jLrrmsKal instrument consists essentially of a vibrating body v — plate, rod. string — and a resonance chamber; a tuning-fork on its resonance box offers a simple illustration. The complex- ity of the air-waves which it sends to the ear may be variously produced. The vibrating body may, like the piano string, be so constituted as to vibrate in halves, thirds, quarters, etc., at the same time that it vibrates as a whole. Or it may be forced into complex movements by the manner in which it is actuated; thus the violin string vibrates as a whole, but also zigzags back and forth as it is drawn forward by the bow and slips away again. Or, lastly, it may vibrate as a simple pendulum, and yet not impart a pendular movement to the air-particles; the metal tongue, for instance, vibrating in an opening which it almost fills, gives rise to extremely complicated motions of the surrounding air. When LIBRARY UNIVERSITY OF CALIFORM.
102 Audition all these possibilities are taken into account, it is not surprising that even relatively pure tones should be of rare occurrence.
The timbre of the compound tone is, in the main, the unana- lysed resultant of the tone-colours of its simple constituents. Bearing in mind the nature of these tone-colours, we have no difficulty in explaining the timbre of most musical instruments. , \A piano tone, for instance, necessarily sounds brighter — and therefore,, to the untrained ear, higher — than a- flute tona_Qf,the_ same pitch, because it contains a longer series of overtones. These are, of course, progressively higher than the fundamental; and high tones have a bright tone-colour. The full and rich tones of open organ-pipes, piano and French horn are due to the presence, at moderate intensity, of the first half-dozen partials. The harsh and penetrating tones of trumpet, bassoon, harmonium are due to the predominance of the higher overtones. The tone of the clarinet contains only the odd-numbered partials. Its nasal character must probably be ascribed to the presence ot beats (§ 26) and to the fact that the difference-tones (§ 27) produced by the partials do not coincide with the constituent simple tones.
If we extend the meaning of timbre to cover everything that helps us to distinguish the tones of the different musical instru- ments, we must further mention, in the first place, the different noises that accompany them. The scrape of the violin, the pluck r t)f the banjo, the thud of the piano, the sish of the wind instru- ■j fnents, are characteristic. So also is the manner in which the \ tones enter consciousness; the large brass instruments lumber into hearing, the flute glides in. Other criteria are pitch, inten- sity, variability, and mode of performance. An instrument that /moves in the ^-octave can hardly be anything else than a piccolo; an instrument that sounds at a certain loudness must be a trumpet. The oboe is distinguished by a peculiar delicacy of dynamic shading. Lastly, many instruments have peculiar features of melody or harmony, rhythm or modulation, so that they may be identified by the nature of their performance. We can hardly think of flute, harp, trumpet, without at the same time thinking § 26. Beats and Intermediate Tones 103 of the special way in which they are played, or the special use to which they are put in orchestral music. — It is sometimes said that tonal stimuli are periodic, noise stim- uli aperiodic movements of the air-particles. But, on the one hand, aperiodic vibrations may produce tonal sensations, as in the ' rising tone ' of the siren; and, on the other, a periodic vibration of short duration or a mixed medley of periodic vibrations may, as we have seen, produce noise. The air-shock ordinarily caused by an explosion is probably a periodic system of many, slightly different wave-numbers and of rapidly decreasing intensity; so that, from the physical point of view, the crack or roar is a mix- ture of incomplete compound tones. In the same way, the continuative noise is probably due to a very large number of vibra- tions, differing relatively little in periodicity but widely in dura- tion. Physically, that is, the hiss must be regarded as a mixture of compound tones, both complete and incomplete. This physi- cal likeness of noise and tone stimuli, which enables them to act upon the same sense organ in much the same way, accounts for the introspective difficulty of distinguishing the tonal and the noisy elements in many instances 'of auditory sensation.
