Formant Tuning Strategies in PrOpera Singers

*Johan Sundberg, Filipa M. B. L~a, and Brian P. Gill, *Stoc

Summary: The term formant tuning is generally used forincides with the frequency of a source spectrum partial. Some authors claim that such coincidence is favorable and be-longs to the goals of classical opera voice training, whereas oThis investigation analyzes the relationships between formantscales on the vowels /a/, /u/, /i/, and /ae/ in a pitch range inclrange of approximately 300400 Hz, applying either of the twand (2) in nonclassical singing, respectively. Formant frequen

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search Centre, SE-10044 Stockholm, Sweden. E-mail: pjohan@speech.kth.se

old, with varying levels of expertise, ranging frdent to international opera singer, voluntarilthis study (Table 2). The singers perfor

Journal of Voice, Vol. 27, No. 3, pp. 278-2880892-1997/$36.00 2013 The Voice Foundationhttp://dx.doi.org/10.1016/j.jvoice.2012.12.002MATERIALS AND METHODS

Participants and protocolA total of eight male classically trained singers, 2342 years

Communication and Arts, INET-MD, University of Aveiro, Aveiro, Portugal; and thezDepartment of Music and Performing Arts Professions, Steinhardt School of Culture,Education and Human Development, New York University, New York, New York.Address correspondence and reprint requests to Johan Sundberg, Department of Speech,

Music and Hearing, School of Computer Science and Communication, KTH Voice Re-ant tuning has been receiving an ever-increasingt of attention over the last decade.7,913 The literaturemant tuning has recently been described in some detailere,14 and hence, only a brief overview will be givenable 1).an be seen in Table 1, different methods have been used inearch. However, all these methods suffer from limitations:

In addition, the results of this research diverge, as can bein the same Table 1. There are at least three sharply conflideas on vocal tract tuning in singing that have emergedworld of vocal pedagogy and voice researchsingers arommended to or found to (1) tune F1 and/or F2 to a harmpartial; (2) keep F1 and F2 constant, independent of F0(3) tune F1 or F2 to a frequency just above its nearest pso that the coincidence between partial and formant is avoAgainst this background, it is clear that vocal tract tunin

serves more research. Thereby, a promising strategy seemexpand our previous, preliminary study of the vowel /a/including also vowels with lower F1 values.

ted for publication December 4, 2012.iminary version of this investigation was presented at the Physiology and Acous-nging conference at KTH; August 2010; Stockholm, Sweden; at the Seattle meet-Acoustical Society of America; May 23 27, 2011; Seattle, Washington; and at

ual Symposium Care of the Professional Voice; May 28 June 2, 2011;hia, PA.he *Department of Speech, Music and Hearing, School of Computer Science andication, KTH Voice Research Centre, Stockholm, Sweden; yDepartment ofhas been found also in some traditional singing.8 source-filter effects, these may be mistakenly eliminated.filtering the acoustic signal. In the classical style, the firstther the first nor the second formant tended to change systeither or both formants was just below, just above, or rightspectrum characteristics of the top tones of the scales withwhether the first formant was slightly lower, slightly highnot seem to be affected.Key Words: Operatic singingNon-classical singingSp

INTRODUCTIONSopranos have been found to avoid the situation where the firstformant (F1) is lower than the fundamental frequency (F0); if F0exceeds the normal value of F1, they increase F1 to a frequencyvery close to F0.

1 The strategy of tuning F1 to a specific spec-trum partial was strongly recommended by singing teacher Cof-fin,2 who developed a vowel chart presenting optimum vowelsof a given pitch range.2 The terms formant tuning or vocaltract tuning have been introduced for this strategy, and it hasbeen found to be applied not only by sopranos but also bysingers of other classifications. For male voices, vocal tract tun-ing is mostly observed in and above the passaggio, that is, nearthe pitches of E4G4, about 330400 Hz.3 Vocal tract tuning in-creases the sound level of the vocal output, and it is assumed tohelp the singer avoid vocal hyperfunction and registerbreaks.2,47 It is not specific to classically trained singers; itther authors have found evidence for advising against it.frequencies and partials in professional singers, who sanguding the passaggio, that is, the fundamental frequencyo singing strategies that are typically used (1) in classicalcies of each note in the scales were measured by inverse-ant tended to be lower than in the nonclassical style. Nei-ically between scale tones, such that on some scale tonesspectrum partial. In many cases, singers produced similarerent first and second formant frequencies. Regardless ofr right on a partial, the properties of the voice source did

umHarmonicsFormant tuning.

