Dept. for Speech, Music and Hearing

Quarterly Progress andStatus Report

An articulatory interpretationof the ’singing formant’

Sundberg, J.

journal: STL-QPSRvolume: 13number: 1year: 1972pages: 045-053

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

STL-QPSR 1/1977. 45.

C. AN ARTICULATORY INTERPRETATION OF THE'SINGING FORlMANl3

J. Sundberg

Abstract - Eats collected frorr- toixograri:~ indicate that a lowered larynx - typical

of profe ssional male singing - increases Ere laryr-zeal ventricle, the sixis p i r i fo rxes and the cross-sect ional a r e a L: the lox-rer pharynx. The effects of such changes on the forrzant frequencies a r e studied by means of neasure- c:eilts on an acoustical tube-model of the vocal t rac t . The resu l t s indicate that the larynx tubc can a c t a s a separate I-Ielxholtz resonator the resonance frequency of which can bc tuned to a freqvency between those of the third and fourth length resonalrces of the vocal t ract . The condition for generat- ing such an ext ra forEant i s that the l a r y n ~ e a l veiitricle and the c r c s s - sectional a r e a in the lower pharynx a r e sufficiently iarge. The sinus p i r i -

I f o r c e s seefi: to iacrease the effective len,n"L~ of the pharynx, thus loweriag those formant frequencies in particular "Lilat a r e due to standing vraves in the pharynx. In this \-Jay the formant frcquency changes accorr-panying a lox-~ering of the larynx appear to explain the "singing forrcant' ' a s well a s other rriajor f o r n a n t frequency differences between spoken and professional - 17 sung vov~els. I I. Introduction

The "2. G kHzJ1 o r tke !'singing formantf i belongs to the acoustical char -

ac ter i s t ics of professionally sung vowels in our culture. More o r l e s s in-

dependent of vowcl and pitch it appears a s a region of high spectral energy

near 3 kHz in rr:ale singing. This spectrum envelope peak s e e m s to be a c -

con~panied by a l i : i ~ i m u ~ slightly higher ir, frequency and often clearly dis-

cernable in the spcctrogran?. In Fig. 111-c-4 a spectrurr:. level difference of

2 0 d B i s observed between a spoken and sung [u).

How can such a "singing formantJ1 be generated? If two o r more fozr.zants

approach each other il: frequency the r e s o n a x e effect will increase and the

spcctrurr, envelope will r i s e . !&r previocs r e s e a r c l ~ attelxpts to rilatc!~

spectra of sung vo:;rels on a forrxant synt>csizer (Sundberg, i970a) she\-led

that five forrr-ants belox*~ 3 kHz a r e requircd in order to generate a "singing

formantt1 with f0ri::ant.s oi2ly. But in nnrizal speech the frequency of the

fifth forrilant generally l i e s around 4. 5 kHz. Therefore, when we interpret

the )'singing for1i:a::t" in t e r m s of forraants only we have to a s su r -~e a dras t ic

compre ssion of higher fori::.ants.

* 1

Expanded version of a paper presected a t the Symposiun; on Formants {

in Singing, National As sociation of Tcacher s of Singing National Con- ! vention, St. Louis, I?/io., USA, Cec. 2 9 , 1971.

VOWEL [u]

SPEECH

3 kHz

Fig. III-C- I. Spectra of the vowel [u] spoken (left) and sung (right) by a professional bass singer.

3 kHz 4

Analyses of the forr;;ant frequencies in vowels spoken and sung by four

trained bass s ingers have shown that in fact such formant conipre ssion does

take place in singing. An illustration of this is given in Fig. III-C-2, where

dashed curves show the forrxant frequencies in vowels spolren by untrained

subjects (Fant e t a l . , 1969) and solid l ines r e fe r to sung vowels a s produced

by trained s ingers (Sundberg, 1968). In singing five formants appear below

the frequency of tllc fourth formant in nori:-,al speech. We a lso note that the

second and third forxants a r e lower in SLXIG front vov~els and that the third

forcant i s slightly raised in sung back vox-rels. Thus, we rcay be reason-

ably sure that the s ingers actually co r lp res s their formants in singing. But

what articulation is required for arr iving at such a formant compression

effect ? The present paper suggests an ansvrer to this question obtained by

studying the ar t iculatory difference s bet;;rceiz spolren and sung vowels and in-

ve stigating their acoustical effects by raeans of an acoustical model of the

vocal t ract .

