Vocal tract resonances and the sound of the Australian didjeridu (yidaki) I. experiment

The didjeridu, or yidaki, is a simple tube about 1.5 m long, played with the lips, as in a tuba, but mostly producing just a tonal, rhythmic drone sound. The acoustic impedance spectra of performers' vocal tracts were measured while they played and compared with the radiated sound spectra. When the tongue is close to the hard palate, the vocal tract impedance has several maxima in the range 1-3 kHz. These maxima, if sufficiently large, produce minima in the spectral envelope of the sound because the corresponding frequency components of acoustic current in the flow entering the instrument are small. In the ranges between the impedance maxima, the lower impedance of the tract allows relatively large acoustic current components that correspond to strong formants in the radiated sound. Broad, weak formants can also be observed when groups of even or odd harmonics coincide with bore resonances. Schlieren photographs of the jet entering the instrument and high speed video images of the player's lips show that the lips are closed for about half of each cycle, thus generating high levels of upper harmonics of the lip frequency. Examples of the spectra of "circular breathing" and combined playing and vocalization are shown.     

Formant frequency estimates for abruptly changing area functions: a comparison between calculations and measurements.

Vocal tract area functions may contain quite abrupt changes in cross-sectional area. In formant frequency calculations for such area functions, an inner length correction (ILC) should be applied. The relevance of this correction was investigated by comparing acoustic measurements obtained from a physical model of the vocal tract with data gathered by means of computer simulations. Calculating formant frequencies without applying internal length corrections caused substantial errors, particularly for area functions representing apical stops just anterior to occlusion. Decentering and axial symmetry in the arrangement of the area elements of the physical model were briefly studied and found to have effects on the formant frequency values.     

A methodological and preliminary study on the acoustic effect of a trumpet player's vocal tract

A methodological study is presented to examine the acoustic role of the vocal tract in playing the trumpet. Preliminary results obtained for one professional player are also shown to demonstrate the effectiveness of the method. Images of the vocal tract with a resolution of 0.5 mm (2 mm in thickness) were recorded with magnetic resonance imaging to observe the tongue posture and estimate the vocal-tract area function during actual performance. The input impedance was then calculated for the player's air column including both the supra- and subglottal tracts using an acoustic tube model including the effect of wall losses. Finally, a time-domain blowing simulation by Adachi and Sato [J. Acoust. Soc. Am. 99, 1200-1209 (1996)] was performed with a model of the lips. In this simulation, the oscillating frequency of the lips was slightly affected by using different shapes of the vocal tract measured for the player. In particular, when the natural frequency of the lips was gradually increased, the transition to the higher mode occurred at different frequencies for different vocal-tract shapes. Furthermore, simulation results showed that the minimum blowing pressure required to attain the lip oscillation can be reduced by adjusting the vocal-tract shape properly.     

Source-tract interaction with prescribed vocal fold motion

An equation describing the time-evolution of glottal volume velocity with specified vocal fold motion is derived when the sub- and supra-glottal vocal tracts are present. The derivation of this Fant equation employs a property explicated in Howe and McGowan [(2011) J. Fluid Mech. 672, 428-450] that the Fant equation is the adjoint to the equation characterizing the matching conditions of sub- and supra-glottal Green's functions segments with the glottal segment. The present aeroacoustic development shows that measurable quantities such as input impedances at the glottis, provide the coefficients for the Fant equation when source-tract interaction is included in the development. Explicit expressions for the Green's function are not required. With the poles and zeros of the input impedance functions specified, the Fant equation can be solved. After the general derivation of the Fant equation, the specific cases where plane wave acoustic propagation is described either by a Sturm-Liouville problem or concatenated cylindrical tubes is considered. Simulations show the expected skewing of the glottal volume velocity pulses depending on whether the fundamental frequency is below or above a sub- or supra-glottal formant. More complex glottal wave forms result when both the first supra-glottal fundamental frequencies are high and close to the first sub-glottal formant.     

Effects of stimulation techniques on vocal responses: Implications for assessment and treatment

During voice evaluation and treatment it is customary for clinicians to elicit samples of the vowel /a/ from clients using various elicitation techniques. The purpose of this study was to compare the effects of four commonly used stimulation tasks on the laryngeal mechanism. Eleven female singing students, studying at a university music school, served as subjects for the study. The subjects phonated the vowel /a/ using 4 vocal stimulation techniques: yawn-sigh, gentle onset, focus, and the use of the voiceless fricative. Videoendoscopic and acoustic evaluations of their productions were done. Results show that, in the first 100 ms following the end of the formant transition, these techniques affected voice differently. The fundamental frequency was found to be highest in the yawn-sigh condition, whereas the maximum frequency perturbation was obtained for the voiceless fricative condition. Planned comparisons were made by comparing the data across 2 dimensions: (1) vowels elicited with voiced contexts versus those elicited with voiceless consonantal contexts and (2) vowels elicited with obstruent versus vowels elicited with nonobstruent consonantal contexts. Some changes in acoustic parameters brought about by these stimulation techniques may be explained on the basis of coarticulatory effects of the consonantal context.     

