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The study addresses the benefit of tuning single harmonics with vocal tract resonances to increase vocal loudness. The loudness of theoretically constructed vocal sounds with variable levels of sound energy in the first, second, and third harmonics is computed on the basis of ISO standard 226:2003. In comparison to increased loudness with changes in overall spectral slope, it is shown that single harmonic tuning requires a greater range of SPL to produce a similar range of loudness. For example, a 10-40 dB increase in the level of a single harmonic produces less than two doublings of loudness, whereas a spectral slope change from -12 dB/octave to -3 dB/octave can produce a similar doubling of loudness with only a 5 dB SPL increase.

The validity of glottal inverse filtering (GIF) to obtain a glottal flow waveform from radiated pressure signal in the presence and absence of source-filter interaction was studied systematically. A driven vocal fold surface model of vocal fold vibration was used to generate source signals. A one-dimensional wave reflection algorithm was used to solve for acoustic pressures in the vocal tract. Several test signals were generated with and without source-filter interaction at various fundamental frequencies and vowels. Linear Predictive Coding (LPC), Quasi Closed Phase (QCP), and Quadratic Programming (QPR) based algorithms, along with supraglottal impulse response, were used to inverse filter the radiated pressure signals to obtain the glottal flow pulses. The accuracy of each algorithm was tested for its recovery of maximum flow declination rate (MFDR), peak glottal flow, open phase ripple factor, closed phase ripple factor, and mean squared error. The algorithms were also tested for their absolute relative errors of the Normalized Amplitude Quotient, the Quasi-Open Quotient, and the Harmonic Richness Factor. The results indicated that the mean squared error decreased with increase in source-filter interaction level suggesting that the inverse filtering algorithms perform better in the presence of source-filter interaction. All glottal inverse filtering algorithms predicted the open phase ripple factor better than the closed phase ripple factor of a glottal flow waveform, irrespective of the source-filter interaction level. Major prediction errors occurred in the estimation of the closed phase ripple factor, MFDR, peak glottal flow, normalized amplitude quotient, and Quasi-Open Quotient. Feedback-related nonlinearity (source-filter interaction) affected the recovered signal primarily when fo was well below the first formant frequency of a vowel. The prediction error increased when fo was close to the first formant frequency due to the difficulty of estimating the precise value of resonance frequencies, which was exacerbated by nonlinear kinetic losses in the vocal tract.

The purpose of this preliminary study was to investigate the feasibility of a tool to compare a severity index of nonlinear events and vocal self-rating over a long period of time. One hundred and ninety-seven phonations were analyzed to quantify the severity of instabilities in the voice attributed to nonlinear dynamic phenomena, including voice breaks, subharmonics, and frequency jumps. Instabilities were first counted; then a severity index was calculated for the instabilities in each phonation. The two quantities were compared to the subject's autoperceptual rating. Generally speaking, the measures derived from nonlinear dynamic analysis of the high-pitched, soft phonations followed the subject's own rating of inability to produce soft voice. These preliminary single subject results provide a foundation for future multi-subject studies to formulate acoustic and autoperceptual measures for the fatiguing effects of prolonged speaking in vocally demanding professions. However, given the number of observations, the results are still useful in showing general relationships. While future work should add additional subjects, a study providing preliminary evidence is useful before attempting to undertake a multi-subject study with complex analysis (i.e., individually selecting the nonlinear events) and with a long observation duration (days, weeks, and months) of subject.

Steady airflow resistances in semi-occluded airways as well as acoustic impedances in vocalization are quantified from the lungs to the lips. For clinical and voice training applications, the primary focus is on two airway conditions, an oral semi-occlusion and a semi-occlusion above the vocal folds. Laryngeal airflow resistance is divided into glottal airflow resistance and epilaryngeal airway resistance. Maximum aerodynamic power is transferred to the vocal tract if the glottal airflow resistance is reduced while the epilaryngeal airway resistance is increased. A semi-occlusion at the lips helps to set up this condition. For the acoustic power transfer, the epilaryngeal airway also serves to match the impedance of the source to the impedance of the vocal tract.

In this tribute article to D.G. Miller, we review some historical and recent contributions to understanding the myoelastic-aerodynamic (MEAD) theory of phonation and the related acoustic phenomena in subglottal and vocal tract. At the time of the formulation of MEAD by van den Berg in late 1950s, it was assumed that vocal fold oscillations are self-sustained thanks to increased subglottal pressure pushing the glottis to open and decreased subglottal pressure allowing the glottis to close. In vivo measurements of subglottal pressures during phonation invalidated these assumptions, however, and showed that at low fundamental frequencies subglottal pressure rather tends to reach a maximum value at the beginning of glottal closure and then exhibits damped oscillations. These events can be interpreted as transient acoustic resonance phenomena in the subglottal tract that are triggered by glottal closure. They are analogous to the transient acoustic phenomena seen in the vocal tract. Rather than subglottal pressure oscillations, a more efficient mechanism of transfer of aerodynamic energy to the vocal fold vibrations has been identified in the vertical phase differences (mucosal waves) making the glottal shape more convergent during glottis opening than during glottis closing. Along with other discoveries, these findings form the basis of our current understanding of MEAD.

Objective This investigation addressed the desirable source–airway interaction obtained with vocalization through a semi-occlusion at the mouth. The semi-occlusion was a flow-resistant tube of varying length and diameter. Method The methodology was strictly computational. Airway shapes resembling those obtained from magnetic resonance or computed tomography imaging were stylized. Supraglottal and subglottal acoustic impedances were calculated, from which inertagrams were plotted over a frequency range of 0–4000 Hz. The inertagrams predict which harmonics are likely to be strengthened. Results The combination of epilaryngeal airway narrowing and lengthening, a pharyngeal expansion, and an oral narrowing behind the tube produce the best overall inertagram for pitch glide exercises. This configuration supports harmonics of the source evenly over a range of 300–4000 Hz. Conclusions For clinical applications, theory predicts that the length of a tube or straw does not matter if the inner diameter is on the order of 3 mm or less. For wider open-ended tubes, greater length can compensate for the wider diameter for the beneficial inertance effect, but the desired steady pressure in the airways for vocal fold posturing cannot be maintained.

