Part 5

The strength of the tone depends on the greater or less breadth of its vibrations, that is, of the waves of sound, the higher or lower pitch of the tones upon the number of the vibrations; that is, the tones are always higher the greater the number of the vibrations, or lower the less the number of the vibrations. A second is used as the unit of time, and by number of vibrations is understood the number of vibrations which the sounding body gives forth in a second of time. The tones used in music lie between 40 and 4000 vibrations per second, in the extent of seven octaves. The tones which we can perceive lie between 16 and 38,000 vibrations to the second, within the compass of eleven octaves. The later pianos usually go as low as C₁ with 33, or even to A₂ with 27½ vibrations; mostly as high as a⁴ or c⁵, with 3520 and 4224 vibrations. The one lined a¹, from which all instruments are tuned, has now usually 440 to 450 vibrations to the second in England and America. The French Academy, however, has recently established for the same note 435 vibrations, and this lower tuning has already been universally introduced in Germany.[8]

The high octave of a tone has in the same time exactly double the number of vibrations of the tone itself. Suppose, therefore, that a tone has 50 vibrations in a second, its octave has 100 in the same time; i.e., twice as many. The octave above this has 200 vibrations, &c. The Pythagoreans knew this acoustic law of the ascending tones, and that the octave of a tone had twice as many vibrations in a second as the tone itself, and that the fifth above the first octave had three times as many; the second octave, four times; the major third above the second octave, five times as many; the fifth of the same octave, six times; the small seventh of the same octave, seven times. In notation it would be thus, if we take as the lowest note C, for example:

1:C 2:c 3:g 4:c¹ 5:e¹ 6:g¹ 7:b♭¹ 8:c² 9:d² 16:c³ 32:c⁴

The figures below the lines denote how many times greater the number of vibrations is than that of the first tone. In the first octave we find only one tone; in the second, two; in the third, all the tones of the major chord with the minor seventh. In the fourth octave we find sixteen tones (which, however, we divide in our system of music into twelve). Likewise, we find in the fifth octave thirty-two tones, which number is doubled in the sixth. Hence, the Greeks had quarter and eighth tones, which we in our equal-tempered tuning have done away with.[9]

The production of a higher pitch in a tone rests in all sounding bodies upon the uniform law which we may observe in the strings of musical instruments, whose tones ascend either by greater tension, by shortening, or through a diminution of the density of the strings.

THE TIMBRE (KLANGFARBE) OF TONES

Strength and pitch were the first two distinctions of different tones. The third is the timbre. When we hear one and the same tone sounded successively upon a violin, trumpet, clarionet, oboe, upon a piano, or by a human voice, &c., although it is of the same strength and of the same pitch, yet the tone of all these instruments is different, and we very easily distinguish the instrument from which it comes. The changes of the timbre seem to be infinitely manifold; for, not to mention the fact that we have a multitude of different musical instruments, all which can give the same tone, letting alone also that different instruments of the same kind as well as different voices show certain differences of timbre, the very same tone can be given upon one and the same instrument, or by one and the same voice, with manifold differences of timbre.[10]

As now the strength of the tone is determined by the breadth of the vibrations, and the pitch by their number, so the varieties of timbre are ascribed to the different forms of the waves of vibration. For as the surface of the water is stirred differently by the falling into it of a stone, by the blowing over it of the wind, or the passing through it of a ship, &c., so the movements of the air take different shapes from sounding bodies. The movement proceeding from the string of a violin over which the bow is drawn, is different from those movements caused by the hammer of a piano or by a clarionet.

OVER-TONES (OBERTÖNE)

That timbre is dependent on the form of the vibrations is confirmed by Helmholtz, and acknowledged as so far correct that every different timbre requires a different vibratory form, but different forms sometimes correspond to nearly the same timbre. But how far the different forms of vibration correspond with different timbres, Helmholtz shows by a fact which has hitherto escaped the notice of physicists, although it forms the foundation of all music. We have learned by the stereoscope that we have two different views of every object, and compose a third view from those two. _Just so the ear perceives different musical tones which come to our consciousness only as one tone._

It is in general, and especially in the case of the human voice, very difficult to distinguish these single parts of tone, because we are accustomed to take the impressions of the external world without analyzing them, and only with a view to their use.

But when we are once convinced of the existence of partial tones (_Partialtöne_), if we concentrate our attention, we can also distinguish them. The ear hears, then, not only that tone, the pitch of which is determined, as we have shown, by the duration of its vibrations, but a whole series of tones besides, which Helmholtz names “_the harmonic over-tones_” of the tone, in opposition to that first tone (fundamental tone) which is the lowest among them all, generally the strongest also, and according to the pitch of which we decide the pitch of the tone. The series of these over-tones is for each musical tone precisely the same; they are, namely, the tones of the so-called acoustic series, arising, as already described, from the doubling of the vibrations. First, the fundamental tone, then its octave with twice as many vibrations, then the fifth of this octave, &c.

