lost sight of the conditions under which the idea grew up, and look upon the continuity of the visual field as a fact of direct perception.
There can be no doubt that this explanation is correct, and that eye movement accounts for the filling up of the bhnd area. There is another circumstance, however, which assists eye move- ment in its task. The blind spots do not occupy the same posi- tion in the two eyes: so that, when we look with both eyes at a landscape, the part to which one eye is blind is seen by the other. This fact makes the continuity of the field a matter of course, when both eyes are used. But it is not sufficient to explain all the facts: it does not explain the continuity of a field seen with only one eye.
(2) Reinverted Visio7i. — The rays of light proceeding from an object in the field of vision do not pass straight through the pupil to the retina, but cross at a point within the eyeball, and thus form upon the retina an inverted image. Since this fact has been known, the question has often been asked: How is it that 1 68 Perception and Idea we see objects the right way up? How does it come about that the retinal image, which is upside down, is set right again, reinverted?
The answer is that we do not see what goes on in our eyes, but what is set before us in space: just as we do not hear what goes on in our ears, but hear the sound which is outside of the ear. Mankind saw things the right way up long ages before any man knew anything of the disposal of light rays upon the retina. We learn the up and the down of things by experience: that is up, which is where our head is; that is down, which is where our feet are. The retinal image need be no more like the thing seen than the shake of the fibre of the basilar membrane is like the sound heard, or the chemical action of salt upon the tongue like the taste of salt in the mouth.
The disposal of light rays upon the retina becomes important only when we wish to examine the mechanism of the eye as a piece of physical apparatus. We find, either by examining an- other person's eye with a special instrument, or by constructing an artificial eye of lenses and ground glass (a camera), that the ' image ' formed by the entering rays is inverted. It is a physical necessity that this be the case, if the eye is to serve the purposes of vision, i.e., if it is to ^ work ' as an optical instrument. But the fact is irrelevant to psychology. Nobody has ever seen his own retinal * image.'
§ 46. Extent of Movement. — Movement is a continuous change of position. The materials for the idea of move- ment are, therefore, in part the same as those for the idea of locality. Our idea of movement is made up, in part, of the ideas of an object in different positions. The other factor in the idea of movement is the persistence of sen- sation after the cessation of stimulus. By the help of an after-image or of memory we are able to perceive an object, as it v^ere, in two places at once: in the place which it has just left, and in the place to which it has just come. Here we have the sense-material for the con- tinuity of change of position which the idea of movement includes.
Our idea of movement is an idea which is at once exten- sive and temporal. Every movement is a movement so far, and also a movement during a certain time. Move- ment has extent, and is therefore an extensive idea; it has rate or rapidity, and is therefore a temporal idea.
Our estimation of the extent of movement may be founded upon sensations from skin, joint or eye.
(i) Skin, — As a stimulus moves over the surface of the skin, it arouses sensations of different local signature. Each of these sensations lasts for a short time after the removal of the stimulus; but the after-image of pressure is very brief, — too brief to be of much assistance to us in forming an idea of the distance passed over by the stimulus. On the other hand, we can remember each impression, for a little while, with great accuracy. Our estimation of the extent of movement, in purely cutaneous terms, is restricted to movements of stimulus which are either so short or so quick that the first local sign has not lapsed from consciousness when the last is reached. In all other cases, we are either entirely un- certain as regards the extent of movement, or make our estimation in terms not of pressure but of sight.
The stimulus must pass from local sign to local sign, />., travel a certain distance, before its movement is remarked at all. And if the pressure is very light, or the movement very slow, we may have no idea of movement; the first local sign may be forgotten when the next is reached. The distance passed over on the fore- arm before movement is noticed may amount to 10 mm.
Method. — Move a charcoal point lightly in different directions over the skin of wrist or forearm, keeping the rate of movement as uniform as you can. Measure the distance which the point travels, in each case, before the subject cries out that it is moving. The distance will be greater if you move it upwards or downwards than if you move it across the limb. This is because localisation, 1^0 Pejxeption and Idea conscious or unconscious (physiological), is less accurate upon the long axis of the body; the local signs are less thickly strewn, so to speak, than they are upon the short axis. And this, in its turn, is because we increase more in height than in breadth as we grow: we grow ' up.' Hence the nerve-endings in the skin are pulled further apart in the up and down directions than they are in the transverse.
