Dept. for Speech, Music and Hearing

Quarterly Progress andStatus Report

Vibrato and vowelidentification

Sundberg, J.

journal: STL-QPSRvolume: 16number: 2-3year: 1975pages: 049-060

http://www.speech.kth.se/qpsr

STL-QPSR 2-3/1975

111. MUSICAL ACOUSTICS

A. VIBRATO AND VOWEL IDENTIFICATION

J. Sundberg

Abstract

The influence of vibrato on vowel identification i s studied in synthesized vowel sounds with fundamental frequencies between 300 and 1000 Hz. Phonetically trained subjects were asked to identify these stimuli presented with and without vibrato a s any of 12 Swedish long vowels. Small and occasional effects a r e ob- served on the mean formant frequencies and the scatter between the responses.

However, the effects a r e greater and more frequent$haai would be expected by chance. In a majority of the cases, where the vibrato affected the responses, the vowel identification became somewhat harder when the stimulus was presented with vibrato.

STL-QPSR 2-3/1975

Introduction

Vibrato occurs in music performed on many types of instruments,

such a s s t r ing and wind instruments and i n singing. Physically it cor - responds to an almost sinusoidal modulatio~t of the fundamental frequency.

Provided that the r a t e and extent of the vibrato i s kept within certain l im-

i t s , the vibrato i s generally considered a useful means of musical ex-

pression in a variety of musical styles. I

Acoustic character is t ics typical of music sounds can be assumed to

serve some purpose in musical communication. One commonly heard

hypothesis i s that the vibrato covers up small e r r o r s in the fundamental

frequency. In a previous investigation no support was found for this hypo-

thesis a s fa r a s the pitch of single tones - and thus not chords - i s con-

cerned (Sundberg 197 2). In the present investigation another commonly

heard hypothesis will be tested, namely that the vibrato facil i tates vowel

identification. This hypothesis seems plausible, because as the part ia ls

move in frequency (e . g. owing to a vibrato) their amplitudes scan small

p a r t s of the vocal-tract t ransfer function, and m o r e information on the , formant frequencies i s communicated. The effect would be particularly

strong in the soprano range where the fundamental frequency may be even

higher than 1000 Hz and the information on the formant frequencies would

be ha rd to decode f r o m the acoustic spectrum.

Experiment

A se r i e s of high-pitched sounds were synthesized with and without

vibrato using a terminal analogue. Six formant-frequency combinations

were used, each of which corresponds to a Swedish long vowel: [u , o,

a , e , i , y ] . The vowel formant frequencies ( s e e Table 111-A-I)

were typical of soprano singing according to previous measurements on

a singer singing a t a fundamental of 262 Hz (Sundberg 1975). Contrary to

what was found in this soprano, each of these s ix combinations of formant

frequencies were used without changes for four different pitches within

the soprano range: 300, 450, 675, and 1000 Hz. In this way the mater ia l

included sounds ranging f rom maximum ease to maximum difficulty a s

regards vowel identification. The vibrato consisted of a sinusoidal modu-

lation of the fundamental frequency. The r a t e was six ondulations per

second, and the extent was 50 cents. These values a r e found in normal

singing, even though the extent i s normally slightly narrower.

Table 111-A-I.

F o r m a n t f requency va lues used for syn thes i s of s t imul i ( lef t)

and a s c r i b e d t o r e s p o n s e vowels ( r ight ) .

I STIMULI RESPONSE VOWELS

Vowel

u

o

a a

a3

E

e

1

Y u

d ce

1 Hz

325

430

640

400

270

250

=2 H z

700

650

1090

2000

1900

1950

F3 H z

F4 H z

= 1 H z

I

2700 1 4000 320

415

700

855

815

625

375

275

275

300

390

565

2820

2800

2700

1950

2510

F2 H z

4000

4000

4000

4000

4000

Hz F3

565

725

1065

1200

2030

2305

2790

2675

2555

1920

2040

1290

2775

2775

3000

2820

3000

3040

3360

3655

3210

2745

2725

2690 J

STL-QFSR 2-3/1975 52.

Four samples of each vowel stimulus were tape recorded a t a constant

overall amplitude. The t ime and the shape of the onsets and decays were

a l l s imilar . The stimuli samples were arranged in random order avoid-

ing m o r e than one repetition of a given stimulus in sequence. The ent i re

tape contained a total of 192 vowel samples: six formant-frequency com-

binations x four fundamental frequencies x four presentations x two cases

(with and without vibrato). Each stimulus had a duration of I sec and was

followed by a silent interval of 4 sec.

