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Acoustic analysis of vocal vibrato: A theoretical interpretation of data
Journal of Voice
Vol. 3, No. 1, pp. 36--43 © 1989 Raven Press, Ltd,, New York
Acoustic Analysis of Vocal Vibrato: A Theoretical Interpretation of Data Yoshiyuki Horii The Recording and Research Center, The Denver Center For The Performing Arts, Denver; Department of Communication Disorders and Speech Science, The University of Colorado, Boulder, Colorado, U.S.A.
Summary: Frequency and amplitude modulations and their phase relationships in vocal vibrato were investigated in an effort to integrate the current body of sometimes contradictory and confusing observations regarding this vocal phenomenon. A resonance-harmonics interaction alone was found to explain sufficiently the various phase relationships between Fo and amplitude modulations as well as the extent of amplitude modulations for most of the present data and many of the observations reported in the literature. Implications were discussed for physiological, aerodynamic, and perceptual investigations of vocal vibrato as well as for investigations comparing pathologic vocal tremor with vocal vibrato. Key Words: Vocal vibrato---Acoustic analysis--Frequency modulations-Amplitude modulations--Resonance-harmonics interaction--Vocal tremor.
Vocal vibrato was the subject of several early experimental studies in music, particularly those by Seashore and colleagues at the University of Iowa (I-3). Seashore (1) described vibrato as a "pulsation of pitch, usually accompanied with synchronous pulsations of loudness and timbre, of such extent and rate as to give a pleasing flexibility, tenderness, and richness to the tone" (p. 33). One area receiving increased attention is acoustic correlates of vocal vibrato (4-16). As the description by Seashore (1) quoted above indicates, acoustic parameters of vocal vibrato include measures of modulation rate, extent of fundamental frequency (F 0) and amplitude modulations, and their phase. Past descriptions of acoustic characteristics of vocal vibrato, however, were often contradictory and confusing at best.
Regarding the rate of Fo modulations in vibrato, some investigators have reported a wide range of 3-12 modulations/s (17), whereas others (6,10,16) have reported a narrower range of 4-7 modulations/ s. Vennard (6), for example, stated that 8-10 modulations/s may be regarded as a maximum. Reports on the extent of F 0 modulations were also variable, ranging from one-half to more than two semitones (6,15,17-21). The pitch and loudness levels at which the vibrato was produced was also indicated as an influence in determining the extent of Fo modulation (3,6,16,21). Although most researchers have agreed that the rate of amplitude modulation is the same as the rate of Fo modulations, some have reported the rate of amplitude modulation twice as large as that of F 0 modulation (6,15,18). Similarly, findings as to the extent of amplitude modulations have been equivocal. Shipp et al. (10) reported an unmeasurably small extent of amplitude modulations, whereas Gemelli et al. (17), as quoted by Luchsinger and Arnold (I6), and Rothman et al. (22) reported a range of a 2-3-dB to an 8-10-dB amplitude modulation. Many authors, however, ap-
Address correspondence and reprint requests to Dr. Y. Horii at Campus Box 409, Department of Communication Disorders and Speech Science, The University of Colorado, Boulder, CO 80309, U.S.A. A shortened version of this paper was presented at the 17th Voice Symposium: Care of the Professional Voice, June 5-10, 1988 at the Manhattan School of Music, New York, New York.
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ACOUSTIC A N A L Y S I S OF VOCAL VIBRATO
pear to accept 2-3 dB as the typical extent of amplitude modulations. Some doubt regarding perceptual significance of amplitude modulations has been also expressed: Vennard (6), for example, stated that "Much of what we seem to hear as variation in intensity is really our ears' interpretation of the pitch variation. However, there is some true intensity vibrato, at least part of the time" (p. 193). Many investigators, in addition, acknowledged the difficulty of accurate measurements of amplitude modulations (10,23,24). In order to describe temporal relationships between F0 and amplitude modulations in vibrato, one has to be able to obtain both Fo and amplitude measures as a function of time. As noted above, and to be discussed later, amplitude modulation measures were often difficult to obtain especially in a decibel scale. Thus, it was a tribute to the early researchers at the University of Iowa, who reported their findings as early as 1922, that they were able to demonstrate the various temporal relationships between F0 and amplitude modulations in vibrato. Initially, the amplitude fluctuations were considered to be synchronous or in phase with the F o fluctuations (1,25). Kwalwasser (26), however, reported both "parallel" and "opposite" vibrato where Fo and amplitude modulations were in phase in the former and out of phase in the latter. In addition, Kwalwasser reported "pitch" vibrato that did not evidence any amplitude modulations, "intensity" vibrato that did not accompany F 0 modulation, and "unusual" situations where a vibrato type changed from " p a r a l l e l " to " o p p o s i t e , " " p i t c h " to "parallel," and so on. These basic notions of frequency and amplitude modulations in vocal vibrato, and reports of various phase relationships between Fo and amplitude can also be found in the current literature. Researchers classify various Fo/amplitude patterns of vibrato into "frequency vibrato" and "amplitude vibrato." Ramig and Shipp (27), for example, categorized their subjects, nine singers, into two groups: three who demonstrated frequency modulations only, and six who demonstrated both frequency and amplitude modulations. None evidenced amplitude modulations alone. These investigators further provided graphic displays of Fo and amplitude where there was no apparent phase relationships between F0 and amplitude and also an example where Fo modulations were in phase with amplitude modulations. The purpose of this article is to offer a theoretical
37
interpretation of the acoustical data on amplitude modulations and phase relationships between amplitude and frequency modulations in vocal vibrato. SOME SPECTROGRAPHIC EXAMPLES VERIFYING THE PAST OBSERVATIONS Various observations regarding the frequency and amplitude modulations and their phase relationships in vocal vibrato were verified in our own data (11-14). Some spectrographic examples are presented below (Figs. 1-5). Spectrograms were made using a sound spectrograph (Digital Sona-graph Model 7800, Kay Elemetrics). Recorded vibrato voices were played into one channel while the rectiffed and smoothed voice signals extracting amplitudes were fed into another channel of the spectrograph. The signal on the first channel was analyzed with a narrowband filter (45 Hz) and displayed on the bottom half of the spectrogram with an expanded frequency scale of 2,000-4,000 Hz. Frequency modulations, therefore, were easier to observe since higher harmonic frequencies magnify the F0 modulations. The upper half of the spectrogram was used to display the extracted amplitude signal. Due to the integration time, the amplitude trace was 30 ms delayed relative to the narrow band spectrogram, as indicated in the figures. Three spectrographic examples of vocal vibrato samples that did not evidence clear amplitude mod-
FIG. 1. Three spectrographic examples for voices with nondefinitive amplitude modulations. Journal of Voice, Vol. 3, No. 1, 1989
38
Y. H O R H
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ulations are shown in Fig. 1. Figure 2 shows three spectrograms of vocal vibrato samples that evidenced amplitude modulations at the same rate as the frequency modulations and which demonstrated an in-phase relationship between the amplitude and frequency modulations (after the 30 ms adjustment). Figure 3, on the other hand, shows three spectrographic examples of the vocal vibrato with an out-of-phase relationship between the amplitude and frequency modulations. Two spectrograms of the vocal vibrato samples with the double-peaked amplitude modulations are shown in Fig. 4. Figure 5 shows drifting phase relationships where amplitude modulations changed from double-peaked to outof-phase in one case (the top spectrogram) while they changed from double-peaked to in-phase relationships in the other case (the bottom spectrogram).
