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Level and Center Frequency of the Singer's Formant
Journal of Voice Vol. 15, No. 2, pp. 176–186 © 2001 The Voice Foundation
Level and Center Frequency of the Singer’s Formant Johan Sundberg Voice Research Centre, Department of Speech Music Hearing, KTH, Stockholm, Sweden
Summary: The “singer’s formant” is a prominent spectrum envelope peak near 3 kHz, typically found in voiced sounds produced by classical operatic singers. According to previous research, it is mainly a resonatory phenomenon produced by a clustering of formants 3, 4, and 5. Its level relative to the first formant peak varies depending on vowel, vocal loudness, and other factors. Its dependence on vowel formant frequencies is examined. Applying the acoustic theory of voice production, the level difference between the first and third formant is calulated for some standard vowels. The difference between observed and calculated levels is determined for various voices. It is found to vary considerably more between vowels sung by professional singers than by untrained voices. The center frequency of the singer’s formant as determined from long-term spectrum analysis of commercial recordings is found to increase slightly with the pitch range of the voice classification. Key Words: Singer’s formant—Vocal loudness—Singer classification.
INTRODUCTION
analyzed its level relative to the level of the first formant and found it reasonably constant within a given operatic voice singing a given vowel at a given degree of vocal loudness at various F0. According to the acoustic theory of voice production, the frequencies of the formants (henceforth denoted Fn, n = formant number) significantly influence the levels of the formant peaks in a spectrum.7,8 Likewise, studies of the voice source have revealed that variation of vocal loudness influences the slope of the voice source spectrum, so that partials at high frequencies gain more in sound level than partials at lower frequencies, when vocal loudness is increased.7,9,10 This paper addresses two issues. The first is how the level of the singer’s formant can be expected to vary with vocal loudness and vowel according to the theory of voice production. The background is that most vowel spectra of normal voices show sound energy near 3 kHz, but the singer’s formant appears as an unusually high spectrum envelope peak. This raises the question of how to define “an
The singer’s formant is a prominent spectrum envelope peak near 3 kHz that appears in voiced sounds sung by classically trained bass, baritone, tenor, and alto singers’ voices. It makes the voice easier to hear in the presence of a loud orchestral accompaniment. It can be explained as a mainly resonatory phenomenon arising from a clustering of formants 3, 4, and 5.1 Its level has been found to vary depending on singer proficiency, vowel, fundamental frequency (F0), vocal loudness, and phonation mode; its center frequency also varies depending on various factors.2-5 Schutte and Miller6 Accepted for publication June 9, 2000. Address correspondence and reprint requests to Johan Sundberg, Voice Research Centre, Department of Speech Music Hearing, KTH, SE-10044 Stockholm, Sweden. A preliminary version of this paper was presented at the Twenty-Eighth Annual Symposium Care of the Professional Voice, Philadelphia, Pennsylvania, USA, June 1999. e-mail: [email protected]
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LEVEL AND CENTER FREQUENCY OF THE SINGER’S FORMANT unusually high peak.” A corrected and expanded version of a previously published method11 for accounting for the influence of F1 and F2 on the level of F3 will be presented. The method consists of two steps. First, the expected level of F3 is predicted from the frequencies of F1 and F2, assuming frequencies of F3, F4, and F5 that are typical for normal speech. Second, the difference between the observed and this predicted level of F3 is calculated and used as a measure of the level of the singer’s formant. The second issue concerns the center frequency of the singer’s formant. Dmitriev and Kiselev12 presented schematized observations of this frequency that suggested that it varies between voice classifications, a result that was later corroborated by synthesis experiments.13 Measurements from long-term average spectrum (LTAS) analysis of commercial recordings of 20 operatic singers of different classifications are reported. Level of the singer’s formant Two factors are decisive in the expected levels of spectrum partials, vocal loudness, and formant frequencies. Bloothooft and Plomp3 studied the rela-
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tion between the level of the singer’s formant, and the overall sound level. They found that this level increased between 16 and 19 dB for a 10 dB increase in the overall sound level, depending on phonation mode, singer, and vowel. Effect of vocal loudness The influence of vocal loudness on the spectrum slope was analyzed in an experiment where classically trained male professional singers were asked to sing a crescendo on various vowels and pitches. No specific instructions were given as to how the singer should sing the crescendo. Two baritones and one bass served as subjects. The recordings were made in an anechoic room. The spectrum slope was analyzed by running the recordings through a B&K (Naerum, Denmark) Model 2307 level recorder twice, one time directly, and the other time after high-pass (HP) filtering [Itaco (Ithaca, NY) Model 4302] at 2 kHz. Figure 1 shows a typical example of the relation between overall sound level and the level of the HP-filtered signal for one of the baritone singers. The correlation is high and the relation generally linear, although it varied with
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[a:] Low F0 [a:] High F0 [i:] Low F0 [i:] High F0 [u:] Low F0 [u:] High F0
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SOUND LEVEL (dB) FIGURE 1. Relation between overall sound level relative to an arbitrary reference, and the level of the singer’s formant in professional, classically trained singers’ crescendos, performed on different vowels and pitches. Journal of Voice, Vol. 15, No. 2, 2001
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vowel and pitch. Data from the analyses of all singers are shown in Table 1, revealing that, when the overall sound level rose 10 dB, the level above 2 kHz rose on average by 16.3 dB. These results are similar to results reported earlier for male classically trained singers.3,9 Effect of formant frequencies Expected L3-L1. The influence of formant frequencies on formants levels (henceforth denoted as Ln, where n = formant number) can be predicted by the acoustic theory of voice production.7,8 The prediction takes into account the fact that a formant level increases if its distance to another formant is decreased, other things being equal. Fant’s equations7 were used for calculating expected values of L3 for different values of F1 and F2. Standard formant bandwidths and a voice source flow spectrum slope of 12 dB/octave were assumed. It was further assumed that F4 = 3.5 kHz and F5 = 4.5 kHz, but F3 was assumed to always be at least 500 Hz higher than F2, and F4 and F5 always at least 1000 Hz higher than F3 and F4, respectively. These values are roughly realistic for speech.
