Characteristics of Velocity Profiles of Speech Movementsnonsense syllable /kokok/ showing standard...

Journal of Experimental Psychology:Human Perception and Performance1985, Vol. 11, No. 4, 457-474

Copyright 1985 by the Am n Psychological Association, Inc.0096-1523/85/100.75

Characteristics of Velocity Profiles of Speech Movements

Kevin G. Munhall, David J. Ostry, and Avraham ParushMcGill University, Montreal, Quebec

The control of individual speech gestures was investigated by examining laryngealand tongue movements during vowel and consonant production. A number oflinguistic manipulations known to alter the durational characteristics of speech(i.e., speech rate, lexical stress, and phonemic identity) were tested. In all cases aconsistent pattern was observed in the kinematics of the laryngeal and tonguegestures. The ratio of maximum instantaneous velocity to movement amplitude,a kinematic index of mass-normalized stiffness, was found to increase systematicallyas movement duration decreased. Specifically, the ratio of maximum velocity tomovement amplitude varied as a function of a parameter, C, times the reciprocalof movement duration. The conformity of the data to this relation indicates thatdurational change is accomplished by scalar adjustment of a base velocity form.These findings are consistent with the idea that kinematic change is produced bythe specification of articulator stiffness.

A fundamental problem in the study ofskilled movement is how to identify the char-acteristics of the functional units of motorcontrol. Nowhere is this problem more ap-parent than in the study of speech production,an activity that involves the coordination ofa number of different articulatory systems aswell as the implementation of a complexsymbol structure. Although there are no uni-versally accepted techniques for the decom-position of such complex systems, a produc-tive strategy has been to identify those aspectsof movements that are invariant to manipu-lations of movement amplitude, duration,accuracy, and so forth. (See Keele, 1981, andKelso & Tuller, 1984, for reviews.) The as-sumption is that these behavioral invariances

Portions of the paper were presented at meetings ofthe Acoustical Society of America, Orlando, Florida,1982, and Norfolk, Virginia, 1984, and at the InternationalConference on the Physiology and Biophysics of Voice,Iowa City, Iowa, 1983.

The research has been supported by grants from theNatural Sciences and Engineering Research Council ofCanada and the FCAR (Formation des Chercheurs etAide a La Recherche) program of the Quebec Departmentof Education.

The authors wish to thank A. A. J. Marley for assistancewith the mathematics related to scaling and velocityprofiles. John Folkins and Carol Fowler made valuablecomments on an earlier version of this paper.

Requests for reprints should be sent to Kevin Munhall,who is now at Haskins Laboratories, 270 Crown Street,New Haven, Connecticut 06511.

reflect the underlying structure responsiblefor coordination.

In the experiments presented here we followthis general line of inquiry of testing forbehavioral invariances. Specifically, we ex-amine the shape of the velocity profile ofmovements across speech production condi-tions in which the spatial and temporal scalesof the speech movements are varied. Thisparticular observable was chosen because theshape of the velocity profile has been shownto distinguish models of motor control thatdiffer in terms of which control variable isoptimized (e.g., movement time, energy, jerk;see Hogan 1984; Nelson, 1983). By lookingat the velocity profiles across different speechconditions, we can test whether any singletype of control exists for movements asso-ciated with different linguistic contexts.

Three situations could be encountered.First, velocity profiles could show no system-atic relation to the manipulated variables,reflecting instead some aspect of the move-ment's organization that is not under exper-imental control. Second, it may be that move-ments of the speech articulators are controlledin a manner that is unique to each particularsound in a language's repertoire so that thesystem optimizes its control for the distinctivegeneration of those sounds. This would argueagainst the observance of any single patternamong velocity profiles. Last, the velocityprofiles of speech movements could be similar

457

458 K. MUNHALL, D. OSTRY, AND A. PARUSH

across a number of linguistic contexts andconsequently across a range of movementrates and amplitudes. This last result wouldsuggest that some single underlying basis couldexist for the organization of speech move-ments.

In Figure 1 a stylized velocity profile isportrayed with instantaneous velocity plottedas a function of time. The apex of the curveis the peak instantaneous velocity. The baseof the curve corresponds to the duration ofthe movement, and the area under the velocitycurve corresponds to the distance moved. Totest for velocity profile shape changes, wemade use of a simple relation among thekinematic variables peak velocity (P), move-ment amplitude (A), and movement duration(T). It can be shown that if a series of velocityprofiles is geometrically similar (i.e., a scalarfamily of curves), then

P/A = C*\/T. (D

The parameter C in Equation 1 serves as anindex of the velocity profile shape. Thus, iftwo movements have the same C value, themovements' velocity profiles are of a similarform, regardless of differences in the ampli-tudes or the durations of the movements (seeAppendix).

In the experiments that follow, velocityprofiles of laryngeal and tongue movementsare examined when stress, speech rate, andconsonant are varied. The framework outlinedabove is used to assess the stability of thevelocity profile shape under these conditions.

General Method

Instrumentation

The data in both studies were collected with a com-

puterized ultrasound recording and analysis system. Theversion of this system used in these experiments isdescribed in Keller and Ostry (1983). An updated versionof the system was reported by Ostry, Munhall, andParush (1983). The system consists of a Picker model104 A-scan ultrasound unit and a Cromemco CS2 mi-crocomputer for data collection, display, and analysis.

The ultrasound transducers are placed beneath thechin for measuring tongue movements and against thethyroid lamina for laryngeal movements. The emittedultrasound pulses thus travel through soft tissue to thearticulator surface. Ultrasound has the property that partof its energy is reflected at changes in acoustic impedance.Reflections occur at changes in tissue density, with almostall of the radiated acoustic energy being reflected at

tissue-air boundaries. The interval between the emissionof the ultrasound pulse and the reception of the largeamplitude reflection from the tongue's surface or the free

margin of the vocal fold is converted to a distanceestimate by assuming an average speed of ultrasound insoft tissue of 1,540 m/s (Goss, Johnston, & Dunn, 1978).