The different timbre of tones thus depends upon the different forms of the vibrations, whence arise various relations of the fundamental tone to the over-tones as they vary in strength. The most thorough inquiries have led to the following results, of the first importance in every formation of tone: _that the appropriate form of the vibratory waves which is the most agreeable to the ear, as well as the fullest, softest and most beautiful timbre which corresponds to that form, is produced when the fundamental tone, and the over-tones following it, so sound that the fundamental tone and the over-tones sound together, the former most strongly, while the latter are heard fainter and fainter in the intervals of the major chord with the minor seventh, so that, with the fundamental tone, still further sound seven over-tones_. If the higher harmonic over-tones grow stronger, and even overpower the fundamental tone, the sound grows shriller, but when the discordant over-tones lying close together, higher than the tones just named, overpower the fundamental tone, the timbre becomes sharp and disagreeable.

But these over-tones are not to be confounded with the earlier known combination-tones (_Combinationstöne_), which arise from the sounding together of two consonant intervals, and likewise have their own over-tones.

Prof. Helmholtz has by means of his Resonance and Electrical apparatus invented aids by which the forms of the vibrations can be perceived as well as the over-tones, and the different degrees of strength of the latter in relation to one another and to the fundamental tone can be exactly measured. In attempting by means of the above-mentioned apparatus to cause the several over-tones to sound more or less strongly with the fundamental tone, and again entirely to veil others, it became possible to Prof. Helmholtz to produce artificially most opposite timbres, as well as all the vowels of speech.

Even when, in the culture of a voice, we have advanced so far that none of the inharmonic but only the harmonic over-tones sound with the fundamental tone, we shall always find that every voice has its own peculiar _Klangfarbe_--i.e., its own characteristic timbre; and it is not possible so to form the tones of a voice that the over-tones sounding with them shall diminish proportionally according to their height. Every voice has one, mostly two, over-tones, which always predominate in every tone, every register, and give the voice its peculiar quality. When, with the first octave, the fifth above it sounds, the voice is full and mellow. A clear, sympathetic, silvery ring is produced by the sounding of the seventh with the octave immediately above it. One of the most beautiful timbres is a result of the prominence of the third with the seventh, etc. This peculiarity appears to be connected with the particular form and structure of the cavity of the mouth. That parts of the cavity of the mouth serve as a sounding-board in the formation of sound, has already been mentioned.[11]

The perfection of a tone at a certain pitch depends, in the resonance of the cavity of the mouth, upon the utterance of some vowel, to which the parts of the mouth are adjusted; and this perfection is considerably affected by even a slight variation in the timbre of the vowel, as it occurs in different dialects of the same language. On the other hand, the peculiar tones of the cavity of the mouth are almost wholly independent of age and sex. The peculiar pitch of the resonance apparatus has also an influence upon the tone. Every one who knows how to play on any instrument knows that some of its tones sound sweeter and are more easily given than others; these are the tones in which the peculiar tone of the instrument and its over-tones sound together. To describe more particularly the natural laws upon which these facts rest would lead us too far away from our present purpose.

THE VOWELS

Every tone in singing usually takes the sound of some vowel. By the greater or less distinctness of one or another of the over-tones, sounding with the fundamental tone, various timbres of the vowel are produced. But certain vowels in certain parts of the scale can be sung far more easily and sweetly than others. The investigation of this fact has taught us that a tone gains in richness when the tone corresponding to the vowel belongs to the over-tones of the fundamental tone. In the human voice, however, the tones favorable to the several vowels do not admit of being precisely determined.

In different languages and dialects the vowels have different shades, and a scarcely perceptible variation, especially in the clearer vowels, is sufficient to cause the over-tones to be heard more or less distinctly. After I had learned, with the kind assistance of Professor Helmholtz, by means of his artificial apparatus for the sharpening of the ear, to find out over-tones and to know their peculiarities, I was soon able, without any artificial help, to discover the vowels favorable to them by the fuller sound of certain tones. In the female voice all tones below the c¹ take the character of _o_. At the c¹, _a_, pronounced as in the English word _hall_, sounds the best, and at d♯¹ e¹ passes in to _a_, as in _man_, and at f¹ into _a_, as in _may_. With the g¹ the _a_ sounds again as in _man_; a¹ b♭¹ b¹ c² are favorable to all the vowels, while d² e♭² e² sound best with _e_. After e² every tone takes the coloring of _a_, as in _father_, and sounds well only with this vowel; b♭² c³ d³ sound again better with _e_. As thus, above e² f² all the tones take the coloring of _a_ in _father_, so the tones below c¹ take the timbre of _o_, and the most skilful artists are not able to sing all the vowels in these tones with equal clearness and purity. The female voice, therefore, has only a few tones more than an octave, upon which every one of the vowels can be distinctly sung; and again, all these tones do not afford an equally sonorous tone with every vowel.

