Tone (acoustics)

“ The author, preparing the way with a chapter on elementary acoustics, states the phenomena of overtones, and then shows their action in determining the tone-character or timbre of the various musical instruments. These overtones also constitute the natural basis for the scales, for melody, tonality, and harmony—in so far as these have a natural basis. For æsthetical influences, local, individual, and transitory, have played the largest part in giving to music its present form. ”

“ Within a certain restricted length of air-waves lies all of the pleasurable sensation which we call musical tone. But as we rise in the scale the tone begins to become uncertain, until the highest note of the instrument is again indefinite noise. ”

“ But the tremendous currents above us, which sweep along the vast masses of vapor, are noiseless until they touch the earth, and some little trifling eddies are made in their lower sweep by hills and trees and houses. It is then only noise. The ear requires yet smaller waves of air to experience the sensation of tone. The lowest note of a piano has barely enough of it to give a definite idea. As the waves become shorter, the ear begins to be pleasantly affected, and the realm of music is reached. ”

“ The third quality of sound is due to the form of the vibrations regardless of the pitch or the loudness. The trained ear recognizes, for instance, in the note of the tuning fork, the violin, the clarionet and the piano, the same tone howsoever made. ”

“ We recognize at once a difference between the sound of a vowel, say ah, sung by different persons to the same note of the piano and with the same loudness. There is a personal element, an individuality, about voices which at once arrests our attention, apart altogether from the tone or loudness. This sound-quality is determined by the form of the wave-motion, that is, by the nature of the movement of the air-particle during its little excursion to and fro in which it takes part in producing a zone of compression or rarefaction in the air and so forms a sound wave. ”

“ In this experiment we notice that tones are high or low, according to the number of their vibrations—the higher the tone the greater the number of its vibrations per second. Again, we observe that we can make the same tone loud or soft, without making it higher or lower. We notice that loudness is obtained by striking with greater force, making the string or fork swing farther from side to side, but still swing the same number of times in a second. ”

“ Other consonants are to be classed with the noises. Like a vowel, and like the timbre of an instrument, a noise is a blend of simple tones; but the fundamental tone in a noise-blend is not so preponderant as to give a clear pitch to the total sound, while the other tones present are often too brief or too unsteady to give a tonal effect. ”

“ Analytical Power of the Ear.—When we listen to a compound tone, we have the power of picking out these partials from the general mass of sound. It is known that the frequencies of the partials as compared with that of the fundamental tone are simple multiples of the frequency of the fundamental, and also that physically the waves of the partials so blend with each other as to produce waves of very complicated forms. ”

“ The low tone must have the power of the loud tone, since it is to be equally understood. The acoustic organs should have nothing to do with the transmission of sound. They must be inert so that the tone may be homogeneous. ”

“ The fact that a repetition of sensations is productive of pleasant effects is not restricted to the realm of the visible. To-day, both the musician and the physicist know that the harmonic or the melodic addition of one tone to another affects us agreeably only when the added tone reproduces a part of the sensation which the first one excited. When I add an octave to a fundamental tone, I hear in the octave a part of what was heard in the fundamental tone. ”

“ As the pressure is increased, the air, passing through the holes, assumes a rhythmical beat, which soon becomes metamorphosed into musical notes. It is evident, therefore, that, by means of this instrument, the number of vibrations which produce a definite tone can be measured with absolute accuracy by any one who has an ear capable of appreciating a musical note. ”

“ This law of sound secures the appropriate resonance for every pitch much more accurately than it could be secured by an effort to develop chest, middle, and head registers through calculating the differences. Again, we need the higher chambers of resonance to reinforce even the low pitch, because every note has its overtones that enrich it, and if these cannot find their proper resonance the tone is impoverished. ”

“ The law is without exception throughout the compass in which our ears can distinguish pitch, and so, of necessity, a string of twice the length of that whose vibrations induce the deepest perceivable sound must stir the air at such a rate as to cause a tone at an 8th below that lowest audible note. ”

“ It depends on the fact that many waves of sound that reach the ear are compound wave systems, built up of constituent waves, each of which is capable of exciting a sensation of a simple tone if it be singled out and reinforced by a resonator (see Sound) , and which may sometimes be heard without a resonator, after special practice and tuition. Thus it appears that the ear must have some arrangement by which it resolves every wave system, however complex, into simple pendular vibrations. When we listen to a sound of any quality we recognize that it is of a certain pitch. ”

“ The Various Qualities of Sound.—Physically, sounds consist of vibrations, and these are, generally speaking, aërial waves. When the waves are non-periodic the result is a{54} noise; when periodic it is what is nowadays called a tone, or note. The loudness of a sound depends on the force of the waves. When they recur periodically a peculiar quality called pitch is the effect of their frequency. ”

“ In the domain of tone-sensations, the harmonic notes, as we know, at first evade our immediate perception, though the timbre they give to the sound is at once noticed by every one, except those portions of the German race whose vocalization is faulty. ”

“ It can only do so by different fibres responding to the constituent vibrations of the sound—one for the fundamental tone being stronger, and giving the sensation of a particular pitch to the sound, and the others, corresponding to the upper partial tones, being weaker, and causing undefined sensations, which are so blended together in consciousness as to terminate in a complex sensation of a tone of a certain quality or timbre. ”

“ 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. ”

