Difference of amplitude (or energy) of sound waves produces difference of loudness in auditory sensation, which thus corresponds to brightness in visual sensation. Sounds can be arranged in order of loudness, as visual sensations can be arranged in order of brightness, both being examples of intensity series such as can be arranged in any kind of sensation.

Difference of wave-length of sound waves produces difference in the _pitch_ of auditory sensation, which thus corresponds to color in visual sensation. Pitch ranges from the lowest notes, produced by the longest audible waves, to the highest, produced by the shortest audible waves. It is customary, in the case of sound waves, to speak of vibration rate instead of wave-length, the two quant.i.ties being inversely proportional to each other (in the same conducting medium).

The lowest audible sound is one of about sixteen vibrations per second, and the highest one of about 30,000 per second, while the waves to which the ear is most sensitive have a vibration rate of about 1,000 to 4,000 per second. The ear begins to lose sensitiveness as early as the age of thirty, and this loss is most noticeable at the upper limit, which declines slowly from this age on.

Middle C of the piano (or any instrument) has a vibration rate of about 260. Go up an octave from this and you double the number of vibrations per second; go down an octave and you halve the number of vibrations. Of any two notes that are an octave apart, the upper has twice the vibration rate of the lower. The whole range of audible notes, from 16 to 30,000 vibrations, thus amounts to about eleven octaves, of which music employs about eight octaves, finding little use for the upper and lower extremes of the {230} pitch series. The smallest step on the piano, called the "semitone", is one-twelfth of an octave; but it must not be supposed that this is the smallest difference that can be perceived. A large proportion of people can observe a difference of four vibrations, and keen ears a difference of less than one vibration; whereas the semitone, at middle C, is a step of about sixteen vibrations.

_Mixture of different wave-lengths_, which in light causes difference of saturation, may be said in sound to cause difference of purity. A "pure tone" is the sensation aroused by a stimulus consisting wholly of waves of the same length. Such a stimulus is almost un.o.btainable, because every sounding body gives off, along with its fundamental waves, other waves shorter than the fundamental and arousing tone sensations of higher pitch, called "overtones". A piano string which, vibrating as a whole, gives 260 vibrations per second (middle C), also vibrates at the same time in halves, thus giving 520 vibrations per second; in thirds, giving 780 per second; and in other smaller segments. The whole stimulus given off by middle C of the piano is thus a compound of fundamental and overtones; and the sensation aroused by this complex stimulus is not a "pure tone" but a blend of fundamental tone and overtones. By careful attention and training, we can "hear out" the separate overtones from the total blend; but ordinarily we take the blend as a unit (just as we take the taste of lemonade as a unit), and hear it simply as middle C of a particular quality, namely the piano quality. Another instrument will give a somewhat different combination of overtones in the stimulus, and that means a different quality of tone in our sensation. We do not ordinarily a.n.a.lyze these complex blends, but we distinguish one from another perfectly well, and thus can tell whether a piano or a cornet is playing. The difference between different instruments, which we have spoken of as a {231} difference in quality or purity of tone, is technically known as _timbre_; and the timbre of an instrument depends on the admixture of shorter waves with the fundamental vibration which gives the main pitch of a note.

Akin to the timbre of an instrument is the _vowel_ produced by the human mouth in any particular position. Each vowel appears to consist, physically, of certain high notes produced by the resonance of the mouth cavity. In the position for "ah", the cavity gives a certain tone; in the position for "ee" it gives a higher tone. Meanwhile, the pitch of the voice, determined by the vibration of the vocal cords, may remain the same or vary in any way. The vowel tones differ from overtones in remaining the same without regard to the pitch of the fundamental tone that is being sung or spoken, whereas overtones move up or down along with their fundamental. The vowels, as auditory sensations, are excellent examples of blends, in that, though compounds, they usually remain una.n.a.lyzed and are taken simply as units. What has been said of the vowels applies also to the semi-vowels and continuing consonants, such as l, m, n, r, f, th, s and sh.

Other consonants are to be cla.s.sed 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.

Comparison of Sight and Hearing

The two senses of sight and hearing have many curious differences, and one of the most curious appears in mixing different wave-lengths.

Compare the effect of throwing two colored lights together into the eye with the effect of {232} throwing two notes together into the ear.

Two notes sounded together may give either a harmonious blend or a discord; now the discord is peculiar to the auditory realm; mixed colors never clash, though colors seen side by side may do so to a certain extent. A discord of tones is characterized by imperfect blending (something unknown in color mixing), and by roughness due to the presence of "beats" (another thing unknown in the sense of sight).

Beats are caused by the interference between sound waves of slightly different vibration rate. 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.