Comparison of vocal tract formants in singing andnonperiodic phonation

The skilled use of nonperiodic phonation techniques in combination with spectrum analysis has been proposed here as a practical method for locating formant frequencies in the singing voice. The study addresses the question of the degree of similarity between sung phonations and their nonperiodic imitations, with respect to both frequency of the first two formants as well as posture of the vocal tract. Using magnetic resonance imaging (MRI), linear predictive coding (LPC), and spectrum analysis, two types of nonperiodic phonation (ingressive and vocal fry) are compared with singing phonations to determine the degree of similarity/difference in acoustic and spatial dimensions of the vocal tract when these phonation types are used to approximate the postures of singing. In comparing phonation types, the close similarity in acoustic data in combination with the relative dissimilarity in spatial data indicates that the accurate imitations are not primarily the result of imitating the singing postures, but have instead an aural basis.     

Vocal tract resonances and the sound of the Australian didjeridu (yidaki) II. Theory

The didjeridu (didgeridoo) or yidaki of the Australian Aboriginal people consists of the narrow trunk of a small Eucalypt tree that has been hollowed out by the action of termites, cut to a length of about 1.5 m, smoothed, and decorated. It is lip-blown like a trumpet and produces a simple drone in the frequency range 55 to 80 Hz. Interest arises from the fact that a skilled player can make a very wide variety of sounds with formants rather like those of human vowels, and can also produce additional complex sounds by adding vocalization. An outline is given of the way in which the whole system can be analyzed using the harmonic-balance technique, but a simpler approach with lip motion assumed shows easily that upper harmonics of the drone with frequencies lying close to impedance maxima of the vocal tract are suppressed, so that formant bands appear near impedance minima of the vocal tract. This agrees with experimental findings. Simultaneous vibration of the player's lips and vocal folds is shown to generate multiple sum and difference tones, and can be used to produce subharmonics of the drone. A brief discussion is given of player preference of particular bore profiles.     

A theoretical study of f0-f1 interaction with application to resonant speaking and singing voice

An interactive source-filter system, consisting of a three-mass body-cover model of the vocal folds and a wave reflection model of the vocal tract, was used to test the dependence of vocal fold vibration on the vocal tract. The degree of interaction is governed by the epilarynx tube, which raises the vocal tract impedance to match the impedance of the glottis. The key component of the impedance is inertive reactance. Whenever there is inertive reactance, the vocal tract assists the vocal folds in vibration. The amplitude of vibration and the glottal flow can more than double, and the oral radiated power can increase up to 10 dB. As F0 approaches F1, the first formant frequency, the interactive source-filter system loses its advantage (because inertive reactance changes to compliant reactance) and the noninteractive system produces greater vocal output. Thus, from a voice training and control standpoint, there may be reasons to operate the system in either interactive and noninteractive modes. The harmonics 2F0 and 3F0 can also benefit from being positioned slightly below F1.     

A comparison of vocal tract perturbation patterns based on statistical and acoustic considerations

The purpose of this study was to investigate the relation between vocal tract deformation patterns obtained from statistical analyses of a set of area functions representative of a vowel repertoire, and the acoustic properties of a neutral vocal tract shape. Acoustic sensitivity functions were calculated for a mean area function based on seven different speakers. Specific linear combinations of the sensitivity functions corresponding to the first two formant frequencies were shown to possess essentially the same amplitude variation along the vocal tract length as the statistically derived deformation patterns reported in previous studies.     

Vocal tract length perturbation and its application to male-female vocal tract shape conversion

An alternative and complete derivation of the vocal tract length sensitivity function, which is an equation for finding a change in formant frequency due to perturbation of the vocal tract length [Fant, Quarterly Progress and Status Rep. No. 4, Speech Transmission Laboratory, Kungliga Teknisha Hogskolan, Stockholm, 1975, pp. 1-14] is presented. It is based on the adiabatic invariance of the vocal tract as an acoustic resonator and on the radiation pressure on the wall and at the exit of the vocal tract. An algorithm for tuning the vocal tract shape to match the formant frequencies to target values, such as those of a recorded speech signal, which was proposed in Story [J. Acoust. Soc. Am. 119, 715-718 (2006)], is extended so that the vocal tract length can also be changed. Numerical simulation of this extended algorithm shows that it can successfully convert between the vocal tract shapes of a male and a female for each of five Japanese vowels.     

