Brad H. Story

Acoustic interactions of the voice source with the lower vocal tract

The linear source-filter theory of speech production assumes that vocal fold vibration is independent of the vocal tract. The justification is that the glottis often behaves as a high-impedance (constant flow) source. Recent imaging of the vocal tract has demonstrated, however, that the epilarynx tube is quite narrow, making the input impedance to the vocal tract comparable to the glottal impedance. Strong interactions can exist, therefore. In particular, the inertance of the vocal tract facilitates vocal fold vibration by lowering the oscillation threshold pressure. This has a significant impact on singing. Not only does the epilarynx tube produce the desirable singers formant (vocal ring), but it acts like the mouthpiece of a trumpet to shape the flow and influence the mode of vibration. Effects of the piriform sinuses, pharynx expansion, and nasal coupling are also discussed.

Acoustic impedance of an artificially lengthened and constricted vocal tract

Voice training techniques often make use of exercises involving partial occlusion of the vocal tract, typically at the anterior part of the oral cavity or at the lips. In this study two techniques are investigated: a bilabial fricative and a small diameter hard-walled tube placed between the lips. Because the input acoustic impedance of the vocal tract is known to affect both the shaping of the glottal flow pulse and the vibrational pattern of the vocal folds, a study of the input impedance is an essential step in understanding the benefits of these two techniques. The input acoustic impedance of the vocal tract was investigated theoretically for cases of a vowel, bilabial occlusion (fully closed lips), a bilabial fricative, and artificially lengthening the tract with small diameter tubes. The results indicate that the tubes increase the input impedance in the range of the fundamental frequency of phonation by lowering the first formant frequency to nearly that of the bilabial occlusion (the lower bound on the first formant) while still allowing a continuous airflow. The bilabial fricative also has the effect of lowering the first formant frequency and increasing the low-frequency impedance, but not as effectively as the extension tubes.

Rules for controlling low-dimensional vocal fold models with muscle activation

A low-dimensional, self-oscillation model of the vocal folds is used to capture three primary modes of vibration, a shear mode and two compressional modes. The shear mode is implemented with either two vertical masses or a rotating plate, and the compressional modes are implemented with an additional bar mass between the vertically stacked masses and the lateral boundary. The combination of these elements allows for the anatomically important body-cover differentiation of vocal fold tissues. It also allows for reconciliation of lumped-element mechanics with continuum mechanics, but in this reconciliation the oscillation region is restricted to a nearly rectangular glottis (as in all low-dimensional models) and a small effective thickness of vibration (<3 mm). The model is controlled by normalized activation levels of the cricothyroid (CT), thyroarytenoid (TA), lateral cricoarytenoid (LCA), and posterior cricoarytenoid (PCA) muscles, and lung pressure. An empirically derived set of rules converts these muscle activities into physical quantities such as vocal fold strain, adduction, glottal convergence, mass, thickness, depth, and stiffness. Results show that oscillation regions in muscle activation control spaces are similar to those measured by other investigations on human subjects.

A parametric model of the vocal tract area function for vowel and consonant simulation

A model of the vocal-tract area function is described that consists of four tiers. The first tier is a vowel substrate defined by a system of spatial eigenmodes and a neutral area function determined from MRI-based vocal-tract data. The input parameters to the first tier are coefficient values that, when multiplied by the appropriate eigenmode and added to the neutral area function, construct a desired vowel. The second tier consists of a consonant shaping function defined along the length of the vocal tract that can be used to modify the vowel substrate such that a constriction is formed. Input parameters consist of the location, area, and range of the constriction. Location and area roughly correspond to the standard phonetic specifications of place and degree of constriction, whereas the range defines the amount of vocal-tract length over which the constriction will influence the tract shape. The third tier allows length modifications for articulatory maneuvers such as lip rounding/spreading and larynx lowering/raising. Finally, the fourth tier provides control of the level of acoustic coupling of the vocal tract to the nasal tract. All parameters can be specified either as static or time varying, which allows for multiple levels of coarticulation or coproduction.

The relationship of vocal tract shape to three voice qualities

Three-dimensional vocal tract shapes and consequent area functions representing the vowels [i, ae, a, u] have been obtained from one male and one female speaker using magnetic resonance imaging (MRI). The two speakers were trained vocal performers and both were adept at manipulation of vocal tract shape to alter voice quality. Each vowel was performed three times, each with one of the three voice qualities: normal, yawny, and twangy. The purpose of the study was to determine some ways in which the vocal tract shape can be manipulated to alter voice quality while retaining a desired phonetic quality. To summarize any overall tract shaping tendencies mean area functions were subsequently computed across the four vowels produced within each specific voice quality. Relative to normal speech, both the vowel area functions and mean area functions showed, in general, that the oral cavity is widened and tract length increased for the yawny productions. The twangy vowels were characterized by shortened tract length, widened lip opening, and a slightly constricted oral cavity. The resulting acoustic characteristics of these articulatory alterations consisted of the first two formants (F1 and F2) being close together for all yawny vowels and far apart for all the twangy vowels.