TABLE 1. Slope, Intercept (Icpt), and Correlation (r) for the Relation Between Overall Sound Level and the Level in a HP Filter at 2 kHz for Crescendo Tones Sung by Professional Classically Trained Singers, Two Baritones (Bar) and One Bass Singer
Vowel
Pitch
Slope
Icpt
r
Bar 1
a
D3
1.53
35.0
0.771
D4
2.27
52.9
0.977
D3
1.88
34.1
0.963
D4
1.71
20.4
0.938
D3
1.36
28.6
0.996
D4
1.29
15.8
0.873
D3
1.56
27.4
0.961
i u Bar 2
a
Bass
a
G3
1.55
24.0
0.969
i
G3
1.36
16.5
0.983
o
G3
1.75
34.6
0.883
Mean
1.63
28.9
0.931
SD
0.29
11.0
0.070
Journal of Voice, Vol. 15, No. 2, 2001
Figure 2 shows how, under these conditions, L3 varies with F2 for the three indicated values of F3, provided F1 = 500 Hz. The influence of these three F3 values was less than 6 dB. Hence these data points can be roughly represented by one single curve. The nomograms in Figure 3 show L3 L1 as a function of F2 for different values of F1, assuming that F3 = 2.5 kHz, but always 0.5 kHz higher than F2, and that F4 = 3.5 kHz and F5 = 4.5 kHz, but always 1 kHz higher than F3 and F4, respectively. Henceforth these values will be referred to as the expected L3 L1. Figure 3 shows that, in the absence of a singer’s formant, the case of F1 = 500 Hz yields an expected L3 L1 of 25 dB for F2 = 1 kHz, but no more than 8 dB for F2 = 1.8 kHz. If the frequency spacing of F3, F4, and F5 is smaller than assumed here, L3 will be higher, suggesting the presence of a singer’s formant. Figure 4 shows expected L3 L1 values for speechlike values of formants 1 5. The values vary widely between vowels, from 38 dB in [u] to 7 dB in [e]. The expected L3 L1, averaged across the 10 vowels in Figure 4, amounted to 19.1 dB [standard deviation (SD) 9.1 dB]. Observed L3 L1 Values. These expected L3 L1 values were compared with data from three sets of recordings. In one, three male speakers read a standard text at conversational loudness in an ordinary room with a microphone distance of 15 cm. Speakers 1 and 2 had untrained voices and speaker 3 was a singer. Spectrum analysis was performed at the middle of the vowel’s duration, and L3 L1 was determined. In the second set, four tenors one baritone, and two basses, all professional opera singers, sang a vowel sequence at a pitch in the middle of the singer’s range at an intermediate degree of vocal loudness. The recordings were made in an anechoic room. Spectrum analysis was carried out in the middle of each of the vowels, and L3 L1 was determined. In the third set of recordings three professional sopranos sang the solo part of a piece for soprano solo and choir, “Hear my Prayer,” by F. Mendelsohn-Bartholdy, pitch range D4-G5, in an anechoic room. The singers heard the choir part in headphones at a realistic loudness. The choir part had been recorded with microphones that were
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F2 (Hz) FIGURE 2. Idealized theoretical values of L3 L1 as a function of F2 for F1 = 500 Hz and the three indicated values of F3, assuming a flow source spectrum envelope slope of 12 dB/octave and standard formant bandwidths. It has further been assumed that F4 = 3.5 kHz and F5 = 4.5 kHz, but that F3 was always at least 500 Hz higher than F2, and that F4 and F5 were always at least 1000 Hz higher than F3 and F4, respectively.
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F2 (Hz) FIGURE 3. Approximative values of L3 L1 as a function of F2 for the indicated values of F1. Here the same assumptions as in Figure 2 are made regarding formant bandwidths, source spectrum slope, and F3, F4, and F5. Journal of Voice, Vol. 15, No. 2, 2001
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L3-L1 (dB)
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u
o
$A A
a
ae VOWEL
e
(E E
i
uç
oe
FIGURE 4. Expected L3 – L1 values for speechlike values of formants 1 – 5.
placed in a dummy head. A series of vowels sung on long notes were selected for spectrum analysis. The level difference between L1, measured as the strongest partial appearing near F1, and L3, measured as the strongest partial in the frequency band 2-4 kHz, was calculated for all spectra. Figure 5A compares expected and observed values of L3 L1 for the three speakers’ data. The variations in vowels are similar to the expected values for the back vowels [u, o, $, a] but were lower than the predicted values for the vowels [(, i, u]. The SD of the observed L3 L1 for these vowels was 9.4 dB and that for the expected L3 L1 was 11.1 dB. For most of the professional male singers the L3 L1 difference varied less with vowel than the expected values, as shown in Figure 5B. The SD of the observed L3 L1 for these vowels was 7.1 dB and was 10.0 dB for the expected L3 L1. The data for the sopranos (Figure 5C) showed great variation. Note that the expected value of L3 – L1 depends on the measured values of F1 and F2. Difference between observed and expected L3 L1 values. The difference between observed and expected L3 L1 values, henceforth denoted as LSF, Journal of Voice, Vol. 15, No. 2, 2001
seems to represent a reasonable measure of the singer’s formant. Figure 6 shows LSF data for the same speakers, male singers, and sopranos as in Figure 5. The thin dotted lines show an approximation of the effect of 10 dB variation in vocal loudness. LSF for the speakers (open symbols) was close to 0 dB or negative, the mean across speakers and vowels being 3.1 dB (SD 5.2 dB). For the male singers, the group mean of LSF was highest for the vowels [u] and [o] and close to 6 dB for the vowels [e, i, ö]. The mean across male singers and vowels was 10.8 dB (SD 7.8 dB). The sopranos exhibited great variability both between and within vowels, and the mean over all data points was 4.0 dB (SD 8.3 dB). Part of the variability would be due to the high F0 and the associated great frequency distance between adjacent partials; under such conditions it is difficult to estimate F1 and F2, and L3 L1 will vary greatly depending on how close a partial is to F1 and F3. In summary, these data show that LSF was negative or close to zero for the speakers, that it was mostly positive but clearly vowel dependent for the male singers, and that it varied considerably for the sopranos. This suggests that LSF is a promising tool
LEVEL AND CENTER FREQUENCY OF THE SINGER’S FORMANT Aa
L3-L1 (dB)
seems less useful. It is likely that a LTAS of a song is a better alternative, as it would be much less dependent on F0.