11. Articulation

The vowel articulation in speech and singing of three of the mentioned

bass s ingers was analyzed frorr, l a te ra l X-ray pictures of the vocal t r a c t

and photographs of the lip opening (Sundberz, f970b). Four important a r -

ticulatory differences \-rere observed to be consistent for a l l sub-jects in

singing a s compared with speech. F i r s t , the larynx was lowered, secondly

the jaw opening was l a rge r , thirdly, the tongue tip was advanced in the back

vo\-rels [u!, [o], and [a], and fourthly, $he l ip s were excessively protruded

in front vowels.

It can be assumed that an acoustic fcatvre such a s the $'singing formant"

which i s common to a l l vol-~els s tems f r o n a region of the vocal t r ac t , that

i s leas t affected bjr the variations of articulatory configurations required

in order to kee-, the vex-rels acoustically distinct. Such a region is the phar-

yllgeal cavity systeir, beloi-J the epiglottis.

The anatorcy of this system can be described a s follovrs. The vocal I

chords constitute the bot tox of a sclall tube vrith a length of about 2 c x , the

larynx tube. This tube i s vertically inserted into a l a rge r tube, the pharynx

tube , that is closed off by the esophagus mouth a t about the level of the vocal - chords. Since the larynx tube i s narrox-rer than the pharynx tube the b o t t o ~ .

par t of the pharynx tube constitutes a cavity surrounding the larynx tube.

FORMANT FREQUENCIES IN SINGING AND NORMAL SPEECH

I I I I I I I I I -

4.0 - - Slnging 7

e- - Normal speech . a\ 3.5 - -

CI

N

3.0 - u

U) W - 2.5- 0 z W

a 2 0 - W a &A

t 1.5 - z 4 I K 0 1.0 - LL

0.5 -

0 - - i I I I t I I I I I 6

[u:I b:I [a:] [=:I led [i:] [y:] [tt:]

V O W E L ( I P A SYMBOLS)

Fig. 111-C-2. Formant frequencies of long Swedish vowels in normal male speech according to Fant e t al. (1969) (dashed lines) and in professional male singing (solid line s) according to Sundbe r g ( 19 68).

STL-CPSR 1/1972 47.

This cavity i s divided into two pockets, one left and one right. These pockets

a r e called the sinus piriformes. Another cavity of relevance i s the laryngeal

ventricle or the sinus Morgagni which i s found a t the bottom of the narrow

larynx tube.

The influence of a 1 arynx lowering on these cavities was examined in one

of the trained singers. Lateral and frontal tornograms were taken when the

subject phonated the sustained vowels t i] and [ a ] with raised and lowered

larynx. Tracings of these torcograms a r e shown in Fig. 111-C-3. A- larynx

lowering i s seen to be associated with t\-ro x a i n effects. F i r s t the sinus

l?riorgagni i s expanded and secondly the sinus piriforme s a re lengthened and

expanded. An additional effect of a larynx lowering not seen in the figure

i s of course an increase in the total length. of the pharynx tube.

111. Acoustic interpretation I The acoustic effect of some of the articulatory differences observed be-

tween speech and singing a r e known already. A lowered jaw raises the f i rs t

forxant frequency ( L i n d b 1 0 ~ and Sundberg, 197 1). In front vowels a length-

ening of the pharynx lowers the second foril-,ant (Fant, 1970) and a lip pro-

trusion lowers the third (Sundberg, 1970b). If the tongue tip i s advanced in

back vowels the third formant frequency \ - f i l l r i se (Sundberg, 1970a).

A s we turn to the influence from the sinus pir iforme s and the larynx

tube we enter a field vrhich has not been equally well explored, In view of

the lack of agreement in the results frorr: earl ier investigations (Beclunann,

19%; Flach, 1961; Flaclz and Schwickardic, 1955; Merrnelstein, 1967;

r a n t , 1970; Sundberg, 1970a) conclusive evidence seems to be needed a s

regards the acoustical effects of these cavities. In the present investigation

such evidence was obtaincd by means of an acoustic tube model of the vocal

t rac t containing simulations of the larynx tube with the sinus Ivlorgagni and

the sinus piriforme s.

Let us first consider the larynx tube. Frorri the tonograms of the lowered

larynx es t ixa tes were made of its dimensions. On the assumption of ellip-

tical shapes in all dimensions the a i r vol~~i-ne contained in the sinus IAorgagni 3 \-/as e s t i ~ a t e d to about . 5 cm . The res t of the larynx tube n a y be regarded

a s a roughly cylindrical tube with a cross-sectional area of about .5 cm2 and I

i a length of slightly =ore than 2 cn;.