(1) it is difficult to interpret spectral data in terms of formantfrequencies because the spectrum is strongly dependent on therelationship between F0 and the frequencies of the formants,and when shifting from modal phonation to ingressive or vocalfry phonation, vocal tract shape, and hence the formant frequen-cies, may change; (2) results of listening tests with synthesizedstimuli are very dependent on how natural the stimuli sound;(3) model work offers accurate predictions only if the model ac-curately reflects all relevant characteristics of the system; (4)broadband excitation at the lip opening during sustained vowelphonation implies that also the subglottal system is to some extentincluded in the resonator because the glottis is open during part ofthe glottal vibratory cycle; and (5) in inverse filtering, the formantringing during the closed phase is eliminated by tuning the fre-quencies of the inverse filters, so if some of this ringing wascaused by factors other than formants, for example, nonlinearofessional Male

kholm, Sweden, yAveiro, Portugal, and zNew York, New York

the case that one of the lowest formant frequencies co-

TABLE 1.Summary Reports of Previous Studies on Formant Tuning Stra

Authors Method

Miller and Schuttel0 Spectral analysis of ingressive phonatvocal fry just after a sung tone

Carlsson andSundberg17

Listening tests with synthesized scalesvowel /a/, with and without formant

Neumann et al7 Spectrum and EGG analysis of /a/ andchest and head register transitio

12 lusiolterof f

thech ton

vow

Johan Sundberg, et al Male Singers Formant Strategies 279descending nine note scales using vowels /ae/, /a/, /u/, and /i/.For each singer, three starting pitches were used, separated bysemitone intervals and chosen so that the singers passaggiorange was reached (pitches E4G4, depending on the voicetype). When reaching their passaggios, they applied either ofthe two different approaches: classical (sung twice) and non-classical, as in for example, musical theater (sung once). The

Titze Computerized model allowing incexclusion of nonlinear source-fiinteraction for predicting effectstuning

Henrich et al8,16 External broad band excitation oftract of 22 singers sustaining eaa scale in comfortable range and/a/, //, //, and /u/

Sundberg et al14 Inverse filtering of scales sung onMadde vowel synthesizer software (custom made by SvanteGranqvist, KTH) was used to supply the reference tone. A totalof 224 (This number was mistakenly reported to be 288 in a pre-vious publication Sundberg et al14) scales were recorded: asthere were three starting pitches and four vowels, there were192 classical and 32 nonclassical versions.

EquipmentAll recordings were made in a sound-treated studio in theSteinhardt School of Culture, Education and Human Develop-ment at New York University. A hybrid system consisting ofa Laryngograph (Laryngograph Ltd, Wallington, Greater

TABLE 2.Singer Subjects Participating in the Experiment

Singer Age Classification Experience

1 30 Tenor Internationally touring2 32 Baritone Nationally touring3 23 Baritone Graduate student4 25 Tenor Graduate student5 24 Baritone Graduate student6 42 Tenor Internationally touring7 38 Baritone Nationally touring8 35 Baritone Graduate studentMean 31.1London, UK) microprocessor and a Glottal Enterprises (Syra-cuse, NY) MS-110 computer interface was used to record au-dio and electrolaryngograph (EGG) signals simultaneously.Audio was picked up by a head-mounted electret microphone(Knowles EK3132, Knowles Headquarters, Itasca, IL). Thesound level was calibrated by means of a 1 kHz sine wave,the sound pressure level of which was measured in dB(C)

tegies

Main Conclusion

ion and .the singerwould tend to adjust resonancesto match one or another harmonic of theglottal source (p. 234)

ontuning

.subjects did not show any preference forthe scales with tuned formants.(p. 259)

// inn

. formant tuning is the most appropriateway of register equalization. (p. 325)

n and

ormant

. a stable harmonic source spectrum is notobtained by tuning harmonics to vocal tractresonances, but rather by placingharmonics into favorable reactanceregions (p. 2733)

vocalone ofvowels

Tenors and baritones generally tune F1 to H2or H3 over at least part of their range, butintersubject variability is great

el /a/ Professional singers did not show anytendency to tune F1 or F2 to a harmonicpartial.next to the recording microphone by means of a sound levelmeter, and the value observed was announced on the recording.Both signals were recorded using Speech Studio software (Lar-yngograph, Laryngograph Ltd, Wallington, Greater London,UK) and stored as wav files.

Analysis

Listening test. Of the recorded scales, 28 were randomly se-lected for a listening test aimed at identifying typical examplesof classical and nonclassical singing styles. The listening testwas carried out with a panel of six experienced listeners (uni-versity singing teachers in USA with the knowledge of vocaltract tuning). The subjects were given the following written in-struction: Here you will listen to a set of ascending-descendingscales sung by different male voices. We ask you to rate howsuccessful the singer is with regard to vocal tract tuning (disre-gard other issues) in transitioning into the pitches in/above thepassaggio in a Classical mode of singing. The subjects gavetheir ratings along visual analog scales (VAS). The test included13 replicated stimuli and all 41 scales were presented in thesame randomized order to all subjects, with a 5-second pausein between, lasting a total of approximately 11 minutes. Thenumber of each stimulus was announced in the test file.