(2) Joint. — The idea of movement which is derived from articular sensations is always the idea of a movement of our own body or some part of it. The just noticeable extent of movement is, of course, the distance which the limb must travel to arrive at a just noticeably different position (§ 44).
Method. — Lay a board, about 50 cm. long and 15 cm. wide, upon a low table. Place the forearm, palm upwards, upon the board, with the elbow projecting just beyond its near end. Close 3^our eyes. Let an assistant raise the far end very carefully and gradually. Measure the height from the table to which the board may be raised before you have any perception of movement from the elbow-joint. To avoid jar at starting, it is best to have the near end of the board hinged to the table, and its far end raised by a cord running through a pulley.
(3) Eye. — The visual idea of extent of movement is differ- ently formed, according as the eyes themselves move or remain stationary.
(yd) If the eyes are fixed, visual movement, like cutaneous, can be estimated only in cases where the sensations first aroused, or their after-images or memories, are still running their course in consciousness when the last make their appearance. The eye has, here as always, the advantage of the skin: retinal sensations per- sist in after-images for longer than cutaneous, and after-images are more reliable than memories.
The just noticeable movement, for the unmoved eyes, is the same as the just noticeable difference of visual position (§ 44).
(Ji) But the head or eyes may move, following the moving stimulus. In this case, the retinal image of the object is kept constantly upon the same portion of the retina, instead of passing from one portion to another. Here, the estimation of movement is of the articular type: the eyes turn in their sockets, or the head upon the shoulders, as the forearm turns in the elbow-joint.
Estimation in terms of eye movement is very uncertain, unless there is somewhere in the field of vision a fixed point, to which we may refer when making it. The fixed point serves the same pur- pose under these circumstances as the persistence of the first sensation does when the eyes are not moved, or when we are form- ing our idea from cutaneous sensations. In the latter cases, the stimulus is spread over all points of its course at once: the move- ment, from starting-point to finish, is filled up with memory, after- image or peripheral sensation. In the present instance we have the fixed object as starting-point, and the final position of the moving object as finishing-point; while the fact of movement it- self is perceived from the series of pressure sensations aroused by the turn of the eyeballs in their sockets, and of strain sensations aroused by changes of ocular convergence.
It may seem strange that eye movement, which is so important in other connections (eye measurement and convergence), should prove to be of such slight assistance in the formation of the idea of the extent of movement. In reality, it is just because of these other functions that the strain sensations are unable to help us now. In eye measurement, the eye moves from a fixed point and sweeps over a line; in convergence, the eyes rest upon a certain fixed point at a definite distance from the body. If we take away the fixed point, as beginning or finishing point of movement, the sensations set up around the eyeball are uncertain guides. Move- ments of the eyes to and fro are very frequent, and very rarely remarked. Hence without the fixed point of reference we may make grave mistakes, even if we base our idea upon the true artic- ular sensations produced by rotation of the head: unnoticed move- ments of the eyes may have added something to or subtracted something from the result of head movement.
Method. — The following experiment shows the uncertainty of estimation of extent of movement when the eyes are allowed to move, in the absence of a fixed point of reference. Seat your- self in a dark room. An assistant holds a dark lantern, by which he can throw a faint spot of Kght on the wall before you. The 1/2 Perception and Idea spot is shown at irregular intervals and for different lengths of time; sometimes it is still, sometimes moved slowly to or fro. You will find that your judgments of its stationariness and move- ment are frequently incorrect.
II. Temporal Ideas § 47. Rhythm. — When we walk, we have a regular alternation of strong and weak sensation complexes. We are resting, perhaps, on the left foot. This means a mass of strong pressures on the sole of that foot, a severe press- ure in knee and hip, etc. The right foot swings forward. This means a complex of weak pressures (after-images, pressure of boot) from the sole of that foot, and a per- ception of movement — with relaxation of pressure, how- ever— in knee and hip. The right foot is then set down: strong. The left leg swings forward: weak. The left foot comes down again: strong, — and so on. A similar alternation is observable in respiration. We inspire, short; expire, long; inspire, short; etc. These alterna- tions of strong and weak, long and short sensation com- plexes are the basis of the idea of rhythm.
The auditory idea of rhythm has been far more highly developed than the tactual. We cannot listen to any fairly rapid succession of sounds without putting rhythm into it (§ 42). Sounds are, indeed, better material for the idea of rhythm than are tactual complexes; for the limbs are fixed to the trunk, and can therefore do no more than oscillate to and fro, pendulum fashion, giving of necessity the most rudimentary form of rhythm, — beat' beat, beat' beat, — whereas a series of sounds can be divided into groups of any complexity. The rhythm: beat" beat beat, beat' beat beat, beat" beat beat, beat' beat beat, could not be formed from tactual impressions, but is easily con- structed when we have a succession of free stimuli, and can place the changes of intensity at any desired point in the succession.
