§ 9. INTENSIVE IDEAS.



1. A combination of sensations in which every element is connected with every other element in exactly the same way is called an intensive idea. Thus for example, a compound clang made up of the tones d, f and a is such an intensive idea. For the immediate perception each of the partial combinations into which this compound clang can be resolved, as df, da, or fd, fa, or ad, af, are all quite equivalent, in whatever order they are considered. We may, accordingly, define intensive ideas, as combinations of sensational elements, in which the order of the elements may be indefinitely varied.

It follows from their nature, that intensive ideas do not have any characteristics arising from the way in which their elements are united, by means of which they can be resolved into separate parts. Such a resolution is possible only through differences in the constituent elements themselves. Thus, we discriminate the elements of the compound clang d f a, only because we hear in it the qualitatively different tones d, f and a. Still, the separate components in such a unitary idea are less clearly distinguishable than in their isolated state. This relative suppression of the elements which is of great importance in all processes of perception, we call in general the fusion of sensations, and in particular, for intensive ideas, intensive fusion. If the connection of one element with others is so close that the single element can be perceived as a part of the whole only through unusual concentration of the attention aided by experimental variation of the conditions, we call the fusion complete. If, on the other hand, the elements are immediately recognized in their proper qualities, and merely recede somewhat into the background in comparison with the impression of the whole, we call the fusion incomplete. If certain particular elements are more prominent in their characteristic qualities than others, we call them the predominating elements. The concept of fusion as here defined is a purely psychological concept which must be assigned to its appropriate place among the processes of association to be discussed later (§ 16, 4).

In reality, every intensive idea always enters into certain spatial and temporal combinations. Thus, for example, a compound clang is always a process having a certain duration, and is at the same time localized by us in some direction or other, though often only very indefinitely. But since these temporal and spatial attributes can be indefinitely varied, while the intensive character of the idea remains the same, we may abstract from space and time in investigating the intensive attributes.

2. Among ideas of the general sense we have intensive fusions in the form of combinations of sensations of pressure with those of heat or cold, or in the form of combinations of pain sensations with those of temperature or pressure. All these fusions are incomplete, and very often there is no decidedly predominating element. The combinations of certain sensations of smell and taste are more intimate. This is obviously favored on the physiological side by the proximity of the sense-organs, and on the physical side by the uniform connection between certain stimulations of the two senses. In such cases the more intense sensations are generally the predominating elements, and when these are the sensations of taste, the composite impression is usually regarded as a taste quality only. Thus, most of the impressions known in ordinary life as "tastes", are in reality combinations of tastes and smells.

The greatest variety of intensive ideas, in all possible gradations of complexity, is presented by the sense of hearing. The relatively most simple of these ideas and those which are most closely related to simple tones, are the single clangs. As more complex forms, we have compound clangs. Complex noises may arise from compound clangs when these are united with sensations of simple noises, and also under certain other circumstances.

3. A single clang is an intensive idea which is made up of a series of tonal sensations regularly graded in quality. These elements, the partial tones of the clang, form a complete fusion, in which the sensation of the lowest partial tone becomes the predominating element. The pitch of the clang is determined by this principal tone. The other elements are higher and are, accordingly, called overtones. The overtones are all grouped together under the name clang-color which is thus recognized as a second determinant of the clang, added to the predominating tone. All the partial tones that go to determine the clang-color are placed along the tonal line at certain regular intervals from the principal tone. The complete series of possible overtones in a clang consists of the first octave of the principal tone, the fifth of this octave, the second octave of the principal tone and the major third and the fifth of this second octave, etc. This series corresponds to the following proportions between the number of objective tonal waves:

1 (principal tone), 2, 3, 4, 5, 6, 7, 8, .... (overtones).
 
 
When the pitch of the principal tone remains constant, only the second determinant of the tonal quality, the clang-color, can vary according to the number, position, and relative intensity of the overtones. In this way we can explain the great variety of clang-colors in musical instruments, as well as the fact that for every instrument the clang-color changes somewhat with the pitch; for in the case of low tones the overtones are generally relatively strong, in the case of high tones relatively weak, while they disappear entirely when they are too high to be audible.