Formant frequency analysis. The formant frequencies inall recorded tones in the ascending part of the scale were

measured by inverse filtering of the audio signal, using theDeCap software (custom made by Svante Granqvist, KTH).This program displays waveform and spectrum in separatewindows (Figure 1). When analyzing an audio signal, it firstconverts the acoustical signal to a flow signal by integration.The frequencies and bandwidths of the inverse filters are setmanually (in the lower window) whereby the classical equa-tions are applied for calculating the transfer function that cor-responds to the given combination of formant frequencies andbandwidths.15 The input signal is filtered with the inverse ofthis transfer function, thus eliminating the effects of the vocaltract transfer function on the input signal, and the resultingwaveform and spectrum are displayed in quasi-real time. Pro-vided that the filters are correctly set, the output then displaysthe waveform and spectrum of the transglottal airflow, includ-ing effects of nonlinear source-filter interaction, if any. Theprogram can also display an additional signal, e.g. the EGGrecorded on a second channel of the input file, with or withoutderivation and with an adjustable time delay.In the upper window of Figure 1, both the transglottal airflow

waveform, that is, the flow glottogram and the derivative of the

note of each of the scales starting on the highest pitch wasthen synthesized, using the frequencies and bandwidths savedin this formant file. This was done for each of the four vowels,using the Madde software. The bandwidths were about 50, 70,100, 110, and 120 Hz for the five lowest formants. The purposeof this synthesis experiment was to test the formant values usedfor the inverse filtering. The values were accepted only if thesynthesized vowel and voice quality sounded similar to vowelsound analyzed, as determined by the authors.The F0 signal was extracted from the EGG, using the FoX op-

tion included in the Soundswell signal workstation software(Hitech Development, Solna, Sweden). For each of the individ-ual scale tones, F0 was averaged over a series of complete vi-brato cycles by means of the histogram option of the samesoftware. In this way, F and formant frequencies data were ob-

solute difference between the first and second ratings of repli-

managed to sing a nonclassical version of the /u/ scale. To in-

Journal of Voice, Vol. 27, No. 3, 2013280EGG signal (dEGG) are displayed. The dEGG was delayed bya time interval of about 1 millisecond corresponding to thetravel time of the sound from the glottis to the microphone.The lower window represents the input audio spectrum andthe spectrum of the flow glottogram.For inverse filtering the formant frequencies and bandwidths

were adjusted according to the three criteria: (1) ripple-freeclosed phase; (2) voice source spectrum envelope as void ofpeaks and valleys as possible; and (3) synchrony between thenegative dEGG peak and the maximum declination rate oftransglottal flow during closure.After completing the tuning of the filters, their frequencies

and bandwidths were saved in a formant data file. The top

FIGURE 1. Example of DeCap display. Upper panel shows thewaveform of the filtered signal and the derivative of the EGG. Lower

panel shows the input audio spectrum and the spectrum of the filtered

flow (gray and heavy curve, respectively). Formant bandwidths are

given on an arbitrary scale along the ordinate. The arrows show the for-

mant frequencies and bandwidths used for the inverse filtering. Thetwo parallel curves represent realistic bandwidths according to Fant.15crease the analysis material, however, formant frequency

TABLE 3.Mean and SD of the Absolute Difference Between theFirst and Second Ratings of Replicated Stimuli and thePearson Correlation (r) Between These Ratings

Rater

Difference (%) Correlation

Mean (%) SD (%) r Slope Intercept (%)

1 11.9 13.4 0.779 0.830 12.22 8.3 10.4 0.931 0.989 0.13 9.1 17.3 0.848 0.828 5.44 9.6 13.6 0.907 0.898 7.45 4.4 5.0 0.979 0.993 0.96 7.1 7.9 0.858 0.825 7.3cated stimuli varied between 4.4% and 11.9% and thecorrelation between 0.779 and 0.979 (Table 3).To assess whether there were significant differences between

the ratings for the classical and nonclassical examples includedin the listening test, a nonparametric paired sample test, Wil-coxon, was performed. This test was used because the datashowed a skewed distribution. Classical versions were scoredsignificantly higher than nonclassical versions for all singers,except for the vowels /u/, as sung by singer 1, and the vowel/a/, as sung by singer 3 (Table 4).

Formant frequenciesSix pairs of scales of the same vowel sung by the same singerin both classical and nonclassical versions were included inthe listening test: three on /a/, one on /ae/, and two on /i/. Nopairs for the vowels /u/ were chosen because none of the singers0

tained, which were as reliable as possible.