Hence it is intelligible that, in cases of conflict, auditory rhythm should outweigh tactual. When we think of the rhythm of walk- ing, we do so as a rule under the form: left' right, left' right, etc., and not under the form: press' swing, press' swing, etc., as given above. This is because we think of walking in terms of hearing, we listen to an imaginary march. The swing is noiseless; and the accent is consequently placed upon one of the two treads.
The simplest auditory rhythms are successions of two or three beats, one of which is stronger than the other or than the other two. The poetical 'feet,' iambus, trochee, dactyl and anapaest, are instances of the four possible forms which these simplest rhythms may take: w_, — w, — ww, ww — The musical 'measure,' which corresponds to the poetical foot, may be far more complicated. Thus we may have twelve impressions, accented as follows: I II I I in music written, perhaps, or accented in this way III I II I I III in music written, perhaps, 1/4 Perception a7id Idea i.e., a succession of four or six simple rhythmical forms, with four degrees of accent or intensity.
Above the foot stands the line or verse; and above the measure the phrase. These represent a further development of the audi- tory idea of rhythm; they are rhythmical wholes, just as are the foot or measure, but rhythmical wholes of a higher order. Neither can contain more than six feet or measures: a seven-footed line or a seven- measured phrase falls to pieces, ceases to be rhythmical.
Once more: above the verse comes the stanza; and above the phrase stands the period. These are rhythmical wholes of a still higher order. Neither can contain more than five verses or phrases; as a general rule, neither contains more than four.
Method. — Set a metronome beating, with an interval of about a quarter of a second between stroke and stroke. Try to throw the beats into all the different possible rhythms, trochaic, iambic, etc. You will find it quite easy to change from rhythm to rhythm, especially if you use movement to assist you, — moving foot or hand when the beats come which you wish to emphasise. Then see how complex a foot or measure you can construct in the vari- ous rhythms.
We found in § 42 that the attention could grasp 40 metronome beats as a single whole, if these were apprehended as 5 impres- sions of 8 beats each. This is the extreme range of attention, under experimental conditions. The measure or foot is here a trochee; the verse or phrase contains four feet or measures accented as follows: v.;.;■.;.
and the stanza or period contains five verses or phrases.
§ 48. Rate of Movement. — Our estimation of the rate, as of the extent, of movement may be founded upon sensa- tions from skin, joint or eye. It is a general rule, in all three sense departments, that quick movement is more readily perceived than slow^.
§ 4^. Rate of Movement 175 (i) Skin. — A stimulus which travels at a uniform rate over the skin does not give rise to the idea of uniform movement. We take the movement to be quicker at parts of the skin upon which localisation is accurate than at parts where it is inaccurate. In the former case more local signs are aroused in the time occu- pied by the movement; the movement has a more varying con- tents. A more diversified contents in a fixed time is perceived as a greater rapidity of movement during that time.
Method. — Draw a pencil point at a uniform rate from shoulder to finger-tips. Its movement will appear to quicken and slacken as it passes over areas of greater and less localising power.
On the other hand, if a thread be drawn by an assistant between your forefinger and thumb, at first quickly and then more slowly, you will not know that the same length of thread has been em- ployed: the thread will seem to be shorter in the first experiment than in the second. If it is pulled quickly, you receive no clear impressions from its irregularities; you have one blurred impres- sion. If it is pulled slowly, you perceive all the roughnesses and unevennesses of its surface; the movement has a more diversified contents. Here, diversified contents in a longer time is inter- preted as a greater extent of thread.
(2) Eye. — The eye can just perceive a movement, in direct vision, if its rate is that of.0028 mm. in the second.
It is difficult to compare the rapidity of two movements, to say which is the quicker and which the slower, if the movements are at all quick. The after-images of the moving stimulus persist so long as to render an estimation almost impossible.
(3) Joint. — All that we know of the rapidity of articular move- ment is the general fact stated above. Quick movements are more readily noticed than slow. This can be shown by the help of the apparatus described in § 46.