Objective This investigation addresses the loudness variations in sones achievable with spectral slope variations (higher harmonic energy) in human vocalization and compares it to the sound pressure level (SPL) variations typically reported in the voice range profile (VRP). Method The primary methodology was computational. The ISO standard 226 was used to convert SPL values to sones for a 125- to 1000-Hz range of fundamental frequency and a –3 dB/octave to –12 dB/octave range of spectral slope. In addition, a retrospective analysis of human subjects' VRPs was conducted, and the experimental results were compared to the theoretical results. Results A very small range of SPL variation (less than 5 dB) in the VRP can produce a large range of loudness. The sensitivity can be on the order of 4 sones per dB SPL change. Conclusion For vocalization in the modal register, loudness variation is not well described by SPL change in dB, especially at high fundamental frequencies where the SPL range in the VRP becomes very small but sizeable loudness variations are still possible.

Long-distance vocal communication by birds and mammals, including humans, is facilitated largely by radiation efficiency from the mouth or beak. Here, this efficiency is defined and quantified. It depends on frequency content of vocalization, mouth opening, head and upper body geometry, and directionality. Each of these factors is described mathematically with a piston-in-a-sphere model. While this model is considered a classic, never before has the high frequency solution been applied in detail to vocalization. Results indicate that frequency content in the 1–50 kHz range can be radiated with nearly 100% efficiency if a reactance peak in the radiation impedance is utilized with adjustments of head size, mouth opening, and beam direction. Without these adjustments, radiation efficiency is generally below 1%, especially in human speech where a high fundamental frequency is a disadvantage for intelligibility. Thus, two distinct modes of vocal communication are identified, (1) short range with optimized information transfer and (2) long range with maximum efficiency for release of acoustic power.

The fluid-structure interaction and energy transfer from respiratory airflow to self-sustained vocal fold oscillation continues to be a topic of interest in vocal fold research. Vocal fold vibration is driven by pressures on the vocal fold surface, which are determined by the shape of the glottis and the contact between vocal folds. Characterization of three-dimensional glottal shapes and contact patterns can lead to increased understanding of normal and abnormal physiology of the voice, as well as to development of improved vocal fold models, but a large inventory of shapes has not been directly studied previously. This study aimed to take an initial step toward characterizing vocal fold contact patterns systematically. Vocal fold motion and contact was modeled based on normal mode vibration, as it has been shown that vocal fold vibration can be almost entirely described by only the few lowest order vibrational modes. Symmetric and asymmetric combinations of the four lowest normal modes of vibration were superimposed on left and right vocal fold medial surfaces, for each of three prephonatory glottal configurations, according to a surface wave approach. Contact patterns were generated from the interaction of modal shapes at 16 normalized phases during the vibratory cycle. Eight major contact patterns were identified and characterized by the shape of the flow channel, with the following descriptors assigned: convergent, divergent, convergent-divergent, uniform, split, merged, island, and multichannel. Each of the contact patterns and its variation are described, and future work and applications are discussed.

Based on the assumption that individual sound intensities of singers are incoherent and add linearly to produce a combined choir intensity, a model of a voice range profile of a choir is produced. It is shown that this model predicts six distinct levels of choir dynamics (pp p mp mf f ff) over two octaves of fundamental frequency in a choir section. The levels are 3-6 dB apart, depending on the individual voice range profiles of the singers. Overall choir size has no effect on dynamic range, unless the size is varied dynamically by not all singers singing all the time. For a non-homogeneousn group of singers, a few loud voices dominate ff if everyone sings, while pp is not achieved effectively without suppressing all voices that cannot sing soft. Furthermore, the dynamic range can be significantly limited when choral blend for loudness is imposed on a non-homogeneous choir.

A fiber-gel vocal fold model is compared to a transversely isotropic stiffness model in terms of normal mode vibration. The fiber-gel finite element model (FG-FEM) consists of a series of gel slices, each with a two-dimensional finite element mesh, in a plane transverse to the tissue fibers. The gel slices are coupled with fibers under tension in the anterior-posterior dimension. No vibrational displacement in the fiber-length direction is allowed, resulting in a plane strain state. This is consistent with the assumption of transverse displacement of a simple string, offering a wide range of natural frequencies (well into the kHz region) with variable tension. For low frequencies, the results compare favorably with the natural frequencies of a transversely isotropic elastic stiffness model (TISM) in which the shear modulus in the longitudinal plane is used to approximate the effect of fiber tension. For high frequencies, however, the natural frequencies do not approach the string mode frequencies unless plane strain is imposed on the TISM model. The simplifying assumption of plane strain, as well as the use of analytical closed-form shape functions, allow for substantial savings in computational time, which is important in clinical and exploratory applications of the FG-FEM model.

A systematic variation of length and cross-sectional area of specific segments of the vocal tract (trachea to lips) was conducted computationally to quantify the effects of source–filter interaction. A one-dimensional Navier–Stokes (transmission line) solution was used to compute peak glottal airflow, maximum flow declination rate, and formant ripple on glottal flow for Level 1 (aero-acoustic) interactions. For Level 2 (tissue movement) interaction, peak glottal area, phonation threshold pressure, and deviation in $f_{{{o}}}$ were quantified. Results show that the ventricle, the false-fold glottis, the conus elasticus entry, and the laryngeal vestibule are the regions to which acoustic variables are most sensitive. Generally, any narrow section of the vocal tract increases the degree of interaction, both in terms of its length and its cross-sectional area. The closer the narrow section is to the vocal folds, the greater the effect.