From a psychological point of view the chief condition for the rise of a single clang, is the complete, or approximately complete, fusion of several tonal sensations with only one predominating element. As a rule, it is impossible to distinguish with the unaided ear the overtones in a clang. They can be made perceptible by the use of resonators which are tuned to the overtones sought, and are thus able to strengthen them through resonant reinforcement. After they have been isolated in this experimental way the stronger overtones can be successively heard in the clang if the attention is directed to them, even without the aid of the resonators. There is a direct correspondence between the complex psychological character of a single clang and the complex physical characteristics of the vibrations which produce the clang. The sensation produced by a simple tone is aroused by a simple regular oscillation such as is represented in Fig. 9, A. The clang has a certain number of additional overtones, which give it a distinctive timbre, and is produced by vibrations of a complex form such as are exhibited in Fig. 9, B and C. Every such complex form of vibration is capable of analysis into simple forms of oscillation, among which the stronger oscillation corresponds to the fundamental and the weaker single vibrations to the overtones of the clang. The experience produced by the clang is in its unity and also in its complexity a subjective parallel of the objective vibration form. The simplicity of the experience corresponds to the unit of the physical process, while the discrimination between the various tone elements corresponds to the possibility of a geometrical analysis of the resultant vibration into simpler elementary vibrations.

4. There are three conditions which must be fulfilled if one element is to be the predominating element in a tonal fusion. First, one tone must be relatively more intense. Second, in its qualitative relations to the other partial tones, the principal tone must be the fundamental of a series whose members are all harmonious. Third, all the partial tones must be sounded at exactly the same time. This coincidence in time is objectively guaranteed by deriving the clang from a unitary source, (that is, producing the clang through the vibrations of one string, one reed-pipe, etc.). A failure to comply with the first condition does not essentially interfere with the experience of a single clang. If, on the other hand, the second condition is not fulfilled the combination becomes a compound clang when the predominating fundamental is wanting, or it becomes a noise when the series of tones is not harmonious, or finally, it becomes a mixed form, between a clang and a noise when both parts of the condition are unfulfilled. If the third condition is not met the single clang may again pass into a compound clang. A series of simple clangs from a number of independent tuning-forks which should unite to form a single clang so far as intensity and quality are concerned, always produces in reality the experience of a compound clang.

5. A compound clang is an intensive combination of single clangs. It is, accordingly, an incomplete fusion with several predominating elements. There are, as a rule, all possible grades of fusion in a compound clang, especially when it is made up of single clangs of composite quality. In such a case, not only does every single clang form a complete fusion in itself, but these single clangs fuse the more completely with one another the more their fundamentals approach the relation of elements of a single clang. So it comes that in a compound clang made up of single clangs rich in overtones, those components whose fundamentals correspond to the overtones of some other single clang in the compound, fuse more completely with the related clang than with others. The other clangs, in turn, fuse the more completely the more their relation approaches that of the first members of a series of overtones. Thus, in the compound clang c e g c' the clangs c and c' form a nearly complete fusion, while the fusions of the clangs c and g, c and e, are incomplete. Still less complete is the fusion between c and eb . A determination of the degree of fusion may be obtained in all these cases by allowing an observer to hear the compound clang for a very brief interval, after which he is to decide whether he perceived only one clang or several. This experiment is repeated many times, and the relative number of judgments in favor of the unity of the clang is a measure for the degree of fusion.

