sundberg et al 2007

Experimental Findings on the Nasal TractResonator in Singing

*Johan Sundberg, †P. Birch, ‡B. Gumoes, ‡H. Stavad, §S. Prytz, and ||A. Karle

*Stockholm, Sweden and †Aarhus and ‡§kCopenhagen, Denmark

Summary: Many professional operatic singers sing the vowel /a/ with avelopharyngeal opening.1 Here resonatory effects of such an opening are an-alyzed. On the basis of CAT scan imaging of a baritone singer’s vocal tractand nasal cavity system, including the maxillary sinuses, acoustic epoxymodels were constructed, in which velopharyngeal openings were modeledby different tubes. The sound transfer characteristics of this model weredetermined by means of sine-tone sweep measurements. In an idealized(iron tube) model, the VPO introduced a zero in the transfer function at thefrequency of the nasal resonance. In the epoxy models, however, the reso-nances of the nasal system, and hence the zero, were heavily damped, partic-ularly when the maxillary sinuses were included in the nasal system. Avelopharyngeal opening was found to attenuate the first formant in /a/, suchthat the relative level of the singer’s formant increased. A similar effect wasobserved in a modified epoxy model shaped to approximate the vocal tractof an /u/ and an /i/, although it also showed a substantial widening of the firstformant bandwidth. Varying the size of the velopharyngeal opening affectedthe transfer function only slightly. It seems likely that singers can enhancehigher spectrum partials by a careful tuning of a velopharyngeal opening.

Key Words: Nasalization—Maxillary sinuses—Nasal resonance—Formants—Singer’s formant.

Accepted for publication November 18, 2005.Presented in part at the 4th Pan-European Voice Conference,

Stockholm, August 2001, and at the Annual Symposium Care ofthe Professional Voice, June 2002, Philadelphia, Pennsylvania.

From the *Voice Research Centre, Department of SpeechMusic Hearing, KTH, Stockholm, Sweden; the †Royal Acad-emy of Music, Aarhus, Denmark; the ‡Royal Academy ofMusic, Copenhagen, Denmark; the §Phoniatric Department,Bispebjerg Hospital, Copenhagen, Denmark; and the ||Depart-ment of Diagnostic Radiology, Bispebjerg Hospital, Copenhagen,Denmark.

Supported by a grant from the Ministry of Culture inDenmark.

Address correspondence and reprint requests to JohanSundberg, Voice Research Centre, Department of SpeechMusic Hearing, KTH, Stockholm SE-100 44, Sweden.E-mail: [email protected]

Journal of Voice, Vol. 21, No. 2, pp. 127–1370892-1997/$32.00� 2007 The Voice Foundationdoi:10.1016/j.jvoice.2005.11.005

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INTRODUCTION

Nasal resonance is generally considered an im-portant component in the formation of vowelsounds in classical singing. For example, singingteachers typically use vocal exercises where nasalconsonants are interleaved with vowels, such as in/mimamu../. This seems to suggest that singingstudents are encouraged to sing with a more orless open velopharyngeal port.

In a previous investigation, the velopharyngealopening (VPO) was analyzed in 17 professional op-era singers, three high sopranos, three sopranos,two mezzo-sopranos, three tenors, two baritones,two bass baritones, and two basses.1 The presenceof a VPO was analyzed by three methods, nasalDC airflow, visual inspection of the velopharyngeal

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128 JOHAN SUNDBERG ET AL

port from above by means of a nasofiberscope, andacoustic analysis of the sound radiated from the na-sal and oral openings. Evidence of a VPO, in termsof a nasal DC airflow and/or a clearly visible open-ing, was found in most male singers and some fe-male singers for the vowel /a/ but more rarely forthe vowels /u/ and /i/. Signs suggesting the presenceof a VPO were found in some other singers. The fi-berscope data revealed that the shape of the VPOvaried both between singers and within singers, de-pending on pitch and vowel, thus supporting obser-vations by Bauer.2

The spectral effect of a singer’s nasalization ofthe vowel /a/ was studied in an informal experi-ment, where a baritone singer (co-author P.B.)attempted to vary what he referred to as ‘‘the degreeof nasal quality’’ in the voice timbre. Figure 1

shows three examples, one without nasal quality,one with an intermediate degree, and one with anexaggerated degree. As can be observed in thefigure, the intermediate degree of nasal qualitywas associated with a substantial boost of the high-er formants. Assuming that ‘‘nasal quality’’ is asso-ciated with the presence of a VPO, this seems tosuggest that singers may gain a boosting of thesinger’s formant by means of a VPO.

