strengthened by the resonance of the air in the air-passages and in the pharyngeal and oral cavities. If mixed—that is, if the tone is compounded of a number of partials—one or more of these will be strengthened by the cavities above the cords acting as a resonator; and so strongly may these partials be thus reinforced that the fundamental one may be obscured, and a certain quality or timbre will be communicated to the ear. Further, Helmholtz has shown that special forms of the oral cavity reinforce in particular certain partials, and thus give a character to vowel tones,—indeed to such an extent that each vowel tone may be said to have a fixed pitch. This may be proved by putting the mouth in a certain form, keeping the lips open, and bringing various tuning forks sounding feebly in front of the opening. When a fork is found to which the resonant cavity of the mouth corresponds, then the tone of the fork is intensified, and by thus altering the form and capacity of the oral cavity its pitch in various conditions may be determined. Thus, according to Helmholtz, the pitch corresponding to the vowels may be expressed:—
| Vowels | OU | O | A | AI | E | I | EU | U |
| Tone | fa2 | si♭3 | si♭4 | sol5 | si♭5 | re6 | do5 | sol5 |
| or | or | or | or | or | ||||
| re4 | fa3 | fa2 | fa3 | fa2 | ||||
| No. of vibrations | 170 | 470 | 940 | 1536 | 1920 | 2304 | 1024 | 1536 |
| or | or | or | or | or | ||||
| 576 | 341 | 170 | 341 | 170 |
R. Koenig has fixed the pitch of the vowels differently, thus:
| Vowels | OU | O | A | E | I |
| Tone | si♭2 | si♭3 | si♭4 | si♭5 | si♭6 |
| No. of vibrations | 235 | 470 | 940 | 1880 | 3760 |
F. C. Donders has given a third result, differing from each of the above; and there is little doubt that much will depend on the quality of tone peculiar to different nationalities. By means of Koenig's manometric flames with revolving mirror the varying quality of tone may be illustrated: with a pure tone, the teeth in the flame-picture are equal, like the serrations of a saw, whilst usually the tone is mixed with partials which show themselves by the unequal serrations. Thus quality of voice depends, not merely on the size, degree of elasticity and general mobility of the vocal cords, but also on the form of the resonating cavities above, and very slight differences in these may produce striking results.
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| Fig. 11. | Fig. 12. | |
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Fig. 11.—Chest Voice, High Tone. Description same as for figs. 7 and 8. (From Mandl.) | ||
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Fig. 12.—Head Voice, Deep Tones. l, tongue; e, epiglottis; pe, pharyngo-epiglottidean folds; ae, ary-epiglottis folds; rs, false cords; ri, true vocal cords; g, pharyngo-laryngeal groove; ar, arytenoid cartilages; c, cuneiform cartilages; o, glottis; r, inter-arytenoid folds. (From Mandl.) | ||
6. Vowel Tones.—A vowel is a musical tone produced by the vibrations of the vocal cords. The tone produced by the vocal cords is a mixed one, composed of a fundamental and partials, and certain of the partials are strengthened by the resonance of the air in the air-passages and in the pharyngeal and oral cavities. In this respect the quality of the human voice depends on the same laws as those determining the quality or timbre of the tones produced by any musical instrument. The pitch of the note of a musical instrument, however, depends on the pitch of the first or fundamental tone, while the partials are added with greater or less intensity so as to give a special character to the sound; and in the case of a vowel tone the pitch does not appear to depend on that of the fundamental tone but on the pitch of the resonance cavity, as adjusted for the sounding of any particular vowel. When we wish to pronounce or sing a vowel the oral cavity must be adjusted to a certain form, and it is only when it has that form that the vowel can be sounded. The nature of vowel tones has been