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FIG. 3. Three spectrographic examples for voices with outof-phase relationships.
my own data (11-14) as well as those reported in the literature led to a hypothesis that most amplitude modulations in vibrato, at least for our voice sampies, are the results of resonance-harmonics interaction rather than an active amplitude oscillation. This hypothesis is commensurate with many current and past observations regarding vocal vibrato as well as the notion of "timbre vibrato," which is described as a periodic change in the strength of individual partials (1,24,28,29). As will be shown,
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RESONANCE--HARMONICS INTERACTION HYPOTHESIS An important consideration in interpreting the resuits on the magnitude of amplitude modulation and the phase relationships between Fo and amplitude modulation are amplitude modulations strictly due to a resonance-harmonics interaction. Review of Journal of Voice, Vol. 3, No. 1, 1989
FIG. 4. Two spectrographic examples of phonations showing double-peaked amplitude modulation for each F0 modulation.
ACO USTIC A N A L YSIS OF VOCAL VIBRA TO SOmsec
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the hypothesis not only supports the vocal tract resonance as a major cause of the presence of amplitude modulations in vocal vibrato, as alluded to by some investigators (23,30), but also predicts quantitatively expected magnitude of amplitude modulations and phase relations between F o and amplitude modulations. An intensity function derived from the resonance-harmonics interaction hypothesis Intensity variations of voice as a function of F0 can be generally estimated by summing the square of harmonic amplitudes falling under a spectral envelope determined by the size and shape of the vocal tract, and converting to decibel (31). As F0 varco
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FIG. 6. An illustration of overall intensity change under a spectral envelope with two different fundamental frequencies (and their harmonics).
ies, harmonic frequencies, which are integer multiples of Fo, vary and their amplitudes are modified by the resonance characteristics of the vocal tract, resulting in changes in the overall intensity as is illustrated in Fig. 6. Figure 7 shows a theoretical intensity function expected strictly from resonance-harmonics interactions using a spectral envelope appropriate for/a/ derived from a transmission line analog of the vocal tract (32,33). In calculating the overall intensity, harmonics up to 2,000 Hz were considered. The abscissa represents fundamental frequency in a logarithmic scale (the magnitude of two semitones is indicated in the figure), and the ordinate represents relative intensity in dB. The general patterns of intensity functions remain the same as the vocal tract lengths are changed, although specific frequency locations of the maxima and minima would be shifted systematically. Predictions by the resonance-harmonics interaction hypothesis The hypothetical intensity function in this figure predicts certain systematic observations regarding the results of the acoustical analysis if the resonance-harmonics interaction alone was assumed responsible for the amplitude modulations in vocal vibrato. More specifically, the following aspects are predicted: (a) phase relationships between Fo and amplitude, (b) size of amplitude modulations ~, and (c) double-peaked amplitude modulations at certain fundamental frequencies. With all other things being equal, the intensity function in Fig. 7 shows that the in-phase relationship occurs if Fo modulates at regions where the intensity function has positive slopes: as Fo inJournal of Voice, Vol. 3, No. 1, 1989
40
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FIG. 8. Theoretical amplitude modulations as a function of time, derived from the intensity function in Fig. 7 when Fo modulates between 260 Hz and 280 Hz (A) and between 228 Hz and 248 Hz
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creases, the overall intensity increases, and as Fo decreases, the overall intensity decreases. The outof-phase relationship results if F 0 modulates at regions where the intensity function has negative slope: as F 0 increases, the overall intensity decreases, and as Fo decreases, the overall intensity increases. The magnitudes of the intensity increase or decrease for one-semitone modulations are often - 2 - 3 dB. Amplitude modulations have smaller magnitudes and may not be discernible if Fo modulations occur at regions where the variation of intensity is minimal in the figure. It is also easily conceivable that the phase relationships may drift from in-phase to out-of-phase or vice versa within one phonation at one pitch level if the vocal tract shapes and, therefore, resonances change while one sings in vocal vibrato. As a special case, if Fo varies exactly around the frequency of an intensity maximum or minimum, there will be two amplitude modulations for each F 0 modulation. Figure 8 shows expected amplitude and Fo traces when Fo oscillates sinusoidally around 270 Hz where a minimum exists (Fig. 8A) and around 238 Hz where a maximum exists (Fig. 8B) in the intensity function. Both amplitude traces were derived from the intensity function in Fig. 7. The double-peaked amplitude traces shown earlier in Fig. 4 appear to exemplify this situation. In particular, it may be noted in Fig. 4 that in the amplitude trace, when the 30-ms delay relative to the harmonic frequency trace is taken into consideration, one amplitude peak coincides with increasing F 0 and the other amplitude peak accompanies with decreasing Fo. This temporal pattern was precisely Journal of Voice, Vol. 3, No. I, 1989
what was predicted by this theoretical model when F o modulated around an intensity maximum. The observation of the double-peaked amplitude modulation in vocal vibrato, however, was not new. Vennard (6), in particular, reported 2 amplitude modulations/Fo modulation and stated that the "tendency for the intensity vibrato to double the rate of the pitch vibrato is seen in varying degrees, depending upon the energy being used in the production. It is difficult to say at this point how significant this discovery is. More analysis including many singers is needed" (p. 202). The resonance-harmonics hypothesis successfully clarifies this once puzzling observation of the double-peaked amplitude modulations. Incidentally, it makes sense that some studies reported greater amplitude modulation rates than F0 modulation rates because of these double peaks of amplitude modulation. Limitations of the resonance-harmonics interaction hypothesis It should be noted that the hypothesis does not state how the frequency modulations be produced. In other words, it does not preclude an active subglottic pressure oscillation as a possible mechanism for vocal vibrato production. As Titze (34) recently reported, subglottic pressure modulations of -10% would produce appropriate sizes of frequency modulations. It should be also noted that there were, of course, a certain number of cases in our data, especially extremely low- or high-pitched phonations and those with varying phase relationships between F 0 and amplitude modulations, to which application of the resonance-harmonics interaction hypothesis produced nondefinitive conclusions. This discrepancy may be due to (a) the lack of knowledge about the exact vocal tract configurations during the phonation, (b) the perturbation of spectral envelopes, (c) possible differences in the laryngeal sound source characteristics at different pitch and intensity levels, and (d) differences in vocal tract resonance characteristics between normal speech and singing. As exemplified in so-called singer's formant (30,35,36), some nondefinitive agreement between the predictions and actual observations is not totally unexpected if the spectral envelope of/aJ in singing is considerably different from the one used in generating the present intensity function. Perturbation of spectral envelopes can be caused by, for example, vertical movements of the larynx or movements of the soft palate and jaw (6). Sung vowel phonations, in addition, may have greater