Transducer Placement

The transducer placement for laryngeal recording isdetermined using a through-transmission procedure(Hamlet, 1981; Holmer & Rundqvist, 1975; Kaneko,Uchida, Suzuki, Komalsu. Kanesaka, Kobayashi, &Naito, 1981). The subject, seated in front of a stand that

holds a pair of matched transducers, has a transducerplaced on each side of the thyroid lamina below thethyroid notch. Maximum through-transmission at thislevel will occur when the folds are in contact. The

location of the vocal folds is identified when a discontin-uous signal is observed during a sustained vowel, and no

signal is observed during noncontact laryngeal maneuverssuch as breathing. (Amplitude modulated signals can be

observed during voicing at a number of locations on thethyroid lamina, and the true location is indicated bydegree of modulation, not simply the detection of thispattern.) Next the amplitude of the through-transmittedultrasound signal is maximized during repetitive syllableproduction at the pitch and amplitude required fortesting. In the experimental trials the system is switchedto a pulsed-echo mode, and unilateral measures with asingle transducer are taken of the distance from thetransducer to the fold's surface.

For the measurement of lingual gestures (Experiment2), the transducer is placed externally below the chin justanterior to the hyoid bone. The transducer is held inposition by a modified sports helmet with an attachedPlexiglas holder for the transducer (see Keller & Ostry,1983). The posterior placement allows the measurementof back vowels and velar consonant articulations. Mea-surement of the movement of more forward portions of

the tongue such as the tip, for example, is hindered bythe air cavity under the anterior tongue body. This air

cavity inhibits the passage of the ultrasound beam.Correct positioning for the measurement of tongue

dorsum movements was determined by first locating aposition and orientation that maximize the observedtongue displacement during the production of the non-sense syllable /ka/. Next the position of the transducer

Maximum instantaneousvelocity

Displacement orextent of movementarea under the curve)

Time

Figure I. Stylized velocity profile with instantaneousvelocity (on the ordinate) plotted as function of movementduration.

VELOCITY PROFILES IN SPEECH 459

was adjusted to ensure that the traditional ordering oftongue heights was maintained for the back vowels /u/,/o/, and /a/. Once an appropriate position and orientationwere established, the transducer was fixed relative to thecranium by means of the helmet and Plexiglas holder.This position was maintained for a complete session.Simultaneous x-ray cinefluorography had indicated thatthe positioning procedures yield reliable transducerplacements that allow the measurement of the verticalcomponent of these gestures (Keller & Ostry, 1983).Further, detailed videotape analysis of subjects in theapparatus has indicated that the transducer and holdingapparatus do not significantly alter the amplitude of jawmovements in the test situation (Keller & Ostry, 1983).

Data Analysis

Natural cubic spline functions were fit to the raw data(Johnson & Riess, 1977). Cubic splines are piecewisepolynomial functions that can be used to approximate aset of data points. These particular functions were chosenfor the present application because their piecewise formmakes no a priori assumptions about the overall shapeof the patterns in the data arid enables the approximationto follow these trends closely. Further, the functions are

differentiable numerically, and thus values for velocityand acceleration as well as position could be obtained.

The standard error due to system resolution is approx-imately 0.1 rnm of tissue (Ostry, Keller, & Pamsh, 1983).The bandwidth of the spline approximation is 23 Hz.This means that the measurement system is sensitive toat least the third harmonic of a 6-Hz movement. Theaverage absolute error of the spline fit is approximately0.2 mm for laryngeal movements and 0.3 mm for tonguemovements.

In both of the studies a standard set of kinematicvariables was examined. These variables are the durationand amplitude of movement, the peak instantaneousvelocity, and the time from the initiation of movementto peak instantaneous velocity. Figure 2 shows the testedvariables for the intervocalic consonant for the nonsensesyllable /ka-kok/ in laryngeal data. This figure will bereferred to in the results sections of the two experiments.

For the purpose of scoring these measures, the position,instantaneous velocity, and acoustic waveform were dis-played as a function of time on a videoscreen. Numericalvalues were obtained with the aid of a moveable cursorand digital readout. Selected values were stored on diskfor subsequent statistical analyses. The measurementstaken are described below.

1.088

a. aae 8.448 8.588 8.728TIME (SECSJ

0.860 1.888

0.300 0.440 0.586 0.720TIME (SECSl

0.860 1.008

Figure 2. Ultrasound record (in seconds) of laryngeal movement amplitude (top panel), instantaneousvelocity (middle panel), and accompanying acoustic signal (lower panel) for a single utterance of thenonsense syllable /kokok/ showing standard measurement variables. (VEL = velocity; POS CM = positionof vocal folds in centimeters [distance from ultrasound transducer]. See text for explanation of intervalsand values [A-H].)


Interval E in Figure 2 is the amplitude of laryngeal

abduction denned as the distance between the zerovelocity point at the beginning of the movement and thezero velocity point at the movement's end. Interval F inFigure 2 is the amplitude of laryngeal adduction dennedsimilarly by the zero velocity points. Intervals A and Bare the movement durations for the laryngeal abductionand adduction movements denned as the temporal inter-vals between the zero velocity positions at the beginningand end of the movements. Points G and H are the peaklaryngeal abduction and adduction instantaneous velocitiesdenned as the highest absolute value in the velocityprofile within a given movement. The times to reachpeak velocity, the temporal interval between the zerovelocity point at the beginning of the movement and the

point of peak instantaneous velocity, are Intervals C andD for laryngeal abduction and adduction.

Experiment 1

In ongoing speech the vocal folds are ap-proximated during the production of vowelsbut open and close rapidly to create theappropriate aerodynamic conditions for theproduction of certain consonants. In thepresent study the velocity profiles of theselaryngeal opening (abduction) and closing(adduction) movements were examined inorder to assess what similarities exist in speechmovement control across various linguisticconditions. Lexical stress, speech rate, andthe phonetic identity of the segment associatedwith an intervocalic (between two vowels)laryngeal gesture were manipulated. Each ofthese manipulations is known to affect theacoustic durations in speech and hence mightalter velocity patterns.

The study of laryngeal adjustments is amost suitable candidate for the assessment ofpossible velocity profile invariance in speech.Laryngeal timing is known to be preciselycontrolled (Sawashima & Hirose, 1983), andits temporal coordination with the activity ofother speech articulators is likewise closelyregulated to effect linguistic contrasts (Lisker& Abramson, 1964, 1967). Further, the sim-plicity of its articulatory maneuvers allowsdetailed study without the complications thata multidirectional and multiform articulatorsuch as the tongue introduces.