investigated by means of the phonograph by Fleeming Jenkin and Ewing, L. Hermann, Pipping, Boeke, Lloyd, McKendrick and others. E. W. Scripture has worked with the gramophone. These observers may be ranged in two divisions—those who uphold the theory of relative as opposed to those who contend for the theory of fixed pitch. Assuming that a vowel is always a compound tone, composed of a fundamental and partials, those who uphold the relative pitch theory state that if the pitch of the fundamental is changed the pitch of the partials must undergo a relative change, while their opponents contend that whatever may be the pitch of the tone produced by the larynx, the pitch of the partials that gives quality or character to a vowel is always the same, or, in other words, vowel tones have a fixed pitch. Helmholtz held that all the partials in a vowel tone were harmonic to the fundamental tone, that is that their periods were simple multiples of the period of the fundamental tone. Hermann, however, has conclusively shown that many of the partials are inharmonic to the fundamental. This practically upsets the theory of Helmholtz. The methods by which this problem can be investigated are mainly two. The pitch of the oral cavity for a given vowel may be experimentally determined, or an analysis may be made of the curve-forms of vowels on the wax cylinder of the phonograph or the disk of the gramophone. By such an analysis, according to Fourier's theorem, the curve may be resolved into the partials that take part in its formation, and the intensity of those partials may be thus determined. The observations of Bonders, Helmholtz, König and others as to the pitch of the resonating cavities gave different results. Greater success has followed the attempts made by Hermann, Boeke, McKendrick, Lloyd and Marichelle to analyse the curves imprinted on the phonograph. (Examples of such phonograms are given by McKendrick in the article on “Vocal Sounds” in Schäfer's Physiology, ii. 1228; see also Phonograph.)
The following is an instructive analysis by Boeke of the curves representing the tones of a cornet, and it illustrates the laws that govern the production of quality in such an instrument:—
| Note | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Partials. | |
| f′ = 170 | vibs. | 1 | 1.05 | 1.22 | 1.15 | 1.01 | 0.80 | 0.53 | 0.28 | 0.13 | 0.10 | „ |
| c′ = 256 | „ | 1 | 0.92 | 0.81 | 0.53 | 0.39 | 0.20 | 0.07 | 0.04 | 0.06 | 0.04 | „ |
| g′ = 384 | „ | 1 | 0.76 | 0.46 | 0.14 | 0.09 | 0.06 | 0.07 | 0.02 | 0.01 | 0.01 | „ |
| c′′ = 512 | „ | 1 | 0.92 | 0.30 | 0.14 | 0.15 | 0.09 | 0.07 | 0.06 | 0.03 | 0.02 | „ |
These figures represent the relative intensities of the partials entering into the formation of the note, and it will be observed that the intensity gradually diminishes. This analysis may be contrasted with that of the vowel āā sung by Boeke (aet. 50) on the notes f and c′, and the same vowel sung on the notes g′ and e′′ by his son (aet. 12).
Man, aet. 50, singing āā.
| Pitch | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Partials. | |
| f′ = 170.6 | vibs. | 1 | 0.86 | 0.46 | 1.74 | 1.90 | 1.55 | 0.51 | 0.54 | 0.43 | 0.44 | „ |
| c′ = 256 | „ | 1 | 0.49 | 1.96 | 1.25 | 0.60 | 0.56 | 0.23 | 0.05 | 0.06 | 0.10 | „ |
Boy, aet. 12, singing āā.
| Pitch | 1 | 2 | 3 | 4 | 5 | 6 | Partials. | |
| g′ = 384 | vibs. | 1 | 1.22 | 2.67 | 0.45 | 0.17 | 0.06 | „ |
| e′′ = 640 | „ | 1 | 8.09 | 1.45 | 0.53 | .. | .. | „ |
It will be observed that in both these cases the intensity of the partials does not fade away gradually as we proceed from the lower to the higher partials, as with the cornet, but that certain partials are intensified more than others, namely, those printed in black. In other words, the form of the resonating cavity develops particular partials, and these modify the quality of the tone. If we multiply the vibrational number of the fundamental tone by the number of the partial we obtain the pitch of the resonance cavity; or if we take the mean of the
