Physical Characteristics of the Singing Voice

A. V. Rabinovich, Moscow

1. General Remarks

The musical merits of the singing voice are determined, obviously, by musical-aesthetic requirements common to all musical instruments. These requirements are essentially the following: beauty of timbre, a large frequency range, a large dynamic range, equal power for all frequencies of the singing voice, musical mobility (the ability to perform any rapid and complex melodic figures), and so forth. For a certain group of musical instruments, including the singing voice, there exists an additional requirement relating to so-called vibration. By vibration is meant a periodic change in the frequency, intensity, and overtone structure of the sound. The vibrations of the singing voice are its inseparable element, organically connected with the whole process of sound production, whereas the vibrations of the other instruments belonging to the aforementioned group—namely, the violin, viola, cello, double bass, and, in part, the saxophone—are created by the musician during performance arbitrarily, obviously in imitation of the singing voice.

As is known, not all human voices can be used as singing voices; certain natural endowments are necessary which, when developed through appropriate training, ensure satisfactory fulfillment of the requirements enumerated above. The determination of these endowments, the determination of training methods and the results obtained—all this is the province of vocal pedagogy. It is generally known, however, that in the field of vocal pedagogy there have hitherto been no, or almost no, firmly established propositions, rigorously verified methods, or working hypotheses based on more or less objective material. There exists an enormous number of vocal-pedagogical theories contradicting one another.

One of the essential causes of the indicated shortcomings of vocal pedagogy is the absence of knowledge concerning the physical nature of the singing voice. Only relatively recently have physicists, with the participation of advanced vocalist-pedagogues, undertaken the study of physical problems; moreover, by the present time a sufficient quantity of experimental, theoretically systematized material has already accumulated.

It must be noted that in this matter investigators have invariably been far from the idea of establishing in advance precisely what physical characteristics a singing voice must have in order to sound good, or of explaining why certain characteristics are good. The idea, set as the basis of the experiments, undoubtedly consisted in taking a large number of unquestionably good and unquestionably poor singing voices and statistically determining the difference in the physical characteristics of the first and second categories; it was then necessary to establish the connection of the physical characteristics with the anatomy and physiology of the vocal apparatus and to trace the change of these characteristics in the process of the singer’s training and development.

The use of the knowledge obtained is possible not only along the line of vocal pedagogy, but also along the line of radio and sound cinema, where admissible

PHYSICAL CHARACTERISTICS OF THE SINGING VOICE

in the design of studios and equipment are closely connected with the physical characteristics of the reproduced musical material.

The present review article has been compiled mainly from the materials of two recently published works: Bartholomew¹ and Wolf, Stanley, and Sette².

2. Power of the Voice

Great power in a singing voice is not a necessary condition for its good quality. Famous singers are known who possessed a relatively quiet voice. In most cases, however, singers with a well-trained voice produce greater power than poor singers. Bartholomew points to this fact without supporting it experimentally. In his opinion, the increase in power is achieved by means of a relatively wide throat, owing to a more intensive action of the vocal cords, and owing to greater tension of the soft walls of the resonant cavities. Wolf, Stanley, and Sette give several examples from which it is evident that, in the course of training, the power of the voice increases: after a course of study singers attain a power 10–15 db higher than the original.

A considerably more important factor determining the quality of the singing voice is its relatively high power over the entire performed frequency range. It may be assumed, as was already said above, that a good singer must be able to sing any required tone with equal force. We know, however, from practice that even the best singers perform the very lowest tones of their register very quietly and are not able to weaken very loudly sounding extreme high tones.

Numerous experiments by Wolf, Stanley, and Sette confirm this fact and establish the regularity, characteristic of good singers, of an increase in sound power with an increase in its frequency. Figure 1 gives

![Figure 1 graph]

Fig. 1. A — vowel “a”, B — vowel “e”, C — vowel “u”, D — vowel “i”.

![Figure 2 graph]

Fig. 2.

curves giving the dependence of the maximum radiated power on frequency (average for 5 good baritones). As is evident from the figure, all four curves are very similar in character.

Figure 2 gives “relative” curves (on the vowel a) A — for all types of male voices (with the exception of bass) and B — for all types of female voices. The points through which the curves have been drawn correspond

maximum powers obtained for the given tone from any of the voices studied.