§ 26. Beats and Intermediate Tones. — Tones are in- trinsically harmonious, as colours are intrinsically antago- nistic. It is this character of tonal sensations which, as we shall see later, has determined the choice of notes in the musical scale and the development of music as melody and harmony. In the meantime, we must take account of two sensory phenomena which result from the blending of tones: the production of beats and intermediate tones, and the production of what are called combinational tones. — If two tones of precisely the same pitch-number are heard at the same time, the resulting sensation differs from its constituents merely in the attribute of intensity. When the trains of air-waves are so timed that crest coin- 104 Audition cides with crest and valley with valley, it is stronger than the single tone; when the crests of the one train overlap the valleys of the other, it is weaker.
If, now, the one of the two simultaneously sounding tones is mistuned, so that its pitch-number is somewhat raised or lowered, the resulting tone is no longer smooth and continuous, but shows rhythmical fluctuations of in- tensity, which are known as beats. So long as the mis- tuning is slight, the beats are slow; the tone surges up to its maximal intensity and gradually subsides again. With increasing difference of the generating tones, the beats become quicker and quicker. At the same time they grow harder and less billowy, so that they may be com- pared to the rattle of a kettle-drum, or even to a rapid succession of hammer-strokes upon an anvil. As the pitch-numbers diverge still further, the separate beats give place to an unanalysable roughness, harshness or hoarse- ness, which with yet wider separation of the generators finally disappears.
The number of beats produced in the i sec. is always equal to the difference between the pitch-numbers of the generating tones. For suppose that we are listening to tones of ioo and 101 vs., and that the two trains of air-waves start in the same phase. At the end of the first half-second, the tone of 101 vs. will be exactly half a vibration in advance of the tone of ioo vs.: crest will coincide with valley, and the resulting tone will be weakened. At the end of the second half-second, the tone of 101 vs. will be exactly one complete vibration in advance of the other: crest will coincide with crest, and the resulting tone will be strengthened. We hear, therefore, one beat, one intensive fluctuation, in the i sec.; and 101 — ioo = i. The same rule will evidently hold for any other pair of generating tones.
Beats are easily distinguished and counted when they occur at § 26. Beats and Intermediate Tones 105 the rate of 3 or 4 in the 1 sec. They may be followed, by a practised ear, from a lower limit of 1 in 180 sec. to an upper limit of some 20 or 30 in the 1 sec. At this point, however, the com- plex is already becoming rough. The impression of roughness or harshness is more pronounced and more persistent in the high than in the low regions of the tonal scale. Thus, the tones CG, Gc, ce, eg, cldl, d1e1, dxe2 produce, all alike, 33 beats in the 1 sec.; but the roughness is increasingly marked as the pitch-numbers grow larger. Similarly, the transition from harshness to smooth- ness occurs in the great octave at about 40, in the four-accented octave only at about 400 beats in the 1 sec.
The surging beats which proceed from a very slight difference of pitch-number are heard as fluctuations of a single tone, whose pitch is indistinguishable from that of the generators. As the difference increases, the single beating tone may be recognised as an intermediate tone, which at first lies near the lower generator, and gradually rises in pitch until it approaches the upper. With a cer- tain amount of difference (in the once-accented octave, a difference of the musical interval of the major second), the two generating tones may be heard alongside of the inter- mediate tone. The upper generator now appears, with occasional intermissions, as a smooth and continuous tone: the intermediate tone, which carries the beats, begins to take on a noisy character: the lower generator, whose identity is somewhat obscured by the presence of differ- ence-tones (§ 27), is less stable than the upper, but seems in general to have little or no share in the production of the beats. Finally, after this stage has been passed, the intermediate beating tone loses its tonality, and we hear the two generators as separate tones, accompanied by a continuative noise, — the harshness or roughness men- tioned above.
io6 Audition io6 Audition The gross phenomena of beats may readily be demonstrated by means of tuning-forks, blown bottles, etc. To distinguish the generators above and below the beating intermediate tone is, however, by no means easy, and requires special practice. This intermediate tone, it may be remarked, is of physical origin } under certain conditions, the superposition of two pendular vibra- tions of nearly the same wave-number gives rise to a resultant vibration of intermediate wave-number.1 If compound tones are sounded together, beats may arise between their overtones. Under certain circumstances, the over- tones of a single compound tone may also beat with one another. Thus, in the case of the C of the harmonium, the partial tones from the seventh (Z;1) onwards are sufficiently near and sufficiently strong to produce sensible beats.