ACOUSTIC A N A L Y S I S OF VOCAL VIBRATO
amplitudes of higher harmonics than normal phonations at the level of laryngeal sound source. Overall, however, there were sufficient agreements between the observed data and predicted behaviors of F0 and amplitude modulations in vocal vibrato. Comments on amplitude measurements
In addition to the variable nature of the extent of amplitude modulation in vocal vibrato, methods of extracting amplitude may be responsible for some discrepancy of results among the studies. We examined in our preliminary study three methods of amplitude extraction. They were an analog method using a Bruel and Kjaer graphic level recorder and two digital methods where root mean square (RMS) and peak amplitudes were derived for each fundamental period. With the graphic level method, the level trace, either by RMS or peak setting with a fast writing speed (1,000 mm/s), did not yield more than 0.5-riB variations, just as Shipp et al. (10) reported. The integration time and full-wave rectification of the intensity analyzer appear to be the main cause of the failure in producing measurable intensity traces for vocal vibrato. The RMS amplitude calculated for each fundamental period was more sensitive to short-term variations than the graphic level measures, but was not as sensitive as the peak amplitude. The pitch-synchronous peak amplitude more closely represented the amplitude envelope of the voice waveform. Extreme caution, therefore, needs to be exercised in comparing data on extent of amplitude modulations in vocal vibrato. In addition, it appears mandatory for researchers to report specifics of their intensity measurement methods in reporting amplitude modulations in vocal vibrato. Implications to future investigations of vocal vibrato In our studies, all singers (15 so far) demonstrated F0 modulations in vocal vibrato, and none evidenced amplitude modulations only or amplitude modulations far exceeding the magnitudes expected from the resonance-harmonics interaction alone. In other words, nonequivocal, pure " a m p l i t u d e vibrato" singers are yet to be found. This raises a, question of whether or not those amplitude modulations reported by a number of researchers in the past referred to the passive amplitude variations caused by the resonance-harmonics interaction. Since the number of subjects in our studies is rather Small, a larger sample of singers might indeed reveal
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a small proportion of singers who use so-called amplitude vibrato. In either case, clearer definitions of "vibrato," "frequency vibrato," and "amplitude vibrato" need to be established and standardized. In view of the results of the current investigation, a modification of the following definition of vibrato, given by U.S.A. Standard Institute (1960) and quoted by Large (24) appears warranted: " a family of tonal effects in music that depend upon periodic variations of one or more characteristics of the sound wave. Note: When the particular characteristics are known, the term 'vibrato' should be modified accordingly, e.g., frequency vibrato, amplitude vibrato, phase vibrato, and so forth." (p. 39.) In order to classify singers as users of amplitude vibrato, the amplitude modulations have to be either present by themselves without concomitant Fo modulation or the amplitude modulations should persist over a wide range of Fo without predicted amplitude magnitudes or predicted phase relationships with F0. Perceptual significance of such amplitude modulations, and discriminability of the amplitude modulations in the presence of F 0 and "timbre" modulations in particular, needs to be further investigated. Undoubtedly, any normal phonation is a result of well-coordinated neuromuscular activities involving respiratory, laryngeal, and articulatory mechanisms with associated physiologic, aerodynamic, acoustic, and perceptual consequences. Thus, there is no reason to suspect that the general regulatory mechanisms of frequency and intensity are not operative during vibrato phonation. The frequencyraising maneuver of the cricothyroid muscles (37), for example, should be involved in producing highpitched phonations. Increased subglottic pressure is also expected at high-pitch conditions as more vocal effort, according to many unsolicited comments of the subjects, was required at these conditions (38-40). An important question, then, is whether or not the same frequency and intensity regulatory mechanisms are responsible for the Fo and amplitude modulations in vocal vibrato. The present results suggest that consideration of an amplitude modulation mechanism may be put on hold for t h e t i m e being, unless particular phonations under study are indeed true "amplitude" or "intensity" vibrato. As to the mechanism of F o modulations in vibrato, it is interesting to note that Ladefoged (41) suggested the possibility of an entirely different physiological mechanism from the cricothyroid-based mechanism Journal of Voice, Vol. 3, No. 1, 1989
42
Y. H O R H