As the frequencies of the formants influence theirlevels, the formant frequencies of these threeversions of the vowel were measured, using acustom-made inverse filtering program ‘‘Decap’’written by Svante Granqvist. The program can dis-play the spectrum and waveform of an input signalalong with the spectrum and waveform of theresidue that results from an inverse filtering of the

FIGURE 1. Example of co-author P.B.’s productions of the vowel /a/ with different degreesof nasal quality.

Journal of Voice, Vol. 21, No. 2, 2007

129NASAL TRACT RESONATOR IN SINGING

signal. The characteristics of this filtering are con-trolled by manually tuning the frequencies andbandwidths of the formants. This analysis revealedthat F1 and F2 were basically identical in all threeversions, whereas F3, F4, and F5 were slightlymore densely clustered in the ‘‘nasalized’’ and ‘‘un-duly nasalized’’ versions. This cannot, however, ex-plain the considerable boosting of the singer’sformant.

The spectral effects of nasalising different vowelshave been studied by many researchers over severaldecades as comprehensively described by Feng andCastelli.3 According to Fant,4 a VPO introduces ze-ros in the transfer function of the vocal tract at theresonance frequencies of the nasal tract. These fre-quencies, however, are influenced by the size of theVPO. Lindqvist-Gauffin and Sundberg5 showedthat the nasal sinuses significantly affected thetransfer function of the nasal tract.

Depending on the frequency locations of thetransfer function zeros, the levels of the variousvowel formants are raised or lowered. Fant4 alsofound that a VPO of 0.16 cm2 could cause an atten-uation of the first formant of the vowel /a/, such thatformants 3, 4, and 5 were enhanced in the oralsound. Stevens6 summarized the effects of nasaliz-ing vowels and showed examples where a nasaliza-tion of the vowel /a/ created a reduced leveldifference between the first and third formants.

Dang et al7 studied the morphology of the nasalcavities in four subjects and noted a marked influ-ence of the morphological variation on the transferfunctions. Moreover, they found that asymmetriesbetween left and right caused pole-zeros in thetransfer function. Also, they calculated the transferfunction for the consonant /n/ and observed effectsof the maxillary sinuses. Feng and Castelli3 calcu-lated transfer functions of vowels with different de-grees of coupling between the nasal and the oraltracts and noted that the coupling affected the fre-quency of the zero. The zero heavily distorted thetransfer function particularly for the vowel /i/.They also studied the influence of attaching to thenasal tract to a 18-cm3 sinus cavity with a resonancefrequency at 650 Hz. The sinus introduced anotherpole-zero pair in the transfer function. Also, a me-dium degree of coupling boosted the third formantpeak as compared with the first formant peak in the

vowels /u/ and /a/. Hawkins and Stevens8 examinedthe perceptual relevance of introducing a pole-zeropair in vowels.

In summary, it is clear that the frequency of thezero caused by nasal tract resonance varies depend-ing on the size of the VPO. As the singers in thecurrent study clearly varied the size and shape oftheir VPO, it seems likely that their acoustic targetwas to tune their nasal tract resonance. The ques-tion posed in this investigation is what the timbralbenefit of a VPO may be. The timbral effects ofnasalizing the vowel /a/ are, however, difficult topredict on the basis of available knowledge, parti-cularly because they depend on morphological fac-tors. For these reasons, the effect on the vocal tracttransfer function was measured on various acousticmodels of the vocal and nasal tracts.

METHOD

Three acoustic models of the vocal tract weremade, one stylized and the other more detailed.The stylized model (Figure 2) consisted of a 20-cm-long iron tube with a quadratic cross-sectionalarea of 2.2 3 2.2 cm2. A hole, with a diameter of1.8 cm, was drilled with its center 11 cm fromthe glottal end. A radial hole of the same dimen-sions was drilled into a second tube, with a lengthof 10 cm, with the same dimension as the longertube. Into this hole, a set of 2-cm-long couplingtubes of different cross-sectional areas were in-serted (Table 1). The connection was sealed bymeans of sticky clay (Plasticine, Creative CompanySverige AB, Gothenburg, Sweden).