LARYNX

LOW

Fig. 111-C-3. Tracings of frontal and la teral tornograms (left and right in each pair respectively) of the larynx in high (left pairs) and low (right pa i rs ) position during phonation of the vowel [ a ] (upper se r i e s ) and [ i ] (lower ser ies ) . (The tornograms were taken by Dr. M. Haverling, Karolinska Sjukhuset, Stockholm. )

Acoustic theory tel ls u s that a tube of these dimensions can be regarded

a s a Helrr,holtz resonator consisting of a volume (s inus ~idorgagni) and a ~ e c k

( r e s t of the larynx tube) (Trolie, 1968). T1;i:len inserted into a la rger tube of

c r o s s - sedona l a r e a A i ts lome st resonance frequency can be calculated with

the following equation:

The effective length ~f the neck 1 can be approxi=ated using a formula n, e

given by Ingsrd ( N 5 3 ) :

c is the specd of sound propagation

A i s the cross-sectional a r e a of the neck n

'n i s the len$h of the neck

V i s the voluxxe

This equation irLplies that the larynx tube ac t s a s a separate resonator:

This i s the case \-ll~eri the cpening a r e a 3f tke larynx tube i s s z a l l e r than

1/6 of the cross-sectional a r e a in the pharyilx. This condition appeared to

be fulfilled in the case of the lowered laryn:: shown in the tornogram-s: when

the larynx i s depressed the pharyngeal cavity appears to be widened. The

resonance frequency of the rzentioned larynx tube was calculated to about 2. $1

kHz. This value gives important information since it indicates that the

fourth formant in sung vov~els w-ay stem froii-i the larynx tube. If so, the

fifth formant in s i q i n g v~ould correspond to the fourth formant in n o r x a l

speech which seesi--s rczr,o:~able. a

I s it reasonable to assume that the s i ~ g e r s ' larynx tubes alx-lays ac t 2 s a

separate r e sonator resonating a t a frequency bet\-reen the third and norx-cal

fourth for;--*ants? The opening a r e a of the larynx tube depends or, the funda-

mental frequency a t which the vocal chor6s vibrate. Thus, the laryrcx tube

opening increases with rising pitch. F i r s t , in order to retain the larynx tube

a s a separate resonator under these conditions i t would be necessary t~ I

acquire 2 \-ride pharynx x-~11ich possibly car: bc achieved by lowering the larynx

excessively. Sccondly, a widening of tilo r~cclc of a I-:eln=holtz resonator in-

c reases i t s resonance frequency. Such a :-~idening of the tube opening 11:ay

be compensated for by an increase in the v o l u ~ e o r neck length. An increase

Experimental data were provided by the node l where the sinus piriformes mere

sixulated by one or two circular tubes of varied lengths and d iane te rs inserted

paralelly to the larynx tube into the closed end of a wider tube sinulating the

pharynx and the mouth. Li Fig. 111-C -5 the calculated data and measured values

can be ccmpared. Note that the main determinant for the zero frequency i s the

depth of the poc1;cts whilst their cross-sectional area i s l ess important. More-

over, sirculating only one instead of both pocliets has a small effect. The zero

zrppears scr-:e~:~here bett-Jec:l 3 and 4 kI-Iz :or a poclret depth of 2 cm. Rccslling

that a spectrum crivelope minimum often can be observed in this frequency

region in spectra oi sung vowels we can conclude that this minimum i s liizely

to stem- f r o m the sinus piriformes.

The sinus piriformes have another effect a s tvell, namely on the fo rxan t

frequencies. This effect \;rill however depend on the area ratio between the

larynx tube opening and the pharynx. If it i s sriialler than 1:6 the sinus piri-

forrnes will ac t a s a lengthening of the pharynx tube and lower the frequencies

of those formants in p a r t i c ~ l a r that corrcspond to resonances in the pharynx

tube, e. g. the second fornan t in front vo\-~cls. Thus the sinus piriforr.3es will

affect the formants in a xanne r that depends on the articulationor the place of

a constriction in the vocal tract.

The effect for various locations of a constriction (length 6 cm, cross-sec- 2

tional area f cm) \-?as studied experimentally in the tube model including sim-

ulation of the larynx tube, the pharynx, and the m-outh. Fig. 1.1-C -6 shol-JS the

observed formant frequencies a s a functioa of the place of constriction. The

fifth formant i s consaiderably lowered for certaiii place s of constriction where - a s the fourth formant acting a s a separate resonator, i s essentially unaffected.