As unfortunately our Song composers do not always keep this fact in view, as the old Italians did, and since words with the most unfavorable vowels often underlie the notes, it as often becomes necessary to mingle with the unfavorable vowel something of the sound (_Klang_) of the vowel properly belonging to the note; as, for example, in the word “ring” upon f², to sing the _i_ with a mixture of the sound (_Klang_) of _a_. Artists do this in a way of which they are for the most part unconscious, and which is always unobserved by the hearer. That in every voice there are several tones upon which every vowel sounds well, finds an explanation in an observation of Professor Helmholtz. The ear is attuned to a certain tone, designated as e⁴ f⁴. To persons with very susceptible nerves these tones are often insupportable, and we often see dogs, whose sense of hearing is especially acute, run howling away when the above e⁴ is struck upon a violin, while to other tones they seem wholly insensible. But all the tones which are accompanied by that tone as an over-tone to which the ear is attuned, sound harmonious even with unfavorable vowels.

PARTIAL TONES

But beside the over-tones, which sound with every good, simple sound, there are other _partial tones_, which, like the long-known combination tones, do not usually present themselves to our consciousness. Combination tones were first discovered in 1745 by the organ-builder, _Sorge_. By an act of concentrated attention one hears these tones at the accord of two different tones. They lie always lower than the interval to which they belong, and arise from the meeting of the nodes of vibration of the tones producing the interval. The node of vibration is the name of that place where, after every completed vibration, the sounding body returns to its former position. When, for instance, we give the third c¹ e¹, we hear the c, lying an octave lower than the third, sounding at the same time as a combination tone. For the tone c¹ a string has two vibrations, while in the same space of time e¹ has three. The vibration node of the c¹ will thus, after two vibrations, coincide with the vibration node of the e¹. By the coincidence of these nodes of vibration is produced the number of vibrations requisite for the c below. Besides these combination tones there are summation tones, discovered by Helmholtz, which arise from the vibrations collectively (_Gesammtzahl_) belonging to the above interval, and are higher than the interval. Both kinds of partial tones have again their faint over-tones.

BEATS (DIE SCHWEBUNGEN)

We have explained the movements of the waves of sound by the movements on the surface of water, and we know that, instead of the billows and hollows that we have in the water, the air is condensed and rarefied. We know further that if two different lines of waves run along with one another, their crests and hollows fall together, and their crests become as high again and their hollows as deep again. So two tones from different sources of sound are twice as strong when they are both equally high, and a new tone of the same height added to them will still further increase the sound. But when two agitations of the surface of the water so move that the crests of one fall into the hollows of the other, their movements neutralize each other. The same thing happens in tones when one is not struck until half the vibrations of the preceding tone are concluded. But if the sounding bodies vary in only a small part of a vibration sound, they will be alternately stronger and weaker, and this is termed beats (_Schwebungen_), which are only produced by tones _very near to each other_. Those intervals whose combination and over-tones so fall together that many beats are produced, sound harsh and disagreeable, and we call them dissonances.

Those intervals in which few or no beats occur are called consonances. As the combination or interfering tones, as well as the beats, have importance and interest only in harmonizing several voices, in tuning pianos, as well as in composition in general, and as we have in view in these pages only the culture of single voices, we cannot further enlarge on these discoveries, interesting as they are. According to the purpose of this little work, I introduce only so much of the latest investigations and discoveries as will help to show the prevailing evils of our mode of teaching singing, and, by their practical application to the business of instruction, serve to improve the vocal art. But whoever has an interest in this branch of science will find in the invaluable work of Helmholtz, “Die Lehre von den Tonempfindungen,” an abundance of most interesting observations and of the most thoroughly scientific illustrations of the theory of music, and of those processes in the domain of tone which we have hitherto always felt, but never understood.