The unique avian vocal organ, the syrinx, is located at the caudal end of the trachea. Although a larynx is also present at the opposite end, birds phonate only with the syrinx. Why only birds evolved a novel sound source at this location remains unknown, and hypotheses about its origin are largely untested. Here, we test the hypothesis that the syrinx constitutes a biomechanical advantage for sound production over the larynx with combined theoretical and experimental approaches. We investigated whether the position of a sound source within the respiratory tract affects acoustic features of the vocal output, including fundamental frequency and efficiency of conversion from aerodynamic energy to sound. Theoretical data and measurements in three bird species suggest that sound frequency is influenced by the interaction between sound source and vocal tract. A physical model and a computational simulation also indicate that a sound source in a syringeal position produces sound with greater efficiency. Interestingly, the interactions between sound source and vocal tract differed between species, suggesting that the syringeal sound source is optimized for its position in the respiratory tract. These results provide compelling evidence that strong selective pressures for high vocal efficiency may have been a major driving force in the evolution of the syrinx. The longer trachea of birds compared to other tetrapods made them likely predisposed for the evolution of a syrinx. A long vocal tract downstream from the sound source improves efficiency by facilitating the tuning between fundamental frequency and the first vocal tract resonance., Author summary The larynx is an important valve in the respiratory system of all air-breathing vertebrates that is located at the upper end of the trachea. In some amphibians, in nonavian reptiles, and in mammals, it has also assumed the function of a vocal organ. In contrast, birds have evolved a new and unique vocal organ, the syrinx, which is located at the lower end of the trachea. The selective forces that underlie the evolution of the syrinx as a novel organ have remained unclear. Among all air-breathing vertebrates, birds have the longest necks, and long necks require a long trachea. With a vocal organ at the base of the trachea, this long tube can act as vocal tract resonator and, therefore, can improve the conversion of aerodynamic energy into acoustic energy if fundamental frequency and a resonance frequency are matched. Here, we conducted experiments with simplified physical models, with real birds and a computational simulation in order to investigate the effect of the two different positions of a sound source within the respiratory tract. We find that sound is produced with greater efficiency by a sound source in syrinx position and that favorable interactions between sound source and vocal tract occur with syringeal position. The data provide support for the hypothesis that a selective pressure for high vocal efficiency may have contributed to the evolution of the syrinx in its unique location within the air tract.

Summary Source-filter interaction is a phenomenon in which acoustic airway pressures influence the glottal airflow at the source (level 1) and the vibration pattern of the vocal folds (level 2). This interaction is most significant when dominant source harmonics are near airway resonances. The influence of acoustic airway pressures on vocal fold vibration (level 2) was studied systematically by changing the supraglottal vocal tract length in human subjects with tube extensions. The subjects were asked to perform fundamental frequency (fo) glides while phonating through tubes of various lengths. An algorithm was developed using the quasi-open quotient extracted from the electroglottograph. Regions of sudden vocal fold vibration pattern change due to source-filter interaction were inferred from contact area changes. The algorithm correctly identified 89% of male and 84.8% of female quantal changes in contact pattern associated with interactions between source harmonics and formants during ascending glides. During the descending glides, the algorithm correctly identified 84% of male and 81.1% of female quantal changes in contact pattern. These results are in comparison with those obtained from the fo-based algorithm (Maxfield et al).

The accuracy of a voice vote was addressed by systematically varying group size, individual voter loudness, and words that are typically used to express agreement or disagreement. Five judges rated the loudness of two competing groups in A-B comparison tasks. Acoustic analysis was performed to determine the sound energy level of each word uttered by each group. Results showed that individual voter differences in energy level can grossly alter group loudness and bias the vote. Unless some control is imposed on the sound level of individual voters, it is difficult to establish even a two-thirds majority, much less a simple majority. There is no symmetry in the bias created by unequal sound production of individuals. Soft voices do not bias the group loudness much, but loud voices do. The phonetic balance of the two words chosen (e.g., “yea” and “nay” as opposed to “aye” and “no”) seems to be less of an issue.

Vocal loudness in sones is quantified on the basis of changes in spectral slope and harmonic tuning in a range of singing fundamental frequencies of 125 Hz to 1000 Hz. Spectral slope of the mouth output pressure is bracketed in the range of -3 dB/octave to -12 dB/octave to reflect a typical glottal spectrum from breathy to pressed adduction. To approximate formant tuning of harmonics, the SPL level of the first three harmonics is raised by 10, 20, and 30 dB. It is shown that spectral slope change is more effective in increasing vocal loudness than tuning a single harmonic with a vocal tract resonance. Some applications to amplified and unamplified vocal production and respective training are given.Vocal loudness in sones is quantified on the basis of changes in spectral slope and harmonic tuning in a range of singing fundamental frequencies of 125 Hz to 1000 Hz. Spectral slope of the mouth output pressure is bracketed in the range of -3 dB/octave to -12 dB/octave to reflect a typical glottal spectrum from breathy to pressed adduction. To approximate formant tuning of harmonics, the SPL level of the first three harmonics is raised by 10, 20, and 30 dB. It is shown that spectral slope change is more effective in increasing vocal loudness than tuning a single harmonic with a vocal tract resonance. Some applications to amplified and unamplified vocal production and respective training are given.

Hydration of vocal fold tissues is essential for self-sustained oscillation. Normal regulatory processes of liquid transport to and from the vocal folds would be expected through the autonomic systems, but the possibility exists that liquid movement may occur locally due to vibrational pressures. Such movement may cause regions of lower or higher concentrations of liquid viscosity and therewith changes in phonation threshold pressure. Hyaluronic acid, a glycosaminoglycan that attracts large quantities of free water, may be a key molecule for transporting or localizing liquids. Some preliminary experiments are reported in which attempts were made to move low-concentration HA liquids with vibration. None of the experiments was conclusive, but collectively they lay some groundwork for future explorations.