Method

Subjects. The subjects were the first two authors, whoare native monolingual speakers of Canadian English(Ontario dialect) with no known speech abnormalities.

Speech sample. Each of the subjects repetitively

produced the nonsense utterance /teCet/, having either/s/ or /t/ as the intervocalic consonant, at two rates, thesubject's preferred rate (slow) and a subject-chosen fasterrate (fast), with either the first or second vowel receivingthe primary stress. The stress manipulation was similarto that observed in the English word conduct whenspoken as either a noun or a verb. Thus, in total, eight

experimental conditions were tested (2 consonants X 2rates X 2 stress levels).

Nonsense utterances were chosen as stimuli becausethey allow the testing of full factorial designs for stress,rate, and phonemic manipulations. Natural speech utter-ances rarely enable such designs to be tested, and with

the additional restrictions that the ultrasound measure-ment places on the suitable corpus, it was not possibleto use natural language productions for these tests. Thisdesign thus sacrifices some generality for experimentalcontrol. It should be noted that this stimulus choice doesnot overly simplify the articulations we measured. Theproduction of nonsense utterances still requires the se-quencing of complex vocal tract configurations as wellas the temporal and spatial coordination of the variousarticulatory systems involved in any speech utterance.

Although we cannot claim to be studying real languageproduction per se, we are nevertheless studying a complex

act of speech motor control.Procedure. The data were collected by recording a

number of 3.5-s trials of vocal fold movements. Thesubject repeated the same token for a complete 3.5-strial. The transducer placement was held constant forone trial in each of the eight conditions (2 rates X 2stress conditions X 2 consonants). Twenty to 30 utteranceswere recorded in each condition.

Results and Discussion

The data were partitioned in terms of thetemporal and spatial variables that are dis-played in Figure 2. As can be seen, only thegestures related to the production of theintervocalic consonants were analyzed.

Kinematics of the intervocalic abductionand adduction gestures. Differences in themovement duration in milliseconds (IntervalsA and B in Figure 2), movement amplitudein millimeters (Intervals E and F in Figure2), and the maximum instantaneous velocity(Points G and H in Figure 2) were examinedfor both abduction and adduction as a func-tion of consonant, rate, and stress. Averagevalues for these variables are presented inTable 1.

Although there is some individual vari-ability in these movement measurements, thereliable kinematic differences were consistentwith findings obtained in different linguisticpopulations and with different instrumenta-tion (e.g., Sawashima, 1970). The measuredglottal movement was larger in the prestress


position than the poststress context for SubjectKM. This was accompanied by higher averagepeak velocities for the larger movements. ForSubject KM the average laryngeal adductionmovement was also larger for fricatives thanfor stops. Both subjects produced longer du-

dition than the unstressed, and Subject DOalso had longer duration movements in theslow condition than the fast.

Relation between movement duration,maximum velocity, and movement amplitude.Peak velocity/amplitude correlations were

ration closing movements in the stressed con- calculated individually for each of the 32

Table 1Average Movement Amplitude, Duration, and Peak Velocity Values as a Functionof Stress Rate and Consonant

Stressed

Fast

Measure

Abduction

/s/AmplitudeDuration

Peak velocity

mAmplitudeDurationPeak velocity

Adduction

/s/AmplitudeDuration

Peak velocity

mAmplitudeDuration

Peak velocity

M

.109102

1.84

.12097

2.08

.126

1331.87

.101

1151.64

SE

.0033

.13

.0093

.15

.0088

.12

.0086

.17

Slow

M

Subject

.168126

2.42

.174117

2.53

.150

1252.33

.142114

2.25

SE

KM

.0125

.19

.0113

.15

.0158

.25

.012

6.22

Unstressed

Fast

M

.104111

1.57

.06185

1.19

.103117

1.52

.05990

1.04

SE

.0115

.15

.0054

.10

.0107

.15

.0935

.09

Slow

M

.095

1091.54

.06394

1.17

.097114

1.52

.056106

0.96

SE

.0116

.17

.004

5.08

.0097

.13

.0044

.08

Subject DO

Abduction

/s/AmplitudeDurationPeak velocity


Adduction

/s/AmplitudeDurationPeak velocity


.143109

2.16

.110101

1.86

.182

1582.22

.123116

1.73

.0084

.12

.0104

.16

.021

9.35

.0147

.21

.136117

2.10

.173137

2.22

.170139

2.28

.176162

1.92

.0088

.15

.015

5.21

.0106

.16

.01311

.21

.134

1132.12

.13497

2.40

.143105

2.55

.13993

2.71

.0186

.28

.0155

.32

.0168

.37

.0166

.37

.213134

3.00

.171106

2.97

.191114

3.13

.188110

2.91

.0229

.49

.0238

.44

.015

9.30

.0269

.28

Note. Movement amplitude values are in centimeters; duration values are in milliseconds; peak velocity values are incentimeters per second.


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Figure 3. Scattergram showing the ratio of maximum velocity to movement amplitude (on the ordinate)as a function of the duration of the movement (in seconds) for Subject KM's laryngeal abduction gestures.(The data represent individual productions of the intervocalic gesture in the nonsense syllables /tetet/ and/teset/, with speech rate and stress being manipulated.)

cells (2 subjects X 2 rates X 2 stress levels X2 consonants X 2 movement directions). In30 of the 32 comparisons the correlationswere reliable (p < .01), with the two excep-tions having probabilities of p < .05. Theaverage value for the 30 reliable comparisonswas r - .843, indicating that the two variablesare strongly linked in the present data. Thisrelation has been found to hold for eyemovements (Carpenter, 1977), tongue move-ments (Ostry, Keller, & Parush, 1983), jawmovements (Stone, 1981), and flexions andextensions about the elbow (Cooke, 1980,1982).

To examine the changes in the individualvelocity profiles, the ratio of maximum ve-locity to movement amplitude was calculatedfor each movement (Equation 1). In Figures3 through 6 scattergrams of these ratios plot-ted against the duration of the movementsare displayed for all treatment combinationsfor both abduction and adduction and forboth subjects. It can be seen that the ratioincreases systematically as duration of themovement decreases.

The linear and quadratic terms of thepolynomial regression were reliable for bothsubjects and for both abduction and adduction(p < .01) across conditions. The overall pro-portions of the variance accounted for were89% and 86% for abduction and 76% and83% for adduction for Subjects KM and DO,respectively.

