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Dept. for Speech, Music and Hearing
Quarterly Progress andStatus Report
Pitch of synthetic sungvowels
Sundberg, J.
journal: STL-QPSRvolume: 13number: 1year: 1972pages: 034-044
http://www.speech.kth.se/qpsr
B. PITCH OF SYNTHETIC SUNG VOWELS++
J , Sundberg
Abstract
Experiments a r e reported in which ~xus ica l ly trained subjects ~ i a t c h the pitch of zl. stimulus tone with a var iablc response tone, both tones being synthesis of a sung vo\vel. The effects on pitch and pitch perception ac - curacy of vibratos of different kinds and tile ' singing formant' a r e exam- ined. The resul t s appear to show that the pitch corresponds to the average fundamental frequency to the f i r s t approximation eventhough deviations from this average occur that may be explained by postulating a time con- stant in the fundamental frequency measuring system of the ea r . Adding I
a vibrato or a ' singing formant ' to a vox- el sound affects neither the pitch perceived nor the accuracy of the pitch perception appreciably. Thc standard deviatioii value s obtained f rom tilc exper i r i~ents a r e considerably smaller than the difference limen for f r e q ~ e n c y probably owing to the subjects' training and to the fact that complex waveforms were used in the experixeiits.
Introduction
In acoustic signals used for the communication of music, acoustic features
can be recognized that appear to characterize a good musician. Probably
such character ist ic s a r e not chosen randol=~ly within a given cultural t radi-
tion, for music - a s \-re11 a s other a r t s - has a long history behind it and i ts
development through the centuries is likely to obey to Darwinistic evolution
principles: Such acoustic features can be expected to survive which a r e in
some meaning adequate from the point of v iev~ of human perception. The
fac t that music can have a forceful impact on emotions can be interpreted
2s a support for this hypothesis. An important task of musical acoustics
would therefore be to map such features and to examine whether their usage
Bas a motivation in the xvay in which humail perception works. Investigations
of this kind may hopefully contribute to the understanding of our sensory and
mcntal behavior.
The present paper repor ts an exploratory study aiming a t an understand-
ing of this kind of two acoustic features characterizing the type of professional
singing that can be hc,zrL in our operas and concert halls. One feature is the
vibrato and the otller i s the spectrum envelope peak near 3 kHz n o r x a l l y oc-
curr ing in professional singing and frequc~ltly called the "singing formanti ' .
Their effects on pitch and pitch perception accuracy will be investigated.
* Paper presented a t Psychoacoustics S y r i ~ p o s i u ~ "Problems of auditive perception", May f 972, Toznah, Poland.
The vibrato corresponds to a periodic lov frequency modulation of the
fundamental frequency. The waveform of this modulation i s generally quite
similar to a sinusoid and i t s periodicity var ies between 5. 5 and 8 cycles per
second. The extent of the rxodulation i s generally between + - 1.5 OJJ and t 3 lo of the fundamental frequency, i. e. betweell -i a quartertone and f - a semitone
(Seashore, 1932). In singing this nodulation of the fundamental frequency i s
accompanied by a 11-lodulation of the overall sound pressure . Sorne authors
have found that the two f inds of rnodulatiox a r e in phase, but others repor t
that this i s not always the case ( ~ c h o e n , I 9 2 3 ; Sacerdote, 1957). The d is -
agreement can probably be explained with reference to the relation between
tile strongest part ia l in the spectrum and the formant lying closest to this
part ia l in frequency. If the formant frequency i s higher than the frequency
of the part ia l the amplitude and frequency r;;odulations can be expected to be
in phase whereas the opposite would occur when the strongest part ia l i s
slightly higher than i ts closest formant frcquency. In any case the anplitude
modulation, whether a consequence of the frcquency modulation o r not, is
believed to be of minor importance a s regards the sound perceived (Baclius,
9969).
The vibrato has been shown to give a pleasing quality to the sound provided
that i t has a periodicity of slightly more than 6 Hz and a total extent of ap-
proximately t 2 70 of the fundamental frequency. In this case one single pitch - i s perceived and even though a s yet not strictly proved, this pitch i s believed
to correspond to the average of the fundamental frequency (Gibian, 1972;
Rax-sdell). It i s a lso assumed that the pitch perceived f rom a vibrato tone
is l e s s certain than the pitch perceived f r o i ~ a steady state signal. It has
been suggested that a function of the vibrato i s to cover up slight e r r o r s in
tuning, which, hov~evcr , has not been brought to a s t r ic t scientific test
(Stevens & Davis, 1 1 3 2 ) .