Acoustic roles of the laryngeal cavity in vocal tract resonance

The acoustic effects of the laryngeal cavity on the vocal tract resonance were investigated by using vocal tract area functions for the five Japanese vowels obtained from an adult male speaker. Transfer functions were examined with the laryngeal cavity eliminated from the whole vocal tract, volume velocity distribution patterns were calculated, and susceptance matching analysis was performed between the laryngeal cavity and the vocal tract excluding the laryngeal cavity (vocal tract proper). It was revealed that the laryngeal cavity generates one of the formants of the vocal tract, which is the fourth in the present study. At this formant, the resonance of the laryngeal cavity (the 1/4 wavelength resonance) induces the open-tube resonance of the vocal tract proper (the 3/2 wavelength resonance). At the other formants, on the other hand, the vocal tract proper acts as a closed tube, because the laryngeal cavity has only a small contribution to generating these formants and the effective closed end of the whole vocal tract is the junction between the laryngeal cavity and the vocal tract proper.     

Experimental Findings on the Nasal Tract Resonator in Singing

SUMMARY: Many professional operatic singers sing the vowel /a/ with a velopharyngeal opening.(1) Here resonatory effects of such an opening are analyzed. On the basis of CAT scan imaging of a baritone singer's vocal tract and nasal cavity system, including the maxillary sinuses, acoustic epoxy models were constructed, in which velopharyngeal openings were modeled by different tubes. The sound transfer characteristics of this model were determined by means of sine-tone sweep measurements. In an idealized (iron tube) model, the VPO introduced a zero in the transfer function at the frequency of the nasal resonance. In the epoxy models, however, the resonances of the nasal system, and hence the zero, were heavily damped, particularly when the maxillary sinuses were included in the nasal system. A velopharyngeal opening was found to attenuate the first formant in /a/, such that the relative level of the singer's formant increased. A similar effect was observed in a modified epoxy model shaped to approximate the vocal tract of an /u/ and an /i/, although it also showed a substantial widening of the first formant bandwidth. Varying the size of the velopharyngeal opening affected the transfer function only slightly. It seems likely that singers can enhance higher spectrum partials by a careful tuning of a velopharyngeal opening.     

Cyclicity of laryngeal cavity resonance due to vocal fold vibration

Acoustic effects of the time-varying glottal area due to vocal fold vibration on the laryngeal cavity resonance were investigated based on vocal tract area functions and acoustic analysis. The laryngeal cavity consists of the vestibular and ventricular parts of the larynx, and gives rise to a regional acoustic resonance within the vocal tract, with this resonance imparting an extra formant to the vocal tract resonance pattern. Vocal tract transfer functions of the five Japanese vowels uttered by three male subjects were calculated under open- and closed-glottis conditions. The results revealed that the resonance appears at the frequency region from 3.0 to 3.7 kHz when the glottis is closed and disappears when it is open. Real spectra estimated from open- and closed-glottis periods of vowel sounds also showed the on-off pattern of the resonance within a pitch period. Furthermore, a time-domain acoustic analysis of vowels indicated that the resonance component could be observed as a pitch-synchronized rise-and-fall pattern of the bandpass amplitude. The cyclic nature of the resonance can be explained as the laryngeal cavity acting as a closed tube that generates the resonance during a closed-glottis period, but damps the resonance off during an open-glottis period.     

Measurement of formant frequencies and bandwidths in singing

That singers under certain circumstances adjust the articulation of the vocal tract (formant tuning) to enhance acoustic output is both apparent from measurements and understood in theory. The precise effect of a formant on an approaching (retreating) harmonic as the latter varies in frequency during actual singing, however, is difficult to isolate. In this study variations in amplitude of radiated sound components as well as supraglottal and subglottal (esophageal) pressures accompanying the vibrato-related sweep of voice harmonics were used as a basis for estimating the effective center frequencies and bandwidths of the first and second formants.     