The relative curves serve for comparing voices with respect to the feature discussed in the present section. Incidentally, we note that the maximum power of the singing voice in the high register of high male and female voices is approximately equal to 1 W. This is considerably greater than the figures indicated by previous investigators.

3. Vibrations

One of the principal characteristics of a good singing voice is the presence of substantial vibrations. The frequency of vibrations in a good singer is

Fig. 3. Timbre spectra obtained at four successive moments of time (baritone of good quality, vowel “a,” fundamental tone 262 Hz—“C” of the first octave).

almost constant. According to Bartholomew’s study they occur 6–7 times per second; according to the investigations of Wolf, Stanley, and Sette—about 6 times per second. It is interesting to compare these figures with the frequency of vibrations in violin playing, where we have on average the figure 6.7 times per second.

According to Bartholomew’s observations, the change in timbre during vibration consists in a periodic strengthening of the overtones now in the higher, now in the lower frequency region. Fig. 3 explains this well.

The presence and great importance of timbre vibrations in the singing voice were established comparatively long ago: Kazansky and Rzhevkin⁴ pri-

introduce numerous examples of vibrations and establish a method for harmonic analysis of vibrating voices, made difficult by the presence of inharmonic overtones.

Poor singing voices do not have significant timbral vibrato, i.e., their timbre remains almost unchanged over a considerable interval of time. For illustration we present four oscillograms (Bartolomeo), sung by a good (a and b) and a poor (c and d) singer (Fig. 4). Between oscillograms a and b, and likewise between oscillograms c and d, an interval of time of \(1/13\) sec. was taken, i.e., about a half-period of one vibration. As we see, in the good voice during this time significant changes in timbre and amplitude occurred, whereas in the poor one both remained almost unchanged.

Fig. 4.

Amplitude changes during vibrato were studied by Wolf, Stanley, and Sette with the aid of an automatic device recording the level of sound intensity.

On the basis of these records it can be established that the change of amplitude during vibrato in good singers occurs smoothly, on average by 4–5 db; in individual cases, when performing “fortissimo” (very loudly), it reaches 12–15 db; when singing “pianissimo” (very softly), the amplitude vibrations become very small.

In poor singers the change of amplitude occurs stepwise, and the vibrato frequency deviates from the norm, reaching up to 8 times per second.

Frequency changes during vibrato in the works under consideration, as in the other works known to us, have been insufficiently studied. Wolf, Stanley, and Sette used for this purpose an acoustic spectrometer, with the aid of which it was, of course, possible to determine only the frequency band affected by the vibrato, but not the character of the frequency change. To determine the latter, it is useful to employ an oscillograph according to the method used by the author of the present article in deciphering violin vibrations³. Wolf, Stanley, and Sette were able only to establish that in good singers the frequency vibrato affects a considerably broader band than in poor ones.

4. Timbre

Kazansky and Rzhevkin, in the work already cited by us, established the difference in the character of the formants between the singing and speaking voice, which reduces to two propositions: 1) the singing voice is characterized

in the region of the formants by a sharp amplification of only one overtone and a very slight amplification of the neighboring ones, whereas in the speaking voice in the region of the formants an entire group of adjacent overtones is amplified (Fig. 5); 2) the amplification of the overtone of the lower formant for all vowels occurs in the region of about 500 Hz; thus, the distinction among vowels in the singing voice is expressed less sharply than in speech. The latter phenomenon was confirmed also in the studies of Bartholomew.

Fig. 5. Above—the spectrum of the sound of a typical singing voice; below, the spectrum of the same sound (vowel “a,” 129 Hz) sung by a non-singer.

The invariability of the strong resonance in the region of about 500 Hz for good singing voices of any timbre and for any vowels was established by him on a large number of observations. According to Bartholomew, this resonance occurs in the pharynx, which during singing expands as a result of stretching of its walls and lowering of the larynx.

Relative level in dB

Numbers of harmonics

Fig. 6. Vowel “a,” 262 Hz. Below—nasal timbre coloration.
——— closed sound, ————— normal sound, -------- open sound.