Aside from discord, a tone blend is really not such a different sort of thing from a color blend. A chord, in which the component notes blend while they can still, by attention and training, be "heard out of the chord", is quite a.n.a.logous with such color blends as orange, purple or bluish green. At the same time, there is a curious difference here. By a.n.a.logy with color mixing, you would expect two notes, as C and E, when combined, to give the same sensation as the single intermediate note D. Nothing of the kind! Were it so, music would be very different from what it is, if indeed it were possible at all. But the real difference between the two senses at this point is better expressed by saying that D does not give the effect of a combination of C and E, or, in general, that no one note ever gives the effect of a combination or blend of notes higher and lower than itself. h.o.m.ogeneous orange light gives the sensation of a blend of red and yellow; but there is nothing like this in the auditory sphere. In light, some wave-lengths give the effect of simple colors, as red and yellow; and other wave-lengths the effect of blends, as greenish yellow or bluish {233} green; but in sound, every wave-length gives a tone which seems just as elementary as any other.

There is nothing in auditory sensation to correspond to white, no simple sensation resulting from the combined action of all wave-lengths. Such a combination gives noise, but nothing that seems particularly simple. There is nothing auditory to correspond with black, for silence seems to be a genuine absence of sensation. There are no complementary tones like the complementary colors, no tones that destroy each other instead of blending. In a word, auditory sensation tallies with its stimulus much more closely than visual sensation does with its; and the main secret of this advantage of the sense of hearing is that it has a much larger number of elementary responses. Against the six elementary visual sensations are to be set auditory elements to the number of hundreds or thousands. From the fact that every distinguishable pitch gives a tone which seems as simple and unblended as any other, the conclusion would seem to be that each was an element; and this would mean thousands of elements.

On the other hand, the fact that tones close together in pitch sound almost alike may mean that they have elements in common and are thus themselves compounds; but still there would undoubtedly be hundreds of elements.

Both sight and hearing are served by great armies of sense cells, but the two armies are organized on very different principles. In the retina, the sense cells are spread out in such a way that each is affected by light from one particular direction; and thus the retina gives excellent s.p.a.ce information. But each retinal cell is affected by any light that happens to come from its particular direction. Every cone, in the central area of the retina, makes all the elementary visual responses and gives all the possible color sensations; so it is not strange that the number of visual {234} elements is small. On the other hand, the ear, having no sound lens, has no way of keeping separate the sounds from different directions (and accordingly gives only meager indications of the direction of sound); but its sense cells are so spread out as to be affected, some by sound of one wavelength, others by other wave-lengths. The different tones do not all come from the same sense cells. Some of the auditory cells give the low tones, others the medium tones, still others the high tones; and since there are thousands of cells, there may be thousands of elementary responses.

Theory of Hearing

The most famous theory of the action of the inner ear is the "piano theory" of Helmholtz. The foundation of the theory is the fact that the sense cells of the cochlea stand on the "basilar membrane", a long, narrow membrane, stretched between bony attachments at either side, and composed partly of fibers running crosswise, very much as the strings of a piano or harp are stretched between two side bars. If you imagine the strings of a piano to be the warp of a fabric and interwoven with crossing fibers, you have a fair idea of the structure of the basilar membrane, except for the fact that the "strings" of the basilar membrane do not differ in length anywhere like as much as the strings of the piano must differ in order to produce the whole range of notes. Now, a piano string can be thrown into "sympathetic vibration", as when you put on the "loud pedal" (remove the dampers from the strings) and then sing a note into the piano. You will find that the string of the pitch sung has been thrown into vibration by the action of the sound waves sung against it.

Now suppose the strings of the basilar membrane to be tuned to notes of all different pitches, within the range of {235} audible vibrations: then each string would be thrown into sympathetic vibration whenever waves of its own vibration rate reached it by way of the outer and middle ear; and the sense cells standing over the vibrating fibers would be shaken and excited. The theory is very attractive because it would account so nicely for the great number of elementary tone sensations (there are over 20,000 fibers or strings in the basilar membrane), as well as for various other facts of hearing--if we could only believe that the basilar membrane did vibrate in this simple manner, fiber by fiber. But (1) the fabric into which the strings of the membrane are woven would prevent their vibrating as freely and independently as the theory requires; (2) the strings do not differ in length a hundredth part of what they would need to differ in order to be tuned to all notes from the lowest to the highest, and there is no sign of differences in stretch or in loading of the strings to make up for their lack of difference in length; and (3) a little model of the basilar membrane, exposed to sound waves, is seen to be thrown into vibration, indeed, and into different forms of vibration for waves of different length, but not by any means into the simple sort of vibration demanded by the piano theory. This theory is accordingly too simple, but it probably points the way towards some truer, more complex, conception.