In order to test whether the shape of thevelocity profile varied across conditions, es-timates of C were calculated for each individ-ual movement and analyzed by analysis ofvariance. The average values can be seen inTable 2.

Analyses of variance of these C valuesrevealed reliable differences for Subject KM'sadduction gestures as a function of consonant,F{\, 151) = 10.83, p < .01, and stress level,F{\, 151) = 10.60, p < .01, with the /s/ andstressed conditions having higher values thanthe /t/ and unstressed conditions. No othermain effects or interactions were reliable.

It is important to note that a single functioncan account for a large proportion of thevariance associated with changes in duration


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Figure 4. Scattergram showing the ratio of maximum velocity to movement amplitude (on the ordinate)as a function of the duration of the movement (in seconds) for Subject KM's laryngeal adduction gestures.(The data represent individual productions of the intervocalic gesture in the nonsense syllables /tetet/ and/tesct/, with speech rate and stress being manipulated.)

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Figure 5. Scattergram showing the ratio of maximum velocity to movement amplitude (on the ordinate)as a function of the duration of the movement (in seconds) for Subject DO's laryngeal abduction gestures.(The data represent individual productions of the intervocalic gesture in the nonsense syllables /tetet/ and/teset/, with speech rate and stress being manipulated.)


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Figure 6. Scattergram showing the ratio of maximum velocity to movement amplitude (on the ordinate)as a function of the duration of the movement (in seconds) for Subject DO's laryngeal adduction gestures.(The data represent individual productions of the intervocalic gesture in the nonsense syllables /tetet/ and/teset/, with speech rate and stress being manipulated.)

as well as the basic form of the velocityprofile across a number of linguistically sig-nificant manipulations. The best-fit estimatesfor C provided very good fits to the ratio of

peak velocity to movement amplitude as afunction of i/T(Equation 1). The percentagesof variance accounted for were 88, 74, 83,and 82 for Subject KM (abduction and ad-

Table 2Mean Values of the Velocity Profile Parameter, C, for Abduction and Adduction as a Functionof Rale, Stress, and Consonant

Stressed Unstressed

Fast

Measure

/s/AbductionAdduction

mAbductionAdduction

/S/AbductionAdduction

mAbductionAdduction

M

1.691.96

1.671.78

1.651.81

1.671.63

SE

.02

.11

.02

.05

.04

.06

.03

.08

Slow

M SE

Subject KM

1.80 .071.90 .08

1.71 .031.73 .04

Subject DO

1.75 .051.86 .15

1.75 .081.68 .15

Fast

M

1.681.72

1.651.65

1.791.66

1.641.71

SE

.04

.06

.03

.03

.05

.08

.03

.03

Slow

M

1.771.79

1.691.66

1.721.80

1.771.74

SE

.05

.04

.03

.06

.06

.07

.06

.05


duction) and Subject DO (abduction andadduction), respectively. Although it is clearfrom Figures 3 to 6 that the residuals increaseas the duration of the movement increases,the overall fit is still good.

In the analysis of the average C values,only Subject KM's adduction gestures showedany reliable differences between experimentalconditions. Although this implies that strictscalar equivalence of the velocity profiles hasnot been observed for this subject, it is inter-esting to note that the condition means donot differ greatly. Realistically the parameter,C, could vary from slightly above 1 to wellabove 2, depending on the physical limitationson acceleration and jerk. As can be seen inTable 2, the values of C vary around overallmeans of 1.74 and 1.72 for Subjects KM andDO, respectively.

The data as a whole suggest that over avariety of manipulations, a single functionaccounts for changes in the ratio of peakvelocity to movement amplitude over changesin movement duration. The scalar or nearscalar adjustments to the velocity profile im-plied by this function suggest that a singleprinciple may underlie the control of thesevarious speech movements.

Previous research (e.g., Cooke, 1980; Feld-man, 1980a, 1980b) has suggested that bio-mechanical characteristics of muscles andjoints change with the behavioral demandsof the movement. For example, Cooke (1980)has shown that when the elbow is modeledby a linear second order system, changes inthe duration of movements can be broughtabout by changes in the static stiffness of thejoint. The kinematic concomitants of thisincrease in stiffness are that the ratio of peakvelocity to movement amplitude increasesand movement duration decreases (i.e., higherstiffness corresponds to shorter durationmovements and greater peak velocity/move-ment amplitude ratios).

In the present data the ratio of peak velocityto movement amplitude increased as move-ment duration decreased. This is consistentwith studies of limb movements (Cooke, 1980;Ostry & Cooke, in press) and other speechgestures (Ostry, Feltham, & Munhall, 1984;Ostry, Keller, & Parush, 1983; Ostry & Mun-hall, 1985). This pattern in the data suggeststhat durational changes associated with dif-

ferences in speech rate, stress, and consonantmay all be produced by altering the overallstiffness of the glottal articulators while pre-serving the form of the base velocity function.

Experiment 2

Even casual observation of the movementsinvolved with the production of speech sug-gests that the articulators are intimately in-terrelated. Not only do their offsets and onsetsof movement show systematic relations (e.g.,Tuller, Kelso, & Harris, 1982) but also theirtrajectories of movement must be related. Anumber of recent reports attest to this inter-articulator coupling.

When the position of the jaw is fixed bythe use of a bite block, other articulators (thetongue and lips) can compensate to providenormal acoustic output (Gay, Lindblom, &Lubker, 1981; Gay &Turvey, 1979; Lindblom,Lubker, & Gay, 1979; Kelso & Tuller, 1983).When brief unanticipated perturbations areapplied to the jaw during speech (Abbs &Gracco, 1984; Folkins & Abbs, 1975, 1976;Folkins & Zimmermann, 1978; Kelso, Tuller,Bateson, & Fowler, 1984), the lips and tonguehave been shown to provide immediate com-pensation so as to preserve not only thetiming but the acoustic quality of the artic-ulation. Although it is clear that some ma-nipulations to the vocal tract are less easilycompensated for (e.g., Hamlet & Stone, 1978)than others, it is also clear that individualspeech movements are produced against abackdrop of interarticulator linkages (Abbs,Gracco, & Cole, 1984).