6. Besides the elements contained in the single clangs of a compound, there always arise from the combination of vibrations in the auditory organ, additional elements which cause new tonal sensations, characteristic of the different kinds of compound clangs. These may also fuse more or less completely with the original clang. They are sensations of difference-tones; they correspond, as their name indicates, to the difference between the number of vibrations in two primary tones. Some of these tones are due to the interference of sound waves in the air, outside of the ear (objective difference-tones). Such tones can be reinforced by inserting in the ear open tubes which are tuned to the tone in question and are known as resonators. Other difference-tones arise within the ear itself, either through the interference of the sound waves in the organs of the outer ear, especially in the tympanic membrane and in the chain of ossicles, or else through interferences in the inner ear. This second class of difference-tones (subjective difference-tones) can not be reinforced by using resonators. Through the presence of these difference-tones compound clangs become very complex psychical compounds, for such difference-tones may result not merely from the interference of the primary tones of the complex clang, but also from the interference of overtones. It is even possible for the difference-tones to interfere with each other, or with the primary tones. To distinguish these various classes of difference-tones they are designated as difference-tones of the first order, second order, third order, etc. The strongest of these difference-tones are those which result from the interference of the primary tones and then follow in general those which are lower in pitch than the primaries 1). The fusion of the difference-tones with the primary tones of the compound clang is the more complete the weaker the difference-tones, and the more nearly they correspond to tones which are harmonious with the original elements of the clang. The difference-tones are, accordingly, as a result of these characteristics, to be compared in respect to their importance for the compound clang as a whole, with overtones in their relation to simple clangs. The fact that in certain interval relations (octave, fifth, and fourth) the difference-tones disappear in part and in part coincide, explains the greater unity which is an important characteristic of consonant complex clangs.

7. A compound clang may pass through all possible intermediate stages into a third form of intensive auditory experiences, namely, experiences of noise. When two tones are no longer included within a series of harmonious tones and when at the same time the difference between the number of their vibrations does not exceed certain limits (for higher tones about sixty vibrations and for lower thirty or even fewer) there arise interruptions in the compound clang, which correspond in number to the difference between the number of vibrations in the primary tones. These interruptions are due to the alternating coincidence of like (Fig. 10, a, b) and opposite phases (Fig. 10, m) of vibration. When the vibrations are of like phase they reinforce each other, when they are in opposite phases they counteract each other. Interruptions of the clang sensations equal in number to the difference between the rates of vibration of the primary tones are called beats when they consist merely in successive weakenings and reinforcements of the clang. When, on the other hand, full breaks appear in the clang, a result which appears most frequently in the case of low tones, we speak of tonal beats. If the differences in the number of vibrations exceed the numbers mentioned, the tones are at first heard as continuous, for the interruptions disappear, but they are harsh. Later the harshness disappears and we have pure dissonance. As a rule beats resulting from the interference of difference-tones are perceived as combined with this impression of roughness and pure dissonance. Ordinary dissonance is, accordingly, made up in a very complex manner, of beats, of roughness from the combined tones, and of pure dissonance. In this complex the various pitches are distinguished only in a very uncertain degree, because of the diffuse form of the tonal excitation. If the elements of dissonance, that is, if beats, tonal beats, and roughness, are combined in sufficiently great numbers through the simultaneous sounding of a great number of tones, the whole complex becomes ultimately a noise. On the psychological side this means that the predominating tonal elements disappear entirely or become mere modifying elements in the total experience. In the case of noises which last for a short interval only, the general pitch of the most intensive elements is determinative for our perception. In the case of noises which last longer, the form of the disturbance resulting from the rapidity of the beats, from the accompanying tonal beats, etc., also has an influence.
 
 

1) In addition to difference-tones there may arise also, as helmholtz has shown, under similar conditions of interference summation-tones, the number of vibrations in which corresponds to the sum of the number of vibrations in the two primaries. The general term combination-tones is used to cover both the difference-tones and the summation-tones. The summation-tones are in general very weak and coincide, for the most part, with the overtones. They have therefore no essential significance in the perception of clangs.

Human articulations are characteristic examples of different forms of noise. The vowels are intermediate between clangs and noises with predominantly clang character; the resonants are noises of long duration, and the proper consonants, noises of short duration. In whispers the vowels become simply noises. The fact that the differences in vowels are perfectly distinct in whispers, goes to prove that the character of vowels depends essentially on their noise elements.

