ism. Latterly the subject has been much discussed, on account of the danger arising from the confusion of red and green signal lights by engineers, pilots, etc.
86 The Quality of Sensation: Vision the base, and which thus begin and end the four colour series. These colours, R, Y, G, B, are the psychological primaries.
For technical and artistic purposes, we must give this title to a different set of colours: R, Y and B. The painter who has these pigments upon his palette is able by their means, with the help of white, to reproduce the various colours of nature.
It is a matter of common experience that the mixture of B and Y paints will give a saturated green. The reason is that the blue pigmentary stals reflect & and 7 jffht, the K crystal.-. G light Thus the B and Y cancel each other, and only the G is left to be seen.
For the physicist, again, the primary colours are. R, G and a certain BV. The mixture of these three spectral olours, in fitting proportions, will not only give colours of every possible hue, but will also give them at a higher degree of saturation than can be obtained from any other three spectral colours.
Lastly, for the physiologist, the primary colours are. the -racteristi- j \ retinal zoi \ purplish red, its complementary bluish green of about 495 h/j., and the Y and B of the intermediate zone. The two latter colours are identical with the psychological primaries. Whether the physiologically pure R is identical with the psychological R is doubtful; but it is certain that the physiological G is not the psychological G: it is rather a distinctly bluish G.
Evidently, then, the term primary is misleading; what it means depends upon the context in which it is used. We may, perhaps, call the psychological R, G, Y, B the principal colours; the artist's IV, R, Y, B the primary § 22. Theories of Vision 87 colours; the physicist's R, G and B V the fundamental colours; and the physiological C, BG, Y and B the invari- able colours.
§ 22. Theories of Vision. — The eye1 is, in all essentials, a little photographic camera. The eyelids form a cap or shutter, closure of which prevents the access of light. Behind the shutter is an automatic diaphragm, the iris, which closes to a pin-hole or opens out, according to the degree of illumination. Behind the diaphragm is a iens, which may be adjusted for near or far objects. This ad- justment is not made by changing the length of the eye- ball, as it were by racking the lens back and forth; the soft substance of the lens is encased in an elastic sheath, which is suspended by radial fibres to muscles set vertically in the wall of the eyeball. When the eye is at rest, the anterior surface of the lens is relatively flat, and the organ is consequently adjusted for far vision; if we wish to focus upon a near object, the muscles contract, the pull on the radial fibres is thereby lessened, and the lens assumes a greater curvature. Behind the lens is a dark chamber, lined with a membrane, the choroid, which is deeply pig- mented by a colouring matter of dark brown. This chamber, together with the smaller chamber in front of the lens, is filled with a clear semi-fluid or fluid substance, which serves to maintain the shape of the eyeball; and the whole eyeball is surrounded by a leathery protective membrane, the sclerotic, which is pierced behind by the optic nerve and 1 Models of the brain and sense-organs are manufactured, in all degrees of elaboration, by a number of firms: Auzoux, Bennin^hoven & Summer, Bock- Steger, Brendel, Deyrolle, etc. The writer uses, as eye-models, the (EU com- plet de tres grande dimension, of the Auzoux series of clastic anatomy, and the models numbered 3 b and 3 / in the Benninghoven & Sommer series.
88 The Quality of Sensation: Vision passes over in front into the transparent cornea. The retina, or sensitive film, is produced by the expansion of the optic nerve over the posterior two-thirds of the internal surface; it is self-renewing, just as the diaphragm and lens are automatic.
The retina, with which we are chiefly concerned, is a very thin but extremely complex membrane. Its terminal structures, which are the sensitive receivers of the physi- cal light stimulus, are known as rods and cones. In general, these are intermingled over the entire retina. There are, however, two areas — the optic disc and the yellow spot — which show a different formation. The optic disc is the point at which the optic nerve enters the eye- ball. Here there is no true retina, but a blind spot, whose situation and dimensions may readily be determined by experiment. The yellow spot or macula lutea lies at the posterior pole of the eyeball: it is peculiarly sensitive to form and contour, and is therefore termed also the spot of clearest vision. At the centre, in the fovea centralis, it shows a depression, where the retina consists of little more than a single layer of attenuated cones. The whole spot is coloured yellow, so that in macular vision the colours of the short-wave end of the spectrum are somewhat darkened. — It is not possible, in the present state of our physiological knowledge, to give an entirely satisfactory explanation of all the facts of visual sensation. The following, however, seem to be the most reasonable hypotheses.