The "singing f o r ~ a n t " has been studicd previously mainly in male singing
(Sundberg, 1970a and b; Sundberg, 1972). It appears to consist of a cluster
of three forlxants. The lowest of these fori::ants corresponds to the third
formant in normal speech and the highest to the fourth. In-between these
formants an extra forrr-ant is found. This forrr-ant can be ascr ibed to the
larynx tube that iy-ay ac t a s a separate I-Ieli:?holt~ resonator under certain
conditions. Thesc conditions involve a v~ide laryngeal ventricle and a v ide
pharynx. Additional conditions fo r generating a "singing formant1' i s to adopt
STL-QPSR 1/1972 3 6 .
a special articulation of some vowels in singing as compared with speech.
Thus, the "singing formant'' i s probably actively pursued by the singer a t
costs a s regards h is normal articulatory habits.
The perceptual function of the "singing formant1' i s not well understood.
It has been shovsn that i t adds to the "beauty1' of the tone and that i t may be
correlated with a perceptual quality labeled "placement in the head" among
singing teachers (Cibian, 1972). An interesting circumstance is also that the I frequency of the "singing forrr,ant9' appro:;iixately coincides with the region of
maxiriial sensitivity of the human ea r . Consequently the p re sencc of the
"singing formant" may make the sung sound eas i e r to perceive, a s suggested
by Winckel (197 1). YTe might expect that it a l so makes i t s pitch eas i e r to
discern.
Experimental procedure
The influence of the vibrato and the "singing formant" on pitch and pitch
perception accuracy was studied by means of t e s t s e r i e s in which subjects
matched the pitch of a given stimulus tone with a variable response tone.
The stiniulus and response tones were repcatedly presented binaurally to the
subjects by means of e a r phones. A pause of . 5 sec separated the stimulus
and the response tones, each of 11 9 sec cliiration. Between the response
tone and the follox-~ing s t i x u lus tone the pause was 1.6 sec (Fig. 111-B- 1).
The subjects adjusted the fundamental freqcency of the response tone by
turning a knob. 77hen they found the pitch of the two signals identical they
pressed a button intempting the signal presentation and triggering two f r e -
quency counters, one for each signal. In the case of vibrato tones the aver - age fundariiental frequency \-/as ~ e a s u r e d .
When not other\-rise stated the stimulus and response tones had the follow-
ing character is t ics . Both \-sere synthescs of a baritone voice singing a n [ a ] .
The synthesis was performed on a forri;lai:t synthesizer using the follox-sing
formant frequencies: F = 520 Hz, F2 = 9 5 5 Hz, F = 2335 Hz, Fq = 2550 Hz, 1 3 and F5 = 3480 Hz. The synthesis was found to be quite ''natural" by a l l sub-
jects. The sound p res su re level in the e a r phones varied around 70 + 3 dB 2
- r e . .0002 dyn/cm dependiiig on the fundai::ental frequency. The r i s e and
fall t i n e of the s t i x u l u s and response t o l ~ e s was C O msec. The vibrato, ex-
clusively used for the stimulus tone, was generated by modulating the funda-
mental frequency sinusoidally a t a ra te of 6 . 5 cycles pe r sec and slot-~ly
Fig. 111-B-I. Oscillogram of the stimulus-rerponre presentation (upper figure) and of the onset of the vibrato rignal (lower figure).
grawing to a maxirnai extent of i- - 1.7 OJo of the fundam~ental frequency ( ~ i g .
III-B- 1). As indicated above the "singins formantu was generated by connect-
i i ~ g an extra forma-?t circuit resonating at a frequency close to the third
formant (F = 2550 HZ). Four fundame~ta i frequency values were used for 4
the stimulus tone: 70 , f 15, 125, and 300 I-2z. These frequencies a r e equally
spaced over the range of a skilled professional bass singer. Each subject
made 5 matching s of each of the se fundacxntal frequencie s in randomized
order in one tes t ser ies . Three o r four such ser ies , each lasting maximally
f 5 min, could be run in one test session x-~ithout extending i ts duration over
60 min. In al l sessions a r e s t of some i=?iautes was offered to the subjects
after each series .
The subjects \-!ere sb: ~ ~ u s i c a l l y traixecl persons in the age of 2 5 to 36
years . Three of them a r e professional i==usicians (MD, 3 T , NS) and a l l of
ther.-: play or sing regularly in ensernble s.