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Method. Approximately 30-s excerpts of four commercial recordings of each of 20 singers (4 sopranos, 4 altos, 4 tenors, 4 baritones, and 4 basses) were analyzed by means of LTAS.14 An LTAS shows the time average of the sound level in adjacent frequency bands. When applied to speech and singing it usually shows a stable and representative curve shape after 20–30 seconds of analysis. If a certain frequency band constantly contains a high sound level, the LTAS will show a high level at that frequency. Therefore, the singer’s formant typically appears as a clearly marked LTAS peak. In most recordings the singers sang with an orchestral accompaniment. The LTAS of this type of accompaniment typically shows a peak near 500 Hz and falls off at a rate of about 9 dB/octave. Thus, an LTAS peak in the frequency range of the singer’s formant can safely be attributed to the singer’s voice.
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a$
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FIGURE 5A. Observed and expected (solid line) L3 L1 values for vowels as produced by three speakers. Speaker 3 had a trained singing voice. B. Observed and expected (solid line) L3 L1 values for seven male professional operatic singers. The heavy dotted curve shows the mean across singers for each vowel. C. Observed and expected (solid line) L3 L1 values for three female professional operatic singers. The thin dashed line represents the overall mean across singers and vowels.
for defining the singer’s formant in male voices. For female, high-pitched voices, however, LSF
Results. LTAS for each of the 20 singers is shown with group mean curves in Figure 7. Both the shape and the level of the main high-frequency peak varied both within and between voice classifications. Figure 8 shows the mean LTAS for the five classifications. The LTAS level near 3 kHz was lowest for the sopranos and showed two rather than one single peak for three of them. For the tenors, baritones, and basses it was clearly marked, less so for the altos. The center frequency of the peak could be determined from these mean LTAS for each of the voice classifications except for the sopranos. The center frequency was measured as the midpoint between the frequencies on each side of the peak, where the level was 3 dB lower than the peak. The resulting values varied systematically between classifications. Figure 9 shows the means of this center frequency for each classification. It was highest for the alto singers (approximately 3 kHz), and was 2.84, 2.55, and 2.42 kHz for the tenors, baritones, and basses, respectively. For comparison, Seidners and coworkers’5 corresponding values, averaged Journal of Voice, Vol. 15, No. 2, 2001
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LEVEL OF SINGER'S FORMANT (dB)
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Group MV Sopr 2 MV Speaker 1 Speaker 3
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a$
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( E
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VOWEL FIGURE 6. LSF (i.e., the difference between observed and expected L3 L1 values) for the same speakers and operatic singers as in Figure 5. Solid and open symbols refer to vowel means for singers and speakers, respectively. Solid diamonds show the group means for the male singers. The thin dotted lines show an approximation of the effect of ±10 dB variation of vocal loudness.
over the vowels they analyzed, are shown in the same figure. The discrepancies would be due to the fact that the data of Seidner et al refer to only one singer in each classification. Dmitriev and Kiselev12 represented the center frequencies in term of frequency bands for the different singer classifications. The middle frequencies of these bands, also shown in Figure 9, are in good agreement with our data for the male singers. DISCUSSION One limitation of the present results is that vocal loudness could not be taken into account because of the lack of SPL data. As mentioned above, an increase in vocal loudness reduces the slope of the source spectrum envelope. The values in Table 1, however, give an idea of how variation in loudness can be expected to affect the spectrum level near 3 kHz; for our male subjects, a 10 dB increase of Journal of Voice, Vol. 15, No. 2, 2001
SPL will yield an average increase of LSF by 16 dB. The nomograms in Figure 3 and the sound level values in Figure 4 were based on the assumption of a flow source spectrum envelope slope of 12 dB/octave, that is, 6 dB/octave in pressure units; these values would be representative of a neutral degree of vocal loudness, that is, an SPL of about 75 dB at 0.3 m distance. This implies that if a vowel is produced at 65 dB at 0.3 m, the LSF in a male voice can be expected to be 6 dB weaker than predicted in Figure 4. These values, however, obviously need corroboration with real data. Another limitation is that F1 and F2 could not be accurately determined for the sopranos because of the high F0. This reduces the accuracy of the predicted L3 value. Moreover, at high F0 the frequency distance between a formant and its closest partial strongly affects the spectrum level at the formant frequency. This contributed significantly to the scatter observed for the sopranos.
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FIGURE 7. LTAS for each of four sopranos, four altos, four tenors, four baritones, and four basses. The heavy curve represents the mean for each group. To facilitate comparison the highest level of all LTAS curves were set to 0 dB.
LEVEL (dB)
SOPRANOS
LEVEL (dB)
0
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LEVEL (dB)
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FREQUENCY (Hz) FIGURE 8. Mean LTAS for the indicated singer classifications. To facilitate comparison the highest level of all LTAS curves were set to 0 dB.