(i) The Theory of Dual Vision. — Many indications point to the conclusion that the rods are the end-organs of twilight, the cones the end-organs of daylight vision. That is to say, the rods are organs which, under stimulation § 22. Theories of Vision 89 by light-waves whose energy is too low to stimulate the cones, furnish us with sensations of light. The blindness of the normal fovea at night-time is due to the fact that the retina is there composed only of cones. The Purkinje phenomenon, and the exceptions to the third law of colour mixture, are to be ascribed to the rods: they mean that the rods are affected by light-waves of different length other- wise than are the cones. The typical retina of the totally colour blind eye is a rod-retina, lacking functional cones, and the complete blindness of the fovea is a necessary result.
We have seen that twilight vision is extremely dependent upon dark-adaptation. It is significant, in this connection, that the terminal members ofjhe rods contain a purplish red substance, the visual purple, which bleaches on exposure to light and is re- formed under the influence of darkness. It is further significant that the distribution of tints in the Purkinje spectrum (lightest region in G) accords with the chemical action of the different light-waves upon the visual purple. Whether, however, the visual purple is essentially concerned in rod-vision, or whether it serves merely to sensitise the visual apparatus, cannot certainly be de-\ cided. The retinas of nocturnal animals — owls, bats, rats, moles — are almost wholly deficient in cones, while their rods are richly supplied with the visual purple. Animals whose eyes lack this rod-pigment — fowls, pigeons — are strictly diurnal in their habits.
(?) The Phenomena of Daylight Vision. — There are two current theories of daylight vision, called respectively the Helmholtz and the Hering theory. Both are adequate to a large proportion of the facts; both have been variously modified to accord with newly discovered facts; neither fits the facts in complete detail. Both, of course, are physio- logical theories; but Helmholtz approaches physiology by way of physics, Hering rather by way of psychology. The go The Quality of Sensation: Vision following account agrees, in its main outlines, with Hering's view.
We assume that the retinal cones contain three visual substances, which are decomposable by light, and which are the vehicles of reversible or antagonistic chemical reactions. We may term them the black-white, the blue- yellew, and the red-green substances. The cones of the central area contain all three; those of the intermediate zone mostly contain the Bk- J^and the B- Fsubstances; and those of the outermost zone mostly contain only the Bk- W « substance. The latter, which is thus the most widely dis- tributed of the visual substances, is affected by every light stimulus which exceeds a certain lower limit of energy; the other two are affected only by the wave-lengths correspond- ing to their names. The six chemical reactions which occur in the three substances give rise to the sensations of black, white, and the four invariable colours. From them and their combinations are derived, with a single exception, all the phenomena of daylight vision.
The exception is the sensation of neutral grey. Since this sensation may persist while the retinal organs are out of function, it must take its origin in the brain. We ascribe it to the molecular motion of heat in the cells of the visual cortex, and are thus able to explain both its constancy and its qualitative character.
According to this view, the retinal processes which arouse the sensations of Bk and IV, B and Y, and invariable R and G are antagonistic and incompatible. If, for instance, by mixing a dark B and a light Y on the colour mixer, we expose a certain area of the intermediate zone to light which affects the Bk-lV and the B-Y substances in equal and opposite ways, no retinal sensation will be set up by the stimulus; we ought, so to speak, to see § 22. Theories of Vision 91 nothing whatever. What we do see is a middle grey, the grey which is to be referred to the cortex. This grey, which mixes with all retinal sensations, is constant, because the heat-energy of the cortex is constant; it is grey because, unlike the sensations of light from the retina, it derives simultaneously from both of the antagonistic Bk- W reactions: — such a simultaneous occurrence of opposed processes is, as physics tells us, precisely the effect produced by heat within a body which is in chemical equilibrium. The office of the cortical grey is to prevent the darker objects in the field of vision from being drowned out by their lighter surroundings.