Thus, the sinus piriformcs a r e in fact able to cozp re s s higher forn:ants. The

second fo rxan t i s l o -x rcd in cases of frontal constriction and the f irst formant

i s slightly lowered in all cases.

These observations iya-jr re=ind us of the observations z a d e in comparing

the forxant frequencies in singing and nor:z-,al speech. The fourth formant r e -

ixains a t about 2 . 3 1:I-Iz for al l articulations, and the fifth approaches the fourth

in singing. The second formant i s lowered \-?hen the place of constriction i s

fronted. 0a the other hand there a r e differences between the foriilant frequency

changes due to the siiius piriformes and those observed between singing and

specch. F i r s t , the formant shifts a r e ~--?rrcl~ greater between speech and sing-

ing, probably owing to the fact t3at thc pharynx lengthening was not simulated

I 1 I I I

6.0 - -

0

N I x V

8 5.0 - - W N LL 0 > U z z " " ~ - w ~ . ~ ,,,,I, ,, .,I ."I"',,-".,. ,-,,-""",,,WY1.L.II

W => 4.0 Q

- W Area of 8.p. x 1.2 c d z LL Area of 8.p. a 2~1.2cm2C2tubes)

Area of 8.p. 3.5 crrf

- Calculated tc14 Le)

3.0 - ct.= 4 e . 7 Gk - : I I I I I

0 0.5 1 .O 1.5 2.0 DEPTH OF SINUS PlRlFORMlS (cm)

Fig. 111-C -5. Frequency of the t ransfer function zero stemming from various types of cavities simulating the sinus piriformis (s. p. ) in the acoustical model.

EFFECT ON FORMANT FREQUENCIES OF S l NUS PlR l FORMiS

1 I I I I I I I I I I

4.0 - *- - * Without s p - t

, ' ', - With s.p.

DISTANCE CONSTRICTION CENTER -OPEN END (cm)

E 'zIzzz b*

Fig. 111-C-6. Formant f requencies obtained f r o m an acoustical model of the vocal t r a c t with (solid l ines) and with- out (dashed l ines) simulation of the sinus pir i formis . The model con isted of a tube with a cross-sect ional 'i a r e a of 7.8 cm and a total length of 19 c m in which the larynx tube was simulated by a sma l l Helmholtz resonator tuned to resonance a t 2.8 kHz and the sinus piriformif by two tubes of a cross-sect ional a r e a of 1 .2 c m and a length of 2 cm.

STL-QPSR 1/1972 5 1.

in the model experiments. Secondly, t l ~ c f i rs t forn-Aant i s raised in singing

and lowered by the sinus piriformes, but a s mentioned t h jaw is lowered in

singing which causes the f i r s t fcrmant to rice. A third difference i s that

the third formant i s not lowered in the sa122e v~ay. This i s certainly due to

the strong dependence of this formant on the tongue tip position and the lip

protrusion that were not s k u l a t e d in t l ~ c :=lode1 experiments. The observa-

tions sugge s t the conclusion that the formant frequency difference s observed

between speech and singing can to a largc extent be explained with reference

to changes in the pharynx and larynx tube associated with a lowcring of the

larynx.

Shifts in formant irequencies a r e accocpanied by alterations of the spec-

trum envelope. Measured changes in thc spectrurfi envelope due to the pres-

ence of a wide sinus Morgagni, the sinus 2iriformes, and to a raise of the

third fcrrzant frequency can be studied in r ig . 111-C -7. The values were ob-

tained f rom the model ~ i ~ u l a t i n g an articulation similar to that of an [u].

A daixping effect frorr, the transfer function zero due to the sinus piriformes

i s clearly seen. The substantial envelope r ise due to the sinus Morgagni i s

reinforced when the third formant i s shifted upwards in frequency. The total

gain in spectrum amplitude around 3 IcI-Is i s about 20 dB. This values agrees

l-~ith the initially observed difference between a spoken and a sung [u]. The

conclusion therefore seems justified that a singer i s capable of generating a

"singing formant" by a e a n s of his sinus Liorgagni, sinus pi r i forzc s, and in

the Eacl: vov~els, his tongue tip. Except for the tongue tip movement these

effects a r e presimabiy all secondary consequences of a lowering of the larynx.