Acoustic impedance measurements-correction for probe geometry mismatch

The effect of evanescent mode generation, due to geometrical mismatch, in acoustic impedance measurements is investigated. The particular geometry considered is that of a impedance probe with an annular flow port and a central microphone, but the techniques are applicable to other geometries. It is found that the imaginary part of the measured impedance error is proportional to frequency, and that the sign of the error is positive for measurements made on tubes with diameter much larger than that of the inlet port, but negative for tubes with diameter close to that of the inlet. The result is a distortion of the measured frequencies of the impedance minima of the duct while the maxima are largely unaffected. There is, in addition, a real resistive component to the error that varies approximately as the square root of the frequency. Experiment confirms the results of the analysis and calculations, and a calibration procedure is proposed that allows impedance probes that have been calibrated on a semi-infinite tube of one diameter to be employed for measurements on components with an inlet duct of some very different diameter.     

Two-dimensional model of vocal fold vibration for sound synthesis of voice and soprano singing

Voiced sounds were simulated with a computer model of the vocal fold composed of a single mass vibrating both parallel and perpendicular to the airflow. Similarities with the two-mass model are found in the amplitudes of the glottal area and the glottal volume flow velocity, the variation in the volume flow waveform with the vocal tract shape, and the dependence of the oscillation amplitude upon the average opening area of the glottis, among other similar features. A few dissimilarities are also found in the more symmetric glottal and volume flow waveforms in the rising and falling phases. The major improvement of the present model over the two-mass model is that it yields a smooth transition between oscillations with an inductive load and a capacitive load of the vocal tract with no sudden jumps in the vibration frequency. Self-excitation is possible both below and above the first formant frequency of the vocal tract. By taking advantage of the wider continuous frequency range, the two-dimensional model can successfully be applied to the sound synthesis of a high-pitched soprano singing, where the fundamental frequency sometimes exceeds the first formant frequency.     

The perceptual effects of child-adult differences in fricative-vowel coarticulation

Earlier work [Nittrouer et al., J. Speech Hear. Res. 32, 120-132 (1989)] demonstrated greater evidence of coarticulation in the fricative-vowel syllables of children than in those of adults when measured by anticipatory vowel effects on the resonant frequency of the fricative back cavity. In the present study, three experiments showed that this increased coarticulation led to improved vowel recognition from the fricative noise alone: Vowel identification by adult listeners was better overall for children's productions and was successful earlier in the fricative noise. This enhanced vowel recognition for children's samples was obtained in spite of the fact that children's and adults' samples were randomized together, therefore indicating that listeners were able to normalize the vowel information within a fricative noise where there often was acoustic evidence of only one formant associated primarily with the vowel. Correct vowel judgments were found to be largely independent of fricative identification. However, when another coarticulatory effect, the lowering of the main spectral prominence of the fricative noise for /u/ versus /i/, was taken into account, vowel judgments were found to interact with fricative identification. The results show that listeners are sensitive to the greater coarticulation in children's fricative-vowel syllables, and that, in some circumstances, they do not need to make a correct identification of the most prominently specified phone in order to make a correct identification of a coarticulated one.     

A physiological and acoustic study on voiced bilabial fricative /β:/ as a vocal exercise

The voiced bilabial fricative /β:/ has been used as a vocal exercise. The present study investigated the effects of the exercise on voice production and voice source. This study compared vowel phonation on the syllable /a:p/ with the production of the exercise and vowel phonation before and immediately after the exercise. The methods were (a) dual-channel electroglottography, from which the vertical laryngeal position was derived, (b) electromyography using surface electrodes, and (c) inverse filtering of the acoustic signal to obtain an estimate of the voice source. In the production of /β:/ as compared with vowel phonation in most of the cases, the vertical laryngeal position seemed to be higher, the muscular activity of the larynx lower, and the slope of the voice source spectrum steeper. In vowel phonation after the exercise, the muscular activity seemed to be lower in most cases, although the voice source remained unchanged. This seems to indicate improved vocal economy.     

Vocal tract area functions and formant frequencies in opera tenors' modal and falsetto registers

According to recent model investigations, vocal tract resonance is relevant to vocal registers. However, no experimental corroboration of this claim has been published so far. In the present investigation, ten professional tenors' vocal tract configurations were analyzed using MRI volumetry. All subjects produced a sustained tone on the pitch F4 (349 Hz) on the vowel /a/ (1) in modal and (2) in falsetto register. The area functions were estimated from the MRI data and their associated formant frequencies were calculated. In a second condition the same subjects repeated the same tasks in a sound treated room and their formant frequencies were estimated by means of inverse filtering. In both recordings similar formant frequencies were observed. Vocal tract shapes differed between modal and falsetto register. In modal as compared to falsetto the lip opening and the oral cavity were wider and the first formant frequency was higher. In this sense the presented results are in agreement with the claim that the formant frequencies differ between registers.