MIDFREQEUNCY OF LTAS PEAK (Hz)
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2400 2200 Soprano
Alto
Tenor
Baritone
Bass
VOICE CLASSIFICATION FIGURE 9. Means of the center frequency of the LTAS peak near 3 kHz for different voice classifications. The bars represent one standard deviation. The open squares show values reported by Seidner et al5 and the thin dotted curve shows data derived from measurements published by Dmitriev and Kiselev.12 Journal of Voice, Vol. 15, No. 2, 2001
LEVEL AND CENTER FREQUENCY OF THE SINGER’S FORMANT In spite of these limitations, the curves shown in Figure 3 clearly demonstrate the need to take F1 and F2 into consideration when judging whether or not a vowel contains a singer’s formant. It is difficult to determine the presence of a singer’s formant from L3 L1 for an isolated vowel, unless F1 and F2, as well as loudness, are known. The relevance of vocal loudness and vowels to the level of the singer’s formant was clearly demonstrated by Bloothooft and Plomp.3 They suggested that a spectrum peak higher than 20 dB below the overall SPL might be useful as a threshold value for a singer’s formant but also reported that vowels sung in a soft voice would then lack a singer’s formant. The male singers showed a much more vowel-dependent LSF than the speakers. The values observed for LSF were almost 20 dB for the vowels [u, o] and close to 6 dB for the other vowels analyzed. Given the fact that L3 is very low in [u, o] this variability probably reflects the striving for equalization of vowel timbre, a major goal in the training of classical singers. This finding relates to observations made by Estill and coworkers.15 They teased out the resonatory and phonatory contributions to the spectrum envelope peak representing the singer’s formant in the vowels [a] and [i] as sung by three singer subjects. They found that the spectrum peak could be accounted for in terms of resonatory effects for the [a], but in the case of the [i] the spectrum level was not much different from what it was in speech. A limitation with the data on the center frequency of the singer’s formant is that they were derived from commercial recordings of singers accompanied by an orchestra. However, as mentioned above, the LTAS peak near 3 kHz is very likely to reflect the singer’s formant in such recordings, since the LTAS of an orchestra typically does not show any peak in this frequency region. The frequency characteristics used during the recording represent another potential source of error. On the other hand, it is unlikely that this characteristic caused any shift in the center frequency of the singer’s formant. First, such a shift would entail a modification of the singer’s voice timbre.13 Second, the values derived from the LTAS analyses of the recordings of male voices agreed closely with those published by Dmitriev and Kiselev.12 For the fe-
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male voices the values of Dmitriev and Kiselev on center frequencies were lower than ours. The reason for this discrepancy may be the choice of singers and/or the filter bank used for the analysis. The LTAS in Figure 8 showed a much higher peak near 3 kHz for the male singers than for the sopranos. Similar observations were made by Bloothooft and Plomp.3 The divided peak in the LTAS for the sopranos probably reflects the averages of normal, that is, nonclustered F3 and F4. This supports the assumption that sopranos do not produce a singer’s formant. Indeed, avoiding a clustering of formants 3, 4, and 5 may even be advantageous under conditions of singing at high pitches. The wide spacing of partials under such conditions is associated with the risk that for some pitches, no partial would fall into the frequency range of the cluster. This would have a clearly perceptible effect on the voice timbre. The risk of producing spectra devoid of a strong partial near 3 kHz is reduced, if the frequency separation of F3 and F4 is wider. It is also relevant that timbre perception is based on the critical bands of hearing. The width of a critical band near 3 kHz is approximately 800 Hz. Therefore, if F3 and F4 are separated by 800 Hz, the voice timbre should be similar, regardless of whether a strong partial appears in F3 or F4. In view of the difficulties caused by high F0 and the associated limited accuracy of the expected L3 L1 values, it seems that LTAS analysis may be a better tool than isolated vowels for deciding whether or not a voice possesses a singer’s formant. For this, a calibration of LTAS curves is required, which should preferably be realized by means of experiments with synthesized singing. CONCLUSIONS The singer’s formant is an unusually high spectrum envelope peak near 3 kHz, the level of which reveals whether or not a voice possesses a singer’s formant. It is suggested that this level be defined as the deviation from an expected level of the third formant. Given the frequencies of the two lowest formants this expected level can be estimated from the nomograms in Figure 3. According to the definition proposed, the level of the singer’s formant is Journal of Voice, Vol. 15, No. 2, 2001
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close to or lower than 0 dB in male speakers, thus suggesting a lack of a singer’s formant. The same applies also to operatic sopranos in most cases, although they show a great variability that is probably due to their high fundamental frequencies. The average level of the singer’s formant in male operatic singers is about 20 dB in [u] and 6 dB in [e]. This would increase the timbral similarity between vowels. However, for accurate measurements it is also necessary to take vocal loudness into account. The center frequency of the singer’s formant varies with voice classification, being lowest for basses and highest for tenors. LTAS analysis of commercial recordings showed a clear peak near 3 kHz. The group average curves for the classifications showed that the level of the peak was highest for baritones, that it was 3 dB lower for basses and tenors, and about 9 dB lower for altos. For most sopranos two peaks were observed, presumably reflecting F3 and F4, thus suggesting that they do not cluster these formants and do not have a singer’s formant. Acknowledgments: The computations underlying the data shown in Figures 2 and 3 were carried out by Dr. Sten Ternström. The recordings used for measuring the center frequency of the singer’s formant were assembled by Anna Maria Söderström and Marie Niska, and the LTAS analyses were carried out by Keyhan Hadjari and Mikael Hirschberg. The author gratefully acknowledges the many valuable comments and suggestions of an anonymous reviewer.
REFERENCES 1. Sundberg J. The Science of the Singing Voice, DeKalb, Ill: Northern Illinois University Press; 1987. 2. Hollien H. The puzzle of the singer’s formant. In: Bless DM, Abbs JH, eds. Vocal Fold Physiology. Contemporary Research and Clinical Issues. San Diego, Calif: College Hill Press; 1983: 368-378.