The detailed models were based on co-authorP.B.’s vocal and nasal tracts. These cavities werephotographed by means of computed tomography(CT) scan, because this technique gives a high res-olution. The CT scan was taken while the subjectformed his vocal tract as for singing the vowel /a/.The CT scans were obtained on a Picker 5000 spiral

FIGURE 2. Schematical model of the vocal and nasal tracts.



scanner (Santax Medico, Arhus, Denmark) depict-ing the entire vocal tract while the upper part ofthe nasal tract was excluded to protect the eyesfrom radiation. The pitch factor was 1.50, the colli-mation 2 mm was interpolated to 1 mm, the scantime was approximately 40 s, and the algorithmwas the standard. All transaxial slices obtainedwere later reconstructed on a workstation toa three-dimensional image, which was then usedfor casting two epoxy models of the vocal tract(VT) and two models of the nasal cavities. Figure 3shows the complete Epoxi model. Both VT modelswere divided into three sections by two cuts, one

TABLE 1. Dimensions of the Tubes, With a Length of2 cm, Used for Modeling Different Sizes of the VPO

Tube # Diameter mm Area mm2

1 5.1 20.42 7.0 38.5

3 7.5 44.24 8.8 60.85 9.0 63.6

6 10.1 80.17 12.2 116.9

FIGURE 3. Subject’s vocal tract as derived from the CT scan.


parallel to the floor of the nasal tract and one paral-lel to the tongue dorsum (Figure 4).

The CT documentation revealed a VPO of about0.15 cm2, which was achieved by a lowering of thevelum, as can be observed in Figure 4. In onemodel, this VPO was kept. In the other, the loweredvelum was eliminated, such that a wide VPO wasobtained, allowing insertion of the coupling tubesmentioned above for modeling VPOs of varioussizes. Also the pharyngeal tongue constrictionwas removed. Plasticine was used to provide an air-tight seal between the coupling tube and the walls.One of the nasal tract models did not include themaxillary sinuses.

When measuring the frequency response ofmodels, Vaseline paste was applied to the contactsurfaces of the three parts of the model to providean airtight seal. The frequency curves of themodels, that is, their transfer functions, were mea-sured by means of a sine sweep obtained from acustom-made computer program, Tombstone,written by Svante Granqvist, that simultaneouslyrecorded and displayed the transfer function. Anearphone fastened to the closed (glottal) end pro-vided the acoustic excitation of the models. Thesound was picked up by a small omnidirectional

FIGURE 4. The three parts of the epoxy model of the sub-ject’s vocal tract.


electret microphone, outer diameter 0.7 cm, thatwas placed radially at a distance of about 1 cmfrom the oral end (Figure 5). The summed transfercharacteristics of the earphone and microphonewere determined by recording a sine sweep infree air. All sound transfer curves were then cor-rected by the response curve thus obtained.

RESULTS

Data on the cross-sectional area for the vocal andnasal cavities were derived from the CT scan. Datafor the nasal cavities are shown in Figure 6 togetherwith the Bjuggren and Fant9 data obtained froma mold taken from a corps. There are great differ-ences that, however, may very well originate fromindividual variation as well as from the drying ofthe mucosa occurring after death. The maxillary si-nuses reach a maximum cross-sectional area ofabout 8 cm2 near 3 cm from the posterior wall.The volume contained in them amounted to about18 cm3 each.

Frequencies and levels of the five lowest for-mants and of the frequency of the zero were mea-sured in the transfer functions obtained from thefrequency sweeps of the models. The reproducibil-ity of these measures was tested by repeated mea-surements on the complete epoxy model. Theresults (Figure 7) showed a good reproducibilityfor frequency data and a somewhat lower reproduc-ibility for level data, particularly for low levels.

FIGURE 5. Setup used for measuring the transfer function ofthe vocal and nasal tracts. The insert graph to the low leftshows the combined sound transfer characteristics of the ear-phone used for the sine sweep and the microphone.