The fact that there are many elementary sensations of hearing is the chief reason why the art of tones is so much more elaborate than the art of color; for while painting might dispute with music as to which were the more highly developed art, painting depends on form as well as color, and there is no art of pure color at all comparable with music, which makes use simply of tones (and noises) with their combinations and sequences.

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Senses of Bodily Movement

It is a remarkable fact that some parts of the inner ear are not connected with hearing at all, but with quite another sense, the existence of which was formerly unsuspected. The two groups of sense cells in the vestibule--the otolith organs--were formerly supposed to be the sense organ for noise; but noise now appears to be a compound of tones, and its organ, therefore, the cochlea. The _semicircular ca.n.a.ls_, from their arrangement in three planes at right angles to each other, were once supposed to a.n.a.lyze the sound according to the direction from which it came; but no one could give anything but the vaguest idea of how they might do this, and besides the ear is now known to give practically no information regarding the direction of sound, except the one fact whether it comes from the right or left, which is given by the difference in the stimulation received by the two ears, and not by anything that exists in either ear taken alone.

The semicircular ca.n.a.ls have been much studied by the physiologists.

They found that injury to these structures brought lack of equilibrium and inability to walk, swim or fly in a straight course. If, for example, the horizontal ca.n.a.l in the left ear is destroyed, the animal continually deviates to the left as he advances, and so is forced into a "circus movement". They found that the compensatory movements normally made in reaction to a movement impressed on the animal from without were no longer made when the ca.n.a.ls were destroyed. They found that something very much like these compensatory movements could be elicited by direct stimulation of the end-organs in the ca.n.a.ls or of the sensory nerves leading from them. And they found that little currents of the liquid filling the ca.n.a.ls acted as a stimulus to these end-organs and so aroused the {237} compensatory movements. They were thus led to accept a view that was originally suggested by the position of the ca.n.a.ls in s.p.a.ce.

[Ill.u.s.tration: Fig. 40.--How the sense cells in a semicircular ca.n.a.l are stimulated by a water current. This current is itself an inertia back-flow, resulting from a turning of the head in the opposite direction. (Figure text: water current, nerve to brain)]

Each "semicircular" ca.n.a.l, itself considerably more than a semicircular tube, opens into the vestibule at each end and thus amounts to a complete circle. Therefore rotating the head must, by inertia, produce a back flow of the fluid contents of the ca.n.a.l, and this current, by bending the hairs of the sense cells in the ca.n.a.l, would stimulate them and give a sensation of rotation, or at least a sensory nerve impulse excited by the head rotation.

When a human subject is placed, blindfolded, in a chair that can be rotated without sound or jar, it is found that he can easily tell whenever you start to turn him in either direction. If you keep on turning him at a constant speed, he soon ceases to sense the movement, but if then you stop him, he says you are starting to turn him in the opposite {238} direction. He senses the beginning of the rotary movement because this causes the back flow through his ca.n.a.ls; he ceases to sense the uniform movement because friction of the liquid in the slender ca.n.a.l soon abolishes the back flow by causing the liquid to move with the ca.n.a.l; and he senses the stopping of this movement because the liquid, again by inertia, continues to move in the direction it had been moving just before when it was keeping pace with the ca.n.a.l. Thus we see that there are conscious sensations of rotation from the ca.n.a.ls, and that these give information of the starting or stopping of a rotation, though not of its steady continuance.

Excessive stimulation of the ca.n.a.ls gives the sensation of dizziness.

The otolith organs in the vestibule are probably excited, not by rotary movements, but by sudden startings and stoppings of rectilinear motion, as in an elevator; and also by the pull of gravity when the head is held in any position. They give information regarding the position and rectilinear movements of the head, as the ca.n.a.ls do of rotary head movements. Both are important in maintaining equilibrium and motor efficiency.

The muscle sense is another sense of bodily movement; it was the "sixth sense", so bitterly fought in the middle of the last century by those who maintained that the five senses that were enough for our fathers ought to be enough for us, too. The question was whether the sense of touch did not account for all sensations of bodily movement.

It was shown that there must be something besides the skin sense, because weights were better distinguished when "hefted" in the hand than when simply laid in the motionless palm; and it was shown that loss of skin sensation in an arm or leg interfered much less with the coordinated movements of the limb than did the loss of all the sensory nerves to the limb.