Experiment I: Test of method
Due to possible effects of auditory phenor-~ena such a s temporal masliing
etc. i t cannot be talcen for certain that snbjects adjust the pitch of the response
tone so that i t s fundamental frequency i s identical with that of the stimulus
tone in an experiment of the type described. Therefore, in one test se r i es
the stimulus and response tones were both presented without vibrato and i-rith
''singing formant", thus not differing fror-? each other. 10 settinzs of each
of the four fundarxental frequencies were x a d e by a l l subjects except
and BT c-~ho made only 5. The resul ts a r e plotted in Fig. III-B-2.a and b
in ter ixs of the icdividual subjects ' means.
Fig. III-B-2. a shows that, on the average, there i s no dir'ference between
the fundamental frequency of the stirr,ulus tone Fa, and that of the response 3
tone F O R . In some cases, however, individual subjects give values of F O R
that differ from F O by more than one standard deviation. lMoreover the S standard deviations vary considerably bet\-reen subjects and fundamental
frequencies betvreen . 05 and .7 7i (Fig. III-B-2. b). Therefore i t seerns
motivated to judge the influence of a given stimulus property on the basis
of the change in pitch and standard deviation that i t inlposes on the values of
the individual subje cts . In the experiments to be described the stiE:ulus and response tones were
both generated by means of a formant synthesizer. Thus, the timbre and
EFFECT OF TEST SITUATION
ON PITCH %o
6 RISE t
4
FO (Hz)
ON PITCH ACCURACY I I I I r I I 1
DECREASE 7
4
MEAN I 2
FO (Hz)
Fig. 111-B-2.a. Difference in fundamental f requency between the s t imulus and response tones observed when they w e r e generated in exactly the s a m e way.
b. Corresponding values of the s tandard deviat ions. Symbols r e p r e s e n t sub jec t s ( 0 = JS; @ = BN;
A = NS; A = EJ; 0 = BT; 1111 = MD).
AMPLITUDE (dB ) AMPLITUDE (dB )
EFFECT OF SlNUSOlDAL VIBRATO
a ON PITCH
FO (Hz)
I I 1 I 1 l 4 O/oo -
-
-
-
ON PITCH ACCURACY r 1 I I I I I 1 OIOO
DROP 4 - - -
I I I 1 I 1
DECREASE f
\
-2
-6
INCREASE 4 '0
50 100 150 200 300 400
FO (Hz)
Fig. 111-B-5. a. Change in the fundamental frequency difference be- tween the stimulus and response tones observed after adding a sinusoidal vibrato to the stimulus tone.
b. Corresponding changes in the standard deviations. The subject symbols a r e the same a s in Fig. 111-B-2.
As regards pitch Fig. 111-B-5. a demonstrates that the vibrato has a very
small effect, if any. The individual differences ascribable to the vibrato
do not reach even a 90 % level of confidence in any case but one. The ap-
propriate concluaio-n, tllerefore seems to be that adding a vibrato has no ef-
fect on the pitch perceived.
As regards pitch perception accuracy the individual differences in the
standard deviatioxs giveri in Fig. 111-33-5. b show that there might be a sm-all
effect when the fundarriental frequency i s a s lo\-J a s 70 o r 115 Hz. F o r these
frequencies the average standard deviation r i ses by . 2 and . 1 70 respectively,
thus by an extra--1ely srzall amount. The extent af the vibrato used in the
c:<perinents i s rather s r a l l : + - 9.7 70 of the fundamental frequency. Values
of f 3 70 do occur in singing. One test sc r i cs was run with one of the subjects
in which the extent of t11c vibrato was incrcascd to + 3 O/o. However, no con-
sistent changes in the standard deviations could be observed. Therefore
the resul ts can hardly be taken a s a support for the hypothesis that a pe r -
ceptual function of the vibrato i s to cover np slight e r r o r s in tuning.
It i s interesting that the pitch perceived of a vibrato tone appears to cor-
respond to the averaged fundamental frequcncy. As long a s a sinusoidal
vibrato i s used it cannot be decided whether this average i s computed a s the
frequency midway between the extremes ill the fundarriental frequency modu-
lation curve or vrl~ether i t i s the linear mean. Lf the modrlation waveforms
a r e distorted a s shown in Fig. 111-B-6 these two averages differ.