The facts of indirect vision are explained by the distribution of the visual substances over the retina. The Bk-lV is, evidently, the oldest, the R-G the youngest, of the three. Hence the R-G is also the most instable. In cases of partial colour blindness, it does not occur at all, while the Bk-W and the B- Y substances are intact. If the light-waves possess a very high degree of energy, it is thrown out of function (§ 16).
The facts of colour mixture may easily be worked out in terms of the three retinal substances and the cortical grey. Take, for instance, the fact that C and BG, mixed in the right proportions, give grey. The stimuli affect the R-G substance in equal and opposite ways. They also affect the Bk- W substance: perhaps equally and oppositely, perhaps both by way of Bk or both by way of IV, perhaps differently, so that the one of these antagonistic processes is stronger than the other. Ln the first case we see simply the cortical grey; in the second, a distinctly dark or a distinctly light grey; in the third, a slightly dark or somewhat light grey, according as the retinal excess has fallen on the side of Bk or of IV. The same sort of analysis may be carried through for the mixture of other light stimuli, in any number and of any wave-length.
To account for contrast, we have merely to suppose that the retinal substances tend towards equilibrium over the whole area of their distribution, so that, directly affected at one point, they are indirectly — and oppositely — affected at all other points, though most noticeably, of course, in the immediate neighbour- 92 The Quality of Sensation: Vision hood of the stimulus. If we look at a red square on a grey ground, we see at once the contrast-fringe of verdigris; it is as if the whole of the R-G substance were up in arms to repel the invasion. The same thing holds of other stimuli, including Bk and IV; all alike call out, indirectly, the antagonistic retinal process.
Lastly, the phenomena of adaptation and after-image follow from the antagonistic character of the reactions in the three sub- stances. As we gaze at the red square, the ^-reaction of the R-G substance is gradually reduced; or, what is the same thing, the ^-reaction is gradually strengthened. Presently, the two reactions are of equal strength; adaptation to the coloured stimulus is com- plete, and we see grey. If, now, the red square is removed, the c?-reaction is suddenly given the ascendancy, and shows itself in the complementary colour of the after-image.
References for Further Reading §§ 14-22. The dual theory of vision was first propounded by the his- tologist M. J. S. Schulze in 1866 {Zur Anatomic und Physiologic der Retina, in Archiv fur mikroskopische Anatomic, ii., esp. 255 f.). Its establishment in recent years has been largely due to the work of J. von Kries, professor of physiology in the University of Freiburg i. Br., who has described it in the chapters entitled Die Gesichtsempfindun- gen, in W. Nagel's Handbuch der Physiologic des Menschen, iii., 1905, 109 ff. Here will also be found a full statement and criticism of the Helmholtz and Hering theories. For the Helmholtz theory, and its debt to Thomas Young, see H. L. F. von Helmholtz. Handbuch der physiologischen Optik, 1896, esp. §§ 20, 23. The theory of E. Hering, who is now professor of physiology in the University of Leipzig, is set forth in Zur I. clue vom Lichtsinne, 1S74, and Grundsugeder Lehrevom Lichtsinn, pts. i.. ii., 1905, 1907 (not yet completed). The cortical ori- gin of the sensation of ^rey was suggested by G. E. Miiller, professor of philosophy at Gottingen, in Zur Psychophysik der Gesichtsempfin- dungen (offprinted from Zeitschrift fur Psychologic und Physiologic der Sinnesorgane), 1897. — Consult also W. H. R. Rivers, Vision, in E..1. Schafer's Text-Book of Physiology, ii.. 1900, 1026; art. Vision, in /. M. Baldwin's Dictionary of Philosophy and Psychology, ii., 1902, 765 ff.; I. M. Bentley, 'Phe Simplicity of Colour Tones, American Journal of Psychology, xiv., 1903, 92; J. W. Baird, The Colour Sen' sitivity of the Peripheral Retina. 1905.
AUDITION §23. The Auditory Qualities. — The world of sound, like the world of sight, is made up of two classes of sensa- tions, the one variegated and of manifold quality, the other sober and monotonous. These are distinguished, in ordi- nary speech, as tones and noises. Tones, which corre- spond to the senations of colour, are the proper material of music; they have a certain clarity and stability which fit them for their place in art. Noises, which correspond to the sensations of light, are dull and instable; if momen- tary, they are abrupt and harsh, if continued, they are rough and turbid. And as in vision, so in audition, the two kinds of sensation are in some measure independ- ent, while at the same time they are intimately related.