Comparison of magnetic resonance imaging-based vocal tract area functions obtained from the same speaker in 1994 and 2002

A new set of area functions for vowels has been obtained with magnetic resonance imaging from the same speaker as that previously reported in 1996 [Story et al., J. Acoust. Soc. Am. 100, 537-554 (1996)]. The new area functions were derived from image data collected in 2002, whereas the previously reported area functions were based on magnetic resonance images obtained in 1994. When compared, the new area function sets indicated a tendency toward a constricted pharyngeal region and expanded oral cavity relative to the previous set. Based on calculated formant frequencies and sensitivity functions, these morphological differences were shown to have the primary acoustic effect of systematically shifting the second formant (F2) downward in frequency. Multiple instances of target vocal tract shapes from a specific speaker provide additional sampling of the possible area functions that may be produced during speech production. This may be of benefit for understanding intraspeaker variability in vowel production and for further development of speech synthesizers and speech models that utilize area function information.

Closed phase covariance analysis based on constrained linear prediction for glottal inverse filtering

Closed phase (CP) covariance analysis is a widely used glottal inverse filtering method based on the estimation of the vocal tract during the glottal CP. Since the length of the CP is typically short, the vocal tract computation with linear prediction (LP) is vulnerable to the covariance frame position. The present study proposes modification of the CP algorithm based on two issues. First, and most importantly, the computation of the vocal tract model is changed from the one used in the conventional LP into a form where a constraint is imposed on the dc gain of the inverse filter in the filter optimization. With this constraint, LP analysis is more prone to give vocal tract models that are justified by the source-filter theory; that is, they show complex conjugate roots in the formant regions rather than unrealistic resonances at low frequencies. Second, the new CP method utilizes a minimum phase inverse filter. The method was evaluated using synthetic vowels produced by physical modeling and natural speech. The results show that the algorithm improves the performance of the CP-type inverse filtering and its robustness with respect to the covariance frame position.

Formant frequency estimation of high-pitched vowels using weighted linear prediction

All-pole modeling is a widely used formant estimation method, but its performance is known to deteriorate for high-pitched voices. In order to address this problem, several all-pole modeling methods robust to fundamental frequency have been proposed. This study compares five such previously known methods and introduces a technique, Weighted Linear Prediction with Attenuated Main Excitation (WLP-AME). WLP-AME utilizes temporally weighted linear prediction (LP) in which the square of the prediction error is multiplied by a given parametric weighting function. The weighting downgrades the contribution of the main excitation of the vocal tract in optimizing the filter coefficients. Consequently, the resulting all-pole model is affected more by the characteristics of the vocal tract leading to less biased formant estimates. By using synthetic vowels created with a physical modeling approach, the results showed that WLP-AME yields improved formant frequencies for high-pitched sounds in comparison to the previously known methods (e.g., relative error in the first formant of the vowel [a] decreased from 11% to 3% when conventional LP was replaced with WLP-AME). Experiments conducted on natural vowels indicate that the formants detected by WLP-AME changed in a more regular manner between repetitions of different pitch than those computed by conventional LP.

A reflex resonance model of vocal vibrato

A reflex mechanism with a long latency (>40 ms) is implicated as a plausible cause of vocal vibrato. At least one pair of agonist-antagonist muscles that can change vocal-fold length is needed, such as the cricothyroid muscle paired with the thyroarytenoid muscle, or the cricothyroid muscle paired with the lateral cricoarytenoid muscle or a strap muscle. Such an agonist-antagonist muscle pair can produce negative feedback instability in vocal-fold length with this long reflex latency, producing oscillations on the order of 5-7 Hz. It is shown that singers appear to increase the gain in the reflex loop to cultivate the vibrato, which grows out of a spectrum of 0-15-Hz physiologic tremors in raw form.

ACOUSTICS OF THE TENOR HIGH VOICE

Frequency spectra of five standard vowels sung at high pitches (F4, G4, A4, and B4) were obtained from six tenors who were in vocal training at Westminster Choir College. Because of the variation of the spectra over the vibrato cycle, measurements were made at the peak, the trough, and the middle of the cycle. Stylized power spectra were generated from averages over the vibrato cycle. A power spectrum model was then used to determine the extent to which tenors ‘‘tune’’ formants to specific harmonics of the source. Results indicate that, aside from the high level of acoustic energy in the region of the singer’s formant, tenors get most of their vocal intensity from the second, third, and fourth harmonics. In some cases, F1 or F2 is specifically tuned to one of these lower harmonics; in other cases, however, the desire to create smooth transitions between vowels seems to favor a distribution of energy across several harmonics. Unlike what has been observed in the soprano high voice, the fundamental almost n...