In principle, this coordination could besimplified if the movements of the differentarticulators shared movement control param-eters. For example, if changes in the move-ment amplitude and duration of differentarticulators' movements were produced bychanging a single parameter or by changingparameters that were systematically related,compensatory adjustments would be com-putationally less demanding. Such a situationcould exist if the velocity profiles of differentarticulators were derivable from some com-mon base form.

In the present experiment the similarity oftongue and vocal fold kinematics was assesseddirectly. The working assumption here is that


similarities in the kinematics point to simi-larities in the overall dynamics and, ulti-mately, in the control structure itself.

Method

Subjects. The subjects were 2 fluent speakers ofEnglish with no known speech abnormalities. SubjectKM is a native Canadian English (Ontario dialect) speaker,whereas Subject AP is a native Hebrew speaker.

Speech sample. Both subjects produced the nonsenseutterance /koiok/ repetitively, with either the first orsecond vowel receiving the primary stress. This particularsequence was used because the ultrasonic measurementof the tongue is limited to posterior articulations by theair cavity below more anterior tongue positions. As inExperiment 1 the stress alternation was similar to thatobserved in the English word conduct when spoken aseither a verb or a noun.

Procedure. Each articulator was measured separatelywithin the same session. The subjects produced the samespeech utterance repetitively during 3.5-s trials at a self-paced speed. The experimental conditions (first vs. secondvowel stressed) were randomized across trials. Twenty to30 observations were obtained in each condition.

Results and Discussion

As in the previous experiment, the datawere analyzed by using regression and analysisof variance. Only the intervocalic laryngealadduction and tongue lowering data will bepresented.

Kinematics of laryngeal adduction andtongue lowering. The movement amplitudes,durations, peak velocities, and times to reachpeak velocity were compared for the twostress levels, separately for the laryngeal andtongue data. Figures 7 and 8 show the meanvalues and standard errors for these compar-isons. Reliable movement duration, ampli-tude, and time to reach peak velocity effectswere observed for both articulators and sub-jects, with the stress condition showing largervalues. The peak velocity value varied onlywith the stress manipulation for Subject AP'slaryngeal adduction although there was a

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Figure 7. Average movement duration in milliseconds (top panel) and movement amplitude in millimeters(bottom panel) for the intervocalic consonant in /kakak/. with either the first or second second vowelbeing stressed. (Values for both subjects and articulators are plotted.)


consistent ordering of the means for all fourcomparisons (2 subjects X 2 articulators).Greater stress levels showed higher averagepeak velocities.

Relation between peak velocity, movementduration, and movement amplitude. As inthe previous experiment, peak instantaneousvelocity and movement amplitude were foundto be strongly related within conditions. Theaverage r1 values (across the two stress levelsand articulators) were .71 and .69, for SubjectsKM and AP, respectively.

The ratio of peak velocity to movementamplitude was again calculated and plottedas a function of movement duration. Equation1, which models this ratio in terms of C* I/T, accounted for large proportions of thevariance. (Subject KM: tongue lowering, 78%;laryngeal adduction, 69%. Subject AP: tonguelowering, 57%; laryngeal adduction, 80%.)

For each gesture the parameter C wascalculated (Figures 9 through 12). Analysisof variance indicated that for both subjectsthere was a main effect of stress level—Subject KM, F(l, 89) = 14.39, p < .01; Sub-ject AP, F(l, 138) = 17.36, p < .01—withboth subjects showing a higher value for Cwith increased stress. There were no reliabledifferences in the value of the parameter foreither subject as a function of articulator,though Subject KM showed a small Stress XArticulator interaction, F(\, 89) = 5.73, p <.05, which was due to the large average Cvalue observed for the laryngeal stressed con-dition (Table 3).

Although stress seems to influence theshape of the velocity profile, it does so in asimilar fashion for the two articulators. Theparameter C increased with stress in bothcases. The same pattern was observed for

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Figure S. Average duration of the interval between the initiation of movement and peak velocity inmilliseconds (top panel) and the value of the peak instantaneous velocity in centimeters per second (bottompanel) for the intervocalic consonant in /kokok/, with either the first or second vowel being stressed.(Values for both subjects and articulators are plotted.)


3.0

2.4

1.8

1.2

0.6

0.0 -

4.0

SUBJECT AP

o Unstressed

• Stressed

6.0 8.0 10.0 12.0

AMPLITUDE OF TONGUE LOWERING MOVEMENT IN MM

Figure 9. The velocity profile parameter, C—(P* T)/A—on the ordinate plotted as a function of movement

amplitude (in millimeters) for Subject AP's tongue lowering data. (Each symbol represents an individualmovement. P = F ,̂, or maximum instantaneous velocity; T = duration; A = movement amplitude.)

Subject KM's laryngeal gestures in Experi-ment 1. The overall similarity in the velocitypatterns of the tongue and. the vocal foldssuggests that the tongue and vocal folds sharecommon principles of control.

General Discussion

In the two experiments reported here vari-ables were manipulated that were known to

yield durational and amplitude changes inindividual speech movements as well as pro-duce changes in the accompanying acousticwaveform. It was shown that these manipu-lations (speech rate, lexical stress, phonemicidentity) produced little change in the overallshape of the movement velocity profile, butthey did alter the movement amplitudes anddurations. In both experiments the ratio of

3.0

1.8

1.2

0.6

0.0 -

SUBJECT AP

o Unstressed

• Stressed

0.4 0.8 1.2 1.6 2.0

AMPLITUDE OF LARYNGEAL ADDUCTION IN MM

Figure 10. The velocity profile parameter, C—(P*T)/A—on the ordinate plotted as a function ofmovement amplitude (in millimeters) for Subject AP's laryngeal adduction data. (Each symbol represents

an individual movement.)


3.0

2.4

1.8

1.2

0.6

0.0 -

SUBJECT KM

o Unstressed

• Stressed

4.0 6.0 8.0 10.0 12.0

AMPLITUDE IN OF TONGUE LOWERING MOVEMENT IN MM

Figure 11. The velocity profile parameter, C—(P*T)/A—on the ordinate plotted as a function ofmovement amplitude (in millimeters) for Subject KM's tongue lowering data. (Each symbol represents anindividual movement.)

peak velocity to movement amplitude wasfound to vary systematically as a function ofmovement duration. This relation was inter-preted as indicating a uniform basis for themotor control of a wide range of laryngealand tongue articulations.