As expected, the nasal tube introduced a zero inthe transfer function. The frequency of this zerowas closely related to the resonance of the nosetube, which, in turn, was dependent on the cross-sectional area of the coupling tube. Figure 8 showsthe relationship for the square-tube model betweenthe area of the coupling tube and the frequencyof the zero Fz, which appeared at

Fzz168)A1799 Hz

where A is the cross-sectional area of the 2-cm-longcoupling tube in centimeters squared.

Figure 9 shows the transfer functions for thethree models of the nasal tract, the iron tube, andthe epoxy models without and with the maxillarysinuses, all with the pharyngeal end closed. Forthe iron model, the lowest resonance appeared at800 Hz, and for the epoxy models at 550 Hz and400 Hz. The bandwidth of this resonance wasmuch wider in the epoxy models than in the irontube model, particularly for the model that includedthe maxillary sinuses. This result was not surprisinggiven the very large circumference-to-area ratio inthe nasal tract,9 but apparently also the sinuses con-tributed substantially to the losses.

Figure 10 shows the transfer functions for thedetailed epoxy model with the original VPO closedand open, respectively. Table 2 compares the fivelowest formants of the complete epoxy model, in-cluding the nasal tract and maxillary sinuses, withthose measured in the subjects’ singing of the vowel/a/. The greatest difference, 223.1%, appeared forF2 because the CT scan and the audio recordingwere made on different occasions. Both measure-ments show, however, that formants 3, 4, and 5were clustered, and F5 and F3 lying about 1-kHzapart, which supports the idea that the productionof a singer’s formant is associated with a clusteringof higher formants.10 The nasal resonance systemintroduced a peak near 350 Hz followed by faintzero near 400 Hz. The peak would boost the funda-mental in the upper part of this subject’s F0 range.

A series of measurements was made with the ep-oxy model of the singer’s /a/, using a VPO tubewith a cross-sectional area of 0.44 cm2 and withthe nasal tract excluding or including the maxillary



FIGURE 6. Area function of the subject’s nasal tract derived from the CT scandata. The data reported by Bjuggren and Fant, 1965, are also shown, forcomparison.

sinuses. The result can be observed in Figure 11.With this VPO tube, the peak and the zero didnot appear that were observed in the low-frequencyregion for the unmodified epoxy model. F1 and F2were only marginally affected by the introductionof the VPO, but the nasal system lowered the levelof the first formant, leaving the levels of the higherformants unaffected. In this way, the VPO raisedthe levels of F3, F4, and F5 by about 4 dB relativeto the level of F1; that is, it raised the level of thesinger’s formant by this amount.

Attemtps were made to modify the epoxy modelin which the back of the tongue had been eliminated,


thus leaving a wide pharynx. Plasticine and a plastictube, ID 5 0.5 cm, l 5 3 cm, were used for creatingarea functions that approximated those of an /u/ andan /i/. Figures 12 and 13 show the transfer functionsof these area functions for three cases, with no nasalcavity, and with a nasal tract excluding or includingthe maxillary sinuses. In the two latter cases, a VPOof 0.44 cm2 was used.

In the case of the /i/ (Figure 12), the opening thevelopharyngeal port widened the bandwidth of F1considerably while its level relative to the higherformants was much less affected, as in the caseof the /a/. When the nasal system included the

FIGURE 7. Reproducibility of measurements of formant frequencies and the levels of zeros ob-tained by two measurement attempts performed on the epoxy model of the subject’s vocal tract with-out and with coupling to the nasal tract by means of a coupling tube of 0.8 cm2 cross-sectional area.


FIGURE 8. Transfer functions (left) and relationship of the cross-sectional area of the coupling tube andthe frequency of the zero observed in an iron tube model with constant cross-sectional area (right).

maxillary sinuses, the levels of the higher formantsdropped considerably relative to that of F1. Thesinuses also widened the bandwidth of F1.

In the case of the /u/ with a nasal tract lacking themaxillary sinuses, the nasal tract lowered the levelof F1 considerably, whereas the levels of the higherformants were much less affected, as in the case ofthe /a/. In other words, also in this vowel, the nasalcavities seemed to raise the level of the singer’s for-mant relative to the level of F1. On the other hand,the bandwidth of F1 was considerably widenedwhen the maxillary sinuses were included in the na-sal tract. Such a widening would affect the timbreof the vowel considerably.