It is well known that a half-sinusoid has no odd harmonics other than the fundamental. If glottal flow in phonation were to approximate this exact waveshape, which is generally unlikely, some misperception of pitch and loss of vowel intelligibility would occur. The sensitivity of the glottal waveshape to this special shape is explored by systematically varying two parameters, open quotient and skewing quotient. Mild asymmetry (open quotient below 0.45 or above 0.55 and/or skewing quotient greater than 2.0) equalizes the odd-even harmonic series. Singers and speakers avoid the exact symmetry by skewing the flow pulse with source-filter interaction.

Intraglottal pressure is the driving force of vocal fold vibration. Theoretically, simultaneous quantification of glottal area and transglottal airflow allows the calculation of the intraglottal pressure waveform during a single vibration cycle. In this study, we show that, by combining photoglottography (transglottal light transmission) and airflow (Rothenberg mask) measurements during sustained vocal emissions in vivo, the intraglottal pressure wave can be approximated in a way similar to what has been done in models. The results confirm in vivo that the intraglottal pressure is systematically larger during the opening phase than during the closing phase, so that over one whole cycle, the driving force performs net positive work, accounting for sustained vocal fold motion. A component of this driving force asymmetry is related to vocal tract inertance, which also accounts for the skewing of the airflow waveform compared with the area waveform. Furthermore, the intraglottal pressure ratio (opening:closing) increases with voicing intensity, reaches a maximum around 76 dB, and significantly decreases at higher intensities. This rise and fall suggests that there is a range of intensity values in which, mechanically, a maximum of the driving force is imparted to the vocal fold mass. This finding could have implications for voice economy in professional speakers.

The traditional source-filter theory of voice production describes a linear relationship between the source (glottal flow pulse) and the filter (vocal tract). Such a linear relationship does not allow for nor explain how changes in the filter may impact the stability and regularity of the source. The objective of this experiment was to examine what effect unpredictable changes to vocal tract dimensions could have on fo stability and individual harmonic intensities in situations in which low frequency harmonics cross formants in a fundamental frequency glide. To determine these effects, eight human subjects (five male, three female) were recorded producing fo glides while their vocal tracts were artificially lengthened by a section of vinyl tubing inserted into the mouth. It was hypothesized that if the source and filter operated as a purely linear system, harmonic intensities would increase and decrease at nearly the same rates as they passed through a formant bandwidth, resulting in a relatively symmetric peak on an intensity-time contour. Additionally, fo stability should not be predictably perturbed by formant/harmonic crossings in a linear system. Acoustic analysis of these recordings, however, revealed that harmonic intensity peaks were asymmetric in 76% of cases, and that 85% of fo instabilities aligned with a crossing of one of the first four harmonics with the first three formants. These results provide further evidence that nonlinear dynamics in the source-filter relationship can impact fo stability as well as harmonic intensities as harmonics cross through formant bandwidths.

Vocal folds are used as sound sources in various species, but it is unknown how vocal fold morphologies are optimized for different acoustic objectives. Here we identify two main variables affecting range of vocal fold vibration frequency, namely vocal fold elongation and tissue fiber stress. A simple vibrating string model is used to predict fundamental frequency ranges across species of different vocal fold sizes. While average fundamental frequency is predominantly determined by vocal fold length (larynx size), range of fundamental frequency is facilitated by (1) laryngeal muscles that control elongation and by (2) nonlinearity in tissue fiber tension. One adaptation that would increase fundamental frequency range is greater freedom in joint rotation or gliding of two cartilages (thyroid and cricoid), so that vocal fold length change is maximized. Alternatively, tissue layers can develop to bear a disproportionate fiber tension (i.e., a ligament with high density collagen fibers), increasing the fundamental frequency range and thereby vocal versatility. The range of fundamental frequency across species is thus not simply one-dimensional, but can be conceptualized as the dependent variable in a multi-dimensional morphospace. In humans, this could allow for variations that could be clinically important for voice therapy and vocal fold repair. Alternative solutions could also have importance in vocal training for singing and other highly-skilled vocalizations., Author Summary Mammals, birds, and reptiles vocalize (make sounds with vocal cords). Various species, and individuals within the species, are identified by pitch, loudness, and other acoustic features they can build into a repertoire of rhythmic and melodic patterns. Range of pitch, or more precisely fundamental frequency, is required to produce a variety of patterns. Whereas the average fundamental frequency is predictable by body size, the range of fundamental frequency depends on two different factors. The first is a freedom of movement factor–how much vocal cord length change can be produced by muscles that rotate or glide cartilages in the larynx. The second is a molecular composition factor–how much collagen density can be produced in the vocal cord ligament. Development and evolution has not been uniform with regard to these factors, suggesting that alternative choices are available for growth, training, and repair.

Semi-occlusion of the vocal tract with a thin straw provides some advantages for assessing the physiological ranges of intensity and fundamental frequency in a voice. Signals can be obtained without concern about room noise, mouth-to-microphone distance, or vocal injury caused by excessive loudness produced by a patient or client. We show that differences between loud and soft phonation into the straw are clearly measureable and reflect the soft-loud differences measured from airborne sound radiating from an open mouth. Using this technique to acquire a traditional voice range profile, the range of fundamental frequency is not limited and risk for injury seems to be less than for traditional methods. In the lower portion of the fundamental frequency range, the steady pressures measured at the mouth constitute a range profile for subglottal (lung) pressure.

SUMMARY The vocal folds of male Rocky Mountain elk (Cervus elaphus nelsoni) are about 3 cm long. If fundamental frequency were to be predicted by a simple vibrating string formula, as is often done for the human larynx, such long vocal folds would bear enormous stress to produce the species-specific mating call with an average fundamental frequency of 1 kHz. Predictions would be closer to 50 Hz. Vocal fold histology revealed the presence of a large vocal ligament between the vocal fold epithelium and the thyroarytenoid muscle. In tensile tests, the stress–strain response of vocal fold epithelium and the vocal ligament were determined. Elasticity of both tissue structures reached quantitative values similar to human tissue. It seems unlikely that the longitudinal stress in elk vocal folds can exceed that in human vocal folds by an order of magnitude to overcome the drop in fundamental frequency due to a 3:1 increase in vocal fold length. Alternative hypotheses of how the elk produces high fundamental frequency utterances,despite its very long vocal fold, include a reduced effective vocal fold length in vibration, either due to bending properties along the vocal fold, or by actively moving the boundary point with muscle stiffening. The relationships between an individual's average fundamental frequency, vocal fold length and body size are discussed.