IV. Discussion

It has been shown that the singer i s able to produce a vowel with a "singing

formant I ' using his vocal chords and vocal t rac t exclusively. Given the ex- I planation sugge sted above the re i s no motivation to postulate "clie s t r e sonance " , ''head resonance", f'cingi:~g in the maskfJ, ctc. , i. e. they appear to lacl:

acoustical relevance for the tone. On the other hand, these terms play a pre-

dominant role in current vocal pedagogy. The reason for this might be that

these terns describe patterns of vibration sensations that appear only when

the tone is properly produced. Perhaps, i-e cognizing the vibrations accom-

panying good tones may be an efficient way to control vocal production.

EFFECT ON SPECTRUM ENVELOPE OF SINUS PlRlFORMlS ARTICULATION: [u] =#

I I 1 I I

FREQUENCY ( k H z )

Fig. 111-C-7. Spectrum envelope changes due to the introduction of sinus pir i formis (s. p. ), sinus Morgagni (s. M. ), and a raised third formant frequency (AF ). The 3 changes were observed in an acoustic model of the vocal t rac t consisting of a 19 cm tube (0 = 3. 1 cm) and including two constrictions so a s to simulate the articulation of a sung [u].

STL-CPSR 1/1972

Frorn the acoustical point of view it i s essential for the generation of the

11, ,inging - formant" that the larynx tube ac ts a s a separate resonator the r e so -

nance of which i s not affected by articulatory r;r^ovements in the r e s t of the

vocal t ract . This i s a c ~ o ~ p l i s h e d only .;lileil the larynx tube opening is c:uch

narrower than the cross-sectional a r e a ill the pharynx. Articulatorily this

effect i s obtained by lowering the larynx ~;/5ich widens the pharynx cavity.

Part icular ly. a t higher pitches where the larynx tube opening i s vide i t

be essential to acquire a wide pharynx.

It was mentioned that .:hen we increaze pitch we also increase the larynx

tube opening. Thk increase has to be co1~1;ensated for by a widening of tile

sinus idorgagni if the larynx tube resonance should remain a t 2 .8 kHz. A

contribution to the widening required i s provided by the stretching of the vocal

folds constituting the bottolx of the sinus I..iorgagni. But probably additional

compensation i s required a s well. If so, the singer will have to lower h is

larynx more and x o r e the higher tile tcne s he sings. This agree s wit11 the

coz--rnonly stated ceed for "covering" high note s , since covering h a s been

sholvn to be associated pheno l~ena si:xilar to the effects observed in

larynx lowering.

There a r e ,nreat individual diiferenccc a s regards the dimecsions of the

vocal chords, the sinus idorgagni, and tlze sinus piriforrrie s. We may con-

clude f rom the present investigations that a good singer needs a large sims

Ivlorgagni and a wide pharynx. One day i:.- future \-re may a r r ive a t the pos-

sibi lity of x e a s u r i n g the se cavitie s f r o 2 tomograr-s talcen with lo\-rered I

larynx and judge -.-.?lether it i s advisable fo r that individual to s t a r t a voice

training aiming a t an operatic c a r r e e r .

V. Conclusion

The acoustically i>~os t essential articulatory difference between speech

a;>d singing appears to be the widening of the pharynx a t the level of tlle larynx

tube apenicg. Sucl a widening ~f the pharynx is probably accompanyi?g a

lcwering of the larynx. Acoustically the pllarynx widening h a s the effect of

isolating the larynx tube from the r e s t of " i ~ e vocal t r ac t so that i ts r e s o n a c e

frequency i s not al tered by articulatory :_-ovements outside it. Its resonance

can be tuned to a frequency between the third and fourth formant in normal

speech by choosing tile volum-e contained il2 the sinus Morgagni in relation to

tlze opening a r e a of the larynx tube. Ar, additional effect of a larynx lovrering

STL-QPSR 1/1972 53.

i s that it increases the dimensions of the sircus piriformes and the length of

the pharynx tube. This mainly lowers the second formant frequency in front

vov~els and in certain articulations a1 so that of the fifth fornant . In this way

a great deal of the acoustical difference s betmeen spoken and sung vowels

can be explained wit11 reference to the larynx lowering, the major articulatory

gesture associated with the production of a "singing formant".

Aclaowledgments I The author i s indebted to B. L i n d b l o ~ , J . Lindqvist, and M. M. Sondhi

for valuable discussions, The tomograms were obtained due to kind coopera-

tion of Dr. 3A. Haverling at the Karolinska S j ukhuset, St ockholm. The work

was supported by the Bank of Sweden Tercentenary Fund under Contract No.

67/46.

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J I

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