The shape of sound: From acoustic wave geometry to synesthetic perception

“ I hear bravuras of birds, bustle of growing wheat, gossip of flames, clack of sticks cooking my meals,
I hear the sound I love, the sound of the human voice,
I hear all sounds running together, combined, fused or following,
Sounds of the city and sounds out of the city, sounds of the day and night,
Talkative young ones to those that like them, the loud laugh of work-people at their meals ”

“ In this region⁠—pondering the relation between sound and shape⁠—the imagination may wander till it grows dizzy, for it leads very soon to the still more wonderful world where sound and colour spin their puzzling web, and the spiritual phenomena of music cry for further explanation. But, for the moment, let only the sound of wind be in our ears; for in wind, I think, there is a sweetness and a variety of music that no instruments invented by men have yet succeeded in approaching so far as sheer thrill and beauty are concerned. ”

“ By various contrivances we can compel the vibrations of the air to declare themselves we know the length and frequency of the sonorous waves, and we have also obtained great mastery over the various methods by which the air is thrown into vibration. We know the phenomena and laws of vibrating rods, of organ-pipes, strings, membranes, plates, and bells. ”

“ The motion of the sonorous wave must not be confounded with the motion of the particles which at any moment form the wave. During the passage of the wave every particle concerned in its transmission makes only a small excursion to and fro.
The length of this excursion is called the amplitude of the vibration.
Sound cannot pass through a vacuum.
A certain sharpness of shock, or rapidity of vibration, is needed for the production of sonorous waves in air. ”

“ Scientific education ought to teach us to see the invisible as well as the visible in nature, to picture with the vision of the mind those operations which entirely elude bodily vision; to look at the very atoms of matter in motion and at rest, and to follow them forth, without ever once losing sight of them, into the world of the senses, and see them there integrating themselves in natural phenomena. With regard to the point now under consideration, we must endeavor to form a definite image of a wave of sound. ”

“ It is like seeing pictures of things to hear you talk. No wonder that all listen to you, for indeed ’tis wonderful the way you have with words. You use them so that ’tis as though they had shapes of their own and colours, and you builded with them. ”

“ The western sky was like a great golden pearl. Far down the harbour was frosted with a dawning moonlight. The air was full of exquisite sounds—sleepy robin whistles, wonderful, mournful, soft murmurs of wind in the twilit trees, rustle of aspen poplars talking in silvery whispers and shaking their dainty, heart-shaped leaves, lilting young laughter from the windows of rooms where the girls were making ready for the dance. The world was steeped in maddening loveliness of sound and colour. ”

“ Sound always travels with uniform velocity in the air in the same temperature. But sound! What is the cause of it? How does it arise? These questions can now be fully answered with reference to the foregoing observations. Phenomena of vibration render themselves visible by light, heat, and sound, and to arrive at some definite ideas of sound vibrations we may compare them to waves, such as may be produced by throwing a stone into a pond. ”

“ Observe a sea-fowl, or, if you are a swimmer, abandon yourself to the action of the waves; you are not carried forward, but simply rocked up and down. The propagation of a wave is the propagation of a form, and not the transference of the substance which constitutes the wave.
The length of the wave is the distance from crest to crest, while the distance through which the individual particles oscillate is called the amplitude of the oscillation. You will notice that in this description the particles of water are made to vibrate across the line of propagation. ”

“ The amount of motion communicated by a vibrating string to the air is too small to be perceived as sound, even at a small distance from the string.
When a broad surface vibrates in air, condensations and rarefactions are more readily formed than when the vibrating body is of small dimensions like a string. Hence, when strings are employed as sources of musical sounds, they are associated with surfaces of larger area which take up their vibrations, and transfer them to the surrounding air. ”

“ We have already learned that what is loudness in our sensations is outside of us nothing more than width of swing, or amplitude, of the vibrating air-particles. Every other real sonorous impression of which we are conscious has its correlative without, as a mere form or state of the atmosphere. ”

“ In wires and bells the bodies themselves produce the sounds we hear. In wind instruments and the voice the air is the cause of the sound.
The very deepest notes are produced by the fewest vibrations. Fourteen or fifteen vibrations will give us a very low note, if not the very lowest. The pipe of sixteen feet, closed at its upper end, will produce sound waves of thirty-two feet. High notes can be formed from vibrations up to 48,000 in a second. Beyond these limits the ear cannot accept a musical sound. ”