The stimuli were presented in head-phones (Sennheiser HD 414) a t an

overall SPL of 70 dB, approximately, to ten phonetically trained subjects.

Their task was to decide which one of 12 given Swedish long vowels [ u, o,

a, a, ;e, E, e, i , y, u, 4 , c e ] sounded most s imilar to the stimulus they

heard and to write that vowel in phonetic symbols on a tes t chart. These

vowels suggested by the subjects a s interpretations of the stimuli will be

r e fe r red to a s response vowels. The test , including three short breaks,

took, i n all , about 30 min.

Evaluation of r e snons e s

I t seems reasonable to hypothesize that the process of identifying an I

isolated stimulus a s a specific vowel involves three major steps. The

f i r s t is a purely sensory one in which the acoustic stimulus i s converted

into some kind of sensory information. The second step involves an ex-

traction of an ensemble of sensory character is t ics f rom this sensory

information. In the third step a comparison i s made between these sen-

sory character is t ics and corresponding character is t ics of vowels s tored

in the subject ' s internal reference. The difficulty of identifying a sound

a s a specific vowel would depend on the degree of s imilar i ty between the

ensemble of sensory character is t ics and the character is t ics in the internal

reference.

The vibrato may affect the sensory information in various ways. Let

us assume that i t affects the extraction of sensory character is t ics . If so,

the responses for a given vibrato stimulus should differ f rom those ob-

tained when the same stimulus was presented without vibrato. In the tes t

responses the effect would then be that the mean formant frequencies of

the response vowels for a given stimulus would differ between the cases

with and without vibrato. In that case the identification difficulties may

STL-QPSR 2- 3/1975 53.

be affected i n various ways, depending on whether the vibrato makes the

sensory character is t ics (1) more s imi lar , (2) l e s s s imi lar , o r (3) equally

s imilar to the subject' s reference features. The cases (1) and (2) would

affect the scatter of the responses.

The above considerations show the need for measures of the average and

scat ter of the response vowels. In order to obtain such measures a set of

formant frequencies was ascr ibed to each of the 12 response vowels in ac-

cordance with data on female speakers , given by Fant (197 3). These values

a r e l is ted in Table 111-A-I. I t should be noted that the same formant f re -

quencies were ascr ibed to a given response vowel regard less of the funda-

mental fr equency of the corresponding stimulus. The formant frequencies

were expressed in .Mels and the mean formant frequencies of the response

vowels were computed for each stimulus.

Resul ts

The responses a r e l is ted in Table 111-A-11. One of the subjects refused

to give an answer to three of the stimuli, a l l of which happened to lack vib-

rato. The inter- subject differences rkgarding the internal reference were

ra ther small: three o r four unique votes on a specific response vowel were

given by the same subject only occasionally, a s can be seen in Table 111-A-II.

The mean formant frequencies of the response vowels a r e shown in Fig.

111-A- 1 and the corresponding standard deviations a r e given in Table 111-A-111.

The relationships between the mean formant frequencies of the r espon-

s e s and the stimulus spectra can be studied in Fig. 111-A-1, where, in

par t icular , the case of the stimuli synthesized with [I?]-formants offer an

i l lustrative example (Fig. 111-A- lc). The mean formant frequencies of the

responses drop with r is ing fundamental frequency up to 675 Hz. The r ea -

son for this is probably that, in o rde r to retain the vowel quality when the

fundamental is ra i sed , i t i s necessary to r a i s e the formant frequencies

slightly. Slawson (19 68) found an average increase of 10 b/o in the formant

frequencies to be required per octave r i s e of the fundamental. If the funda-

mental i s ra i sed while the formant frequencies a r e kept constant, a s was

done in our experiment, the vowel quality will shift towards a vowel with

lower formant frequencies. This effect can be seen i n the case of Fig.

111-A- 1 c. Presumably, the subjects identified the two lowest formant f re -

quencies correctly, and the formant frequencies ascr ibed to the response

vowels contain an e r r o r which i s dependent on the fundamental frequency.