We are apt to think of tones as coming from a musical instrument, piano or violin. Musi- cal tones are, however, complicated mixtures of tones and noises_(§ 25). To obtain sensibly pure tones, elementary tonal FIG. ii. Tuning-fork on Resonance Box, and Glass Bottle, fitted with mouthpiece for blovvprocesses, we must ing The pitch of the bottle.tone may be have recourse tO Spe- raised or lowered by pouring in or letting out cial apparatus: the best are weakly sounding tuning-forks standing on their resonance boxes, and weakly blown bottles. If we 93 94 Audition work through a long series of such pure tones, we notice, first, that they differ qualitatively as high and low; they show differences of pitch. These terms are, of course, spatial in origin, and it is not altogether easy to see how they came to be applied to tonal qualities.1 At any rate, they are in current use, and we understand their meaning. We notice, secondly, that the tones differ qualitatively in what we must call — again in spatial terms — size or diffusion. This attribute runs, in general, parallel with the attribute of TREBLE BASS Fig. 12. The Tonal Pencil, representing the sum-total of tonal qualities, as the Colour Pyramid represents the sum-total of visual qualities. The horizontal di- mension corresponds to the attribute of pitch, the vertical to the attribute of volume.
pitch; but at the ends of the scale it changes more quickly, in the middle region more slowly, than pitch, so that deep tones appear very large and diffuse, and high tones very small and concentrated, while the intermediate tones seem all to be more or less of the same size.
As we have already said (§ 1 1), some psychologists believe that tones have a truly spatial attribute of volume, while others think that the low tones merely remind the hearer of large things and the high tones of small. This second view contains, undoubtedly, a good deal of truth. The deepest tones from the organ, for in- stance, are not only heard, but are also felt as a thrill over the 1 The composer Berlioz remarked that, on the piano, high means right and low means left in the horizontal plane; and that, if the violinist's hand rises, for high tones, the cellist's drops. The whole question is discussed by C. Stumpf, Tonpsychologic, i., 1883, § XI.
§ 23. The Auditory Qualities 95 whole body; and the size of musical instruments varies with the height of their tones. Children call deep and high tones big and little, old and young: evidently because the former come from the large grown-up people, and the latter from their small play- mates. At the same time there can be no doubt that what we have termed diffusion and concentration is an inherent attribute - of tones; only, we need no more regard it as really spatial than the other attribute of height or pitch. In trying to specify the ultimate characters of sensation, we have to take language as we find it, and to use metaphor and analogy. We speak of colour-tone and of colour-depth, but we do not mean that the hues sound dif- ferently, or that we can drop a stone into them. So we shall speak presently of tone-colour, without implying that tones are red or green. Pitch and size stand for certain qualitative aspects of tonal sensation, and neither can be understood literally in terms of space. — There seems, in the musical scale, to be a periodical recurrence of tonal quality; the corresponding notes of successive octaves, if struck together, sound in unison. It has therefore been suggested that the tonal system must be represented, not by a straight line, but by a line which returns upon itself, a spiral line. This resem- blance of a note to its octave is not, however, a matter of pure sensation; it depends upon conditions which we discuss in Pt. II. If the finger is run in a glissando over the white keys of the piano, the impression obtained is that of a linear series of tonal qualities. Hence our sensations of tone may be represented by a straight line which tapers, in three divisions, from bass to treble, being broadest for the diffuse deep tones and narrowest for the small and concentrated high tones.
The noises that we hear in everyday life are of two kinds, explosive and continuative. For the former, we have such words as crack, pop, snap; for the latter, such words as hiss, sputter, rumble. It seems, at first thought, that the continuative noises might very well be regarded as repeated explosions; a rattle or clatter, for instance, is I- ;/ g6 Audition I- ;/ g6 Audition simply a quick succession of raps or shocks. This reduc- tion cannot, however, be carried through. Such noises as the hiss of escaping steam, the soughing of wind in the trees, the rustle of a newspaper, — complex as they cer- tainly are, — refuse to be analysed by introspection into series of explosions; and in the pattering of rain, or the sizzle of frying fat, we distinguish the rapidly recurring taps or clicks from the steady hiss of the background. There are, then, two types of noise sensation, the__gnarj and the hiss, to be set alongside of the sensations of tone.