of frequency adjustment. Ladefoged suggested that pitch adjustment in vibrato "involves some adjustment of the position o f the arytenoid cartilages" and stated that " t h e i r spacing (their distance apart) is varied as well as their tension" (p. 262). He attributed pitch modulation to this tension variation and intensity modulation to the spacing of the a r y t e n o i d cartilages, which c a u s e s variation o f amount of force as the vocal folds come together. In relation to amplitude modulation in vocal vibrato, Large (24) and Large and Iwata (42) reported that airflow was synchronous with amplitude modulations in vibrato. Mason and Zemlin (20) reported that the activity of the cricothyroid muscle was generally in phase with the crest of the frequency and intensity vibrato, which they found at all times. Zemlin (37), furthermore, suggested that the subglottic air pressure fluctuations may account for the amplitude vibrato. These findings and statements need to be interpreted in a new light if the resonance-harmonics interaction indeed accounts for most of the amplitude modulations and their phase relationships with Fo modulations. In particular, it appears necessary to differentiate clearly amplitude modulations due to the resonance-harmonics interaction and those amplitude modulations actively produced by singers. Implications for future comparative studies of vocal vibrato and pathological vocal tremor T h e s a m e p r o b l e m in d e f i n i n g " a m p l i t u d e vibrato" articulated above applies also to studies of pathologic vocal tremor. Several researchers, including myself, reported that vocal modulations in sustained vowel phonations, produced presumably "as steadily as possible" by individuals with spastic dysphonia and with neurological disorders (such as Parkinson's disease, amyotrophic multiple sclerosis, head injury, etc.), were characterized predominantly by amplitude modulations (9-12,27). Often such investigations compare frequency and amplitude modulations observed in the tremorous phonations to those of singers' vibrato and proceed to speculate on underlying physiological and neurological mechanisms of vibrato and tremor. In this process, again, it appears important to differentiate a m p l i t u d e m o d u l a t i o n s due to the r e s o n a n c e harmonics interaction and amplitude modulations unaccounted for by the interaction both for singers' vibrato and pathologic vocal tremor. Without going into detail, it may be noted that results o f comparisons of the present findings with those of pathoJournal of Voice, Vol. 3, No. 1, 1989
logic vocal tremor (11,12) strengthened the claim that vocal modulations in sustained phonations by pathologic speakers are both frequency and amplitude modulations, the latter o f which originates from an additional source (possibly more active contributions of the respiratory components) to the resonance--harmonics interaction. Acknowledgment: This work was supported in part by the National Institutes of Health, grant number RO 1NS24409. REFERENCES 1. Seashore CE. The vibrato. Iowa City, Iowa: University of Iowa Press, 1932:30-7. 2. Seashore CE, Tiffin J. Summary of the established facts in experimental studies in the vibrato up to 1932. University of Iowa, studies in psychology of music. Iowa City: University of Iowa Press, 1932:344-76. 3. Seashore CE. The psychology of music. New York: McGraw-Hill, 1938. 4. Lawrence V, Weinberg B, eds. Care of the professional voice. New York: The Voice Foundation, 1979. 5. Large J, ed. Contributions of voice research to singing. Houston, Texas: College-HillPress, 1980. 6. Vennard W. Singing. New York: Carl Fischer, 1967. 7. Wyke B, ed. Ventilatory and phonatory control systems. New York: Oxford University Press, 1974:248--64. 8. Deutsch D, ed. The psychology of music. New York: Academic Press, 1982. 9. Izdebski K, Dedo HH. Characteristics of voice tremor in spastic dysphonia: a preliminary study. In: Lawrence V, Weinberg B, eds. Transcripts of the eighth symposium on care of the professional voice. 1979:Part III, 17-23. 10. Shipp T, Leanderson R, Sundberg J. Vocal vibrato. In: Lawrence V, Weinberg B, eds. Transcripts of the eighth symposium on care of the professional voice. 1979:Part I, 46-9. 11. Horii Y. Correlation between fundamental frequency and intensity in vibrato and vocal tremor. Presented at the XXth international congress of logopedics and phoniatrics, Tokyo, Japan, August 1986. 12. Horii Y. Sustained phonations produced by dysarthric patients. ASHA 1986;28:145. 13. Horii Y, Hata K. Phase relationships between frequency and amplitude modulations in vocal vibrato. Folia Phoniatr (Basel) (in press). 14. Horii Y. Vowel differences in vibrato frequency/amplitude modulations. ASHA 1987;29:78. 15. Sj6strom L. Experimentell-phonetischeuntersuchungen des vibratophanomens der singstimme, lOth Nord otolaryngol Kongr, Stockholm, 1947. 16. Luchsinger R, Arnold G. Voice--speech--language. Belmont: Wadsworth, 1965. 17. Gemelli A, Sacerdote G, Bellussi G. Analisi elettroacustica della voce cantata. Boll Soc ltal Fonet Sperim 1954;4:3-8. 18. PommezJ. Etude acoustique du vibrato de la voix chantee. Rev Laryngol Otol Rhinol (Bord) 1962;83:249--64. 19. Mason RM. A study of the physiologicalmechanisms of vocal vibrato [Dissertation]. University of Illinois, 1965. 20. Mason R, Zemlin W. The phenomenon of vocal vibrato. The NATS Bulletin 1966;37:12-7. 21. Winckel F. Physikalische kriterien fur objektive stimmbeurteilung. Folia Phoniatr (Basel) I953;5:232. 22. Rothman HB, Nielson K, Hicks JW Jr. Perceptual classifi-
A C O U S T I C A N A L YSIS O F V O C A L V I B R A T O
23.
24. 25. 26. 27. 28. 29. 30. 31.
cation of voice movements. In: Lawrence V, Weinberg B, eds. Transcripts of the eighth symposium on care of the professional voice. 1979:Part I, 57-9. Coleman RF. Acoustic and perceptual factors in vibrato. In: Lawrence V, Weinberg B, eds. Transcripts of the eighth symposium on care of the professional voice. 1979:Part I, 36-7. Large J. An air flow study of vocal vibrato. In: Lawrence V, Weinberg B, eds. Transcripts of the eighth symposium on care of the professional voice. 1979:Part I, 39-45. Schoen M. The pitch factor in artistic singing. Psychol Med [Monogr Suppl] 1922;31:230-359. Kwalwasser J. The vibrato. Psychol Med [Monogr Suppl] 1926;36:84-108. Ramig LA, Shipp T. Comparative measures of vocal tremor and vocal vibrato. Presented at the fifteenth symposium on care of the professional voice, New York, June 1986. Potter R, Kopp G, Kopp H. Visible speech. New York: D. Van Nostrand, 1947. Stevens KN. Physical aspects of ventilatory and phonatory behavior. In: Wyke B, ed. Ventilatory and phonatory control systems. New York: Oxford University Press, 1974. Sundberg J. Studies of the soprano voice. Research in Singing 1977;1:25-35. House AS. A note on optimal vocal frequency. J Speech Hear Res 1959;2:55-60.
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32. Dunn HK. The calculation of vowel resonances, and an electrical vocal tract. J Acoust Soc A m 1950;22:740-53. 33. Stevens KN, House AS. An acoustical theory of vowel production and some of its implications. J Speech Hear Res 1961 ;4:303-20. 34. Titze I. Singing synthesis with models of phonatory and articulatory kinematics. J Acoust Soc Am 1988;83:$30. 35. Sundberg J. Formant structure and articulation of spoken and sung vowels. Folia Phoniatr (Basel) 1970;22:28--48. 36. Wolf SK, Stanley D, Sette WJ. Quantitative studies on the singing voice. J Acoust Soc Am 1934;6:25-33. 37. Zemlin WR. Speech and hearing science. Englewood Cliffs, New Jersey: Prentice-Hall, 1968. 38. Isshiki N. Regulatory mechanism of voice intensity variation. J Speech Hear Res 1964;7:17-29. 39. Isshiki N. Vocal intensity and air flow rate. Folia Phoniatr (Basel) 1965;17:92-104. 40. Large J, Iwata S, yon Leden H. The primary female register transition in singing: aerodynamic study. Folia Phoniatr (Basel) 1970;22:285-396. 41. Ladefoged P. Respiration, laryngeal activity and linguistics. In: Wyke B, ed. Ventilatory and phonatory control systems. New York: Oxford University Press, 1974:29%314. 42. Large J, Iwata S. Aerodynamic study of vibrato and voluntary "straight tone" pairs in singing. Folia Phoniatr (Basel) 1971 ;23:50--65.