§ 27. Combinational Tones. — If we sound together two precisely similar tones from the upper region of the tonal scale, and slowly mistime the one without changing the other, we shall hear, according to the statements of the previous section, first a single smooth tone, then a surging, and presently a hammering tone. When the beats have reached a frequency of some 30 in the 1 sec, we hear ai? entirely new, very deep tone, whose pitch-number corre- sponds to the difference between the pitch-numbers of the two generators. If we term the upper generating tone //, and the lower /, we hear, in general, a third tone whose pitch-number is u — I. This is known as the first differ- ence tone, Dv Under favourable circumstances, a single pair of tones will give rise to no less than five difference tones, whose pitch-numbers correspond to the successive differences between the pitch-numbers of the lowest tones present in the complex. Thus, let u be a tone of 1328 and /a tone of 1024 vs. (c3). Then we have § 2J. Combinational Tones Fig. 16. Set of Quincke Tubes.
all of which may be rendered audible to the practised ear.
Difference tones may be demonstrated by means of high forks, Galton whistles, Quincke tubes, a double bicycle whistle, etc. To hear them, one must neglect the high tones of the instru- ments, and listen for some- thing lower and larger. Sometimes the difference tone seems to be diffused through the room, like the humming of a top; sometimes it seems to be a deep booming within the ear. A very striking demonstration may be given with two Galton whistles, the one of stationary and the other of varying pitch. Since a difference of a certain number of vs. means a much wider interval in the region of the difference tone than in that of the generators, a slight change of the whistle will produce a pro- nounced change in the difference tone, which accordingly sounds as the howling of the wind, or as the tone of a fog-siren. — To hear the whole series of difference tones requires special training.
The difference tone, unlike the intermediate tone of the preced- ing section, cannot be obtained by the superposition of pendular vibrations. It must, therefore, if it exists outside the ear at all, be set up by some secondary vibration of the sonorous body. Objective difference tones are, as a matter of fact, generated by instruments, like the harmonium, in which the two primary tones are produced by the same air-blast, and by certain forms of vibrat- ing membranes. The great majority of difference tones are, however, subjective, — ear tones and not air tones. They aw occasioned by the mechanism of the ear itself.
io8 Audition It is noteworthy that difference tones behave, in tonal complexes, precisely as their generators. A difference tone, that is, may beat with another difference tone or with a generating tone; and two difference tones, or a difference tone and a generating tone, may give rise to an intermediate tone and to new difference tones. So far as hearing is concerned, the difference tones are on an equality with the tones aroused by air-waves.
Difference tones have been known to science since the middle of the eighteenth century. In 1856, Helmholtz an- nounced the discov- ery of another kind of Fig. 17. R. Koenig's Apparatus for the Dem- combinational tone, onstration of Difference Tones. — Quel-...j. v gues Experiences <FAcousHq«e, 1882, 165. which he liatTied the summation tone; its pitch-number is // + /, the sum of the pitch-numbers of the two generators. The summation tone is faint, and diffi- cult to distinguish; indeed, many investigators have ques- tioned its existence. Recent observations seem, however, to leave little doubt that Helmholtz' statement is correct.
It has been suggested, in particular, that the summation tone is simply a difference tone of a higher order, generated by the first overtone of u and the first difference tone; for 211 — Dx = 2u — (»—/) = »+/. As, however, an objective summation tone is § 28. Theory of Audition 109 produced and produced only by those instruments which produce objective difference tones, it is clear that the physical conditions for the arousal of the two kinds of combinational tones are the same. And as the ear has shown itself able to originate difference tones, we may naturally suppose that it can also originate the summation tone. Moreover, the presence of the summation tone has been recorded under circumstances which seem to preclude the possi- bility of its generation by an overtone. Owing to its faintness, it is much less important, psychologically, than are the difference tones.