“ We see light, the waves of which, or ether vibrations, are transversal; air waves or sound vibrations are longitudinal.
We have spoken of radiant heat. Light acts in the same way through the ether; and when we consider Sound we shall learn that a certain number of vibrations of a string give a certain sound, and the quicker the vibration the shriller the tone. So in light. The more quickly the waves of luminosity travel to our eye, and the faster they strike it, the greater the difference in the colour, or what we call colour. ”

“ The only condition necessary to the production of a musical sound is that the pulses should succeed each other in the same interval of time. No matter what its origin may be, if this condition be fulfilled the sound becomes musical. If a watch, for example, could be caused to tick with sufficient rapidity—say one hundred times a second—the ticks would lose their individuality and blend to a musical tone. And if the strokes of a pigeon’s wings could be accomplished at the same rate, the progress of the bird through the air would be accompanied by music. ”

“ Noise affects us as an irregular succession of shocks. We are conscious while listening to it of a jolting and jarring of the auditory nerve, while a musical sound flows smoothly and without asperity or irregularity. How is this smoothness secured? By rendering the impulses received by the tympanic membrane perfectly periodic. A periodic motion is one that repeats itself. The motion of a common pendulum, for example, is periodic, but its vibrations are far too sluggish to excite sonorous waves. ”

“ It is also proportional to the square of the maximum velocity of the vibrating air-particles.
When sound issues from a small body in free air, the intensity diminishes as the square of the distance from the body increases.
If the wave of sound be confined in a tube with a smooth interior surface, it may be conveyed to great distances without sensible loss of intensity.
The velocity of sound in air depends on the elasticity of the air in relation to its density. The greater the elasticity the swifter is the propagation; the greater the density the slower is the propagation. ”

“ Double Refraction of Light explained by the Wave Theory.
The two elements of rapidity of propagation, both of sound and light, in any substance whatever, are elasticity and density, the speed increasing with the former and diminishing with the latter. The enormous velocity of light in stellar space is attainable because [Pg 109] the ether is at the same time of infinitesimal density and of enormous elasticity. Now the ether surrounds the atoms of all bodies, but it is not independent of them. ”

“ Flame or incandescent gas presents gaseous matter in a visible form, admirably adapted for experimental investigation; and, when produced by a jet, should be amenable to the principles of Plateau’s theory. According to this view, the pulsations or beats which I observed in the gas-flame when under the influence of musical sounds, are produced by the conflict between the aërial vibrations and the “forces of figure” (as Plateau calls them) giving origin to periodical fluctuations of intensity, depending on the sonorous pulses. ”

“ The end of a rod vibrating longitudinally may be caused to agitate a column of air contained in a tube, compelling the air to divide itself into ventral segments. These segments may be rendered visible by light powders, and from them the velocity of sound in the substance of the vibrating rod, compared with its velocity in air, may be inferred. ”

“ If the opposing forces be equal, particles so solicited will move neither backward nor forward, the aërial rest which corresponds to silence being the result. Thus it is possible, by adding the sound of one fork to that of another, to abolish the sounds of both. We have here a phenomenon which, above all others, characterizes wave-motion. ”

“ LIGHT ADDED TO LIGHT MAKES DARKNESS.
In a precisely similar manner two systems of sonorous waves can be caused to interfere and mutually to destroy each other: thus, by adding sound to sound, silence may be produced. Two beams of light also may be caused to interfere and effect their mutual extinction: thus, by adding light to light, we can produce darkness. Here indeed we have a critical analogy between sound and light—the one, in fact, which compels the most profound thinkers of the present day to assume that light, like sound, is a case of undulatory motion. ”

“ The answer to this question involves one of the most important physical conceptions that the mind of man has yet achieved: the conception of a medium filling space and fitted mechanically for the transmission of the vibrations of light and heat, as air is fitted for the transmission of sound. This medium is called the luminiferous aether. Every vibration of every atom of our platinum wire raises in this aether a wave, which speeds through it at the rate of 186,000 miles a second. ”