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3. Bloothooft G, Plomp R. The sound level of the singer’s formant in professional singing, J Acoust Soc Am. 1986; 79:2028-2033. 4. Schultz-Coulon H, Battmer R, Riechers H. Der 3-kHzFormant, ein Mass fur die Tragfähigkeit der Stimme? I. Die untrainierte Stimme, II. Die trainierte Stimme, Folia Phoniatr. 1979;31:291-313. 5. Seidner W, Schutte H, Wendler J, Rauhut A. Dependence of the high singing formant on pitch and vowel in different voice types. In: Askenfelt A, Felicetti S, Jansson E, Sundberg, J, eds. Proceedings of the Stockholm Music Acoustics Conference (SMAC 83):I. Stockholm, Sweden: Royal Swedish Academy of Music, Publication No. 46(1); 1985: 261-268. 6. Schutte H, Miller R. Individual parameters of the singer’s formant, Folia Phoniatr. 1985; 37:31-35. 7. Fant G. Acoustic Theory of Speech Production. The Hague, Netherlands: Mouton; 1960. 8. Fant G. On the predictability of formant levels and spectrum envelopes from formant frequencies. In: For Roman Jakobson. The Hague, Netherlands: Mouton; 1970:109120. 9. Cleveland T, Sundberg J. Acoustic analysis of three male voices of different quality. In: Askenfelt A, Felicetti S, Jansson E, Sundberg, J, eds. Proceedings of the Stockholm Music Acoustics Conference (SMAC 83):I. Stockholm, Sweden-Royal Swedish Academy of Music, Publication No. 46(1);1985:143-156. 10. Gauffin J, Sundberg J. Spectral correlates of glottal voice source waveform characteristics. J Speech Hear Res. 1989;32:556-565. 11. Sundberg J. The singer’s formant revisited. Voice. 1995;4:106-119. 12. Dmitriev L, Kiselev A. Relationship between the formant structure of different types of singing voices and the dimension of supraglottal cavities. Folia Phoniatr. 1979;31: 238-241. 13. Berndtsson G, Sundberg J. Perceptual significance of the center frequency of the singer’s formant. Scand J Logop Phoniatr. 1995;20:35-41. 14. Sundberg J, Niska Thörnvik M, Söderström AM. Age and voice quality in professional singers. Logop Phoniatr Vocol. 1998;23:169-176. 15. Estill J, Fujimura O, Erickson D et al. Vocal tract contributions to voice qualities. In: Friberg A, Iwarsson J, Jansson E, Sundberg, J, eds. Proceedings of the Stockholm Music Acoustics Conference (SMAC 93), Stockholm, Sweden: Royal Academy of Music, Publication No. 79; 1994:161165.
Level and Center Frequency of the Singer’s Formant Johan Sundberg Voice Research Centre, Department of Speech Music Hearing, KTH, Stockholm, Sweden
Summary: The “singer’s formant” is a prominent spectrum envelope peak near 3 kHz, typically found in voiced sounds produced by classical operatic singers. According to previous research, it is mainly a resonatory phenomenon produced by a clustering of formants 3, 4, and 5. Its level relative to the first formant peak varies depending on vowel, vocal loudness, and other factors. Its dependence on vowel formant frequencies is examined. Applying the acoustic theory of voice production, the level difference between the first and third formant is calulated for some standard vowels. The difference between observed and calculated levels is determined for various voices. It is found to vary considerably more between vowels sung by professional singers than by untrained voices. The center frequency of the singer’s formant as determined from long-term spectrum analysis of commercial recordings is found to increase slightly with the pitch range of the voice classification. Key Words: Singer’s formant—Vocal loudness—Singer classification.
INTRODUCTION
analyzed its level relative to the level of the first formant and found it reasonably constant within a given operatic voice singing a given vowel at a given degree of vocal loudness at various F0. According to the acoustic theory of voice production, the frequencies of the formants (henceforth denoted Fn, n = formant number) significantly influence the levels of the formant peaks in a spectrum.7,8 Likewise, studies of the voice source have revealed that variation of vocal loudness influences the slope of the voice source spectrum, so that partials at high frequencies gain more in sound level than partials at lower frequencies, when vocal loudness is increased.7,9,10 This paper addresses two issues. The first is how the level of the singer’s formant can be expected to vary with vocal loudness and vowel according to the theory of voice production. The background is that most vowel spectra of normal voices show sound energy near 3 kHz, but the singer’s formant appears as an unusually high spectrum envelope peak. This raises the question of how to define “an
The singer’s formant is a prominent spectrum envelope peak near 3 kHz that appears in voiced sounds sung by classically trained bass, baritone, tenor, and alto singers’ voices. It makes the voice easier to hear in the presence of a loud orchestral accompaniment. It can be explained as a mainly resonatory phenomenon arising from a clustering of formants 3, 4, and 5.1 Its level has been found to vary depending on singer proficiency, vowel, fundamental frequency (F0), vocal loudness, and phonation mode; its center frequency also varies depending on various factors.2-5 Schutte and Miller6 Accepted for publication June 9, 2000. Address correspondence and reprint requests to Johan Sundberg, Voice Research Centre, Department of Speech Music Hearing, KTH, SE-10044 Stockholm, Sweden. A preliminary version of this paper was presented at the Twenty-Eighth Annual Symposium Care of the Professional Voice, Philadelphia, Pennsylvania, USA, June 1999. e-mail: [email protected]
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LEVEL AND CENTER FREQUENCY OF THE SINGER’S FORMANT unusually high peak.” A corrected and expanded version of a previously published method11 for accounting for the influence of F1 and F2 on the level of F3 will be presented. The method consists of two steps. First, the expected level of F3 is predicted from the frequencies of F1 and F2, assuming frequencies of F3, F4, and F5 that are typical for normal speech. Second, the difference between the observed and this predicted level of F3 is calculated and used as a measure of the level of the singer’s formant. The second issue concerns the center frequency of the singer’s formant. Dmitriev and Kiselev12 presented schematized observations of this frequency that suggested that it varies between voice classifications, a result that was later corroborated by synthesis experiments.13 Measurements from long-term average spectrum (LTAS) analysis of commercial recordings of 20 operatic singers of different classifications are reported. Level of the singer’s formant Two factors are decisive in the expected levels of spectrum partials, vocal loudness, and formant frequencies. Bloothooft and Plomp3 studied the rela-
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tion between the level of the singer’s formant, and the overall sound level. They found that this level increased between 16 and 19 dB for a 10 dB increase in the overall sound level, depending on phonation mode, singer, and vowel. Effect of vocal loudness The influence of vocal loudness on the spectrum slope was analyzed in an experiment where classically trained male professional singers were asked to sing a crescendo on various vowels and pitches. No specific instructions were given as to how the singer should sing the crescendo. Two baritones and one bass served as subjects. The recordings were made in an anechoic room. The spectrum slope was analyzed by running the recordings through a B&K (Naerum, Denmark) Model 2307 level recorder twice, one time directly, and the other time after high-pass (HP) filtering [Itaco (Ithaca, NY) Model 4302] at 2 kHz. Figure 1 shows a typical example of the relation between overall sound level and the level of the HP-filtered signal for one of the baritone singers. The correlation is high and the relation generally linear, although it varied with
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SOUND LEVEL (dB) FIGURE 1. Relation between overall sound level relative to an arbitrary reference, and the level of the singer’s formant in professional, classically trained singers’ crescendos, performed on different vowels and pitches. Journal of Voice, Vol. 15, No. 2, 2001
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vowel and pitch. Data from the analyses of all singers are shown in Table 1, revealing that, when the overall sound level rose 10 dB, the level above 2 kHz rose on average by 16.3 dB. These results are similar to results reported earlier for male classically trained singers.3,9 Effect of formant frequencies Expected L3-L1. The influence of formant frequencies on formants levels (henceforth denoted as Ln, where n = formant number) can be predicted by the acoustic theory of voice production.7,8 The prediction takes into account the fact that a formant level increases if its distance to another formant is decreased, other things being equal. Fant’s equations7 were used for calculating expected values of L3 for different values of F1 and F2. Standard formant bandwidths and a voice source flow spectrum slope of 12 dB/octave were assumed. It was further assumed that F4 = 3.5 kHz and F5 = 4.5 kHz, but F3 was assumed to always be at least 500 Hz higher than F2, and F4 and F5 always at least 1000 Hz higher than F3 and F4, respectively. These values are roughly realistic for speech.
