spectrum of the output sound correlated well with minima in the impedance spectrum (a correlation coefficient of 0.98 for 46 measurements on three players).

In the sound file, the sound is clearly that of a yidaki with a pitch below that of the normal human voice. Nevertheless, it sounds a little like someone alternating between the sound "ee" (the vowel in the English word "heed") and an indistinct vowel something like "aw" (the vowel in "hoard" or "hot"). In a previous study (Epps et al, 1997), we measured the resonances of the vocal tracts during speech. Vocal tracts pronouncing "heed" have a strong resonance at about 1.8 kHz, corresponding to the formant in Fig 1, while tracts pronouncing "hoard" or "hot" have no resonances between 1 and 2 kHz.

In our paper on the yidaki, we briefly discuss the importance of the glottis (the aperture left open between the vocal folds) in the production of strong resonances in the vocal tract in the kHz region. When the vocal folds are nearly closed, as they are for speech, the reflection coefficient for sound waves travelling down the vocal tract is high for all but very low frequencies. When the vocal folds are relaxed and open, the reflection coefficient for frequencies near 1 kHz is much lower: sound waves in the upper airway are more readily transmitted to the lower airway and to the highly lossy lungs. Consequently, the resonances of the vocal tract are weaker.

It is both practically and ethically problematic to measure, with a nasendoscope, the opening of the glottis of a human yidaki player during performance. For this and other reasons, we have made studies using an artificial system for playing the yidaki, in which the "glottis" opening in the artificial vocal tract can be accurately controlled. Measurements on such systems show weaker resonances and weaker formants when the glottis is open. This is in agreement with simple mathematical models. Both the artificial playing system and the physical models are the subjects of extended papers to be presented elsewhere.

Alex Tarnopolskya), Neville Fletchera,b), Lloyd Hollenbergc), Benjamin Langea), John Smitha), Joe Wolfea)

a) School of Physics, University of New South Wales, Sydney NSW 2052, Australia

a) Research School of Physical Science and Engineering, Australian National University, Canberra 0200, Australia

c) School of Physics University, of Melbourne, Parkville, Vic 3010, Australia

Reference

Epps, J., Smith, J.R. & Wolfe, J. Measurement Sci. and Technol. 8, 1112-1121 (1997).