Two test ser ies \-rere run in which thc stimulus had a vibrato obtained
v~i th the modulation v~aveforms shown in Fig. 111-B-6. The rate of the vibrato
was lcept to 6. 5 cycles per sec and the eiiteilt to f 1.7 73 of the fundamental - frequency. 1
The individual mean values obtained from these test se r i es tail be cox-
pared with those f rom the te s t where both stilxulus and response lacked a
vibrato in Fig. 111-3-7. a and b. This figare shows the effects of adding a
vibrato of these ::inds t9 the stimulus toile. A s regards pitch there seems to
be an effect of these distortions of the sincsoidal vibrato type. !?hen the
fundamental f r e q u e ~ c y ~zlalte s 20s itive deviations tile r e sponse tone was ad-
justed slightly lover than the linear averxzc, and when the vibrato =;rave-
form was inverted the opposite applies. Thus, the fundamental frequency
of the response tone x-jal; in both cases deviating from the linear average in
FUNDAMENTAL FREQUENCY MODULATION WAVEFORMS
PERIODICITY: 6 . 5 PER SECOND
Fig. 111-B-6. Two waveforms used for the fundamental frequency modulation.
EFFECT OF VIBRATO TYPE
ON PITCH
Fig
. S \
A AA
'. 4 DROP / ' \ 2
1 I I I I 1 +
VIBRATO : - -4 - - A -.-.- w
-1 5 -0- v
- v RISE f -
ON PlTCH ACCURACY
O/oo
8
l o t DECREASE 7 VIBRATO.-,^--^ 6
A -. -.- r\/ 1
I INCREASE 1 -I-"
FO (Hz)
. 111-B-7. a. Change in the difference in fundamental frequency between the stimulus and response tones observed after adding to the stimulus tone vibratos of the waveforms shown in Fig. 111-B-4.
b. Corresponding changes in the standard deviations.
STL-QPSR 1/1972 40.
the direction of the steady state portion of the modulation wavefor=. This
deviation rcay vary with the fundamental frequency since the mean curves
separate more a t h i ~ l ~ e r frequcncies. Fron Fig. 111-R-7. b it can be seen
that, on the average, there seems to be no cffect on the standard deviation
values. This indicates that the subjects dicl not find it more difficult to
match the pitch of a stimulus with these tyijcs of vibrato than wit11 a sinus-
oidal vibrato.
The resul ts clearly show that the fundamental frequency determining
the pitch of a vibrato tone i s not the frequency midv~ay betweer, the extremes I in the modulation curve. The linear avcragc appears to be a better approxi-
mation, but the steady state portion of the ~iodula t ion curve seems to be of
sorcewhat greater importance than the r c st of the curve.
Exper irzent 111. Effect of the "singing formant"
In a l l experirncnts described above thc stimulus and r e sponse tones con-
tained a "singing formantu. In one test scr ies the stimulus and response
tones were presented 1-~ithout this spectrul= envelope peak. These signals
were generated by sir-ply omitting the extra formant a t 2550 Hz in the syn-
thesizer. The idealized spectrum envelopes a r e sl~own in Fig. 111-B-8. The
stimulus tone had a sinusoidal vibrato. The effect of adding a "singing for - rA.antl' can therefore be studied by comparing the data collected in this ex-
periment with the data obtained when the stixxulus and response signals con-
tained a "singing forl;nantl'. Fig, 111-B-?. a and b shows sucI1 a comparison.
The intersubject 1::ean curve indicates that there might be an effect on
the pi-ccl~ perceived and that this effect dei>cilds on the fundamental frequency.
Ho\i.zver, statistically significant differcnccs were found only in two cases
(out of 24). Consequently the correct col~clusion seems to be that the
"singing formant'! does not affect the pitch. Sirfiilarly Fig. 111-B-9. b in-
dicates that i t does not affect the accuracy with -3hich the pitch i s perceivcd.
As previously mentiomd it has been sr:ggcsted that the $'singing formant"
~nalces the sound easier to perceive in large halls. Therefore i t may be a s -
sulxed that an cffcct could be observed if thc stimulus tone is presented a t a
considerably lov~cr sound pressure level than the response tone. In this case
the "singing formant" -:rould possibly facilitate the pitch perception. This I
hypothesis was tested in a t e s t . The stir?,ulus tone was presented a t a sound 2 1
pressure level of 4 5 d B re l . ,0002 dyn/crx , i. e. 25 dB below the level of I
IDEALIZED SPECTRUM ENVELOPE
FREQUENCY (kHz)
Fig. 111-B-8. Idealized spectral envelopes used for the stimulus and r e - sponse tones in studying the effects of the "singing formant".