RESULTS

Listening testA Pearson correlation was used to test the consistency of theparticipating experts ratings. For the individual experts, the ab-Abbreviation: SD, standard deviation.

, Z); *In

Johan Sundberg, et al Male Singers Formant Strategies 281measurements were made also on two more classical versionsof /i/ scales and four classical versions of /u/ scales. Thus, a totalof 18 scales were selected for formant frequency analysis.Figure 2AC show the formant frequencies obtained.

Figure 2A pertains to the vowel /a/, described in our previous re-port,14 complemented by newdata for vowel /ae/. As can be seenin the graph, the mean ratings of the classical versions of thesescales exceeded 75% of VAS length, whereas the mean ratingsfor the nonclassical versions varied between 10% and 32%. Es-pecially in and above the passaggio range,F1 andF2 were lowerin the classical version than in the nonclassical version of the /ae/,just as in the /a/. In the classical version, all singers lowered F1for the top scale tone or scale tones, whereas in the nonclassicalversion,F1was just above, just below, or right onH2. F2was just

TABLE 4.Med, IQR, in % VAS, and Significance Level (Wilcoxon TestIntentionally Sung in the Classical and Nonclassical Styles

Subject Vowel

Classical

Med IQR

1 /a/ 84.3 15.2/u/ 80.5 22.4

2 /a/ 83.6 9.8/ae/ 90.0 10.2

3 /a/ 34.3 31.1/u/ 80.0 16.1

4 /a/ 76.1 28.3/i/ 60.7 25.8

5 /u/ 42.5 47.56 /i/ 56.6 19.47 /ae/ 30.7 41.38 /ae/ 56.1 28.9

Abbreviations: Med, median; IQR, interquartile range.above, just below, or right on H3 for the top pitches in the clas-sical versions. In these versions, all singers tuned F1 almost ex-actly to H2, at least in one of the scale tones. However, with fewexceptions, neither F1 nor F2 changed markedly between scaletones, thus suggesting that the singers did not attempt to tunethese formants to the frequencies of spectrum harmonics ofthe individual scale tones. In other words, the coincidence be-tween formant and harmonic seemed to occur unintentionally.However, singer 2 tuned his F2 exactly to H3 in /a/, both in theclassical and nonclassical versions of his highest note.Figure 2B shows the F1 and F2 values observed for the vowel

/u/, all in the classical versions. Singers 1, 2, 3, and 4 all tunedF1 midway between H1 and H2 for the top pitches. Singers 1and 3 kept F2 rather constant throughout the scale, with F2 co-inciding with H3 on the penultimate note for singer 1 and thetop note for singer 3. Singer 6 by contrast, changed F2 in thelower part of the scale such that it was close to H4 and H3.Singer 2 provided a clear example of vocal tract tuning; F1tracked H2 for the four lowest scale tones, whereas for thehigher tones, he tuned F2 to H3.The F1 and F2 values observed for /i/ are shown in Figure 2C.

A common trait is that all singers reduced F2 more or less forthe top pitches, both in the classical and nonclassical versions.Singers 1 and 2 produced a similar difference between classicaland nonclassical for F1. However, the difference was quitesmall in the case of singer 1, and, interestingly, also the meanratings of these examples were not very different, 48% and78%. Singers 4 and 6 produced clear examples of vocal tracttuning, placing F1 just above H1 for the highest scale tones.Their F2, by contrast, remained basically independent of F0.Singers 1 and 2 increased F1 with increasing F0, singer 2 tuningit almost midway between H1 and H2 in the upper part of thescale.Singers have been found to tune their formant frequencies

with an accuracy of about 20 Hz.16 Therefore, if applyingformant tuning, they may not tune F1 exactly to a partial

of the Difference in Mean Ratings Between Scalesdicate Significant Differences

Nonclassical Wilcoxon Test

Med IQR Z P

7.9 24.2 2.201 0.028*71.1 37.3 1.214 0.22513.0 28.5 2.201 0.028*5.0 9.6 2.207 0.027*16.4 33.2 1.363 0.17359.6 32.8 2.201 0.028*28.6 35.2 2.201 0.028*36.4 19.5 2.201 0.028*11.6 12.4 1.992 0.046*37.3 34.6 2.201 0.028*7.7 16.2 2.201 0.028*20.0 30.4 2.201 0.028*but only to the vicinity of a partial. In the investigationjust referred to, the criterion for formant tuning appliedwas that the distance between the formant and its closest par-tial should not be wider than 50 Hz. This corresponds toabout 2 semitones in the range of the pitch of E4. If singersapply formant tuning with this accuracy, one would expectthat the average of this distance would be close to 0 semitonein our material. As formant tuning is assumed to be requiredfor tones in the upper part of the passaggio, this should applyat least to the top note of the scales.9 Formant tuning mayconcern both F1 and F2. For these reasons, we measuredthe frequency ratios, expressed in semitones, between theseformants and their closest partials. The results are shownin the box plots in Figure 3. For the vowel /a/ in the classicalversion, the median distance was clearly negative for F1 andsmall and positive for F2. Thus, F1 was typically lower thanits nearest partial. For /i/, F1 and F2 were about 1 semitoneabove and below the nearest partials, respectively. For thevowel /u/, the median was 0 for both F1 and F2, but the scat-ter was considerable. For the nonclassical versions, the me-dians for /a/ and /i/ were close to 0. These results showthat depending on the vowel, the formant may be below,