“ The chemists who recoil from these notions of atoms and molecules accept without hesitation the Undulatory Theory of Light. Like you and me they one and all believe in an ether and its light producing waves. Let us consider what this belief involves. Bring your imaginations once more into play and figure a series of sound-waves passing through air. Follow them up to their origin, and what do you there find? A definite, tangible, vibrating body. It may be the vocal chords of a human being, it may be an organ-pipe, or it may be a stretched string. ”

“ We have been picturing atoms and molecules and vibrations and waves which eye has never seen nor ear heard, and which can only be discerned by the exercise of imagination. This, in fact, is the faculty which enables us to transcend the boundaries of sense, and connect the phenomena of our visible world with those of an invisible one. Without imagination we never could have risen to the conceptions which have occupied us here to-day ”

“ Whereby the lips and heart are fire;
No look the linked glances read
That held the springs of deep desire.
And yet the sounds her glad lips gave
Are on my soul vibrating still;
Her eyes that swept me as a wave
Shine my soul's worship to fulfil.
Her hair, her eyes, her throat and chin—
Sweet hair, sweet eyes, sweet throat, so sweet,
So fair because the ways of sin
Have never known her perfect feet—
By what far ways and marvellous
May I such lovely heaven reach?
What dread, dark seas and perilous
Lie 'twixt love's silence and love's speech? ”

“ You cannot have good matter with bad style. Examine the point more closely. A man wishes to convey a fine idea to you. He employs a form of words. That form of words is his style. Having read, you say: "Yes, this idea is fine." The writer has therefore achieved his end. But in what imaginable circumstances can you say: "Yes, this idea is fine, but the style is not fine"? The sole medium of communication between you and the author has been the form of words. The fine idea has reached you. ”

“ Sound builds; sound destroys; and invisible sound-vibrations affect concrete matter. For all sounds produce forms--the forms that correspond to them, as you shall now see. Within every form lies the silent sound that first called it into view--into visible shape--into being. Forms, shapes, bodies are the vibratory activities of sound made visible."
"My goodness!" exclaimed Spinrobin, who was listening like a man in a dream, but who caught the violence of the clergyman's idea none the less. ”

“ Sound for most of us lies between, say, thirty and many thousand vibrations per second--the cry of the earthquake and the cricket; it is our limitation that renders the voice of the dewdrop and the voice of the planet alike inaudible. We even mistake a measure of noise--like a continuous millwheel or a river, say--for silence, when in reality there is no such thing as perfect silence. ”

“ Sound travels in air at about 1130 feet per second, and if the vibrating body, giving out the sound, oscillates sixteen times in one second, it follows that, spreading over this 1130 feet, there will be sixteen waves, giving a length of about 70 feet to each wave. This is the lowest sound that the human ear can appreciate as a musical note, and is, what may be called, the fourth Octave above one vibration in one second. When the number of vibrations in a second sinks below sixteen, the ear no longer appreciates them as a musical sound, but is able to hear them as separate vibrations or beats. ”

“ The drums of insect ears, and the tubes, etc., connected with them, are so minute that their world of sounds probably begins where ours ceases; that the sound which appears to us as continuous is to them a series of separated blows, just as vibrations of ten to twelve per second appear to us. We begin to hear such vibrations as continuous sounds when they amount to about thirty per second. The insect’s continuous sound probably begins beyond three thousand. The blue-bottle may thus enjoy a whole world of exquisite music of which we know nothing. ”

“ And so one comes to a further suggestive reflection: that objects all possess their own particular sound or voice that the winds love to set free; their essential note⁠—that specific set of vibrations lying buried in their form⁠—of which, as some curious doctrines of the old magic assert, their forms, indeed, are the visible expression. ”

“ The particles which fill the cavity of the ear are finally driven against the tympanic membrane, which is stretched across the passage leading from the external ear toward the brain. This membrane, which closes outwardly the “drum” of the ear, is thrown into vibration, its motion is transmitted34 to the ends of the auditory nerve, and afterward along that nerve to the brain, where the vibrations are translated into sound. How it is that the motion of the nervous matter can thus excite the consciousness of sound is a mystery which the human mind cannot fathom. ”