The possibility that the use of repetitivestimuli could have introduced a uniformity

into the velocity profiles that is not normallypresent should be considered. In principle,the form of rhythmical movements could begreatly influenced by the rhythm itself andnot reflect the strategies used in normalspeech control. This does not appear to bethe case in the present data. The utteranceswere not composed of simple cycles of uni-

3.0

2.4

1.8

1.2

0.6

0.0 -

SUBJECT KM

i •

o Unstressed

• Stressed

0.4 1.2 1.6 2.0

AMPLITUDE OF LARYNGEAL ADDUCTION IN MM

Figure 12. The velocity profile parameter, C—(P* T)/A—on the ordinate plotted as a function ofmovement amplitude (in millimeters) for Subject KM's laryngeal lowering data. (Each symbol representsan individual movement.)


Table 3

The Velocity Profile Parameter, C, as a Functionof Articulator and Stress Level

Unstressed Stressed

Subject and movement M SE M SE

KMTongue towering 1.72 .02 1.76 .05Laryngeal adduction 1.71 .02 1.93 .05

APTongue lowering 1.69 .02 1.81 .02Laryngsal adduction 1.67 .04 1.73 .03

form amplitude and period. The utterancesin both experiments were modulated by thestress pattern, and half of the stimuli inExperiment 1 involved a consonantal alter-nation. The stimuli thus had sufficient inher-ent complexity to rule out any simple rhyth-mical explanation of the findings.

As a further check, we reanalyzed tonguegestures (Parush, Ostry, & Munhall, 1983) inwhich the utterances were spoken in thecarrier phrase "Say /pVCVp/ again." Subjectsproduced both /g/ and /k/ as the intervocalicconsonant and /u/, /o/, and /a/ as the sur-rounding vowels. In these data the samepattern of results was observed as in theexperiments presented here. The subjectsproduced C values close to 1.7 with the sametendency for C to increase slightly with move-ment duration (see also Ostry & Munhall,1985).

Some departures from the strict equivalenceof velocity profiles were evident in the presentdata. Changes in lexical stress, in particular,seemed to alter the base velocity profile sys-tematically. It is not clear from the experi-ments presented here whether these small,albeit reliable, differences in the movementpatterns are significant in a control sense. AsYates (1982) suggests, it is difficult to knowwhat degree of constancy and stability shouldbe expected from biological systems. In thepresent speech data the nervous system mayhave acted as if the velocity profile shape wasconstant and as I/the scaling was linear overthe full extent of its operating range with fewserious repercussions from small nonlineari-ties or deviations from strict scalar adjust-ment.

There may be many reasons why this de-parture from scalar equivalence is observed.Evolution may act according to a "goodenough" principle where evolving changesare judged by their efficacy in the usualworking range, not by their optimality acrossthe whole functional range (Partridge, 1982).Further, optimal solutions may be too costlyfor the received benefits. In the present datait may be possible to maintain the form ofthe velocity profile across all durational ad-justments, but the acoustic consequences ofthis may be insignificant. If there are somecosts in energy output, for example, in main-taining strict velocity profile constancy, slightdeviations that are acoustically irrelevant maybe preferable. A finding consistent with thissuggestion is Perkell and Nelson's (1982, 1984)demonstration that tongue dorsum positionvariation in the production of various vowelsis greater in acoustically irrelevant directions.

Lastly, these departures from scalar equiv-alence may indicate that geometric similaritycannot hold over a large range of movementspeeds. In rapid movements, the dampingrequirements may be sufficiently differentfrom those in slower movements that thevelocity profile is altered. The need to preventterminal oscillations may thus supercede geo-metrical similarity of the velocity profile.

In speech production and some other com-plex motor activities, equivalence of velocityprofiles might aid in the coordination betweenarticulators. Freund and Budingen (1978)have made a similar suggestion based on theirobservation of constant electromyographicrise time for maximally rapid movements.Consistent with this suggestion is the dem-onstration by Kelso and his colleagues (Kelso,Putnam, & Goodman, 1983; Kelso, Southard,& Goodman, 1979) that in simultaneoustwo-armed movements both limbs show sim-ilar movement durations and trajectories evenwhen the movement demands differ acrosshands.

The question remains, however, as to thenature of the physiological coherence isolatedby these manipulations and of the physiolog-ical nature of the scaling process itself. In thepresent data a kinematic index of mass-normalized stiffness (PIA) was seen to increasesystematically as the duration of the move-


ment decreased. Differences in speech rate,lexical stress, and phonetic identity were allfound to produce changes along this function(Equation 1). To the extent that this ratio isan adequate index of articulator stiffness, thedata indicate that stiffness differs for variousspeech manipulations. Further, the data sug-gest that velocity profiles can be held constantor nearly constant when stiffness is altered toaffect durational change. To a first approxi-mation, this pattern is consistent with thenotion of speech articulators being controlledas lumped parameter second-order systemsin which stiffness can be specified (Ostry &Munhall, 1985).

Although the present proposals account forthe observed P/A pattern and the relativeinvariance of the velocity profile, they do notaddress the issue of why a particular velocityprofile is observed. Nelson (1983) has shownthat velocity profiles differ, depending on thenature of the optimized control variable. Forexample, when energy output is minimized,Nelson showed that the velocity profile re-sembled a partial sinusoid. Although thepresent experiments do not identify the vari-able responsible for the velocity profile shape,some recent evidence from the study of limbmovements is relevant. Velocity profiles sim-ilar in shape to those in the present experi-ments have been observed in both single joint(Ostry, Cooke, & Munhall, 1984; Ostry &Cooke, in press) and multijoint arm move-ments (Soechting, 1984). This suggests thatthe velocity profile form may reflect optimi-zations that are motoric rather than linguistic.

Changes in the shape of the velocity profilewarrant further study. First, the variation inthe velocity profile with increased movementamplitude or duration, such as caused by thestress manipulation in these experiments,should be examined. The study of size andits consequences has proved to be a usefulwindow into the processes that govern bio-logical form (Gould, 1966), and a more for-mal characterization of changes in the scaleof movement amplitudes and durations mayyield similar insights. Secondly, manipulationsthat cause large changes in the velocity profileshould be explored. For example, Soechting(1984) has recently shown that when theaccuracy requirements for arm movements

are manipulated, the velocity profile variesin form. Differences between discrete andrepetitive movements may also provide aninteresting contrast.