TABLE 1. Slope, Intercept (Icpt), and Correlation (r) for the Relation Between Overall Sound Level and the Level in a HP Filter at 2 kHz for Crescendo Tones Sung by Professional Classically Trained Singers, Two Baritones (Bar) and One Bass Singer
Vowel
Pitch
Slope
Icpt
r
Bar 1
a
D3
1.53
35.0
0.771
D4
2.27
52.9
0.977
D3
1.88
34.1
0.963
D4
1.71
20.4
0.938
D3
1.36
28.6
0.996
D4
1.29
15.8
0.873
D3
1.56
27.4
0.961
i u Bar 2
a
Bass
a
G3
1.55
24.0
0.969
i
G3
1.36
16.5
0.983
o
G3
1.75
34.6
0.883
Mean
1.63
28.9
0.931
SD
0.29
11.0
0.070
Journal of Voice, Vol. 15, No. 2, 2001
Figure 2 shows how, under these conditions, L3 varies with F2 for the three indicated values of F3, provided F1 = 500 Hz. The influence of these three F3 values was less than 6 dB. Hence these data points can be roughly represented by one single curve. The nomograms in Figure 3 show L3 L1 as a function of F2 for different values of F1, assuming that F3 = 2.5 kHz, but always 0.5 kHz higher than F2, and that F4 = 3.5 kHz and F5 = 4.5 kHz, but always 1 kHz higher than F3 and F4, respectively. Henceforth these values will be referred to as the expected L3 L1. Figure 3 shows that, in the absence of a singer’s formant, the case of F1 = 500 Hz yields an expected L3 L1 of 25 dB for F2 = 1 kHz, but no more than 8 dB for F2 = 1.8 kHz. If the frequency spacing of F3, F4, and F5 is smaller than assumed here, L3 will be higher, suggesting the presence of a singer’s formant. Figure 4 shows expected L3 L1 values for speechlike values of formants 1 5. The values vary widely between vowels, from 38 dB in [u] to 7 dB in [e]. The expected L3 L1, averaged across the 10 vowels in Figure 4, amounted to 19.1 dB [standard deviation (SD) 9.1 dB]. Observed L3 L1 Values. These expected L3 L1 values were compared with data from three sets of recordings. In one, three male speakers read a standard text at conversational loudness in an ordinary room with a microphone distance of 15 cm. Speakers 1 and 2 had untrained voices and speaker 3 was a singer. Spectrum analysis was performed at the middle of the vowel’s duration, and L3 L1 was determined. In the second set, four tenors one baritone, and two basses, all professional opera singers, sang a vowel sequence at a pitch in the middle of the singer’s range at an intermediate degree of vocal loudness. The recordings were made in an anechoic room. Spectrum analysis was carried out in the middle of each of the vowels, and L3 L1 was determined. In the third set of recordings three professional sopranos sang the solo part of a piece for soprano solo and choir, “Hear my Prayer,” by F. Mendelsohn-Bartholdy, pitch range D4-G5, in an anechoic room. The singers heard the choir part in headphones at a realistic loudness. The choir part had been recorded with microphones that were
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F2 (Hz) FIGURE 2. Idealized theoretical values of L3 L1 as a function of F2 for F1 = 500 Hz and the three indicated values of F3, assuming a flow source spectrum envelope slope of 12 dB/octave and standard formant bandwidths. It has further been assumed that F4 = 3.5 kHz and F5 = 4.5 kHz, but that F3 was always at least 500 Hz higher than F2, and that F4 and F5 were always at least 1000 Hz higher than F3 and F4, respectively.
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F2 (Hz) FIGURE 3. Approximative values of L3 L1 as a function of F2 for the indicated values of F1. Here the same assumptions as in Figure 2 are made regarding formant bandwidths, source spectrum slope, and F3, F4, and F5. Journal of Voice, Vol. 15, No. 2, 2001
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ae VOWEL
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i
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oe
FIGURE 4. Expected L3 – L1 values for speechlike values of formants 1 – 5.