A theory of interaction between the source of sound in phonation and the vocal tract filter is developed. The degree of interaction is controlled by the cross-sectional area of the laryngeal vestibule (epilarynx tube), which raises the inertive reactance of the supraglottal vocal tract. Both subglottal and supraglottal reactances can enhance the driving pressures of the vocal folds and the glottal flow, thereby increasing the energy level at the source. The theory predicts that instabilities in vibration modes may occur when harmonics pass through formants during pitch or vowel changes. Unlike in most musical instruments (e.g., woodwinds and brasses), a stable harmonic source spectrum is not obtained by tuning harmonics to vocal tract resonances, but rather by placing harmonics into favorable reactance regions. This allows for positive reinforcement of the harmonics by supraglottal inertive reactance (and to a lesser degree by subglottal compliant reactance) without the risk of instability. The traditional linear source–filter theory is encumbered with possible inconsistencies in the glottal flow spectrum, which is shown to be influenced by interaction. In addition, the linear theory does not predict bifurcations in the dynamical behavior of vocal fold vibration due to acoustic loading by the vocal tract.

Nonlinear source-filter coupling has been demonstrated in computer simulations, in excised larynx experiments, and in physical models, but not in a consistent and unequivocal way in natural human phonations. Eighteen subjects (nine adult males and nine adult females) performed three vocal exercises that represented a combination of various fundamental frequency and formant glides. The goal of this study was to pinpoint the proportion of source instabilities that are due to nonlinear source-tract coupling. It was hypothesized that vocal fold vibration is maximally destabilized when F(0) crosses F(1), where the acoustic load changes dramatically. A companion paper provides the theoretical underpinnings. Expected manifestations of a source-filter interaction were sudden frequency jumps, subharmonic generation, or chaotic vocal fold vibrations that coincide with F(0)-F(1) crossovers. Results indicated that the bifurcations occur more often in phonations with F(0)-F(1) crossovers, suggesting that nonlinear source-filter coupling is partly responsible for source instabilities. Furthermore it was observed that male subjects show more bifurcations in phonations with F(0)-F(1) crossovers, presumably because in normal speech they are less likely to encounter these crossovers as much as females and hence have less practice in suppressing unwanted instabilities.

Summary This paper discusses the effects of measurement uncertainties when calculating elastic moduli of laryngeal tissue. Small dimensions coupled with highly nonlinear elastic properties exacerbate the uncertainties. The sensitivity of both tangent and secant Young's Modulus was quantified in terms of the coefficient of variation, which depended on measurement of reference length and cross-sectional area. Uncertainties in the measurement of mass, used to calculate cross-sectional area of a small tissue sample, affected Young's Modulus calculations when tissue absorption of the hydrating solution was not accounted for. Uncertainty in reference length had twice the effect on elasticity than other measures. The implication of these measurement errors on predicted fundamental frequency of vocalization is discussed. Refinements on isolated muscle experimental protocols are proposed that pay greatest attention to measures of highest sensitivity.

The forces and torques governing effective two-dimensional (2D) translation and rotation of the laryngeal cartilages (cricoid, thyroid, and arytenoids) are quantified on the basis of more complex three-dimensional movement. The motions between these cartilages define the elongation and adduction (collectively referred to as posturing) of the vocal folds. Activations of the five intrinsic laryngeal muscles, the cricothyroid, thyroarytenoid, lateral cricoarytenoid, posterior cricoarytenoid, and interarytenoid are programmed as inputs, in isolation and in combination, to produce the dynamics of 2D posturing. Parameters for the muscles are maximum active stress, passive stress, activation time, contraction time, and maximum shortening velocity. The model accepts measured electromyographic signals as inputs. A repeated adductory-abductory gesture in the form /hi-hi-hi-hi-hi/ is modeled with electromyographic inputs. Movement and acoustic outputs are compared between simulation and measurement.

The National Center for Voice and Speech (NCVS) data bank on voice dosimetry was used to study the distributions of continuous voicing periods and silence periods in 31 teachers over the duration of two weeks. Recordings were made during all awake hours of the day. Voicing periods were grouped into half decades, ranging from 0.0316 to 0.10 s for the shortest periods of phonation to 31.6-100 s for the longest periods of phonation. Silence periods were grouped into similar half decades, but ranged up to periods of several hours. On average, the teachers had 1800 occurrences of voicing (onset followed by offset) per hour at work and 1200 occurrences per hour while not at work. Voicing occurred 23% of the total time at work, dropping to 13% during off-work hours and 12% on weekends. The greatest accumulation of voicing occurred in the 0.316-1.0 s voicing periods, whereas the greatest accumulation of silence occurred in the 3-10 s silence periods. The study begins to lay the groundwork for understanding vocal fatigue in terms of repetitive motion and collision of tissue, as well as recovery from such mechanical stress. (c) 2007 Acoustical Society of America.