Wolf, Stanley, and Sette did not find such a narrowly limited region of resonance amplification. Their harmonic analyses (Fig. 6) indicate a considerable amplification of several (2–3) harmonics in the region from 500 to 1000 Hz. The position of this formant determines the shades of timbre: lowering is characteristic of a closed sound, raising—of an open or “white” sound. With a “nasal” shade of timbre the resonance peaks are sharper.

In addition to the lower formant, Bartholomew also established the existence of an upper formant in the region of 2800–2900 Hz for the male voice and 3200 Hz for the female voice. This formant is still more characteristic of the singing voice than the lower one. Wolf, Stanley, and Sette came to the same conclusion, although the region indicated by them is somewhat broader—from 2000 to 3300 Hz (this formant is clearly visible in Fig. 6).

The upper formant, like the lower one, remains unchanged when the pitch of the fundamental tone, changes in timbre and type of voice, or the vowel being sung are varied. Tables 1 and 2 give an idea of the experiments carried out by Bartholomew in this direction.

The exception is high female voices, mainly coloratura soprano, whose timbre is significantly simpler than that of male...

PHYSICAL CHARACTERISTICS OF THE SINGING VOICE

...and low female voices; the high formant is very weakly expressed. When singing in falsetto, the high formant is entirely absent.

The high formant can be found both in a bad voice and in a good one; however, the better the voice, the stronger the resonant amplification in this region. The influence of the high formant on the quality of the singing voice is enormous. It is precisely this that gives the voice its characteristic brilliance, roundness, and metallic quality.

The constancy of the frequency of the high formant gives grounds for supposing that its appearance is caused by the resonance of some cavity whose volume remains unchanged under all conditions. Bartholomew assumes that such a cavity can only be the laryngeal cavity, since it is difficult to suppose that the narrow and more or less soft nasal resonators could produce such a high and sharp resonance. In this connection Bartholomew cites the theory of voice production of Eimer and Willis. The vocal cords open sharply and immediately close again, remaining open only for a small fraction of each period of the fundamental tone of the voice. The wave arising from the opening of the cords propagates to the upper folded edge formed by the larynx and the supralaryngeal cartilage, and, reflected from it, returns again to the vocal cords, which by this time have already managed to close. Thus, at each opening of the vocal cords, natural damped oscillations are excited in the air column enclosed between the aforementioned folded edge and the closed vocal cords. To illustrate what has been said, we present a series of damped oscillations (Fig. 7), obtained by blowing air through the freshly excised larynx of a donkey. The fundamental tone is determined by the number of cycles per second; the high formant by the frequency of the damped oscillations. The latter, consequently, is a function of the dimensions of the larynx.

Table 1

Baritone, vowel “a”

Table 2

Tenor, vowel “o”

In the speaking voice or in poor singers the folded edge is insufficiently tense, and the vocal cords do not close quickly enough. Therefore the laryngeal resonance is weakened, and the high formant becomes less clearly expressed.

As has already been said above, during vibrations the timbre changes periodically. Consequently, both formants periodically change their position, but over a larger part of the vibration period remain in the frequency regions indicated by us.

5. Conclusion

Thus, we see that in many questions concerning the physical characteristics of the singing voice, considerable clarity has been achieved and the results obtained at different times by various investigators and by means of various methods coincide. Individual discrepancies merely indicate that a more detailed treatment of one question or another is required. This is the case, for example, with the determination of the frequency range of the low formant.

Fig. 7.

What, then, from the physical point of view, constitutes a good singing voice? Let us summarize briefly: a voice of sufficient power, with a smooth increase in the latter as the pitch rises; a voice possessing considerable vibrato, about 6 times per second, especially intensified in loud singing; a voice with two clearly expressed formants in the regions of about 500 and about 3000 Hz.

It is quite understandable that there are still other, purely musical merits of the singing voice that are not amenable to physical analysis.

LITERATURE

1. W. Bartolomew, J. Ac. Soc. Am. 4, 25, 1934.
2. S. Wolf, D. Stanley a. W. Sette, J. Ac. Soc. Am. 4, 255, 1935.
3. A. V. Rabinovich, “Oscillographic Method of Melody Analysis,” Muzgiz, 1932.
4. V. Kazansky and S. Rzhevkin, Zh. prikl. fiziki 5, 87, 1928.