References

Abbs, J. H., & Gracco, V. L. (1984). Control of complexmotor gestures: Orofacial responses to load perturba-tions of the lip during speech. Journal of Neurophysi-ology, 51, 705-723.

Abbs, J. H., Gracco, V. L., & Cole, K. J. (1984). Controlof multimovement coordination: Sensorimotor mech-anisms in speech motor programming. Journal ofMotor Behavior, 16, 195-232.

Carpenter, R. H. S. (1977). Movement of the eyes. London:Pion.

Cooke, J. D. (1980). The organization of simple, skilledmovements. In G. Stelmach & J. Requin (Eds.), Tu-torials in motor behavior (pp. 199-212). Amsterdam:North-Holland.

Cooke, J. D. (1982). Position-velocity-torque relationsduring human arm movement. Society for NeuroscienceAbstracts, 8,131.

Feldman, A. G. (1980a). Superposition of motor programs:1. Rhythmic forearm movements in man. Neuroscience,5, 81-90.

Feldman, A. G. (19805), Superposition of motor pro-grams: 2. Rapid forearm flexion in man. Neuroscience,5, 91-95.

Folkins, J. W., & Abbs, J. H. (1975). Lip and jaw motorcontrol during speech: Responses to resistive loadingof the jaw. Journal of Speech and Hearing Research,IS, 207-220.

Folkins, J. W., & Abbs, J. H. (1976). Additional obser-vations on responses to resistive loading of the jaw.Journal of Speech and Hearing Research, 19, 820-821.

Folkins, J. W., & Zimmermann, G. N. (1978). Jawmuscle activity during speech with the mandible fixed.Journal of the Acoustical Society of America, 69, 1441-1445.

Freund, H.-J., & Budingen, H. J. (1978). The relationshipbetween speed and amplitude of the fastest voluntarycontractions of human arm muscles. ExperimentalBrain Research, 31, 1-12.

Gay, T., Lindblom, B., & Lubker, J. (1981). Productionof bite-block vowels: Acoustic equivalence by selectivecompensation. Journal of the Acoustical Society ofAmerica, 69, 802-810.

Gay, X, & Turvey, M. T. (1979). Effects of efferent andafferent interference on speech production: Implicationsfor a generative theory of speech motor control. Pro-ceedings of the Ninth International Congress of PhoneticSciences, 2, 344-350.

Goss, S. A., Johnston, R. L., & Dunn, F. (1978). Com-prehensive compilation of empirical ultrasonic prop-erties of mammalian tissues. Journal of the AcousticalSociety of America, 64, 423-457.

Gould, S. J. (1966). Allometry and size in ontogeny andphylogeny. Biological Reviews, 41, 587-640.

Hamlet, S. L. (1981). Ultrasound assessment of phonatoryfunction. Proceedings of the Conference on the As-


sessment of Vocal Pathology, A.S.H.A. Reports, 11,128-140.

Hamlet, S. L, & Stone, M. (1978). Compensatory alveolarconsonant production induced by wearing a dental

prosthesis. Journal of Phonetics, 6, 227-248.Hogan, N. (1984). An organizing principle for a class of

voluntary movements. The Journal of Neuroscience,4, 2745-2754.

Holmer, N. G., & Rundqvist, H. E. (1975). Ultrasonicregistration of the fundamental frequency of a voiceduring normal speech. Journal of the Acoustical Societyof America, 58, 1073-1077.

Johnson, L. W., & Riess, R. D. (1977). Numerical

analysis. Reading, MA: Addison-Wesley.Kaneko, X, Uchida, K., Suzuki, H., Komatsu, K., Ka-

nesaka, N., Kobayashi, & Naito, J. (1981). Ultrasonicobservations of vocal fold vibration. In K. N. Stevens& M. Hirano (Eds.), Vocal fold physiology (pp. 107-118). Tokyo: University of Tokyo Press.

Keele, S. W. (1981). Behavioral analysis of movement.In J. M. Brookhart, V. B. Mountcastle, & V. B. Brooks(Eds.), Handbook of physiology: Volume 2, motor

control (pp. 1391-1414). Bethesda, MD: AmericanPhysiological Society.

Keller, E., & Ostry, D. J. (1983). Computerized measure-ment of tongue dorsum movements with pulsed echoultrasound. Journal of the Acoustical Society of America,73, 1309-1315.

Kelso, J. A. S., Putnam, C. A., & Goodman, D. (1983).On the space-time structure of human interlimb co-

ordination. Quarterly Journal of Experimental Psy-chology, 35A, 347-375.

Kelso, J. A. S., Southard, D. L., & Goodman, D. (1979).On the coordination of two-handed movements. Journal

of Experimental Psychology: Human Perception andPerformance, 5, 229-238.

Kelso, J. A. S., & Tuller, B. (1983). "Compensatoryarticulation" under conditions of reduced afferent in-formation: A dynamic formulation. Journal of Speech

and Hearing Research, 26, 217-224.Kelso, J. A. S., & Tuller, B. (1984). A dynamical basis

for action systems. In M. S. Gazzaniga (Ed.), Handbook

of cognitive neuroscience (pp. 319-356). New York:

Plenum.Kelso, J. A. S., Tuller, B., Bateson, E.-V., and Fowler,

C. A. (1984). Functionally specific articulatory cooper-ation following jaw perturbations during speech: Evi-dence for coordinative structures. Journal of Experi-

mental Psychology: Human Perception and Performance,10, 812-832.

Lindblom, B., Lubker, J., & Gay, T. (1979). Formant

frequencies of some fixed-mandible vowels and a modelof a speech motor programming by predictive simu-lation. Journal of Phonetics, 7, 147-161.

Lisker, L., & Abramson, A. (1964). A cross-languagestudy of voicing in initial stops: Acoustical measure-ments. Word. 20. 384-422.

Lisker, L., & Abramson, A. (1967). Some effects ofcontext on voice onset time in English stops. Language

and Speech. 10, 1-28.Munhall, K. G., & Ostry, D. J. (in press). Ultrasonic

measurements of laryngeal kinematics. In I. Titze &R. Scherer (Eds.), Vocal fold physiology: Biomechanics,acoustics, andphonatory control. Denver: Denver Centerfor the Performing Arts.