There can be no question that sensations of tone may be had without accompanying noise. It is much more difficult to decide whether sensations of noise occur without accompanying tones. In the first place, all explosive noises have a certain, more or less definite pitch. A hand-clap sounds lower than a snap of the fingers, the crack of a rifle lower than the spit of a revolver. This statement holds of the simplest noises that we can produce in the laboratory. Thus, if soap-bubbles are filled with a mixture of air and hydrogen, and touched off" with a match, the large bubbles give a deeper pop than the small. Or if tuning-fork tones are cut down to mere momentary puffs of sound, we hear short, dry strokes which are deeper for the large forks than for the small. It would seem that, in such cases, we are listening to simple, toneless noises, — in which event we must say that these noises show differences of pitch akin to the pitch-differences of tones, though of a coarser kind. But there is an alternative. If a bar of wood is dropped upon a wooden table, we hear a thud which sounds merely noisy. If, however, we drop a series of bars, cut to the right lengths, we hear, over and above the noise, a series of definite tones, an air played in a certain key. The single Ithud contains a true tone, but a tone of such short duration that introspection fails at first to find it. And the same thing may be true of the noises from the soap-bubbles and the tuning-forks. If, again, we pass the finger-nail slowly over the ribbed binding of a book, we hear a succession of plucks or taps; but, if we move more quickly, a distinctly tonal scroop. The pitch of the separate fj taps may, then, itself have been tonal.
In the second place, it seems safe to say that no continuative noises are known which do not contain recognisably tonal ele- ments. The buzz of voices in a crowded room, the beat of waves upon a beach, the scrape of a book against others as it is returned to the shelf, the whisper of an S, the drag of matting over a floor, all alike contain various tones which can be singled out by the trained ear.1 And, contrariwise, a continuative noise may be gen- erated from a medley of tonal stimuli. If you press down, all to- gether, an octave of notes in the bass of a piano, — better still, if you press suddenly upon the loud pedal, without striking the key- board,— you hear a harsh, booming or rumbling noise with but little trace of tone.
In fine, introspection distinguishes between tones and noises; and, among noises, distinguishes such things as hiss, murmur, sigh, I purl, crash, rumble from such things as snap, puff, knock, clack, \ roar. But we have, as yet, no means of determining with accuracy the nature and number of the elementary noise qualities. >- § 24. The Dependence of Auditory Sensation upon Wave- number of Sound. — Sound-waves, like light-waves, differ in respect of wave-length, wave-amplitude or energy, and wave-form or composition. We are not here concerned with their energy, since this has no influence upon the quality of auditory sensation. And we shall speak, not of wave-length, but rather of the wave-number — the number of complete waves in the 1 sec. — which is defi- nitely correlated with it. As referred to the tones them- selves, this is usually termed pitch-number; as referred 1 Stumpf narrates that, in listening to a mountain brook, he heard a clear and steady tone of/lt, with neighbouring tones playing about it; further, a clucking and gurgling, made up of momentary deeper tones; and behind all the noisy plash which could not be analysed. Tonfisychologie, ii., 1890, C02.
H 98 Audition /S c> cc> to the motion of sonorous bodies, it is termed vibration-rate.
Wave-number determines the quality, the pitch and size, of tonal sensations. The tones of the musical scale range between the limits ot about 40 and 4000 vs. in the 1 sec. The range of audible tones is much wider, from about 12 to about 50000 vs. Between these extremes the trained ear can distinguish some 11000 different tones.
Wave-number also influences the inten- sity of tonal sensations. High tones are intrinsically loud, and low tones intrinsi- cally weak, — very much as, in the spec- trum, Y is a light and V a dark colour.