§28. Theory of Audition. — Sound-waves are received into the outer ear-passage, and impinge upon the tympanic membrane or drum-skin, which forms the boundary between the external and the middle ear.1 The vibrations of this membrane are transmitted by the auditory ossicles, with diminished amplitude of excursion but increased energy, to the oval window. Here they are transferred to the lymph with which the internal ear is filled.
The cochlea of the internal ear, with which, as the end- organ of hearing, we are here concerned, is a structure of great complexity. If we unroll it, we have a long inelastic tube, filled with water; both ends are closed, but the one end contains two windows, filled with elastic membranes, — the oval window above and the round window below. Between the windows lies a horizontal shelf or partition, which divides the tube into an upper and a lower half, and 1 The author uses, as ear-models, the Auzoux Oreille de ires grande dimension; the model numbered 4 b in the Benninghoven & Sommer series; a pair of very large models of the internal ear, from the Bock-Steger series (these seem not to have been advertised of late years, but are probably still procurable; they are excellent for purposes of demonstration); and Helm- holtz' model of the middle ear. Natural preparations of the temporal bone, and casts of these preparations (with enlarged models of the ossicles), may also be obtained. The Ludwig or Merk model of the organ of Corti is useful for a detailed demonstration.
no Audition no Audition which extends throughout almost its whole length. The partition, which we may conceive of as a long narrow rectangle, consists partly of bone and partly of membrane. The bone is widest at the windows and narrowest at the far end of the cochlea; the membrane forms a triangle with its apex at the windows. This triangular membrane, known as the basilar membrane, carries the hair-cells with which the fibres of the auditory nerve are connected, and which thus correspond to the rods and cones of the retina. Finally, the upper half of the tube is subdivided by a membranous cross-partition, stretched obliquely between the oval window and the hair-cells, as if to protect these from the direct impact of the waves set up by the push of the ossicles.
We have seen that the ear is an analyser, that it is able to split up a compound wave-motion into simple pendular vibrations, or to resolve a compound tone into simple partial tones. According to the theory of Helmholtz, this analysis is performed by the basilar membrane. Histolo- gists tell us that the membrane is composed, in essentials, of a large number of cross-fibres — variously estimated at 13400 to 24000 — which range in length from 0.041 to 0.49 mm., a ratio of 1:12. The fibres represent a system of stretched strings, like those of a harp or a piano, and will accordingly respond by vibration to the wave-movements to which they are tuned. Suppose, then, that a wave- motion of a certain frequency is set up at the oval window. The motion is transmitted, through the membranous cross- partition, to the basilar membrane. A certain basilar fibre (the fibre whose natural period of vibration is the same as that of the incoming wave) is set vibrating; this vibratory movement is imparted to the hairs of the cells which rest § 28. Theory of Audition in upon the fibre; and the agitation of the hairs acts as stimulus to the fibrils of the auditory nerve. The wave- motion, having thus done its work upon the basilar mem- brane, spends itself at the round window, and the whole system comes to rest again.
The Helmholtz theory regards the fibres of the basilar mem- brane as resonators, and is therefore known as the. resonance theory of audition. Just as the strings of a piano respond selectively when a tone is sung into the instrument, so do the basilar fibres vibrate in sympathy with the wave-motion which corresponds to their natural period of vibration. The tuning of the fibres and their selective response to stimulus must not, how- ever, be thought of as absolute. Neighbouring basilar fibres differ but little in length, and are closely bound together. Hence we must suppose that, if a simple pendular vibration is set up at the oval window, it is not a single fibre but rather a narrow strip of the basilar membrane which falls into sympathetic vibration. The sensation of simple tone results from the agitation of the hairs of a little group or field of hair cells.
To account for the sensation of noise, we need only assume that a broader strip, or perhaps that several broad strips of the basilar membrane at the same time are thrown into brief vibration. The compound tone will be produced by the simultaneous vibration, at different amplitudes, of a number of narrow strips, each one of which, if it vibrated alone, would give us the sensation of a simple tone.