APPLICATION OF THE NATURAL LAWS LYING AT THE FOUNDATION OF MUSICAL SOUNDS TO THE CULTURE OF THE VOICE IN SINGING

The parts of the human voice that generate tones are the membranous vocal ligaments or chords, which are subject to the same natural laws as all sounding bodies; of this we may satisfy ourselves by observing the different registers of the voice by means of the laryngoscope. The lower, stronger tones of both series of the chest register show the ligaments in full vibration, and becoming more strongly stretched with every higher tone. In the second series the glottis appears, by the inaction of the arytenoid cartilages, to be shortened. In the falsetto register the vibrating body is diminished, as only the edges vibrate, while the same processes are repeated as in the chest register by the greater stretching of the ligaments and the shortening of the glottis. The head register, likewise, shows the glottis partly closed, and the vibrating ligaments gradually stretched more and more.

The vocal ligaments are made to vibrate by the air coming from the lungs through the trachea, to which they present resistance. These vibrations are communicated to the air in the mouth and outside, and are felt by the ear as sound.

As the strength of the tone depends upon the amplitude of the waves of sound, they, in their turn, depend upon the structure of the organ of singing, and of the parts of the mouth serving as a sounding-board or resonant apparatus, but, above all, upon the skilful management of the vibrating air. And although a fine timbre of the tones and due skill in increasing the amplitude of the vibrations may cause the voice to appear fuller and stronger, yet it is not in our power, when once the vocal organs have been fully developed, to make a strong voice out of a weak one.

Always to strike the true pitch fully and clearly requires persevering attention, as well from the teacher as from the pupil. And long practice is often required before the intonations become as pure as is indispensably necessary to good singing. For only upon the basis of a full, pure tone is a beautiful timbre (_Klangfarbe_) possible.

But the most important thing in the culture of the voice is the timbre of the tones, for _here it is in our power to form out of a sharp, hard and disagreeable voice, a voice sweet and pleasing_.

We have seen that the timbre is dependent on the forms of the vibrating waves, and the different degrees of strength and number of the over-tones arising from these forms. It has been further shown that the simple round form of the waves of vibration produces the softest, fullest timbre. By this form the fundamental tone is the strongest, and the over-tones are heard ascending to the third octave with decreasing degrees of strength. Such a tone is natural to certain voices. In most cases it must be more or less acquired.

A good tone in singing is formed,

1. By controlling and correctly dividing the air or breath as it is expired;

2. By a correct direction of the vibrating column of air; this is done by the right touch (_Tonansatz_);

And, 3. By a very distinct, quick and elastic _touch_.

THE CONTROL OF THE BREATH

By a too great pressure of the breath, the form of the waves of sound most favorable to a good tone is disturbed. One then hears the high over-tones sounding strongly up to the sixteenth, while the lower over-tones with the fundamental tone sound weak or not at all. Thus the tone takes a shrill, sharp and disagreeable sound when the form of the vibrating waves is more or less disturbed by too great a pressure of air. Too little breath deprives the tone only of its strength, but not of its agreeable sound.

_Thus every tone requires for its greatest possible perfection only a certain quantity of breath, which cannot be increased or diminished without injury to its strength in the one case, and its agreeable sound in the other._

In looking carefully through the histories of music, and studying the old Italian schools, we find that it was upon this point--the control and right division of the breathing--that the old masters in the summer of song laid the greatest stress, and this it was to which in teaching they gave the most time and labor. The rules which they followed in this respect, in order to obtain a fine tone, accord perfectly with the results of the latest scientific investigations. And it would be far better for the art of singing if in this respect we had followed the old Italians more faithfully, and not have forsaken so entirely the right way.

According to the old Italian method, which must not be confounded with the modern, the pupil was required at first to breathe just as he was wont to breathe in speaking, and care was taken, by frequent resting-points in the exercises, that the breath should always be renewed at the right time. Accordingly, if the crowding, or pressure, of his breathing was too great, he was required to learn to hold it back. Until the organs were sufficiently practised in the formation of a good tone, and the ear had become familiarized to its sound, pupils were allowed to sing _only_ _piano_. As soon as the pupil had a feeling for a pure tone awakened in him, and could of himself distinguish the finer variations of timbre, he was taught to fill his lungs more and more. But this was to be done, as much as possible, imperceptibly, noiselessly, slowly, and soon enough for him to be able properly to control the quiet breathing in the beginning of a song. Only the sides of the body were in so doing to expand, and breathing with raised chest was allowed only in exceptional cases, as where long passages were to be sung with special passion. For these places, where breath must be taken, there were certain rules which were strictly observed.

After we have learned the natural laws which are applicable in music, and which lie at the basis of a full, rich tone in singing, and that a tone is, strictly speaking, only vibrating air, upon the fine and skilful management of which its beauty and fulness depend, and have considered the careful way in which the old Italians taught the control of the breathing, we cannot but be struck with the rude and negligent manner of using the breath in our present mode of singing.