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Journal of Voice, Vol. 3, No. 1, 1989
Vol. 3, No. 1, pp. 36--43 © 1989 Raven Press, Ltd,, New York
Acoustic Analysis of Vocal Vibrato: A Theoretical Interpretation of Data Yoshiyuki Horii The Recording and Research Center, The Denver Center For The Performing Arts, Denver; Department of Communication Disorders and Speech Science, The University of Colorado, Boulder, Colorado, U.S.A.
Summary: Frequency and amplitude modulations and their phase relationships in vocal vibrato were investigated in an effort to integrate the current body of sometimes contradictory and confusing observations regarding this vocal phenomenon. A resonance-harmonics interaction alone was found to explain sufficiently the various phase relationships between Fo and amplitude modulations as well as the extent of amplitude modulations for most of the present data and many of the observations reported in the literature. Implications were discussed for physiological, aerodynamic, and perceptual investigations of vocal vibrato as well as for investigations comparing pathologic vocal tremor with vocal vibrato. Key Words: Vocal vibrato---Acoustic analysis--Frequency modulations-Amplitude modulations--Resonance-harmonics interaction--Vocal tremor.
Vocal vibrato was the subject of several early experimental studies in music, particularly those by Seashore and colleagues at the University of Iowa (I-3). Seashore (1) described vibrato as a "pulsation of pitch, usually accompanied with synchronous pulsations of loudness and timbre, of such extent and rate as to give a pleasing flexibility, tenderness, and richness to the tone" (p. 33). One area receiving increased attention is acoustic correlates of vocal vibrato (4-16). As the description by Seashore (1) quoted above indicates, acoustic parameters of vocal vibrato include measures of modulation rate, extent of fundamental frequency (F 0) and amplitude modulations, and their phase. Past descriptions of acoustic characteristics of vocal vibrato, however, were often contradictory and confusing at best.
Regarding the rate of Fo modulations in vibrato, some investigators have reported a wide range of 3-12 modulations/s (17), whereas others (6,10,16) have reported a narrower range of 4-7 modulations/ s. Vennard (6), for example, stated that 8-10 modulations/s may be regarded as a maximum. Reports on the extent of F 0 modulations were also variable, ranging from one-half to more than two semitones (6,15,17-21). The pitch and loudness levels at which the vibrato was produced was also indicated as an influence in determining the extent of Fo modulation (3,6,16,21). Although most researchers have agreed that the rate of amplitude modulation is the same as the rate of Fo modulations, some have reported the rate of amplitude modulation twice as large as that of F 0 modulation (6,15,18). Similarly, findings as to the extent of amplitude modulations have been equivocal. Shipp et al. (10) reported an unmeasurably small extent of amplitude modulations, whereas Gemelli et al. (17), as quoted by Luchsinger and Arnold (I6), and Rothman et al. (22) reported a range of a 2-3-dB to an 8-10-dB amplitude modulation. Many authors, however, ap-
Address correspondence and reprint requests to Dr. Y. Horii at Campus Box 409, Department of Communication Disorders and Speech Science, The University of Colorado, Boulder, CO 80309, U.S.A. A shortened version of this paper was presented at the 17th Voice Symposium: Care of the Professional Voice, June 5-10, 1988 at the Manhattan School of Music, New York, New York.
36
ACOUSTIC A N A L Y S I S OF VOCAL VIBRATO
pear to accept 2-3 dB as the typical extent of amplitude modulations. Some doubt regarding perceptual significance of amplitude modulations has been also expressed: Vennard (6), for example, stated that "Much of what we seem to hear as variation in intensity is really our ears' interpretation of the pitch variation. However, there is some true intensity vibrato, at least part of the time" (p. 193). Many investigators, in addition, acknowledged the difficulty of accurate measurements of amplitude modulations (10,23,24). In order to describe temporal relationships between F0 and amplitude modulations in vibrato, one has to be able to obtain both Fo and amplitude measures as a function of time. As noted above, and to be discussed later, amplitude modulation measures were often difficult to obtain especially in a decibel scale. Thus, it was a tribute to the early researchers at the University of Iowa, who reported their findings as early as 1922, that they were able to demonstrate the various temporal relationships between F0 and amplitude modulations in vibrato. Initially, the amplitude fluctuations were considered to be synchronous or in phase with the F o fluctuations (1,25). Kwalwasser (26), however, reported both "parallel" and "opposite" vibrato where Fo and amplitude modulations were in phase in the former and out of phase in the latter. In addition, Kwalwasser reported "pitch" vibrato that did not evidence any amplitude modulations, "intensity" vibrato that did not accompany F 0 modulation, and "unusual" situations where a vibrato type changed from " p a r a l l e l " to " o p p o s i t e , " " p i t c h " to "parallel," and so on. These basic notions of frequency and amplitude modulations in vocal vibrato, and reports of various phase relationships between Fo and amplitude can also be found in the current literature. Researchers classify various Fo/amplitude patterns of vibrato into "frequency vibrato" and "amplitude vibrato." Ramig and Shipp (27), for example, categorized their subjects, nine singers, into two groups: three who demonstrated frequency modulations only, and six who demonstrated both frequency and amplitude modulations. None evidenced amplitude modulations alone. These investigators further provided graphic displays of Fo and amplitude where there was no apparent phase relationships between F0 and amplitude and also an example where Fo modulations were in phase with amplitude modulations. The purpose of this article is to offer a theoretical
37
interpretation of the acoustical data on amplitude modulations and phase relationships between amplitude and frequency modulations in vocal vibrato. SOME SPECTROGRAPHIC EXAMPLES VERIFYING THE PAST OBSERVATIONS Various observations regarding the frequency and amplitude modulations and their phase relationships in vocal vibrato were verified in our own data (11-14). Some spectrographic examples are presented below (Figs. 1-5). Spectrograms were made using a sound spectrograph (Digital Sona-graph Model 7800, Kay Elemetrics). Recorded vibrato voices were played into one channel while the rectiffed and smoothed voice signals extracting amplitudes were fed into another channel of the spectrograph. The signal on the first channel was analyzed with a narrowband filter (45 Hz) and displayed on the bottom half of the spectrogram with an expanded frequency scale of 2,000-4,000 Hz. Frequency modulations, therefore, were easier to observe since higher harmonic frequencies magnify the F0 modulations. The upper half of the spectrogram was used to display the extracted amplitude signal. Due to the integration time, the amplitude trace was 30 ms delayed relative to the narrow band spectrogram, as indicated in the figures. Three spectrographic examples of vocal vibrato samples that did not evidence clear amplitude mod-
FIG. 1. Three spectrographic examples for voices with nondefinitive amplitude modulations. Journal of Voice, Vol. 3, No. 1, 1989
38
Y. H O R H
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FIG. 2. Three spectrographic examples for voices with in-phase relationships.
ulations are shown in Fig. 1. Figure 2 shows three spectrograms of vocal vibrato samples that evidenced amplitude modulations at the same rate as the frequency modulations and which demonstrated an in-phase relationship between the amplitude and frequency modulations (after the 30 ms adjustment). Figure 3, on the other hand, shows three spectrographic examples of the vocal vibrato with an out-of-phase relationship between the amplitude and frequency modulations. Two spectrograms of the vocal vibrato samples with the double-peaked amplitude modulations are shown in Fig. 4. Figure 5 shows drifting phase relationships where amplitude modulations changed from double-peaked to outof-phase in one case (the top spectrogram) while they changed from double-peaked to in-phase relationships in the other case (the bottom spectrogram).