To account for beats, we must suppose that the strips set in motion by the two generating tones partially overlap. So long as the generators are near together, we hear only a single tone, — the intermediate tone, due to the superposition of the primary vibra- tions. The portions of the strips which do not overlap are so small that they cannot vibrate independently and give rise to independent tonal sensations. The beating of the intermediate tone results from the interference of the different oscillatory motions impressed upon the fibres. As the generators diverge, we > 112 Audition hear them sounding smoothly above and below the beating inter- mediate tone. It is now only a comparatively small portion of the vibrating strips that overlaps; so that the major portions on either side vibrate singly, each in its proper period, and con- sequently arouse each its proper sensation of tone.
Helmholtz himself explained combinational tones as due to the movements of the drum-skin and ossicles. Attempts have since been made to derive them from the vibration of the basilar fibres; but recent investigation seems to show that Helmholtz may have been right, and that these tones may take their physical origin in the middle ear.
There is nothing in audition that is analogous to colour blindness in vision. On the other hand, the resonance theory receives strong support from pathology. Cases are known in which, while the outer and middle ears are intact, the range of hearing is greatly reduced: all that is left of the tonal scale is a tonal ' island,' extending perhaps over a couple of octaves, perhaps only over two adjacent semitones. Other cases occur in which the range of hearing is normal, but the tonal scale is not continuous; there are tonal 'gaps,' large or small, — parts of the scale where the patient is completely deaf to tonal stimuli, though he can perfectly well hear the tones above and below. Both of these defects of hearing point to the existence, in the internal ear, of a series of end-organs that are separately stimulable by tones of different pitch-number; and end-organs of this sort are provided by the basilar fibres and the hair-cells which they support.
The principal objection urged against the Helmholtz theory is that the basilar fibres are too minutely small to serve as resonators, especially for the tones of the lower region of the scale. To this the reply is made that they are loaded, by the arches of Corti and the adjacent cells, and that their frequency of vibration is thus very considerably reduced. We cannot at present say either that the objection is fatal to the theory or that the reply is convincing in its favour. No other theory has, however, been proposed which covers so wide a range of facts or explains these facts so satis- factorily as the resonance theory.
References for Further Reading 113 References for Further Reading §§ 23-28. A general summary of facts and theories is given by K. L. Schaefer, professor of physiology at Berlin, in NagePs Handbuch, iii., 1905, 476 ff. More detailed treatment of the subject will be found in the Tonpsychologie of C. Stumpf, professor of philosophy at Berlin. On the character of auditory sensations at large, see i., 1883, §§ 10, 11; ii., 1890, § 28: on tone-colour and timbre, ii., § 28: on beats, ii., § 27: on combinational tones, ii., 243 ff., and other passages cited in the index. Another classical work is Helmholtz' On the Sensations of Tone, translated by A. J. Ellis, 1895. Parts i. and ii. deal with the subject-matter of these sections; the author's theory is worked out on pp. 128 ff., 158. — Consult also A. Barth, Zur Lehre von den Tonen und Gerauscken, in Zeitschrift f. Ohrenheilkunde, xvii., 1887, 81; art. Hearing, in Baldwin's Diet., i., 1901, 443 ff.; W.Wundt, Physiologische Psychologies ii., 1902, 63 ff., 370.
It has been known for some time that the vowel-sounds of the human voice owe their timbre, not to a regular series of overtones, but to cer- tain concomitant tones, whose pitch remains relatively constant what- ever the fundamental may be upon which the vowel is spoken or sung. These tones, called by L. Hermann 'formants,1 apparently represent the proper tones of the buccal resonance chambers; they are usually inharmonic both to the fundamental and to one another; and they may attain to a high degree of intensity. Recent investigations, now, seem to show that the timbre of the wind instruments may also be due to the presence of formants: "instead of a characteristic series of harmonics, it seems that each instrument possesses rather a characteristic tone or tones...of constant pitch for all notes of its scale " (D. C. Miller, Science, N. S., xxix., 1909, 171; cf. R. Wachsmuth und G. Meissner, Arch. f. d. gesatn/nte Physiologie, cxvi., 1907, 543; E. Herrmann-Goldap, Annalen d. Physifc, xxiii., 1907, 979). If this result is confirmed, the account given of timbre in § 25 must be correspondingly modified. Negative results have, however, been obtained by W. Kdhler, Aknstische Untersuchungen, in Zeits.f. Psych., liv., 1909, 241 ff.