Voiced obstruents and phonation into tubes are widely used as vocal exercises. They increase the inertive reactance of the vocal tract in the 200-1000 Hz range and thereby reinforce vocal fold vibration. But the effect is strong only when the epilarynx tube is also narrowed. The present study focused on the effects of a 'resonance tube' (27 cm in length, 0.5 cm2 cross-sectional area, hard walls) on vocal tract reactance and the accompanying economy of voice production (defined as maximum flow declination rate (MFDR), divided by maximum area declination rate (MADR)). The vowel /u/ and phonation into the tube were simulated with a computer model. Three values were given to the cross-sectional area of the epilarynx tube (0.2 cm2, 0.5 cm2, and 1.6 cm2), which is at the opposite end of the vocal tract from the artificial 'resonance tube'. The degree of glottal adduction was varied in order to find the economy maximum for each epilarynx tube setting. Results showed that the 'resonance tube' lowered F1 from 300 Hz to 150 Hz and doubled the vocal tract inertive reactance at F0=100 Hz. The largest economy with the 'resonance tube' was obtained when the epilarynx tube was narrowed (relative to the rest of the vocal tract) and sufficiently tight adduction was used. Most importantly, the intraoral acoustic pressure (calculated at 0.8 cm behind the lips) was tripled with the tube. The results suggest that by optimizing the vibratory sensations in the face that are attributed to increased intraoral acoustic pressure, phonation into a tube may assist a trainee in finding an optimal glottal and epilaryngeal setting for the greatest vocal economy.

Voice production is an inefficient process in terms of energy expended versus acoustic energy produced. A traditional efficiency measure, glottal efficiency, relates acoustic power radiated from the mouth to aerodynamic power produced in the trachea. This efficiency ranges between 0.0001 % and 1.0 %. It involves lung pressure, and hence would appear to be a useful effort measure for a given acoustic output. Difficulty in the combined measurement of lung pressure and tracheal airflow, however, has impeded clinical application of glottal efficiency. This paper utilizes the large data base from Schutte (1980) and a few new measurements to validate a pressure conversion ratio (PCR) as a substitute for glottal efficiency. PCR has the potential for wide application due to low cost and ease of use in clinics and vocal studios.

Toward a consensus on symbolic notation of harmonics, resonances, and formants in vocalization

Analytical and computer simulation studies have shown that the acoustic impedance of the vocal tract as well as the viscoelastic properties of vocal foldtissues are critical for determining the dynamics and the energy transfer mechanism of vocal fold oscillation. In the present study, a linear, small-amplitude oscillation theory was revised by taking into account the propagation of a mucosal wave and the inertive reactance (inertance) of the supraglottal vocal tract as the major energy transfer mechanisms for flow-induced self-oscillation of the vocal fold. Specifically, analytical results predicted that phonation threshold pressure ( P th ) increases with the viscous shear properties of the vocal fold, but decreases with vocal tract inertance. This theory was empirically tested using a physical model of the larynx, where biological materials (fat, hyaluronic acid, and fibronectin) were implanted into the vocal fold cover to investigate the effect of vocal foldtissueviscoelasticity on P th . A uniform-tube supraglottal vocal tract was also introduced to examine the effect of vocal tract inertance on P th . Results showed that P th decreased with the inertive impedance of the vocal tract and increased with the viscous shear modulus ( G ″ ) or dynamic viscosity ( η ′ ) of the vocal fold cover, consistent with theoretical predictions. These findings supported the potential biomechanical benefits of hyaluronic acid as a surgical bioimplant for repairing voice disorders involving the superficial layer of the lamina propria, such as scarring, sulcus vocalis, atrophy, and Reinke’s edema.

Time-domain computer simulation of sound production in airways is a widely used tool, both for research and synthetic speech production technology. Speed of computation is generally the rationale for one-dimensional approaches to sound propagation and radiation. Transmission line and wave-reflection (scattering) algorithms are used to produce formant frequencies and bandwidths for arbitrarily shaped airways. Some benchmark graphs and tables are provided for formant frequencies and bandwidth calculations based on specific mathematical terms in the one-dimensional Navier–Stokes equation. Some rules are provided here for temporal and spatial discretization in terms of desired accuracy and stability of the solution. Kinetic losses, which have been difficult to quantify in frequency-domain simulations, are quantified here on the basis of the measurements of Scherer, Torkaman, Kucinschi, and Afjeh [(2010). J. Acoust. Soc. Am. 128(2), 828–838].

How accurately can sound pressure levels (SPLs) of speech be estimated from skin vibration of the neck? Measurements using a small accelerometer were carried out in 27 subjects (10 males and 17 females) who read Rainbow and Marvin Williams passages in soft, comfortable, and loud voice, while skin acceleration levels (SALs) and SPLs were simultaneously registered and analyzed every 30 ms. The results indicate that the mean SPL of voiced speech can be estimated with accuracy better than +/- 2.8 dB in 95% of the cases when the subjects are individually calibrated. This makes the accelerometer an interesting sensor for SPL measurement of speech when microphones are problematic to use (e.g., noisy environments or in voice dosimetry). The estimates of equivalent SPL, which is the logarithm of averaged relative energy of voiced speech, were found to be up to 1.5 dB less accurate than the mean SPL. The estimation accuracy for instantaneous SPLs was worse than for the mean and equivalent SPLs (on average +/- 6 and +/- 5 dB for males and females, respectively). (c) 2005 Acoustical Society of America.

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.

An experimental method for quantifying the amount of voicing over time is described in a tutorial manner. A new procedure for obtaining calibrated sound pressure levels (SPL) of speech from a head-mounted microphone is offered. An algorithm for voicing detection (kv) and fundamental frequency (F0) extraction from an electroglottographic signal is described. The extracted values of SPL, F0, and kv are used to derive five vocal doses: the time dose (total voicing time), the cycle dose (total number of vocal fold oscillatory cycles), the distance dose (total distance travelled by the vocal folds in an oscillatory path), the energy dissipation dose (total amount of heat energy dissipated in the vocal folds) and the radiated energy dose (total acoustic energy radiated from the mouth). The doses measure the vocal load and can be used for studying the effects of vocal fold tissue exposure to vibration.