The following plan might be followed to test how accurately we can compare the rate of articular movements. Lay the right hand upon a low table. Bend the three last fingers and the thumb, leaving only the forefinger extended. Insert the tip of this finger in a metal cap, which is carried upon a smoothly running wheel. The wheel must be run by clockwork, or by weights hung below 1/6 Perception and Idea the table; and its speed must be variable, and known in each experiment. Let an assistant set it so that it carries the finger over the same distance in two successive movements, but at dif- ferent rates. Find the smallest difference of rate which is percep- tible with a constant extent of movement.
If the whole body is moved, without jar and at a uniform rate, the movement passes entirely unnoticed. If the movement slows or quickens, however, it is perceived at once. The perception may be due to the inertia of the body: we are carried forward as the movement slows, and jerked backward as it quickens. The suggestion has also been made that the acceleration of movement sets up a wave in the endolymph of the internal ear, and that we consequently owe its perception to the static sense (§ 20). If this is correct, the static sense has two qualities, giddiness and a peculiar pressure, and the latter unites with the sensations pro- duced by the inertia of the body to give us the idea of increased or decreased rate of movement.
III. Qualitative Ideas § 49. Clangs. — A clang is an assemblage of tones. It is the conscious process v^hich corresponds to a compound air-wave, as the tone corresponds to a simple wave-move- ment of the air particles.
When we hear a chord of three or four notes struck upon the piano, we realise that it is a chord, i.e., a percep- tion, and not a single tone, a sensation. But we realise, also, that the notes of the chord somehow fit together, belong to one another, form a single impression. If we sound three or four neighbouring notes, we obtain a very different effect: the complex 'falls to pieces,' the notes seem mutually repellent. As compared with a single note, the chord is complex; as compared with a discord, it is a single impression.
But not even the note is a sensation, an unanalysable elementary process; it is a chord, composed of a number of tones. The strongest tone gives name and character to the note, but other, weaker tones are always present in it. To a trained ear there is as much difference between a note and a tone as to the untrained ear between a note and a chord or a chord and a discord.
It is clear from these instances that under certain cir- cumstances tone qualities can mix or blend together, their mixture giving rise to a single total impression, a single perception; while under other circumstances they remain separate, and are distinctly sensible in the complex impres- sion. In the note we have the highest degree of tonal fusion, as it is called: one of the constituent tones is so strongly predominant as to give its own quality to the whole assemblage. In the chord we have a less complete fusion. It is true that each of the component notes loses something of its qualitative distinctness, and that the chord is a single perception. But the hearer cannot doubt, as he can in the case of the note, that the perception is a complex of simple processes; with a little trouble he can distinguish these, the tones, in the total mass of sound. Lastly, in the discord we have the lowest degree of fusion, the refusal to blend: the component notes stand out side by side.
The note is known technically as the simple clang; the chord and discord as compotmd clangs.
The strongest tone in the note is termed the * fundamental.' The other, weaker tones are ' overtones.' When a violin string is plucked, it vibrates not only as a whole, but in sections as well: half, third, quarter, etc. The fundamental is the tone of the whole 178 Perception and Idea string; the overtones are the tones corresponding to the vibrations of the half-string, third-string, quarter-string, etc.^ What holds of the viohn string holds of any vibrating body: metal rod, mass of air, etc. We always have a fundamental tone and a series of overtones. As a general rule, the overtones be- come weaker, the farther they are removed from the fundamental: the vibration of the quarter-string gives rise to a weaker tone than the vibrations of the half-string and third-string. But the relative strength of the overtones is different in the case of different vibrat- ing bodies. Thus the air masses of the viola and clarionette vibrate in thirds, fifths, sevenths, etc., more strongly than in halves, quarters, sixths, etc.; the hammer strikes the piano string in such a way that the sixth overtone does not sound; the reed-pipes of an organ give a regular series of overtones, which decrease in intensity, in accord- ance with the general rule, from the lowest upwards. The note of each musical instrument thus has a peculiar character or colouring; 1 As the overtones correspond to the vibrations of the half, third, quarter, etc., of the vibrating body, their vibration rates will be twice, three times, four times, etc., that of the fundamental. If we represent the fundamental vibration rate by I, the overtones will have the vibration rates 2, 3, 4, 5, 6, etc.; if we represent it by 2, the overtones will form the series 4, 6, 8, 10, 12, etc.