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FIG. 3. Three spectrographic examples for voices with outof-phase relationships.
my own data (11-14) as well as those reported in the literature led to a hypothesis that most amplitude modulations in vibrato, at least for our voice sampies, are the results of resonance-harmonics interaction rather than an active amplitude oscillation. This hypothesis is commensurate with many current and past observations regarding vocal vibrato as well as the notion of "timbre vibrato," which is described as a periodic change in the strength of individual partials (1,24,28,29). As will be shown,
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RESONANCE--HARMONICS INTERACTION HYPOTHESIS An important consideration in interpreting the resuits on the magnitude of amplitude modulation and the phase relationships between Fo and amplitude modulation are amplitude modulations strictly due to a resonance-harmonics interaction. Review of Journal of Voice, Vol. 3, No. 1, 1989
FIG. 4. Two spectrographic examples of phonations showing double-peaked amplitude modulation for each F0 modulation.
ACO USTIC A N A L YSIS OF VOCAL VIBRA TO SOmsec
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the hypothesis not only supports the vocal tract resonance as a major cause of the presence of amplitude modulations in vocal vibrato, as alluded to by some investigators (23,30), but also predicts quantitatively expected magnitude of amplitude modulations and phase relations between F o and amplitude modulations. An intensity function derived from the resonance-harmonics interaction hypothesis Intensity variations of voice as a function of F0 can be generally estimated by summing the square of harmonic amplitudes falling under a spectral envelope determined by the size and shape of the vocal tract, and converting to decibel (31). As F0 varco
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FIG. 6. An illustration of overall intensity change under a spectral envelope with two different fundamental frequencies (and their harmonics).
ies, harmonic frequencies, which are integer multiples of Fo, vary and their amplitudes are modified by the resonance characteristics of the vocal tract, resulting in changes in the overall intensity as is illustrated in Fig. 6. Figure 7 shows a theoretical intensity function expected strictly from resonance-harmonics interactions using a spectral envelope appropriate for/a/ derived from a transmission line analog of the vocal tract (32,33). In calculating the overall intensity, harmonics up to 2,000 Hz were considered. The abscissa represents fundamental frequency in a logarithmic scale (the magnitude of two semitones is indicated in the figure), and the ordinate represents relative intensity in dB. The general patterns of intensity functions remain the same as the vocal tract lengths are changed, although specific frequency locations of the maxima and minima would be shifted systematically. Predictions by the resonance-harmonics interaction hypothesis The hypothetical intensity function in this figure predicts certain systematic observations regarding the results of the acoustical analysis if the resonance-harmonics interaction alone was assumed responsible for the amplitude modulations in vocal vibrato. More specifically, the following aspects are predicted: (a) phase relationships between Fo and amplitude, (b) size of amplitude modulations ~, and (c) double-peaked amplitude modulations at certain fundamental frequencies. With all other things being equal, the intensity function in Fig. 7 shows that the in-phase relationship occurs if Fo modulates at regions where the intensity function has positive slopes: as Fo inJournal of Voice, Vol. 3, No. 1, 1989
40
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FIG. 8. Theoretical amplitude modulations as a function of time, derived from the intensity function in Fig. 7 when Fo modulates between 260 Hz and 280 Hz (A) and between 228 Hz and 248 Hz
(B).
creases, the overall intensity increases, and as Fo decreases, the overall intensity decreases. The outof-phase relationship results if F 0 modulates at regions where the intensity function has negative slope: as F 0 increases, the overall intensity decreases, and as Fo decreases, the overall intensity increases. The magnitudes of the intensity increase or decrease for one-semitone modulations are often - 2 - 3 dB. Amplitude modulations have smaller magnitudes and may not be discernible if Fo modulations occur at regions where the variation of intensity is minimal in the figure. It is also easily conceivable that the phase relationships may drift from in-phase to out-of-phase or vice versa within one phonation at one pitch level if the vocal tract shapes and, therefore, resonances change while one sings in vocal vibrato. As a special case, if Fo varies exactly around the frequency of an intensity maximum or minimum, there will be two amplitude modulations for each F 0 modulation. Figure 8 shows expected amplitude and Fo traces when Fo oscillates sinusoidally around 270 Hz where a minimum exists (Fig. 8A) and around 238 Hz where a maximum exists (Fig. 8B) in the intensity function. Both amplitude traces were derived from the intensity function in Fig. 7. The double-peaked amplitude traces shown earlier in Fig. 4 appear to exemplify this situation. In particular, it may be noted in Fig. 4 that in the amplitude trace, when the 30-ms delay relative to the harmonic frequency trace is taken into consideration, one amplitude peak coincides with increasing F 0 and the other amplitude peak accompanies with decreasing Fo. This temporal pattern was precisely Journal of Voice, Vol. 3, No. I, 1989
what was predicted by this theoretical model when F o modulated around an intensity maximum. The observation of the double-peaked amplitude modulation in vocal vibrato, however, was not new. Vennard (6), in particular, reported 2 amplitude modulations/Fo modulation and stated that the "tendency for the intensity vibrato to double the rate of the pitch vibrato is seen in varying degrees, depending upon the energy being used in the production. It is difficult to say at this point how significant this discovery is. More analysis including many singers is needed" (p. 202). The resonance-harmonics hypothesis successfully clarifies this once puzzling observation of the double-peaked amplitude modulations. Incidentally, it makes sense that some studies reported greater amplitude modulation rates than F0 modulation rates because of these double peaks of amplitude modulation. Limitations of the resonance-harmonics interaction hypothesis It should be noted that the hypothesis does not state how the frequency modulations be produced. In other words, it does not preclude an active subglottic pressure oscillation as a possible mechanism for vocal vibrato production. As Titze (34) recently reported, subglottic pressure modulations of -10% would produce appropriate sizes of frequency modulations. It should be also noted that there were, of course, a certain number of cases in our data, especially extremely low- or high-pitched phonations and those with varying phase relationships between F 0 and amplitude modulations, to which application of the resonance-harmonics interaction hypothesis produced nondefinitive conclusions. This discrepancy may be due to (a) the lack of knowledge about the exact vocal tract configurations during the phonation, (b) the perturbation of spectral envelopes, (c) possible differences in the laryngeal sound source characteristics at different pitch and intensity levels, and (d) differences in vocal tract resonance characteristics between normal speech and singing. As exemplified in so-called singer's formant (30,35,36), some nondefinitive agreement between the predictions and actual observations is not totally unexpected if the spectral envelope of/aJ in singing is considerably different from the one used in generating the present intensity function. Perturbation of spectral envelopes can be caused by, for example, vertical movements of the larynx or movements of the soft palate and jaw (6). Sung vowel phonations, in addition, may have greater