Nelson, W. L. (1983). Physical principles for economiesof skilled movements. Biological Cybernetics, 46, 135-147.

Ostry, D. J., & Cooke, J. D. (in press). Kinematicpatterns in speech and limb movements. In E. Keller& M. Gopnik (Eds.), Motor and sensory language

processes. Hillsdale, NJ: Erlbaum.Ostry, D. J., Cooke, J. D., & Munhall, K. G. (1984).

Movement duration is controlled in similar ways inlimb and speech systems. Society for NeuroscienceAbstracts, 10, 804.

Ostry, D. J., Feltham, R. F., & Munhall, K. G. (1984).

Characteristics of speech motor development in chil-dren. Developmental Psychology, 20, 859-871.

Ostry, D. J., Keller, E., & Parush, A. (1983). Similaritiesin the control of speech articulators and the limbs:

Kinematics of tongue dorsum movement in speech.Journal of Experimental Psychology: Human Perception

and Performance, 9, 622-636.Ostry, D. J., & Munhall, K. G. (1985). Control of rate

and duration of speech movements. Journal of the

Acoustical Society of America, 77, 640-648.Ostry, D. J, Munhall, K. G., & Parush, A. (1983, May).

Computerized pulsed-ultrasound techniques for the

measurement of lingual, laryngeal, and lateral pharyn-

geat wall movements. Paper presented at the 106thmeeting of the Acoustical Society of America, SanDiego, CA.

Partridge, L. D. (1982). The good enough calculi ofevolving control systems: Evolution is not engineering.American Journal of Physiology, 242, RI73-R177.

Parush, A., Ostry, D. J., & Munhall, K. G. (1983). Akinematic study of lingual coarticulation in VCVsequences. Journal of the Acoustical Society of America,

74, 1115-1125.Perkell, J. S., & Nelson, W. L. (1982). Articulatory targets

and speech motor control: A study of vowel production.In S. Grillner et al. (Eds.), Speech motor control (pp.187-204). New York:Pergamon.

Perkell, J. S., Nelson, W. L. (1984, November). Relation-

ships between articulatory and acoustic measurements

from an x-ray microbeam study of variability in the

production of the vowels ft/ and /a/. Paper presentedat the 107th meeting of the Acoustical Society ofAmerica, Norfolk, VA.

Sawashima, M. (1970). Glottal adjustments for Englishobstruents. Haskins Laboratories Status Report on

Speech Research SR-21/22, 187-200.Sawashima, M., & Hirose, H. (1983). Laryngeal gestures

in speech production. In P. F. MacNcilage (Ed.), The

production of speech (pp. 11-38). New York: Springer-Verlag.

Soechting, J. F. (1984). Effect of target size on spatialand temporal characteristics of a pointing movementin man. Experimental Brain Research, 54, 121-132.

Stone, M. (1981). Evidence for a rhythm pattern inspeech production: Observations of jaw movement.Journal of Phonetics, 9, 109-120.

Tuller, B., Kelso, J. A. S., & Harris, K. S. (1982).Interarticulator phasing as an index of temporal reg-ularity in speech. Journal of Experimental Psychology:

Human Perception and Performance, 8, 460-472.Yates, F. E. (1982). Outline of a physical theory of

physiological systems. Canadian Journal of Physiologyand Pharmacology, 60. 217-248.


Appendix

Time

Figure AI. Four hypothetical scalar families of velocityprofiles. (The curves within each of the four families canbe transformed into one another by expansion or con-traction on one or both axes.)

The parameter, C, in Equation 1 serves as anindex of the form of the velocity profile. Forexample, Figure Al shows four hypothetical scalar

families of velocity profiles. The upper left profilesare triangular in form (i.e., acceleration is constant),and as movement duration decreases, the peakvelocity increases so as to keep the distance movedconstant. The upper right profiles are partial si-nusoids in which peak velocity is constant, andthus the distance moved decreases as the durationof movement decreases. The bottom left profilesare semicircular; the movement duration equalsthe circle diameter, and the peak velocity equalsthe circle radius. The bottom right profiles aresquare wave (i.e., acceleration is instantaneous),and, as with the depicted partial sinusoids, themaximum velocity is constant as movementschange in duration. These families of velocityprofiles were chosen for the purpose of illustration,not because they have any specific role in modelingmovement data. However, the partial sinusoid isthe velocity profile predicted by a second orderlinear mass-spring system with negligible damping(Munhall & Ostry, in press), and the square-wavefamily of curves is quite similar to the velocitypattern observed for slow bowing movements inviolin playing (Nelson, 1983).

Each of these families can be fit by Equation 1

52

48

44

40

36

32

28>. 24u0 20<t>

i l61 12

I 8

'/T

.._ n>r2T

m

50 100 150 200

Movement duration in msec

250 300

Figure A2 The ratio of peak velocity (P) to movement amplitude (A; in seconds) plotted as a function of

movement duration (T; in milliseconds) for the four hypothetical scalar families of velocity profiles shown

in Figure A1. (2/T = triangular velocity profile; T/2T = sinusoidal velocity profile; 4/irT = semicircular

velocity profile; l/T = square-wave velocity profile. When durational change is accomplished by scalar

adjustment of a base velocity profile (C) on the time axis, the functions are of the form P/A = C* l/T,

where C varies with the shape of the base function.)


with different C values. This can be seen in FigureA2. In this figure the predicted curves for theratios of peak velocity to movement amplitude areshown as a function of movement duration foreach of the hypothetical families of velocity profiles.For each of the predicted functions, the velocityprofile characteristics remain unchanged across

different movement durations; that is, each functioncharacterizes a base velocity profile that is beingscaled on the time or on both axes. The value ofthe parameter (C) varies with the shape of thebase velocity profile for the family. Thus, triangularvelocity profiles will always have a constant C =2, partial sinusoids will have a constant C = w/2,and so forth. Note that this is true independent of

the manner in which the height of the velocityprofile changes with movement duration. The tri-angular velocity profiles in Figure A1 could havedecreased in height and therefore in peak velocity,or peak velocity could have remained constant asthe movement duration decreased, and the valueof C in Equation 1 would still be 2. Taking the

ratio, P/A, removes any variation due to heightscaling and thus reduces the dimensionality of thedata by transforming velocity profiles to the height

of the standard curve.

Received August 28, 1984Revision received March 4, 1985

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