The three attributes of pitch, size and inten- sity, in so far as intensity is dependent not on energy but on pitch-number, constitute together what is known as tone-colour. High tones have a lighter or brighter, low tones a darker or duller Qri colouring. Where we are dealing with relatively simple tones, the introspective analysis of tone- Fig 13 The c°l°ur is not very difficult. The single term be- Series of Auditory comes useful, however, when we are considering Qualities. The the compound tones employed in music.
keyboard of a _.,.,,.
grand piano ex- °ver the greater part of the musical scale — tends from the A.2 from the lowest tones to tones of about 3000 vs. of 27.5 vs. to the — tNV0 complete sound-waves suffice to arouse a , tonal sensation, while stimuli of less than two smaller piano key- board ranges be- tween the <\ of 33 vs. and the a4 of 3520 vs. Helmhcltz" lower limit of orchestral music is the E\ of 41.25 vs. (double bass); his higher limit, the a* of 4752 vs. (piccolo flute). The organ has a range of 9 octaves: Q (16.5 vs ) to c6 (8448 vs.). The highest note of the violin is the e* (2640 vs.). The range of audition is, approximately, from the (7a of 12.35 vs. to the/8 of 45056 vs.
0 e* a1 Ei MM A.
§ 24- The Limits of Tonal Sensation 99 VJ waves give rise to a snap or stroke. Physically, then, this explo- sive noise is merely an incomplete tone. The probable character of noise stimuli in general is discussed in the following § 25. — The lower limit of tonal hearing may be determined by means of tuning-forks or of a steel lamella. Giant tuning-forks have been constructed, which vibrate very slowly; the rate of vibration may be varied by the adjustment of sliding weights upon the tines. The weighted wire forks, a specimen of which is shown in Fig. 14, are more manageable. The lamella is a blade of soft steel, clamped in a wooden vise, and ac- tuated by the finger; a scale engraved on the blade indicates the rate of vibration.
The upper limit may be determined by means of very small tuning-forks, actuated by a bow, or more easily by means of the Galton whistle shown in Fig. 14. The whistle is a very small stopped labial pipe, actuated by the squeeze of a rubber bulb, and closed by a piston which is adjustable by a micrometer screw.
The series of distinguishable auditory qualities, between the upper and lower limits, may be worked out in part by means of a set of weighted wire forks and of a Galton whistle. For the middle region of the scale we may use a tonometer: a series of delicately adjusted tuning-forks, or a series of metal tongues of minimally different lengths thrown into vibration by a bellows. A less expensive apparatus is the Stern variator shown in Fig. 15. This consists essentially of a blown brass bottle, whose pitch may FIG. 14. Weighted Wire Fork and Galton Whistle.
IOO A udition be varied, little by little, through the introduction or withdrawal of a piston.
§ 25. The Dependence of Auditory Sensation upon Com- position of Sound. — The train of sound-waves which arouses a sensation of tone is a periodic vibration of simple har- monic form; the motion of the air-particles is a simple pendular motion. Periodic vibrations of any other form may be analysed, mathematically, into a series of superposed simple harmonic vi- brations, whose wave-numbers are multiples of the wave-number of the given vibration. That is to say, the complex wave may be regarded as made up of a group of simple waves, whose wave- numbers — if the wave-number of the complex wave is taken as 1 — stand in the ratios 1: 2: 3: 4, etc. All musical tones or, as we may call them, compound tones are aroused by trains of waves of this complex kind. The_ear, unlike the eve, is an an:ih>ing organ; and it is therefore possible, within limits and after practice, to single out the simple tones which together constitute the compound tone, — to repeat in sensation the analysis already performed by mathematics. The compound tone then splits up into partial tones, the lowest of which is FIG. 15. Stern's Variator.
" § 25. Timbre of Compound Tones 1 01 termed the fundamental, and the rest the upper partials. Sometimes the upper partials are distinguished as the overtones of the fundamental: this usage is a little con- fusing, since the second partial becomes the first overtone, and so on. The partial tones, when thus singled out by the attention, have the simple character of the tones pro- duced bv tuning-forks or blown bottles; they sound, that is, as pure tones, and do not differ with the different in- struments from which they come.
Most of us, however, lack the training, and some lack the ability, to resolve a compound tone into its simple components. Under these circumstances, the tone is itself heard as simple, but has upon it a certain colouring or timbre, which varies with the various instruments. The tone of the organ is full and rich, that of the trumpet is hard and rasping, that of the clarinet is hollow and ^~ nasal. These differences of timbre are primarilv due to X the differences in the number and relative intensity of the overtones which accompany the fundamental.