Journal of Voice, Vol. 27, No. 3, 2013282above, and right on a partial, although the proximity betweenF1 and F2 and their closest partials tended to be greater in thenonclassical versions.

FIGURE 2. A. F1 and F2 observed for the indicated vowels in the classicspectively). Diagonal dashed lines refer to the frequencies of spectrum partia

over a set of adjacent complete vibrato cycles. The mean ratings are given in

et al.14 B. New data, plotted the same way observed for the vowel /u/. C. NIt also is relevant to compare the formant tuning data with themean ratings of how successful the singers were with regard tovocal tract tuning, when they transitioned into the pitches in and

al and nonclassical versions of the scale (solid and dashed curves, re-

ls, calculated as n*MF0, where n is an integer and MF0 is F0 averaged

% of VAS length. The graphs for the /a/ vowel are taken from Sundberg

ew data, plotted the same way for the vowel /i/.

2. (c

Johan Sundberg, et al Male Singers Formant Strategies 283FIGUREabove the passaggio in the classical mode of singing. This rat-ing can be assumed to apply to the top note of the scale. More-over, formant tuning would imply that either F1 or F2, or both,are tuned to the close neighborhood of a partial. Hence, we cal-culated, for the top tone, the minimum of the distance betweenF1 and its nearest partial and the distance between F2 and itsnearest partial and then the minimum of these two values wasselected. These minimum values can be compared with themean ratings in Figure 4. No relationship can be seen with

FIGURE 3. Distance between F1 and its closest partial and betweenF2 and its closest partial for the vowels /a, /i/, and /u/ averaged across

singers for the top pitch of the scale exercise. The frequency of the har-

monic was calculated as n3MF0, where n is an integer and MF0 is F0averaged over a set of adjacent complete vibrato cycles.ontinued).the mean ratings, but almost all values lie within a range of1.5 semitones from the closest partial. Thus, the ratingsseemed independent of the frequency separation between F1or F2 and their closest partial.

Flow glottogram waveformWhen formants coincide with the frequencies of harmonics,nonlinear source-filter interaction can be expected to occur.11

In such cases, the flow glottogram would show deviations

FIGURE 4. Mean ratings plotted as function of the minimum dis-tance of F1 and F2 to their closest partial, for the top note of the scales.

Filled and open symbols refer to tones intended as sung in classical and

nonclassical style.

from the typical shape, for example, in terms of a ripple in theclosed phase or a dent in the flow pulse. Such interaction wouldalso imply that the source spectrum partial that coincides witha formant may become boosted or attenuated, so that such par-tials can be expected also to deviate from a smoothly fallingsource spectrum envelope.Figure 5 shows a typical set of flow glottograms obtained

from the top tones of the scales sung on the vowels /a/, /u/,and /i/. The samples exemplify the situation that F1 is just be-low, right on, or just above H1, H2, or H3. A small ripple inthe close phase occurred for the /a/ when F1 was 58 Hz aboveH2 (1.5 semitones), for the /u/ when F2 was 60 Hz above H1(1.1 semitones), and for the /i/ when F1 was 26 Hz above H1(1.3 semitones). In the last mentioned case, the ripple did notseem related to F1 being just above a harmonic because the rip-ple remained also when F1 was right on or just below a har-monic. It cannot be excluded that the ripple was caused bysome external resonance; the ripple corresponded to a frequencyof about 1200 Hz, and in the vowel /i/, this frequency is locatedin a spectrum region where the partials are weak, thus allowingan external resonance to have a noticeable effect on the flowglottogram.

singer 3 and 6 tuned it just below and just above H2, respec-tively. Also with regard to F2, different strategies can be ob-served: singers 1, 3, and 6 placed F2 almost right on H3,whereas singers 2 and 4 placed it just below this same partial.One might imagine that singers possessing a strong singers

formant cluster would tend to tune F1 or F2 to a partial to pro-mote a favorable spectral balance. Singers possessing a weaksingers formant cluster would promote spectrum balance bynot tuning a formant to a partial. This would imply that the levelof difference between the strongest spectrum partial and thesingers formant cluster would show a relationship with thesmallest distance between F1 or F2 and its closest partial.This relationship was examined: the coefficient of determina-tion was 0.108. Thus, there was no correlation between formanttuning and the level of the singers formant cluster.