[Ill.u.s.tration: Fig. 41.--(From Cajal.) A "tendon spindle," very similar to the muscle spindle spoken of in the text, but found at the tendinous end of a muscle instead of embedded in the muscle substance itself, "a" indicates the tendon, and "e" the muscle fibers; "b" is a sensory axon, and "c" its end-brush about the spindle. Let the tendon become taut in muscular contraction, and the fine branches of the sensory axon will be squeezed and so stimulated.]

Later, the crucial fact was established {239} that sense organs (the "muscle spindles") existed in the muscles and were connected with sensory nerve fibers; and that other sense organs existed in the tendons and about {240} the joints. This sense accordingly might better be called the "muscle, tendon and joint sense", but the shorter term, "muscle sense", bids fair to stick. The Greek derivative, "kinesthesis", meaning "sense of movement", is sometimes used as an equivalent; and the corresponding adjective, "kinesthetic", is common.

The muscle sense informs us of movements of the joints and of positions of the limbs, as well as of resistance encountered by any movement. Muscular fatigue and soreness are sensed through the same general system of sense organs. This sense is very important in the control of movement, both reflex and voluntary movement. Without it, a person lacks information of where a limb is to start with, and naturally cannot know what movement to make; or, if a movement is in process of being executed, he has no information as to how far the movement has progressed and cannot tell when to stop it. Thus it is less strange than it first appears to learn that "locomotor ataxia", a disease which shows itself in poor control of movement, is primarily a disease affecting not the motor nerves but the sensory nerves that take care of the muscle sense.

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EXERCISES

1. Outline the chapter, rearranging the material somewhat, so as to state, under each sense, (a) what sense cells, if any, are present in the sense organ, (b) what accessory apparatus is present in the sense organ, (c) what stimuli arouse the sense, (d) what are the elementary responses of the sense, (e) peculiar blends occurring within the sense or between this sense and another, (f) what can be said regarding adaptation of the sense, and (g) what can be said regarding after-images of the sense.

2. Cla.s.sify the senses according as they respond to stimuli (a) internal to the body, (b) directly affecting the surface of the body, (c) coming from a distance.

3. What distinctive _uses_ are made of each sense?

4. Explore a small portion of the skin, as on the back of the hand, for cold spots, and for pain spots.

5. Try to a.n.a.lyze the smooth sensation obtained by laying the finger tip on a sheet of paper, and the rough sensation obtained by laying the finger tip on the surface of a brush, and to describe the difference in terms of the elementary skin sensations.

6. Is the pain sense a highly developed sense, to judge from its sense organ? Is it highly specialized? highly sensitive? How does its peculiarity in these respects fit it for its use?

7. Separation of taste and smell. Compare the taste of foods when the nostrils are held closed with the taste of the same food when the nostrils are opened.

8. Make a complete a.n.a.lysis of the sensations obtained from chocolate ice cream in the mouth.

9. Peripheral vision. (a) Color sense. While your eyes are looking rigidly straight ahead, take a bit of color in the hand and bring it slowly in from the side, noticing what color sensation you get from it when it can first be seen at all, and what changes in color appear as it moves from the extreme periphery to the center of the field of view, (b) Form sense. Use printed letters in the same way, noticing how far out they can be read, (c) Sense of motion. Notice how far out a little movement of the finger can be seen. Sum up what you have learned of the differences between central and peripheral vision. What is the use of peripheral vision?

10. Light and dark adaptation. Go from a dimly lighted place into bright sunlight, and immediately try for an instant to read with the sun shining directly upon the page. Remaining in the sunlight, {242} repeat the attempt every 10 seconds, and notice how long it takes for the eye to become adapted to the bright light. Having become light-adapted, go back into a dimly lighted room, and see whether dark-adaptation takes more or less time than light-adaptation.

11. Color adaptation. Look steadily at a colored surface, and notice whether the color fades as the exposure continues. Try looking at the color with one eye only, and after a minute look at the color with each eye separately, and notice whether the saturation appears the same to the eye that has been exposed to the color, and to the eye that has been shielded.

12. Negative after-images. Look steadily for half a minute at a black cross upon a white surface, and then turn the eyes upon a plain gray surface, and describe what you see. (b) Look steadily for half a minute at a colored spot upon a white or gray background, and then turn the eyes upon a gray background, and note the color of the after-image of the spot. Repeat with a different color, and try to reach a general statement as to the color of the negative after-image.

13. Positive visual after-images. Look in the direction of a bright light, such as an electric light, holding the hand as a screen before the eyes, so that you do not see the light. Withdraw the hand for a second, exposing the eyes to the light, and immediately screen the eyes again, and notice whether the sensation of the light outlasts the stimulus.

14. Tactile after-images. Touch the skin lightly for an instant, and notice whether the sensation ends as soon as the stimulus is removed. If there is any after-image, is it positive or negative?