placed in a dummy head. A series of vowels sung on long notes were selected for spectrum analysis. The level difference between L1, measured as the strongest partial appearing near F1, and L3, measured as the strongest partial in the frequency band 2-4 kHz, was calculated for all spectra. Figure 5A compares expected and observed values of L3 L1 for the three speakers’ data. The variations in vowels are similar to the expected values for the back vowels [u, o, $, a] but were lower than the predicted values for the vowels [(, i, u]. The SD of the observed L3 L1 for these vowels was 9.4 dB and that for the expected L3 L1 was 11.1 dB. For most of the professional male singers the L3 L1 difference varied less with vowel than the expected values, as shown in Figure 5B. The SD of the observed L3 L1 for these vowels was 7.1 dB and was 10.0 dB for the expected L3 L1. The data for the sopranos (Figure 5C) showed great variation. Note that the expected value of L3 – L1 depends on the measured values of F1 and F2. Difference between observed and expected L3 L1 values. The difference between observed and expected L3 L1 values, henceforth denoted as LSF, Journal of Voice, Vol. 15, No. 2, 2001
seems to represent a reasonable measure of the singer’s formant. Figure 6 shows LSF data for the same speakers, male singers, and sopranos as in Figure 5. The thin dotted lines show an approximation of the effect of 10 dB variation in vocal loudness. LSF for the speakers (open symbols) was close to 0 dB or negative, the mean across speakers and vowels being 3.1 dB (SD 5.2 dB). For the male singers, the group mean of LSF was highest for the vowels [u] and [o] and close to 6 dB for the vowels [e, i, ö]. The mean across male singers and vowels was 10.8 dB (SD 7.8 dB). The sopranos exhibited great variability both between and within vowels, and the mean over all data points was 4.0 dB (SD 8.3 dB). Part of the variability would be due to the high F0 and the associated great frequency distance between adjacent partials; under such conditions it is difficult to estimate F1 and F2, and L3 L1 will vary greatly depending on how close a partial is to F1 and F3. In summary, these data show that LSF was negative or close to zero for the speakers, that it was mostly positive but clearly vowel dependent for the male singers, and that it varied considerably for the sopranos. This suggests that LSF is a promising tool
LEVEL AND CENTER FREQUENCY OF THE SINGER’S FORMANT Aa
L3-L1 (dB)
seems less useful. It is likely that a LTAS of a song is a better alternative, as it would be much less dependent on F0.
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Method. Approximately 30-s excerpts of four commercial recordings of each of 20 singers (4 sopranos, 4 altos, 4 tenors, 4 baritones, and 4 basses) were analyzed by means of LTAS.14 An LTAS shows the time average of the sound level in adjacent frequency bands. When applied to speech and singing it usually shows a stable and representative curve shape after 20–30 seconds of analysis. If a certain frequency band constantly contains a high sound level, the LTAS will show a high level at that frequency. Therefore, the singer’s formant typically appears as a clearly marked LTAS peak. In most recordings the singers sang with an orchestral accompaniment. The LTAS of this type of accompaniment typically shows a peak near 500 Hz and falls off at a rate of about 9 dB/octave. Thus, an LTAS peak in the frequency range of the singer’s formant can safely be attributed to the singer’s voice.
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FIGURE 5A. Observed and expected (solid line) L3 L1 values for vowels as produced by three speakers. Speaker 3 had a trained singing voice. B. Observed and expected (solid line) L3 L1 values for seven male professional operatic singers. The heavy dotted curve shows the mean across singers for each vowel. C. Observed and expected (solid line) L3 L1 values for three female professional operatic singers. The thin dashed line represents the overall mean across singers and vowels.
for defining the singer’s formant in male voices. For female, high-pitched voices, however, LSF
Results. LTAS for each of the 20 singers is shown with group mean curves in Figure 7. Both the shape and the level of the main high-frequency peak varied both within and between voice classifications. Figure 8 shows the mean LTAS for the five classifications. The LTAS level near 3 kHz was lowest for the sopranos and showed two rather than one single peak for three of them. For the tenors, baritones, and basses it was clearly marked, less so for the altos. The center frequency of the peak could be determined from these mean LTAS for each of the voice classifications except for the sopranos. The center frequency was measured as the midpoint between the frequencies on each side of the peak, where the level was 3 dB lower than the peak. The resulting values varied systematically between classifications. Figure 9 shows the means of this center frequency for each classification. It was highest for the alto singers (approximately 3 kHz), and was 2.84, 2.55, and 2.42 kHz for the tenors, baritones, and basses, respectively. For comparison, Seidners and coworkers’5 corresponding values, averaged Journal of Voice, Vol. 15, No. 2, 2001
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LEVEL OF SINGER'S FORMANT (dB)
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Group MV Sopr 2 MV Speaker 1 Speaker 3
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VOWEL FIGURE 6. LSF (i.e., the difference between observed and expected L3 L1 values) for the same speakers and operatic singers as in Figure 5. Solid and open symbols refer to vowel means for singers and speakers, respectively. Solid diamonds show the group means for the male singers. The thin dotted lines show an approximation of the effect of ±10 dB variation of vocal loudness.
over the vowels they analyzed, are shown in the same figure. The discrepancies would be due to the fact that the data of Seidner et al refer to only one singer in each classification. Dmitriev and Kiselev12 represented the center frequencies in term of frequency bands for the different singer classifications. The middle frequencies of these bands, also shown in Figure 9, are in good agreement with our data for the male singers. DISCUSSION One limitation of the present results is that vocal loudness could not be taken into account because of the lack of SPL data. As mentioned above, an increase in vocal loudness reduces the slope of the source spectrum envelope. The values in Table 1, however, give an idea of how variation in loudness can be expected to affect the spectrum level near 3 kHz; for our male subjects, a 10 dB increase of Journal of Voice, Vol. 15, No. 2, 2001
SPL will yield an average increase of LSF by 16 dB. The nomograms in Figure 3 and the sound level values in Figure 4 were based on the assumption of a flow source spectrum envelope slope of 12 dB/octave, that is, 6 dB/octave in pressure units; these values would be representative of a neutral degree of vocal loudness, that is, an SPL of about 75 dB at 0.3 m distance. This implies that if a vowel is produced at 65 dB at 0.3 m, the LSF in a male voice can be expected to be 6 dB weaker than predicted in Figure 4. These values, however, obviously need corroboration with real data. Another limitation is that F1 and F2 could not be accurately determined for the sopranos because of the high F0. This reduces the accuracy of the predicted L3 value. Moreover, at high F0 the frequency distance between a formant and its closest partial strongly affects the spectrum level at the formant frequency. This contributed significantly to the scatter observed for the sopranos.
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FIGURE 7. LTAS for each of four sopranos, four altos, four tenors, four baritones, and four basses. The heavy curve represents the mean for each group. To facilitate comparison the highest level of all LTAS curves were set to 0 dB.