Two competing views of regulating glottal airflow for maximum vocal output are investigated theoretically. The maximum power transfer theorem is used as a guide. A wide epilarynx tube (laryngeal vestibule) matches well with low glottal resistance (believed to correspond to the "yawn-sigh" approach in voice therapy), whereas a narrow epilarynx tube matches well with a higher glottal resistance (believed to correspond to the "twang-belt" approach). A simulation model is used to calculate mean flows, peak flows, and oral radiated pressure for an impedance ratio between the vocal tract (the load) and the glottis (the source). Results show that when the impedance ratio approaches 1.0, maximum power is transferred and radiated from the mouth. A full update of the equations used for simulating driving pressures, glottal flow, and vocal tract input pressures is provided as a programming guide for those interested in model development.

Vowel selection is important in differentiating between singing styles. The timbre of the vocal instrument, which is related to its frequency spectrum, is governed by both the glottal sound source and the vowel choices made by singers. Consequently, the ability to modify the vowel space is a measure of how successfully a singer can maintain a desired timbre across a range of pitches. Formant range profiles were produced as a means of quantifying this ability. Seventy-seven subjects (including trained and untrained vocalists) participated, producing vowels with three intended mouth shapes: (1) neutral or speech-like, (2) megaphone-shaped (wide open mouth), and (3) inverted-megaphone-shaped (widened oropharynx with moderate mouth opening). The first and second formant frequencies (F1 and F2) were estimated with fry phonation for each shape and values were plotted in F1-F2 space. By taking four vowels of a quadrangle /i, ae, a, u/, the resulting area was quantified in kHz2 (kHz squared) as a measure of the subject's ability to modify their vocal tract for spectral differences.

The origin of vocal registers has generally been attributed to differential activation of cricothyroid and thyroarytenoid muscles in the larynx. Register shifts, however, have also been shown to be affected by glottal pressures exerted on vocal fold surfaces, which can change with loudness, pitch, and vowel. Here it is shown computationally and with empirical data that intraglottal pressures can change abruptly when glottal adductory geometry is changed relatively smoothly from convergent to divergent. An intermediate shape between large convergence and large divergence, namely, a nearly rectangular glottal shape with almost parallel vocal fold surfaces, is associated with mixed registration. It can be less stable than either of the highly angular shapes unless transglottal pressure is reduced and upper stiffness of vocal fold tissues is balanced with lower stiffness. This intermediate state of adduction is desirable because it leads to a low phonation threshold pressure with moderate vocal fold collision. Achieving mixed registration consistently across wide ranges of F0, lung pressure, and vocal tract shapes appears to be a balancing act of coordinating laryngeal muscle activation with vocal tract pressures. Surprisingly, a large transglottal pressure is not facilitative in this process, exacerbating the bi-stable condition and the associated register contrast.

A quantitative output-cost ratio (OCR) is proposed for objective use in voice production and is defined as the ratio of the acoustic output intensity to the collision intensity of the vocal folds. Measurement of the OCR is demonstrated in a laboratory experiment using 5 excised larynges and a transducer designed for use on human subjects. Data were gathered at constant fundamental frequency (150 Hz). Subglottal pressure was varied from 1.0 to 1.6 kPa, and glottal width at the vocal processes was varied from a pressed condition to a 2-mm gap. The OCR was plotted as a function of glottal width. With no vocal tract, the excised larynx experiments yielded a broad maxima in the OCR curves, across all subglottal pressure conditions, at about 0.6 mm. Computer simulations indicate that sharper maxima may occur when the influence of the vocal tract is taken into account. The potential clinical utility of the OCR is discussed for treatment of a wide range of voice disorders, including those involving both hyper- and hypoadduction.

Although advances in techniques for image acquisition and analysis have facilitated the direct measurement of three-dimensional vocal tract air space shapes associated with specific speech phonemes, little information is available with regard to changes in three-dimensional (3-D) vocal tract shape as a function of vocal register, pitch, and loudness. In this study, 3-D images of the vocal tract during falsetto and chest register phonations at various pitch and loudness conditions were obtained using electron beam computed tomography (EBCT). Detailed measurements and differences in vocal tract configuration and formant characteristics derived from the eight measured vocal tract shapes are reported.

Newly developed glottographic sensors, utilizing high-frequency propagating electromagnetic waves, were compared to a well-established electroglottographic device. The comparison was made on four male subjects under different phonation conditions, including three levels of vocal fold adduction (normal, breathy, and pressed), three different registers (falsetto, chest, and fry), and two different pitches. Agreement between the sensors was always found for the glottal closure event, but for the general wave shape the agreement was better for falsetto and breathy voice than for pressed voice and vocal fry. Differences are attributed to the field patterns of the devices. Whereas the electroglottographic device can operate only in a conduction mode, the electromagnetic device can operate in either the forward scattering (diffraction) mode or in the backward scattering (reflection) mode. Results of our tests favor the diffraction mode because a more favorable angle imposed on receiving the scattered (reflected) signal did not improve the signal strength. Several observations are made on the uses of the electromagnetic sensors for operation without skin contact and possibly in an array configuration for improved spatial resolution within the glottis.

A classical vocal exercise called "messa di voce" (Italian for "placing the voice") was used to study the symmetry of intensity increase and decrease in six trained singers. Ideally, the exercise is performed as a symmetric triangle, a linear increase in loudness, followed by a linear decrease. Given that some physiologic variables, like lung volume, undergo unidirectional change rather than a symmetric reversal, there is reason to believe that symmetries may not exist. It was found that highly trained singers who use large SPL ranges tend to abbreviate the decrescendo phase in comparison with the crescendo phase. In a few other cases, a plateau in SPL is reached, but an increase in loudness may still be perceived on the basis of a stronger vibrato or changes in timbre.