ACOUSTIC A N A L Y S I S OF VOCAL VIBRATO
amplitudes of higher harmonics than normal phonations at the level of laryngeal sound source. Overall, however, there were sufficient agreements between the observed data and predicted behaviors of F0 and amplitude modulations in vocal vibrato. Comments on amplitude measurements
In addition to the variable nature of the extent of amplitude modulation in vocal vibrato, methods of extracting amplitude may be responsible for some discrepancy of results among the studies. We examined in our preliminary study three methods of amplitude extraction. They were an analog method using a Bruel and Kjaer graphic level recorder and two digital methods where root mean square (RMS) and peak amplitudes were derived for each fundamental period. With the graphic level method, the level trace, either by RMS or peak setting with a fast writing speed (1,000 mm/s), did not yield more than 0.5-riB variations, just as Shipp et al. (10) reported. The integration time and full-wave rectification of the intensity analyzer appear to be the main cause of the failure in producing measurable intensity traces for vocal vibrato. The RMS amplitude calculated for each fundamental period was more sensitive to short-term variations than the graphic level measures, but was not as sensitive as the peak amplitude. The pitch-synchronous peak amplitude more closely represented the amplitude envelope of the voice waveform. Extreme caution, therefore, needs to be exercised in comparing data on extent of amplitude modulations in vocal vibrato. In addition, it appears mandatory for researchers to report specifics of their intensity measurement methods in reporting amplitude modulations in vocal vibrato. Implications to future investigations of vocal vibrato In our studies, all singers (15 so far) demonstrated F0 modulations in vocal vibrato, and none evidenced amplitude modulations only or amplitude modulations far exceeding the magnitudes expected from the resonance-harmonics interaction alone. In other words, nonequivocal, pure " a m p l i t u d e vibrato" singers are yet to be found. This raises a, question of whether or not those amplitude modulations reported by a number of researchers in the past referred to the passive amplitude variations caused by the resonance-harmonics interaction. Since the number of subjects in our studies is rather Small, a larger sample of singers might indeed reveal
41
a small proportion of singers who use so-called amplitude vibrato. In either case, clearer definitions of "vibrato," "frequency vibrato," and "amplitude vibrato" need to be established and standardized. In view of the results of the current investigation, a modification of the following definition of vibrato, given by U.S.A. Standard Institute (1960) and quoted by Large (24) appears warranted: " a family of tonal effects in music that depend upon periodic variations of one or more characteristics of the sound wave. Note: When the particular characteristics are known, the term 'vibrato' should be modified accordingly, e.g., frequency vibrato, amplitude vibrato, phase vibrato, and so forth." (p. 39.) In order to classify singers as users of amplitude vibrato, the amplitude modulations have to be either present by themselves without concomitant Fo modulation or the amplitude modulations should persist over a wide range of Fo without predicted amplitude magnitudes or predicted phase relationships with F0. Perceptual significance of such amplitude modulations, and discriminability of the amplitude modulations in the presence of F 0 and "timbre" modulations in particular, needs to be further investigated. Undoubtedly, any normal phonation is a result of well-coordinated neuromuscular activities involving respiratory, laryngeal, and articulatory mechanisms with associated physiologic, aerodynamic, acoustic, and perceptual consequences. Thus, there is no reason to suspect that the general regulatory mechanisms of frequency and intensity are not operative during vibrato phonation. The frequencyraising maneuver of the cricothyroid muscles (37), for example, should be involved in producing highpitched phonations. Increased subglottic pressure is also expected at high-pitch conditions as more vocal effort, according to many unsolicited comments of the subjects, was required at these conditions (38-40). An important question, then, is whether or not the same frequency and intensity regulatory mechanisms are responsible for the Fo and amplitude modulations in vocal vibrato. The present results suggest that consideration of an amplitude modulation mechanism may be put on hold for t h e t i m e being, unless particular phonations under study are indeed true "amplitude" or "intensity" vibrato. As to the mechanism of F o modulations in vibrato, it is interesting to note that Ladefoged (41) suggested the possibility of an entirely different physiological mechanism from the cricothyroid-based mechanism Journal of Voice, Vol. 3, No. 1, 1989
42
Y. H O R H
of frequency adjustment. Ladefoged suggested that pitch adjustment in vibrato "involves some adjustment of the position o f the arytenoid cartilages" and stated that " t h e i r spacing (their distance apart) is varied as well as their tension" (p. 262). He attributed pitch modulation to this tension variation and intensity modulation to the spacing of the a r y t e n o i d cartilages, which c a u s e s variation o f amount of force as the vocal folds come together. In relation to amplitude modulation in vocal vibrato, Large (24) and Large and Iwata (42) reported that airflow was synchronous with amplitude modulations in vibrato. Mason and Zemlin (20) reported that the activity of the cricothyroid muscle was generally in phase with the crest of the frequency and intensity vibrato, which they found at all times. Zemlin (37), furthermore, suggested that the subglottic air pressure fluctuations may account for the amplitude vibrato. These findings and statements need to be interpreted in a new light if the resonance-harmonics interaction indeed accounts for most of the amplitude modulations and their phase relationships with Fo modulations. In particular, it appears