LEVEL (dB)
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LEVEL (dB)
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FREQUENCY (Hz) FIGURE 8. Mean LTAS for the indicated singer classifications. To facilitate comparison the highest level of all LTAS curves were set to 0 dB.
MIDFREQEUNCY OF LTAS PEAK (Hz)
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Alto
Tenor
Baritone
Bass
VOICE CLASSIFICATION FIGURE 9. Means of the center frequency of the LTAS peak near 3 kHz for different voice classifications. The bars represent one standard deviation. The open squares show values reported by Seidner et al5 and the thin dotted curve shows data derived from measurements published by Dmitriev and Kiselev.12 Journal of Voice, Vol. 15, No. 2, 2001
LEVEL AND CENTER FREQUENCY OF THE SINGER’S FORMANT In spite of these limitations, the curves shown in Figure 3 clearly demonstrate the need to take F1 and F2 into consideration when judging whether or not a vowel contains a singer’s formant. It is difficult to determine the presence of a singer’s formant from L3 L1 for an isolated vowel, unless F1 and F2, as well as loudness, are known. The relevance of vocal loudness and vowels to the level of the singer’s formant was clearly demonstrated by Bloothooft and Plomp.3 They suggested that a spectrum peak higher than 20 dB below the overall SPL might be useful as a threshold value for a singer’s formant but also reported that vowels sung in a soft voice would then lack a singer’s formant. The male singers showed a much more vowel-dependent LSF than the speakers. The values observed for LSF were almost 20 dB for the vowels [u, o] and close to 6 dB for the other vowels analyzed. Given the fact that L3 is very low in [u, o] this variability probably reflects the striving for equalization of vowel timbre, a major goal in the training of classical singers. This finding relates to observations made by Estill and coworkers.15 They teased out the resonatory and phonatory contributions to the spectrum envelope peak representing the singer’s formant in the vowels [a] and [i] as sung by three singer subjects. They found that the spectrum peak could be accounted for in terms of resonatory effects for the [a], but in the case of the [i] the spectrum level was not much different from what it was in speech. A limitation with the data on the center frequency of the singer’s formant is that they were derived from commercial recordings of singers accompanied by an orchestra. However, as mentioned above, the LTAS peak near 3 kHz is very likely to reflect the singer’s formant in such recordings, since the LTAS of an orchestra typically does not show any peak in this frequency region. The frequency characteristics used during the recording represent another potential source of error. On the other hand, it is unlikely that this characteristic caused any shift in the center frequency of the singer’s formant. First, such a shift would entail a modification of the singer’s voice timbre.13 Second, the values derived from the LTAS analyses of the recordings of male voices agreed closely with those published by Dmitriev and Kiselev.12 For the fe-
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male voices the values of Dmitriev and Kiselev on center frequencies were lower than ours. The reason for this discrepancy may be the choice of singers and/or the filter bank used for the analysis. The LTAS in Figure 8 showed a much higher peak near 3 kHz for the male singers than for the sopranos. Similar observations were made by Bloothooft and Plomp.3 The divided peak in the LTAS for the sopranos probably reflects the averages of normal, that is, nonclustered F3 and F4. This supports the assumption that sopranos do not produce a singer’s formant. Indeed, avoiding a clustering of formants 3, 4, and 5 may even be advantageous under conditions of singing at high pitches. The wide spacing of partials under such conditions is associated with the risk that for some pitches, no partial would fall into the frequency range of the cluster. This would have a clearly perceptible effect on the voice timbre. The risk of producing spectra devoid of a strong partial near 3 kHz is reduced, if the frequency separation of F3 and F4 is wider. It is also relevant that timbre perception is based on the critical bands of hearing. The width of a critical band near 3 kHz is approximately 800 Hz. Therefore, if F3 and F4 are separated by 800 Hz, the voice timbre should be similar, regardless of whether a strong partial appears in F3 or F4. In view of the difficulties caused by high F0 and the associated limited accuracy of the expected L3 L1 values, it seems that LTAS analysis may be a better tool than isolated vowels for deciding whether or not a voice possesses a singer’s formant. For this, a calibration of LTAS curves is required, which should preferably be realized by means of experiments with synthesized singing. CONCLUSIONS The singer’s formant is an unusually high spectrum envelope peak near 3 kHz, the level of which reveals whether or not a voice possesses a singer’s formant. It is suggested that this level be defined as the deviation from an expected level of the third formant. Given the frequencies of the two lowest formants this expected level can be estimated from the nomograms in Figure 3. According to the definition proposed, the level of the singer’s formant is Journal of Voice, Vol. 15, No. 2, 2001
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close to or lower than 0 dB in male speakers, thus suggesting a lack of a singer’s formant. The same applies also to operatic sopranos in most cases, although they show a great variability that is probably due to their high fundamental frequencies. The average level of the singer’s formant in male operatic singers is about 20 dB in [u] and 6 dB in [e]. This would increase the timbral similarity between vowels. However, for accurate measurements it is also necessary to take vocal loudness into account. The center frequency of the singer’s formant varies with voice classification, being lowest for basses and highest for tenors. LTAS analysis of commercial recordings showed a clear peak near 3 kHz. The group average curves for the classifications showed that the level of the peak was highest for baritones, that it was 3 dB lower for basses and tenors, and about 9 dB lower for altos. For most sopranos two peaks were observed, presumably reflecting F3 and F4, thus suggesting that they do not cluster these formants and do not have a singer’s formant. Acknowledgments: The computations underlying the data shown in Figures 2 and 3 were carried out by Dr. Sten Ternström. The recordings used for measuring the center frequency of the singer’s formant were assembled by Anna Maria Söderström and Marie Niska, and the LTAS analyses were carried out by Keyhan Hadjari and Mikael Hirschberg. The author gratefully acknowledges the many valuable comments and suggestions of an anonymous reviewer.
REFERENCES 1. Sundberg J. The Science of the Singing Voice, DeKalb, Ill: Northern Illinois University Press; 1987. 2. Hollien H. The puzzle of the singer’s formant. In: Bless DM, Abbs JH, eds. Vocal Fold Physiology. Contemporary Research and Clinical Issues. San Diego, Calif: College Hill Press; 1983: 368-378.
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