Apart from the vocal and nasal tract shapes, alsothe size of the VPO can be assumed to be a relevantfactor. For this reason, a set of measurements wascarried out where the cross-sectional area of thecoupling tube was varied. As the effect of connect-ing the nasal cavity to the vocal tract by a VPOshould be small, when the vocal tract has a largecross-sectional area in the velar region, the experi-ment was carried out on the epoxy model that wasmodified to approximate the vocal tract shape used

FIGURE 9. Transfer functions of the indicated nasal tractmodels, all closed in the velar end.



for the vowel /u/. The results, which are shown inFigure 14, revealed that the effects of varying theVPO cross-sectional area on F1 and F2 were mar-ginal. On the other hand, clear effects were ob-served on the level difference between F1 and F3,a factor that might be relevant to the prominenceof the singer’s formant.

DISCUSSION

The results of the current investigation are lim-ited in important respects. One limitation, acceptedfor practical reasons, is that they were derived fromanalyses of one single subject. On the other hand, itdid not prevent analysis of the effect of a VPO onthe transfer function of a vowel. Another limitationwas that the acoustic properties of the epoxymodels differed from those of a real vocal tract, be-cause the epoxy model had hard walls, whereas thevocal tract had soft walls that absorb sound energy.Also, the fine details of the cavities are not accu-rately replicated, and therefore, the frequencies of

TABLE 2. Formant Frequencies Measured for theSubjects’ Sung /a/ and for the Epoxy Model Including

the Nasal Tract and Maxillary Sinuses

Subject (Hz) 510 1080 2530 3200 3450Model (Hz) 530 830 2190 2860 2940Difference % 3.9 223.1 213.4 210.6 214.8

FIGURE 10. Transfer functions for the unmodified epoxymodel with the original VPO closed and open (lower and uppergraph, respectively).


the higher formants, in particular, may be unrealis-tic in the epoxy models.

Despite these limitations, the results support theidea that singers’ can use a VPO in the vowel /a/for enhancing the singer’s formant or the higherspectrum partials in general. This effect can beachieved without substantially changing the vowelquality determinants F1 and F2. In other words,a VPO may enhance the singer’s formant withoutcompromising vowel quality. An additional effect,observed at least under some conditions, was an en-hancement of F0 in the frequency range 300–400Hz. This effect may favorably add to the voicequality, because a strong voice source fundamentalis typically associated with flow phonation, a phona-tory mode that classically trained singers seem tocultivate.11

In the previous investigation,1 it was found thatmost male singer subjects showed clear indicationsof a VPO for the vowel /a/, but rarely for the vowels/i/ and /u/. Above, it was observed that a VPO ex-panded the bandwidth of the first formant of /i/ and/u/ considerably. A notorious experience from vowelsynthesis is that such a bandwidth widening pro-duces a marked nasal timbre. This may be the reasonwhy in the previous investigation only a few singerswere found to use a VPO in /u/ and /i/.

In the previous investigation,1 also several differ-ent shapes of the VPO were observed. In the currentstudy, it was found that the size of a VPO may af-fect the transfer function. It seems likely thatsingers’ differing VPO shapes reflect attempts totune the resonance characteristics of their nasaland vocal tracts such that a desired timbral effectis obtained. It also seems likely that the effect ofa VPO will show inter-individual differences de-pending on the shape of the nasal resonance system,known to vary substantially between persons. Inother words, the same VPO may lead to differenttimbral effects in different singers, even if F0 andformant frequencies are identical.

In some previous investigations VPOs have beenobserved in combination with a sheet of mucuscovering the opening, which did not necessarilyburst during phonation.12 It implies that the resis-tance in the nasal tract may be so high that it arreststhe air stream. The measurements of the transferfunction of the model of the subject’s nasal tract


FIGURE 11. Transfer functions of the epoxy model of the vowel /a/, without VPO (left), with a VPO of 0.44cm2 (middle and right graphs). The middle graph represents the case of a nasal cavity lacking the maxillarysinuses and the right graph a nasal cavity including the maxillary sinuses.

system showed a high degree of attenuation. Ac-cording to Bjuggren and Fant,9 the extremely highcircumference-to-area ratio of the nasal passage isthe source of this resistance. In any event, the com-monly accepted assumption that the absence oftransnasal airflow is a reliable criterion of a com-pletely closed velum does not seem to hold.