necessary to differentiate clearly amplitude modulations due to the resonance-harmonics interaction and those amplitude modulations actively produced by singers. Implications for future comparative studies of vocal vibrato and pathological vocal tremor T h e s a m e p r o b l e m in d e f i n i n g " a m p l i t u d e vibrato" articulated above applies also to studies of pathologic vocal tremor. Several researchers, including myself, reported that vocal modulations in sustained vowel phonations, produced presumably "as steadily as possible" by individuals with spastic dysphonia and with neurological disorders (such as Parkinson's disease, amyotrophic multiple sclerosis, head injury, etc.), were characterized predominantly by amplitude modulations (9-12,27). Often such investigations compare frequency and amplitude modulations observed in the tremorous phonations to those of singers' vibrato and proceed to speculate on underlying physiological and neurological mechanisms of vibrato and tremor. In this process, again, it appears important to differentiate a m p l i t u d e m o d u l a t i o n s due to the r e s o n a n c e harmonics interaction and amplitude modulations unaccounted for by the interaction both for singers' vibrato and pathologic vocal tremor. Without going into detail, it may be noted that results o f comparisons of the present findings with those of pathoJournal of Voice, Vol. 3, No. 1, 1989
logic vocal tremor (11,12) strengthened the claim that vocal modulations in sustained phonations by pathologic speakers are both frequency and amplitude modulations, the latter o f which originates from an additional source (possibly more active contributions of the respiratory components) to the resonance--harmonics interaction. Acknowledgment: This work was supported in part by the National Institutes of Health, grant number RO 1NS24409. REFERENCES 1. Seashore CE. The vibrato. Iowa City, Iowa: University of Iowa Press, 1932:30-7. 2. Seashore CE, Tiffin J. Summary of the established facts in experimental studies in the vibrato up to 1932. University of Iowa, studies in psychology of music. Iowa City: University of Iowa Press, 1932:344-76. 3. Seashore CE. The psychology of music. New York: McGraw-Hill, 1938. 4. Lawrence V, Weinberg B, eds. Care of the professional voice. New York: The Voice Foundation, 1979. 5. Large J, ed. Contributions of voice research to singing. Houston, Texas: College-HillPress, 1980. 6. Vennard W. Singing. New York: Carl Fischer, 1967. 7. Wyke B, ed. Ventilatory and phonatory control systems. New York: Oxford University Press, 1974:248--64. 8. Deutsch D, ed. The psychology of music. New York: Academic Press, 1982. 9. Izdebski K, Dedo HH. Characteristics of voice tremor in spastic dysphonia: a preliminary study. In: Lawrence V, Weinberg B, eds. Transcripts of the eighth symposium on care of the professional voice. 1979:Part III, 17-23. 10. Shipp T, Leanderson R, Sundberg J. Vocal vibrato. In: Lawrence V, Weinberg B, eds. Transcripts of the eighth symposium on care of the professional voice. 1979:Part I, 46-9. 11. Horii Y. Correlation between fundamental frequency and intensity in vibrato and vocal tremor. Presented at the XXth international congress of logopedics and phoniatrics, Tokyo, Japan, August 1986. 12. Horii Y. Sustained phonations produced by dysarthric patients. ASHA 1986;28:145. 13. Horii Y, Hata K. Phase relationships between frequency and amplitude modulations in vocal vibrato. Folia Phoniatr (Basel) (in press). 14. Horii Y. Vowel differences in vibrato frequency/amplitude modulations. ASHA 1987;29:78. 15. Sj6strom L. Experimentell-phonetischeuntersuchungen des vibratophanomens der singstimme, lOth Nord otolaryngol Kongr, Stockholm, 1947. 16. Luchsinger R, Arnold G. Voice--speech--language. Belmont: Wadsworth, 1965. 17. Gemelli A, Sacerdote G, Bellussi G. Analisi elettroacustica della voce cantata. Boll Soc ltal Fonet Sperim 1954;4:3-8. 18. PommezJ. Etude acoustique du vibrato de la voix chantee. Rev Laryngol Otol Rhinol (Bord) 1962;83:249--64. 19. Mason RM. A study of the physiologicalmechanisms of vocal vibrato [Dissertation]. University of Illinois, 1965. 20. Mason R, Zemlin W. The phenomenon of vocal vibrato. The NATS Bulletin 1966;37:12-7. 21. Winckel F. Physikalische kriterien fur objektive stimmbeurteilung. Folia Phoniatr (Basel) I953;5:232. 22. Rothman HB, Nielson K, Hicks JW Jr. Perceptual classifi-
A C O U S T I C A N A L YSIS O F V O C A L V I B R A T O
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cation of voice movements. In: Lawrence V, Weinberg B, eds. Transcripts of the eighth symposium on care of the professional voice. 1979:Part I, 57-9. Coleman RF. Acoustic and perceptual factors in vibrato. In: Lawrence V, Weinberg B, eds. Transcripts of the eighth symposium on care of the professional voice. 1979:Part I, 36-7. Large J. An air flow study of vocal vibrato. In: Lawrence V, Weinberg B, eds. Transcripts of the eighth symposium on care of the professional voice. 1979:Part I, 39-45. Schoen M. The pitch factor in artistic singing. Psychol Med [Monogr Suppl] 1922;31:230-359. Kwalwasser J. The vibrato. Psychol Med [Monogr Suppl] 1926;36:84-108. Ramig LA, Shipp T. Comparative measures of vocal tremor and vocal vibrato. Presented at the fifteenth symposium on care of the professional voice, New York, June 1986. Potter R, Kopp G, Kopp H. Visible speech. New York: D. Van Nostrand, 1947. Stevens KN. Physical aspects of ventilatory and phonatory behavior. In: Wyke B, ed. Ventilatory and phonatory control systems. New York: Oxford University Press, 1974. Sundberg J. Studies of the soprano voice. Research in Singing 1977;1:25-35. House AS. A note on optimal vocal frequency. J Speech Hear Res 1959;2:55-60.
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32. Dunn HK. The calculation of vowel resonances, and an electrical vocal tract. J Acoust Soc A m 1950;22:740-53. 33. Stevens KN, House AS. An acoustical theory of vowel production and some of its implications. J Speech Hear Res 1961 ;4:303-20. 34. Titze I. Singing synthesis with models of phonatory and articulatory kinematics. J Acoust Soc Am 1988;83:$30. 35. Sundberg J. Formant structure and articulation of spoken and sung vowels. Folia Phoniatr (Basel) 1970;22:28--48. 36. Wolf SK, Stanley D, Sette WJ. Quantitative studies on the singing voice. J Acoust Soc Am 1934;6:25-33. 37. Zemlin WR. Speech and hearing science. Englewood Cliffs, New Jersey: Prentice-Hall, 1968. 38. Isshiki N. Regulatory mechanism of voice intensity variation. J Speech Hear Res 1964;7:17-29. 39. Isshiki N. Vocal intensity and air flow rate. Folia Phoniatr (Basel) 1965;17:92-104. 40. Large J, Iwata S, yon Leden H. The primary female register transition in singing: aerodynamic study. Folia Phoniatr (Basel) 1970;22:285-396. 41. Ladefoged P. Respiration, laryngeal activity and linguistics. In: Wyke B, ed. Ventilatory and phonatory control systems. New York: Oxford University Press, 1974:29%314. 42. Large J, Iwata S. Aerodynamic study of vibrato and voluntary "straight tone" pairs in singing. Folia Phoniatr (Basel) 1971 ;23:50--65.
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Journal of Voice, Vol. 3, No. 1, 1989