SynthesisThe top tones were synthesized by means of the singing synthe-sizerMadde, as mentioned. This allowed for a more detailed ex-amination of the contributions of nonlinear source-filterinteraction to the audio signal in these tones because this syn-thesizer represents a completely linear source-filter model. It

Journal of Voice, Vol. 27, No. 3, 2013284SpectraIn pedagogical practice, spectrum characteristics are sometimesused to provide a visual feedback to the student.9 Figure 6 illus-trates howF1 andF2 were tuned for the top pitch of the vowel /a/in five cases, all rated as good examples of the classical style ofsinging. All these examples shared the characteristic of a risingaudio spectrum envelope over partials 1, 2, and 3. However, thischaracteristic was achieved by means of different combinationsof F1 and F2 and their distances to the closest partials. Singers 1,2, and 4 placed F1 well above H1 and well below H2, whereasFIGURE 5. Flow glottograms for the indicated relations between F0 ansimply filters a source spectrum, which has an envelope fallingwith an adjustable number of dB/octave, and its transfer func-tion is calculated from the given frequencies and bandwidthsof the formants. Thus, the differences between the real andthe synthesized versions of a vowel would show the contribu-tions from nonlinear factors. In these measurements, spectrumsections were taken at the upper turning point of the vibrato cy-cle, and F0 of the synthesis was adjusted to that F0 value.Figure 7 compares the levels of the first 10 audio spectrum

partials produced by the singer and by the synthesizer, forfour cases, where either F1 or F2 coincided with a spectrumd its closest harmonic observed for the indicated singers and vowels.

soft

enci

Johan Sundberg, et al Male Singers Formant Strategies 285partial. In three of the four cases, the singers fundamental wasweaker than that of the synthesizer. It can be noted that in noneof these cases, a particularly great discrepancy appeared for thepartial that coincided with a formant (circled in the graph).Thus, the source spectrum seemed to be rather unaffected bythe resonator in these cases.

FIGURE 6. Audio and voice source spectra obtained from the DeCapsingers (refer caption of Figure 1). The bold arrows represent the frequFigure 8 shows the audio spectra of these same tones. In thecase of the /u/ sung by singer 3, the very strong third partial re-quired that the bandwidth of the inverse filter corresponding toF2 was set to no more than 19 Hz, which is an unrealisticallylow value. A possible explanation is that this partial wasboosted by nonlinear source-filter interaction. For the othervowels, the bandwidths of the inverse filters were all withinor very near the realistic limits, represented by the two parallelcurves in the DeCap graphs (Figure 1).It can also be noted that the spectrum peak constituting the

singers formant cluster was produced by clustering formants3, 4, and 5 in the synthesis. The levels of these partials in thesingers spectra did not differ markedly from those of the syn-thesis. This implies that by and large, the singers formant clus-ter could be completely explained by the classical source-filtertheory.

DISCUSSIONThis investigation leans heavily on the assumption that inversefiltering is applicable also in the presence of a nonlinearsource-filter interaction. There seems to be no reason to doubtthis assumption. It is a well-established fact that the transferfunction of the vocal tract can be accurately predicted, giventhe frequencies and the bandwidths of the formants.15 Inversefiltering merely computes this transfer function and filters thesignal with the transfer function inverted. The transfer func-tion will not be affected by a nonlinear source-filter interac-tion. Therefore, the source waveform and spectrum willfaithfully reflect the effects of such interaction, providedthat realistic formant frequencies and bandwidths were usedwhen adjusting the inverse filter. For this reason, we were

ware for the vowel /a/ sung at the top tone of the scale by the indicated

es and bandwidths of the inverse filters.careful only to use formant frequencies and, with the one sin-gle exception mentioned above, also bandwidths typical of thevowels analyzed. It should also be noted that the inverse filterwas adjusted such that the ripple during the closed phase waseliminated. During this phase, the folds prevents coupling ofthe vocal tract to the subglottal airways. In other words, underthese conditions, the resonator system includes only the vocaltract. Moreover, the flow glottograms obtained showeda closed phase that started at the moment of vocal fold con-tact, as evidenced by the spike of the dEGG waveform. Thesefacts support the assumption that our results represent reliableinformation and that the inverse filtering data accuratelywould reflect any significant effects of a nonlinear source-filter interaction.It is obviously important to compare our findings with those

reported by others. Echternach18 converted magnetic reso-nance imaging data for the vowel /a/ to area functions andcalculated the formant frequencies of premiere tenors pas-saggio. He found that they progressively lowered F1 with ris-ing F0. Henrich et al