A correction would be needed, but i t i s not known exactly how this cor rec-

tion should be made. F o r instance, Slawson's correction of 10 % in-

c rease in formant frequency pe r octave r i s e in the fundamental does not

FUNDAMENTAL FREQUENCY (kHz)

Fig. 111-A-la-c. Evaluation of response vowels in t e r m s of their two lowest main formant frequencies. Fil led and open c i r c l e s per ta in to s t imul i presented with and without vibrato, r e spec - tively. The thin horizontal dashed lines, show the formant f requencies used in s y n - thesizing the st imuli . Each of the s ix graphs r e f e r s to the r e sponses collected for a given combination of synthesis formant frequencies (cf. Table 111-A-I).

MEAN FORMANT FREQUENCY OF RESPONSES (MEL)

8 8 8 b 8 0 0 0

t I I 1 I I

I I I \ \\, k - I

P

& cn

$

s - I

1 I

I I

1 I I 1 I

1 I I I 1 \\ i I 1 I I I I I i I

k - I I I

- ( I

-* I cn ' I

I I @

t~ 1 4 I \ I

1 \ I ;5 - d 1 b 1

1 I I

I I I - I I I I 1 I I I - 1 I I 1 I I I I I 1 1

1 tl 6 1 I

STL-OPSR 2-3/1975 54. Table 111-A-11. (See text on next page)

STL-OPSR 2-3/1975

Table 111-A-11.

STIMULUS FORMANTS

Response u o a e i Y

Number of votes on the response vowels collected for the stimuli indicated. The stimuli a r e given in t e r m s of the formant-freluency combination used in synthesizing them ( see Table 111-A-I), - and t indicate that the stimulus lacked or had vibrato, respectively. Sc indicates that a l l votes s tem f rom one subject only.

STL-QPSR 2 - 3 / 1 9 7 5

Standard deviations for the mean formant frequencies in Mels of the response vowels. The stimuli are given in terms of their formant frequency combinations (FN) and fundamental frequency (I?*).

STL-QPSR 2-3/1975 57.

fully compensate the effect in Fig. III-A- lc. I t should a l so be mentioned,

that a lmost invariably, a l l stimuli with a fundamental of 67 5 Hz gave r e -

sponse vowels in which one of the (assumed) formants matched one of the

stimulus par t ia ls in frequency almost perfectly. This fact may tempt us

to speculate that the formant frequencies ascr ibed to the response vowels

may be cor rec t when the pitch i s very high. Some additional support for

the same speculation may be found in the close frequency agreement be-

tween the formants of the responses and those of the stimulus in the case

of the 1000 Hz fundamental in Fig. 111-A- l c . However, i t s eems definite-

ly unsafe to study the relationships between the stimulus spectrum and the

mean formant frequencies of the responses i n our material . These f re -

quencies should not be compared between stimuli with differing funciamental

frequency.

A comparison of the mean formant frequencies of the response vowels

obtained with and without vibrato would inform u s on the effect that the vibrato

may have on the extraction of sensory character is t ics , a s mentioned. Such

comparisons can be made i n Fig. III-A-2. I t shows the difference in the

mean formant frequencies of the response vowels. Negative values indi-

cate that the mean dropped when the stimulus had a vibrato. According to

a t - tes t the difference i s significant above a 90 O/o level in 13 cases out of

72. This suggests that, under cer tain conditions, the vibrato has an effect

on the extraction of the charactexistics f r o m the sensory information on

the stimulus.

The scat ter between the responses can be computed a s the mean per -

ceptual distance between them. Recently Lindblom (1 97 5) following ideas

of Plomp (1970) has established that the perceptual distance D between any

two Swedish vowels can be approximated a s

where A M i s the frequency difference in d s in the n:th formant between n the two vowels. Using this equation the perceptual distance between the

mean formant frequencies of the response vowels ( see Fig. III-A- 1)

and the individual responses was calculated for each stimulus, and the

average was determined. These mean perceptual distances between the

responses can be studied in Fig. III-A- 3. They can be assumed to r e -

flect the difficulty with which the stimulus is identified a s a specific

FUNDAMENTAL FREQUENCY (kHz)

Fig. 111-A-2. Difference in the first (left), second (middle), and third (right) mean formant frequencies in Mels of the response vowels collected from a given stimulus when it was presented with and without vibrato. The circled dots represent differences that are significant above a 90 O/o level.