The subject’s maxillary sinuses played an impor-tant role in determining the transfer function of thenasal system. Their influence should, however, de-pend heavily on the size of their orifices into theepi-pharynx cavity. For example, they may be en-tirely different when the mucosa is swollen. Itwould explain why some vocal artists experiencedifficulties to retrieve their habitual voice quality

in connection with colds, even in cases when thevocal folds are not affected.

There may also be other advantages of singingwith a VPO. According to Titze,13 an increased vo-cal tract resistance, originating from a narrow con-striction, is favorable for the functioning of theglottal oscillator. The great resistance observed inthe nasal tract suggests that phonating also on nasalconsonants such as /m, n, ng/ may exert a favorableinfluence on the glottal oscillator. Also, there seemsto be a reflectory connection between the upper andlower part of the pharynx.

The inter-individual variability of the shape ofthe nasal tract and cavities indicates that the resultsgained from the current study cannot be

FIGURE 12. Transfer functions of the epoxy model, modified to approximate the area function of the vowel /i/. The left graphrefers to the case of a closed velopharyngeal port, and the middle and right graphs to the case of a VPO of 0.44 cm2. Themiddle graph represents the case of a nasal cavity lacking the maxillary sinuses and the right graph a nasal cavity includingthe maxillary sinuses.



FIGURE 13. Transfer functions of the epoxy model, modified to approximate the area function of the vowel /u/. The leftgraph refers to the case of a closed velopharyngeal port, and the middle and right graphs to the case of a VPO of 0.44 cm2.The middle graph represents the case of a nasal cavity lacking the maxillary sinuses and the right graph a nasal cavityincluding the maxillary sinuses.

generalized. On the other hand, the acoustic theoryof the vocal tract of course is universally applica-ble. Thus, a transfer function zero can be expectedas a consequence from a VPO, but its frequencyand depth can be expected to vary.14 Furthermore,a high resistance would belong to the characteris-tics of the nasal system. Different singers mayhave to use different VPO strategies, but it is seemspossible that a vocally gifted singer can locate and


learn to explore the VPO strategy that has the besteffect on her/his vocal timbre.

CONCLUSIONS

Singers may profit from producing vowels witha VPO for several reasons. In the singer subjectstudied in the current investigation, its acousticeffect in the vowel /a/ was to lower the level of

FIGURE 14. Transfer functions of the epoxy model, modified to approximatethe area function of the vowel /u/ (upper left panel) and with (upper right andlower panels) the indicated cross-sectional areas of the VPO coupling tube.


the first formant, mainly. It enhances the singer’sformant or the strength of spectrum partials near3 kHz in general. In vocal tract models approximat-ing the vocal tract shapes for the vowels /u/ and/i/, a VPO lowered the level of the first formantbut also widened its bandwidth. The latter of theseeffects is likely to produce a nasal quality. A VPOwould also increase the vocal tract resistance,which, in turn, has been shown to be beneficialfor the glottal vibratory system.

Acknowledgments: Per Larsen at the Panum Instituteand Rolf Berholdt Hansen, Technology Park, Aarhusprovided the computer processing of the CT scan dataand the molding of the epoxy model. The authors alsogratefully acknowledge valuable advice and discussionwith Dr. Brad Story.

REFERENCES

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nasalized vowels: a target for vowel nasalization. J AcoustSoc Amer. 1996;99:3694–3706.

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5. Lindqvist-Gauffin J, Sundberg J. Acoustic properties of thenasal tract. Phonetica. 1976;33:161–168.

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12. Gramming P, Sundberg J, Elliot N, Nord L. Does the noseresonate in singing? In: Friberg A, Iwarsson J, Jansson E,Sundberg J, eds., SMAC 93 (Proceedings of the StockholmMusic Acoustics Conference 1993), Stockholm, RoyalSwedish Academy of Music, 1994;79:166–171.

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