16 observed a great intersubject variationin their group of singers, which included both amateurs andprofessionals. In their male singers, they observed formanttuning in the top of the singers ranges. We observed some ex-amples of this.The representativeness of the data is another important as-

pect of our findings. There are three reasons to assume that

Journal of Voice, Vol. 27, No. 3, 2013286our subjects were good representatives of classically trained op-era singers: (1) the examples selected for analysis were thosereceiving the highest and lowest mean ratings as classical inthe listening test, whereby those receiving the lowest mean rat-ings were regarded as typical of nonclassical; (2) the subjectswere all singing at professional/semiprofessional level, someat the Metropolitan opera; and (3) all singers tried to followthe instructions given to provide the nonclassical and classicalversions.Given these reasons for assuming that the data observed are

representative, two main questions need to be considered: (1) isthere a common tuning strategy that male singers use to suc-cessfully navigate through their passaggio and (2) where arethe formants in relation to the partials?Regarding the first question, the answer is in the negative; al-

though there were spectral similarities, there was no commonformant tuning strategy that our male singers used to success-fully manage their passaggio. Such variability was observedalso by Henrich et al.16 This suggests that perhaps, insteadof a formant tuning rule that all male singers should applyto negotiate passaggio notes, they apply personal strategies,presumably tailored to their own anatomical-physiologicalcharacteristics.On the other hand, three common denominators were

found for vocal techniques perceived as classical and non-

FIGURE 7. Levels of the first 10 audio spectrum partials produced by thevalues observed for partials coinciding with either F1 or F2.classical. First, in the top notes of the classical examples,F1 and F2 were lower than in the nonclassical examplessung by the same singer, perhaps due to a lowering of the lar-ynx, lip protrusion, and/or decreased jaw opening. Second,F1 in /a/ was lowered for the top notes, thus suggestingthat a principle of formant detuning rather than formant tun-ing was applied. Third, all top notes on /a/ perceived asclearly representing the classical singing technique sharedthe characteristic of a rising spectrum envelope over thethree lowest spectrum partials of the audio signal, which pos-sibly produces a desirable timbral effect in this style ofsinging.It is noteworthy, however, that the sensitivity of the audio

spectrum to the vibrato phase is quite large, particularly whena formant is tuned to the close proximity of a spectrum partial.Figure 9 presents an example of a spectrum taken at the peakand at the valley of the same vibrato cycle for an /a/ sung atthe pitch of F#4. For example, assuming a bandwidth of50 Hz for the vowel /a/ and an H2 located 25 Hz below F1, a vi-brato peak-to-peak extent of 5% would lead to a sound levelmodulation of about 6 dB for that partial. In other words, thespectrum envelope over the three lowest spectrum partialsmay vary greatly over a vibrato cycle. It is not clear how the cri-terion of a rising spectrum envelope over harmonics 1, 2, and 3is applied under such conditions.

indicated singer and by theMadde synthesizer. The circles indicate the

. Th

um,

Johan Sundberg, et al Male Singers Formant Strategies 287With regard to the second question, where the formants are inrelation to the partials, it is clear that F1 was never below H1.This finding is in agreement with earlier studies.1,12,16 On theother hand, in and above the passaggio range, we found onlyfew examples of F1 and/or F2 being tuned to a partial.Mostly, the formant frequencies remained the same or similarbetween scale tones, so coincidence between F or F and

FIGURE 8. Audio and source spectra of the tones shown in Figure 5filters (refer caption of Figure 1). In the case of the bottom left spectr

more than 19 Hz, which is an unrealistic low value.1 2

a partial appeared rather to happen by chance. Thus, ourresults fail to support the claim that such tuning is animportant principle in the classical style of singing.7,9,16 Withregard to F1, it was tuned to a frequency well above, justabove or right on H1 in /i/. In /a/ and //, it was lowered toa frequency below H2 for the highest pitches, which is inaccordance with earlier reports.4,7,18 In /u/, we found F1 to betuned midway between H1 and H2, an observation markedlydeviating from results reported by Henrich et al.16 With respect