- - .- -
STL-QPSR 1/1972 41.
the response tone. In one test ser ies the stimulus and response tones con-
tained a "singing formant", in another not. The stimulus tone was presented
\-{it11 a sinusoidal vibrato. All subjects but one (EJ) participated in these
series.
Fig. 111- B - 10. a and b shov~s the change s in the fundamental frequency of
the rcssonse tone and in the standard deviations observed when a "singing
forri=antl' was added to the stirr-ulus tone. Fig. 111-3- 10. a indicates that
different subjects react very differently 1-~llen the "singing formant" i s intro-
duced. At the same time there i s no clear effect on the pitch accuracy. This
i s indicated by the very srr-all changes in the standard deviation values a s
seen in Fig. 111-E- 40. b. r"cvcrt11eless significant changes in pitch occurs I only spuriously. Thus it does not seem 1il:ely that the "singin3 formant" has
any effect neither on pitch, nor on the accuracy with which the pitch i s per-
ceived even when added to a vowel of weak intensity. I In a previous investigation it was observed that the dependence on inten-
sity of the pitch appeared to be different in complex sounds a s compared with
sinusoids (Lindqvist S Sundberg, 19711). 1:Thereas the pitch of a sinusoid
below about .5 kHz r i ses if the intensity i s decreased, the pitch of a complex
wave was found to drop with decreasing intensity. If this observation i s ap-
plicable also to vowel sounds, subjects 1-~ould match the pitch of the mealcer
sounds wit11 a lower fundamental frequency than in the case when the stirn-
ulus and response tone \-{ere equally loud. Fig. III-B-11. a confirms that this
i s the case in t e rms of intersubject neans of the fundamental frequency
difference between the response tone and the stimulus tone. l'll~en the stim-
ulus and response tones have the same intensity they differ very little in
fundamental frequexcy. Vhen the s t h u l u s i s 25 dB wealcer than the response
tone the pitch appears to drop considerably, nc matter if a Itsinging formant"
i s p e s e n t or not. It i s interesting that this large shift in pitch i s not ac-
companied by an in the accuracy of pitch perception, a s indicated
by the close agreement between the standard deviations given in Fig. 111-B- 11. b.
Discussion
According to tllc findings reported in this investigation the pitch per -
ce j ved from a vibrato tone appears to c o r n spond approximately to the aver - age fundamental frequency. Moreover, the vibrato does not appear to affect
tile certainty with which the pitch i s perceived, since the vibrato \.ras not found
EFFECT OF "SINGING FORMANT"
a STIM. 45d0, RESP. 70dB
ON PITCH
FO (Hz)
b ON PITCH ACCURACY h I I 1 I I
10 - DECREASE t
INCREASE 4
FO (Hz )
Fig. 111-B-10. a. Change in the fundamental frequency difference between the stimulus and response tones observed after adding a "singing formant" to the stimulus tone. The sound pressure level of the stimulus tone was 25 dB below that of the response tone.
b. Corresponding changes in the standard deviations. The subject symbols a r e the same a s in Fig. 111-B-2.
EFFECT OF SPL
a ON PITCH
' --t S.F. STIM. 45 dB SPL 0 -*o.- - S.E RESP. 7 0 6 0 SPL
-.*.- 1 S.E STIM.4 RESP. 70dB SPL 4-14
FO ( H z )
ON PITCH ACCURACY r I I I I I I 1 O ~ o O
6 - *'- S.P STIM. & RESF! 70dB SPL
I- z U Y -- . - . V)
-0 2
FO (Hz )
.g. 111-B- I I. a. Intersubject averaged difference between the s t im- ulus and the response tones. The stimulus tone was presented a t two intensities and a t the lower intensity with and without a "singing formant".
b. Cor re sponding averages of the standard deviations.
STL-GPSR 1/1972
to increase the standard deviations in the pitch matching experiments appreciab-
ly. Consequently, the vibrato can hardly reduce the demands on intonation ac-
curacy in singing. These findings agrec 1-jitll the results of recent investiga-
tion in vrhich the relations between fundamental frequency in singing and sab-
jects3 i n ~ p r e ssion of bad intonation were examined: if the mean value of the
f u n d a ~ e n t a l frequency never coincide s with the theoretically correct value
during the course of a to-cre, niusically trained subjects tend to judge the tone
a s #'out of tune", no matter if the theoretically correct value l ies x-~ithin the
frequency swing of the vibrato (Lindgren 8 Sundberg, 1972). On the other
hand, the s t ixulus tones in our experim-ents certainly differ froxx the signals
reaching the listeners' e a r s in a concert. For instance, one difference i s that
the average fundamental frequency c;f the stirmlu s tone remained constant
(or , in the test with non-sinusoidal vibrato, almost constant) in the tests.