A set of ten vowel area functions, based on MRI measurements, has been parameterized by an “empirical orthogonal mode decomposition” which accurately represents each area function as the sum of the mean area function and proportional amounts of a series of orthogonal basis functions. The mean area function was found to possess a formant structure similar to that of a uniform tube (i.e., nearly equally spaced formants) suggesting that empirical orthogonal modes are perturbations on the mean (∼neutral) vowel shape much like past vocal tract analyses have considered perturbations on a uniform tube. The acoustic characteristics of the two most significant empirical orthogonal modes were examined, showing that both modes tend to increase the first formant as the modal amplitude coefficients are both increased from negative to positive values. However, the second formant was found to decrease in frequency for increasing values of the first modal coefficient and to increase for increasing values of the second mode coefficient. Next, a mapping between F1-F2 formant pairs and vocal tract area functions is proposed which is largely one-to-one but was initially limited by a constant vocal tract length. A possible method to include variable vocal tract length and higher ordered orthogonal modes in the mapping is given. The mode-to-formant mapping suggested the possibility of an inverse mapping to determine physiologically realistic area functions from a speech waveform and a simple example is presented. Finally, empirical orthogonal modes for a collection of ten vowels and eight consonants were derived and showed many similarities to those for the vowel-only case.

Magnetic resonance imaging (MRI) was used to acquire vocal tract shapes of ten vowels /i, I, [symbol: see text] a, [symbol: see text], o, [symbol: see text] u/ and two liquid approximants /3[symbol: see text], 1/ for a 27-year-old adult female. These images were complemented with additional images acquired with electron beam computed tomography (CT) of /i/ and /a/. Each 3-D shape was condensed into a set of cross-sectional areas of oblique sections perpendicular to the centerline of the vocal tract's long axis, resulting in an "area function." Formant frequencies computed for each area function showed reasonable similarity to those determined from the natural (recorded) speech of the imaged subject, but differences suggest that some of the imaged vocal tract shapes were articulated differently during imaging than during recording of natural speech, and also that imaging procedures may have compromised some accuracy for a few shapes. The formant calculations also confirmed the significant effect that the piriform sinus can have on lowering the formant frequencies. A comparison is made between area functions derived using both MRI and CT methods for the vowels /i/ and /a/. Additionally, the area functions reported in this study are compared with those from two previous studies and demonstrate general similarities in shape but also obvious differences that can be attributed to anatomical differences of the imaged subjects and to differences in imaging techniques and image processing methods.

An experiment with excised larynges was undertaken to investigate the interaction between acoustic pressures in a pseudotrachea and the amplitude of vibration of the vocal folds. Pressure was measured beneath the vocal folds at three specific moments of the vibratory cycle: (a) when the superior margin of the vocal folds began to separate, (b) when the vocal folds were maximally apart, and (c) when the inferior margin of the vocal folds began to touch. Results indicate that in half the larynges investigated, the maximum amplitude of vibration increased as a function of: (a) increased positive pressure at the moment of opening, and (b) reduced subglottal pressure when the vocal folds were maximally apart. The implications of these experiments regarding involuntary register transitions related to trachea resonance are discussed in light of a previously proposed register theory.

A method is reviewed for conversion of a microphone signal into calibrated Sound Pressure Level (SPL) units. The method follows American National Standards Institute (ANSI) standard for S1.4 SPL meters and requires an accurate SPL meter and an accurate calibration sound source for conversion. Accuracy and validation data from test signals and human phonation are provided. The results indicate that under typical speech conditions, an absolute accuracy of plus or minus 1.6 dB (type 1 SPL meter) can be obtained with a miniature head-mounted microphone.

This paper reports results of further experimentation on a previously developed physical model of the vocal-fold mucosa [Titze et al., J. Acoust. Soc. Am. 97, 3080-3084 (1995)]. The effects of vocal-fold thickness, epithelial membrane thickness, and prephonatory glottal geometry on phonation threshold pressure were studied. Phonation threshold pressures in the range of 0.13 to 0.34 kPa were observed for an 11-mm-thick vocal fold with a 70-micron-thick "epithelial" membrane for different "mucosal" fluid viscosities. Higher threshold pressure was always obtained for thinner vocal folds and thicker membranes. In another set of experiments, lowest offset threshold pressure was obtained for a rectangular or a near-rectangular prephonatory glottis (with a glottal convergence angle within about +/- 3 degrees). It ranged from 0.07 to 0.23 kPa for different glottal half-widths between 2.0 and 6.0 mm. The threshold for more convergent or divergent glottal geometries was consistently higher. This finding only partially agrees with previous analytical work which predicts a lowest threshold for a divergent glottis. The discrepancy between theory and data is likely to be associated with flow separation from a divergent glottis.

The Ritz method is used to calculate eigenmodes and eigenfrequencies in a continuum model of the vocal folds. The investigation represents a rectification and extension of previous studies, emphasizing the indispensability of utilizing natural boundary conditions when computing the characteristic modes of a system. Concurring with previous assertions, two of the lower-order eigenmodes are theorized to play a major role in facilitating self-oscillation of the folds during phonation. One mode, related to vertical phasing, is shown to have a more direct control over glottal convergence/divergence than indicated in previous calculations. Unlike lumped element models, the continuum model predicts that the eigenfrequencies of the two modes are closely spaced over an extensive range of tissue sizes and stiffnesses. This finding may help explain why the two modes entrain so naturally over a wide range of phonatory adjustments in human phonation.

The effect of convergent and divergent prephonatory glottal geometries on phonation threshold pressure was investigated using a previously reported physical model of the vocal fold mucosa [Titze et al., J. Acoust. Soc. Am. 97, 3080–3084 (1995)]. Lowest offset phonation threshold pressure in the range of 0.07 to 0.23 kPa was obtained for a rectangular or a near‐rectangular glottis (with convergent or divergent angle ≤3°) across different glottal half‐widths between 2.0 and 6.0 mm. Phonation threshold pressure for more convergent or divergent glottal geometries was consistently higher. This finding only partially agrees with previous analytical work which predicts a lowest phonation threshold pressure for a divergent glottis [I. R. Titze, J. Acoust. Soc. Am. 83, 1536–1552 (1988) and J. C. Lucero, J. Acoust. Soc. Am. 98, 779–784 (1995)]. The discrepancy between theory and data is likely to be associated with flow separation from a divergent glottis. [Work supported by NIH.]