FIGURE 9. Audio spectra of the vowel /a/ as sung by singer 3 at the pitch oand at the valley of the vibrato curve, respectively.to F2, it coincided with or was in the vicinity of H3 for /a/ and//, whereas for /i/ and /u/, it seemed independent of F0 in allsingers except one (singer 2). Although Neumann et al7 notedthat F2 in /a/ was tuned to H4 in the high range of the chestregister, we found that this situation happened at single pitches,when F0 was in the appropriate range for this to happen by co-incidence, that is, it occurred without any marked changes of F

e bold arrows represent the frequencies and bandwidths of the inverse

the bandwidth of the inverse filter corresponding to F2 was set to no2

between scale tones.As mentioned, F1 or F2 coincided with a harmonic in sev-

eral scale tones. According to Titze,12 this may cause insta-bility because of nonlinear source-filter interaction, at leastwhen no vertical phase difference can be seen in the vocalfold vibration, such as in falsetto register. However, innone of these cases, instability was noted, presumably be-cause singers used only modal register. Apparently, singersare able to avoid instabilities caused by such interaction, as

f F#4 in classical style. The left and right panels were taken at the peak

Journal of Voice, Vol. 27, No. 3, 2013288suggested by Titze.12 A relevant remaining question is howthis can be done.Nonlinear source-filter interaction is likely to boost certain

partials in the radiated spectrum. Inverse filtering merely im-plies that the effects of the vocal tract transfer function on theradiated sound are eliminated, as mentioned. A nonlinearsource-filter interaction would then manifest itself as irregular-ity of the source spectrum envelope obtained from the inversefiltering analysis. One example of this was illustrated inFigure 8, where F2 was almost identical with H3 in the /u/sung by singer 3. In the inverse filtering, the very strong H3was here compensated by an unrealistically narrow bandwidthof F2. No similar examples were observed in the classical ver-sions of the scale. On the other hand, irregularities were oftennoted in the source spectrum envelope of the nonclassical ver-sions. This again raises the question what tricks singers canmake to avoid nonlinear source-filter interaction.It is noteworthy that the source spectrum envelope did not

show any irregularities in the region of the singers formantcluster. The generation of this spectrum envelope peak wasthus compatible with a normal voice source and the clusteringof F3, F4, and F5 assumed in the inverse filtering analysis.Such clustering does not seem unrealistic; it was observedalso in an acoustical model of the vocal tract, which containeda representation of the pyriform sinuses and of the larynx tubeincluding a laryngeal ventricle. Thus, it seems that a singersformant cluster can be produced without the help of nonlinearsource-filter interaction.Formant tuning, meaning tuning of formants to partial, must

be strongly influenced by F0 and the normal value of F1 and F2.The male passaggio is limited to the F0 range of 300400 Hz,approximately, and F1 for the vowel /i/ is typically near300 Hz. This automatically brings it to the vicinity of H1 inthe passaggio. Likewise, F1 for the vowel /a/ is about 700 Hz,which implies that distance between F1 and H2 will automati-cally be small in the passaggio. It is thought-provoking thatin the classical versions, the singers tended to decrease F1 inthe passaggio, thus, contrary to formant tuning, expandingthe separation between F1 and H2. In this case, the term formantdetuning seems more appropriate than formant tuning.

CONCLUSIONSThe main results of the present investigation can be summa-rized as follows. (1) The classical and nonclassical styles ofsinging differed with respect to formant frequencies in a consis-tent and clearly perceptible way, and for all vowels, F1 and F2tended to be lower in the classical than in the nonclassical style.This difference was most pronounced at high F0. (2) In twocases, of a total of 18, examples of formant tuning were found,occurring at high pitches for the vowel /i/ and both at low andhigh F0 for the vowel /u/. (3) A rising spectrum envelope overthe three lowest partials was a common denominator of thehighest tones sung on /a/ and /ae/ in classical style, even thoughit was produced with slightly differing combinations of formantfrequencies and the spectrum varied greatly during the vibratocycle. (4) F1 coincided with H2 at some scale tones in allsingers classical as well as in their nonclassical versions ofthe scale. (5) Almost without exception, inverse filtering analy-sis of the tones produced in the classical style showed no clearsigns of a nonlinear source-filter interaction, neither when F1 orF2 coincided with a spectrum partial nor when F1 was slightlylower than a partial. Thus, in most cases, the major characteris-tics of the spectra produced by these singers with the classicalformant tuning strategy could be explained by the classical lin-ear source-filter theory of voice production. On the other hand,in examples produced with a nonclassical formant tuning strat-egy, some source spectrum irregularities were found that mayreflect such interaction.

AcknowledgmentsThe kind cooperation of the singers is gratefully acknowledged.The authors profited greatly from discussions with Dr SvanteGranqvist, KTH, on inverse filtering and are indebted to theSchering Health Care Ltd. & Bayer Portugal for providing themeans to acquire the equipment and to the Gomes TeixeiraFoundation for support.

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Formant Tuning Strategies in Professional Male Opera SingersIntroductionMaterials and methodsParticipants and protocolEquipmentAnalysisListening testFormant frequency analysis

ResultsListening testFormant frequenciesFlow glottogram waveformSpectraSynthesis

DiscussionConclusionsAcknowledgmentsReferences