SMELL SMELL § 29. Sight and Hearing: Taste and Smell. — If you were asked to make out a list of the senses, you would probably begin with sight and hearing. These two seem, naturally, to go together: they are the ' higher ' as con- trasted with all the other, ' lower ' senses. The word ' higher ' may then mean one of two things: that the sense-organs, eye and ear, have attained to the highest degree of biological development; or that the sensations derived from them are put to the highest intellectual pur- poses. The second meaning is, perhaps, that which is the more familiar to common sense. Sight and hearing have an obvious twofold value to the organism: a commercial value, as the vehicle of communication, of written and spoken language; and a cultural value, as the vehicle of the fine arts, painting and sculpture, literature and music.
From this point of view, the bracketing together of sight and hearing is both natural and right: only, of course, while we talk in terms of common sense, we must think in terms of parallelism. On the other hand, it is worth while to remember that, psychologically, the differences between the two senses are very great. Visual sensations form a manifold of three dimensions; sensations of tone, a manifold of two dimensions. Colour mixtures appear themselves as simple sensations, while mixtures of tones are analysable into their constituents. Again, there is no § 29. Sight and Hearing: Taste and Smell 1 1 5 such thing as tonal contrast, or a negative after-image of tone. The phenomenon of beats has been compared to that of flicker; but there is nothing in vision that resem- bles the combinational tones. And when we turn from description to explanation, we find that_antagonism is the keynote of visual, and _syinpathetic re^onance_the^key_note ofau^itoiy_theory. — Wemay sum up these differences between sight and hearing, in a single word, by saying that_the: formeris~a~cTiermrcin a mechanical sense.
sense.
Next after sight and hearing, in a list of the senses, stand taste and smell. These, too, seem to go together as a matter of course. Psychologically, indeed, they have good right to go together. Both alike are chemical senses, and the two groups of sensations are intimately connected in experience: so intimately, that in everyday life we are constantly attributing to taste what really belongs to smell. Most meats and vegetables are taste- less.
I_f__you hold your nose, you cannot _dis tin guish a bit of apple from ra^vpoJatoJ_pj^yine^a£_Jrojn_da^eX A cold in the head does not affect taste, as we ordinarily suppose; what really happens is that the accumulation of mucus in the nose cuts off the sense of smell. It is clear that such gross confusion would not be possible unless the qualities of taste and smell were very much alike: nobody would confuse a colour with a tone! As a matter of fact, it may well be doubted if the scent of lavender and the taste of sugar do not stand, psychologically, nearer together than the taste of sugar and the taste of quinine.
On the biological side, also, the senses of taste and smell are closely related. Both of them, though in slightly dif- ferent ways, stand guard over the great function of nutri- *ll6 Smell y tion, inviting the organism to what is wholesome and warning it of what is deleterious.
The sense of smell is of peculiar interest: partly on account of the problems which it sets to psychology, and which — as we shall see in the following sections — are still very far from solution; partly on account of the role that it has played in the course of organic evolution. Far back in the history of life, among the reptiles, the cortex appears as little more than an annex to the organ of smell. As development proceeded, the sense retained its importance as the servant of nutrition and reproduction: we know, for instance, how largely it bulks in the mental life of the carnivorous mammals. It is, however, essentially a land-sense: the mammals which live wholly or partially in the water — whale, dolphin, seal — possess a very rudimentary organ of smell, and are probably without smell sensations. The sense-organs in fishes which have been described as organs of smell differ in structure from the corresponding organs of land animals, and apparently furnish sensations, not of smell, but of something akin to taste. It is also a ground-sense: birds have, in general, very obtuse smell; and our own disregard of smell sensations is largely due to our assumption of the upright position.