- -

MEAN PERCEPTUAL DISTANCE BETWEEN RESPONSES (MEL)

STL-QPSR 2- 3/1975 58.

vowel. In the back vowels the identification seems to be simple when the

fundamental is 300 Hz, and a s the fundamental i s ra i sed , the identification

becomes m o r e difficult. In the front vowels the identification is ha rd even

when the fundamental i s low. This i s certainly a consequence of the fact

that the formant frequencies used in synthesizing these stimuli were rath-

e r devient f rom those which a r e typical of normal speech. Rather they

a r e typical of the type of singing which i s often called "covered". In

these stimuli the uncertainty of the identification is not substantially af-

fected by the fundamental frequency. Comparing the values pertaining to

the cases of with and without vibrato revea ls that the identification of vib-

r a to stimuli is harder in approximately a s many cases a s i t i s simpler.

However, the cases of particular interest a r e those which, according to

the t - tes t , changed signfikantly in the mean formant frequency of the r e -

sponse vowels. This occurred in ten cases , and he re the outstanding

features shifted somewhat when the stimulus was presented with a vibrato.

Out of these ten cases the identification became more uncertain in seven

cases. This seems to support the assumption that the vibrato may have

a slight effect on the difficulty with which a sound i s identified a s a vowel,

and the effect i s that the identification i s somewhat harder to per form

when the sound has a vibrato. However, the effect is ve ry weak in our

material .

I t may be argued that the stimuli used in our experiment a r e typical

neither of singing, nor of speech, and hence the subjects' react ions have

l i t t le relevance to the pract ical situation. I t is then interesting to com-

p a r e our resu l t s with data collected f rom similar experiments where the

stimuli were natural, non- synthesized vowels. Such re su l t s have been

presented by Stumpf ( 19 2 6 ) . In h is experiments untrained and profession-

a l s ingers sang high-pitched vowels, and a jury attempted to identify the

intended vowels. Stumpf gave h is r e su l t s in t e r m s of a confusion ma t r ix

and they vYrer e converted into mean per ceptual distance between response

vowels in exactly the same way a s the resu l t s f rom our experiment.

Stumpf' s data a r e a l so given in Fig. 111-A-3. I t is clear f rom the figure

that our stimuli did not give extreme re su l t s a s compared with the natural

stimuli. Thus, vowel identification was not m o r e difficult in our experi- .

ment than i t may be in practice.

STL -0PSR 2- 3/ 197 5 60.

vibrato may change the vowel quality slightly. In such cases , the identifica-

tion of the sound a s a specific vowel seems to be slightly m o r e difficult

when the stimulus h a s a vibrato. I t i s believed that in pract ice, a singer

may profit systematically f rom this effect of the vibrato so a s to reduce

the per ceptability of her deviations f rom the formant frequencies of normal

speech.

Acknowledgments

Stefan Paul i is acknowledged for h i s assis tance in computer program-

ming. The work was supported by The Bank of Sweden Tercentenary

Foundation.

References

CARLSON, R. , FANT, G. , and GRANSTROM, B (1973): "Two-formant models, pitch and vowel perception", paper presented a t the Symp. on Auditory Analysis and Perception of Speech, Leningrad 1973; to be publ. by Academic P r e s s , London 1975.

FANT, G. (1973): Speech Sounds and Fea tures , MIT-Press , Cambridge, Mass . , p. 36 and p. 84.

FLANAGAN, J. L . (1955): "A difference l imen for vowel formant f r e - quency", J.Acoust.Soc.Am. - 27:3, p. 613.

LINDBLOM, B. (197 5): "Experiments in sound structure", paper presented a t the 8th Int. Congr. of Phonetic Sciences, Leeds, Aug.

PLOMP, R. (1970): "Timbre a s a multidimensional attribute of complex tones", in Frequency Analysis and Periodicity Detection in Hearing, ed. by R. Plomp and G . F. Smocrenburg, A. W . Sijthoff, Leiden, p. 397.

SLAWSON, A. W. ( 1968): "Vowel quality and musical t imbre a s functions of spectrum envelope and fundamental frequencyt1, J. Acoust. Soc. Am. 43:1, p. 87. 7

STUMPF, C. (1926): Die Sprachlaute, Springer, Berlin, pp. 77-85. I SUNDBERG, J. ( 1970): "Formant s t ructure and articulation in spoken and

sung vowels", Fol. Phon. 22: 1, p. 28. - SUNDBERG, J. (1972): "Pitch of synthetic sung vowels", STL-QPSR

1/1972, p. 34. ! SUNDBERG, J. (197 5): "Formant technique in a professional female

singer", Acustica 32:3, p. 90. -