“ The resonance of the bugles and the far-reaching vibrations of the bells, with their overtones and harmonics, were specially noted by the young musician, and used by him later in his music. It is a well-known fact that every tone or sound is accompanied by a whole series of other sounds; they are the vibrations resulting from the fundamental tone. If the tone C is played in the lower octave of the piano, no less than sixteen overtones vibrate with it. ”

“ The full tones themselves, however, which we shall henceforth call tones or notes, [137] may not be able to make the impression upon the nerves of hearing needful for conveying a sense of sound to the brain within. The tone produced by any number of vibrations less than sixteen a second is wholly inaudible except by the help of the microphone, and even this number of vibrations brings out so deep a pitch as to be scarcely perceptible. ”

“ The presence of overtones determines the quality of the sound produced. If the string vibrates as a whole merely, the tone given out is simple, and seems dull and characterless. If, on the other hand, it vibrates in such a way that overtones are present, the tone given forth is full and rich and the sensation is pleasing. A tuning fork cannot vibrate in more than one way, and hence has no overtones, and its tone, while clear and sweet, is far less pleasing than the same note produced by a violin or piano. ”

“ The use of the word tone, both for a sound and for the interval between two sounds or tones, is confusing, but is common — almost universal.
Nearly every musical sound is composite, consisting of several simultaneous tones having different rates of vibration according to fixed laws, which depend upon the nature of the vibrating body and the mode of excitation. ”

“ For a single sound to become a musical sound, that is to say, a tone corresponding to one of the intonations of the musical scale, it is necessary that the impulse and, consequently, the undulations of the air should be exactly similar in duration and intensity, and that they should return after equal intervals of time. ”

“ Sounding bodies are of two kinds; those unelastic ones, which being struck, return but a single sound; and those more elastic returning a succession of sounds, which uniting together form a tone. This tone may be considered as a number of sounds produced one after the other by the same body, as we find in a bell, which continues to sound for some time after it is struck. A continuing tone may be also produced from a non-elastic body, by repeating the blow quick and often, as when we beat a drum, or draw a bow along the string of a fiddle. ”

“ Chladni’s Tonometer: the Iron Fiddle, Musical Box, and the Kaleidophone
And now let us shorten our rod, so as to bring its vibrations into proper relation to our ears. When it is about four inches long, it emits a low musical sound. When further shortened, the tone is higher; and, by continuing to shorten the rod, the speed of vibration is augmented, until finally the sound becomes painfully acute. These musical vibrations differ only in rapidity from the grosser oscillations which a moment ago appealed to the eye. ”

“ And thus each letter may be distinguished from every other by hearing.
Thirdly, It is agreeable to all this, that it is difficult at great distances to distinguish the tone of one musical instrument from another, or of any from the tone of a human voice, cæteris paribus; or to distinguish articulate sounds from one another. For at great distances the vibrations of the air are circular to sense, and all the ascents, descents, eruptions and interruptions of sound, which distinguish one compound sound from another, are confounded by numberless reflections from the intermediate bodies. ”

“ We are now prepared to realize the error of the common notion that loudness of tone is due entirely to increase of breath pressure on the vocal cords. Simple experiments with the tuning-fork have shown that while the volume of sound it gives forth is due in part to the amplitude of its vibrations, its loudness is chiefly due to the character of the resonance provided for it.
The larger the resonance chamber the greater is its reinforcing capacity. The largest air chamber in the body is the chest, which serves not only as a wind-chest, but as a resonance chamber. ”

“ No human voice, however, has so great a range of tone; the highest soprano notes of women correspond to [282] but 1000 vibrations a second, and the deepest bass of men falls but to 80 vibrations a second.
While the human voice is limited in its production of sound,—rarely falling below 80 vibrations a second and rarely exceeding 1000 vibrations a second,—the ear is by no means limited to that range in hearing. ”

“ If, however, this could be done so rapidly as to make more than eighteen beats to the second, then the ear would cease to recognize each individual stroke and would perceive a musical tone. The more rapid the vibrations the higher the tone, until the limit of human hearing is reached, which is about 48,000 vibrations to the second. ”

“ If you tune two whistles one vibration apart and sound them together, you get a tone that swells once a second; tune them ten vibrations apart and you get ten swellings or beats per second, and the effect is rough and disagreeable. ”

“ Most men produce all their tones at rates of between 90 and 500 a second, and women between 200 and 800 a second. Not every different vibration rate is heard as a tone of different pitch; the ear is not sensitive enough for that. The interval between one note and the next includes several vibrations, more the higher one goes in the scale. A perfectly true tone has exactly the rate called for; a departure of one or two vibrations a second may not be noticed, but if the error is greater the singer is sharping or flatting his tone, according as he is above or below the true rate. ”

“ If the tone is to have life, it must always be able to conform to any vowel sound. The least displacement of the form or interruption of the breath breaks up the whirling currents and vibrations, and consequently affects the tone, its vibrancy, its strength, and its duration. ”

“ Thus, although vocal tone originates within the larynx, it sets the resonance-cavities into sympathetic vibration, and these produce the harmonics that give the fundamental tone its timbre; the resonance-cavities being to the vocal cords or lips what the body or resonance-box of the violin and the sounding-board of the pianoforte are to their strings, the tube of a cornet or horn to the lips, the body of the clarinet to its reed—the resonating factor which determines the overtones and through these the timbre. ”