This seems to be r a r e in ~~,zusical perforxances. Transients in the average
fundarilental frequency may be of relevance to the effect of a vibrato a s regards
the pitch and the accuracy of pitch perception Thus, a vibrat, c . 2 ~ be
rc lcvmt :-?kc3 the sinzcr' r accuracy in t;:::ing i s uncertain. Another dif - ference is that a voice is often accompanied by instruments or other voices
in music. It i s likely that a vibrato i s capable of hiding beats between n i s -
tuned sounds under these conditions. Therefore, it may in such situations
have a function of covering e r r o r s in tuning.
The average fundamental frequency uscd by the ea r in pitch perception ap-
pears to be closer to the linear average than the frequency lying =id\-ray be-
tween the extremes in the modulation curve. On the other hand, the experi-
x x n t s wit11 the non-sinusoidal vibratos also showed that the steady state
portion of the f u n d a ~ e n t a l frequency modulation waveform seems to be cf
slightly greater ircportance than the rapidly changing portions when the ea r
compute s the average determining the pitch perceived. An interpretation of
this cannot be m-ade on the basis of the available set of data. However, it seerri s
reasonable to assume that the c.xplanation deals with some time constant in
the fundamental frequency measuring sys t ex of the ear ; this system might
be too slow to follox-r the rapid changes in fundamental frequency occurring
in the distorted l-nodulation waveforms. ?his interpretation is in agreement
with earl ier findings \-/here subjects matcl~ed the extreme s in pitch between
which a vibrato tone appeared to swing. These pitches correspond to f re -
quencies slightly closer to the average frequency than the actual frequencies
STL-QPSR 1/1972
of the extremes (Makepeace, 1 931, cit. in Vennard, 1967). Further experi-
ments with sy ster=,atically varied shapes of the fundamental frequency modu-
lation waveform may elucidate the propcrtie s of the fundamental frequency
measuring s y s t e a of the ear .
The &'singing formanttt seems to have no appreciable influence neither on
the pitch nor on the accuracy of pitch pcrccption. Thus no explanation to its
presence in professional singing has been found. Another hypothetical ex-
planation to be tested in future r e search i s that it matches the average
spectrum of an orchestral accompaniment iil such a way that the tone sung
I i s i ~ o t masked.
I
The standard deviation values in all cxpcriments described in this in-
vestigation a r e astonishingly small and a p p a r to be rather unsensitive to
variations of stimulus properties. The standard deviations in a test of this
liind cannot be expected to be identical \ -~ i t l~ the difference limen for frequency,
but they could be cxpectecl to be of the sx:e order of magnitude. However, I
the standard deviations a r e about 5 to 10 t h e s smaller than the difference
l i n e n reported for sinusoids. One possibility of explaining this discrepancy
i s to assume that the difference limen for frequency reported in the literature
i s too large (Ralcot-zslri, 1172). I t i s also possible that the pitch of a complex
sound i s perceived wit11 higher accuracy t h n the pitch of a sinusoid. In pre -
vious experiments i~us i ca l l y trained subjects set the octave of given stim-
ulus tones. In these experiments the s t a ~ d a r d deviatior s were approxir-~ately
only doubled when the stimulus tone was shifted from a complex wave signal
to a sinusoid (Lindqvist & Sundberg, $971). Consequently it seer-1s reasonable
to assume that musical training i s of appreciable importance to tile difference
lirsen fcr frequency. Piost probably then the extremely small standard devia-
tions found in the present te s t ser ies a r e d ~ e to the musical training of the
scbjects and to the fact that the stimulus tone as a compkx wave.
Conclusions
The pitch perceived from a vibrato tolie appears to correspond to the
average fundamental frequency to the fir s t approximation. However, the
~ e a s u r i n g system cf the ea r i s probably :lot capable of tracking very rapid
changes in the fundamental frequency so that slight discrepancies c a y occur
between the physical average and the average giving the pitch. The pitch 1
perceived does not seem to be affected by the presence of a "singing formanttt,
1