The relation of the overtone to its fundamental must not be confused with the relation of the two tones composing a musical interval. The sixth over- tone, e.g., does not make with its fundamental the musical interval of the sixth. The notes of the musical scale are named a, b, c, d, c, f, g. The musical inter- vals are calculated by reference to these names. Thus a-c, b-d, d-f, e-g, f-a are all thirds: three notes are involved in the composition of each. So a-e, b-f, c-g, etc., are all fifths: five notes are involved in the composition of each one.
The vibration rates of the chief musical intervals form the following ratios: octave, 1:2; fifth, 2:3; fourth, 3:4; major sixth, 3:5; minor sixth, 5:8; major third, 4:5; minor third, 5:6; second, 8:9; major seventh, 8:15; minor seventh, 5: 9.
We can now state the relation of overtone to fundamental in terms of the musical intervals. The series, with i as fundamental, is: Fundamental and first overtone constitute an octave; fundamental and second overtone, an octave and a fifth; fundamental and third overtone, two octaves; fundamental and fourth overtone, two octaves and a major third; fundamental and fifth overtone, two octaves and a fifth, etc.
or, technically, the clangs of different instruments have different clang-tints.
It is a difference of clang-tint which differentiates the vowel sounds of the human voice. The larynx, the primitive musical instrument, is thus seen to be in reality a number of instruments: an ^-instrument, an ^-instrument, an //-instrument, etc. This fact accounts, in part, for the superiority of the voice over any string or wind instrument in the matter of expression. The viohn approaches nearest to the voice, since the violinist can vary the overtones of his instrument, within wide Hmits, by striking the strings at different points; and can thus evoke notes or chords of different clang-tint.
Method. — The analysis of a note into its constituent tones is most easily performed by the aid of a sonometer and a set of re- sonators, such as are used in the physical laboratories. The sono- meter is an instrument somewhat resembling a single-stringed vio- lin; and the resonators are bottles of glass or metal, each of which contains a mass of air whose vibration corresponds to a particular tone. The sonometer string is plucked, and its vibrations give rise to a clang. The resonators are applied to the ear in quick succession, during the sounding of the clang. All those whose peculiar tone is among the overtones of the clang send a loud sound into the ear: the others are silent.
If you have not these instruments, try the following experiment with a piano. The middle c of the scale contains in it a number of overtones, the loudest of which are the c^ and g' of the next octave, and the <r", g" and <?" of the octave above that. Sound one of these last notes softly by itself; and when you have it 'in your head,' strike the key of the middle c. You will be able, with a httle practice, to hear the overtone, which you have just Hstened to separately, ring out from the body of the clang.
Experiments upon compound clangs, chords and discords, are best made with a set of tuning-forks. Tuning-forks give pure tones; not clangs. If they are not available, you can again make use of a piano. Let an assistant strike the various musical ' inter- vals ' within the middle octave of the scale, in haphazard order. Record your judgment of the composition of each clang sounded, your judgment, i.e., as to whether it contain two notes or only i8o Perception and Idea one; and note further whether you decide promptly or hesitat- ingly. If you feel that it is impossible to judge impartially when you know that two notes will be given in each experiment, let the assistant intersperse the series of intervals with occasional single notes. In this way you will avoid the expectation error.
You will find that the interval of the octave {^c-c^) is most often taken to be a single note; less often the fifth {c-g); still less often the fourth {c-f); seldom the thirds and sixths {c-e, c-Ve, c-a, e-ka); never the second and sevenths (c-d, c-b, c-Vb^. The oetave shows the highest degree of fusion, the second and sevenths the lowest.
You can then go on to experiment with groups of three and four tuning-fork tones or piano notes, arranging these more com- plex clangs in the order of fusion, from the highest to the lowest degree. Or you can alter the intensity, either of all the compo- nent tones or notes, or of some one of them; and see whether the degree of fusion is changed by these changes of intensity.
Clangs are typical of qualitative ideas in general: of the ideas built up from sensations of smell and taste, of the qualitative com- plexes of pressure and temperature, of the mixtures of pressure with organic sensations (resistance, impact, etc.), and of the mixt- ures of colour and brightness; and they furnish the best illustra- tion of the way in which quahtative ideas are formed. For (i) we are or can be as familiar with the elementary component pro- cesses as we are with their mixture; whereas we never get colour apart from brightness, and only with difficulty get strain, articular pressure, etc., separate in experience; (2) the universal distribu- tion of musical instruments makes it possible for any one to examine them; and (3) they show all degrees of blending, from an almost unanalysable singleness of impression (the tuning-fork octave) to an unmistakable complexity (second or seventh).