7a. The process of "fusion" occurs here, in the case of intensive tonal fusion, under the simplest possible conditions. We shall come upon fusions of a somewhat different form when we take up spatial and temporal ideas. In the case of tonal fusions the compound resulting from the fusion process differs relatively less from a simple addition of its elements, than do the extensive fusions. The general characteristics which distinguish an intensive tonal fusion from a mere sum of the single tones which enter into the fusion, are three in number. First, many or all (as for example in many noises) of the elements sink into insignificance as compared with the total impression of the whole compound. Second, there is a union of all the elements into a single unitary idea with a unitary affective value, as may be seen with especial clearness in harmonious chords. Third, and finally, certain dominating elements stand out above the others, as for example, the fundamental tone in a single clang. The first and second characteristics are constant, the third is variable. In the case of complex clangs the third characteristic is less noticeable than in the case of single clangs, and in the case of noises it is entirely absent. Furthermore, it will be noted that all of these characteristics are psychological, so that the concept fusion is also a psychological concept. And since like, or analogous, phenomena appear whenever we find psychological elements combining with each other, there is no reason for seeking to find in these characteristics anything except an expression of a certain regular form of psychological action. Some investigators have strayed from the simple empirical facts in their use of the concept "tonal fusion", and have regarded the synthesis of the elements into a fusion-product as a logical act added to the sum of the sensory elements — as a kind of judgment of unity. Some have even sought to find a physiological ground for this judgment of unity in some kind of physical processes of fusion in an hypothetical organ in the brain. (stumpf.) In opposition to this view it is to be recognized most clearly that tonal fusions present themselves as examples of elementary psychical processes of fusion which include no judgment whatsoever. The incorrect logical theory obviously arises from the confusion of logical reflections about psychical experiences with the experiences themselves — a form of confusion which is so frequently, even to-day, carried over from popular psychology into scientific psychology (p. 14). The assumption of a nervous organ of fusion is obviously a resort to a purely artificial hypothesis made up for the occasion.

The resonance hypothesis formulated by helmholtz (sec p. 42 and 56) was the first which attempted to give any account of one of the most important of the phenomena which appear in tonal fusions, namely the synthesis into a single clang experience of all the elementary tonal sensations into which a clang may be separated even in its objective nature. It is assumed that certain parts of the auditory organ are so tuned that tonal waves of a given rate always set in sympathetic vibration only the part correspondingly tuned. This explains in a general way the analyzing ability of the auditory sense.

There are certain difficulties which confront this hypothesis because of the existence of so-called subjective difference-tones. These can arise, however, through the existence of certain vibrations which are produced in parts of the ear capable of taking up certain additional vibrations from the primary tone. The assumption of helmholtz that the organs of the middle ear, (tympanic membrane and chain of ossicles), are the vibrating parts which explain these difference-tones can no longer be accepted, for it has been observed by the aurists that difference-tones are perceived by patients in whom these organs of the middle ear are destroyed, (dennert), and also by the fact that sometimes difference-tones may exceed in intensity the primary tones (hermann). These objections to the theory can be overcome if the resonance hypothesis is modified in such a way as to explain the reception of the stimulations which give rise to difference-tones, (and possibly also beats), not by organs which lie in front of the resonance apparatus (in the internal meatus), but behind it (in the cochlea). It may be assumed that the axis of the cochlea is set into direct vibration or is set into vibrations by the basilar membrane, and that these induced vibrations are carried over to the auditory fibers which pass through the fine canals in the bone. This additional hypothesis can, of course, be worked out only when the assumption of strict specific energy of the single auditory fibers is given up as well as the assumption that auditory fibers are aroused to action only through the vibrations of the basilar membrane. It has never been possible to explain the phenomena of clang analysis with the same degree of completeness by means of any of the theories of hearing which have not accepted the resonance hypothesis. There is nothing, however, in the fact that the resonance hypothesis has proved itself up to this time indispensable, which could stand in the way of an effort to supplement the hypothesis in the manner described.

For a treatment of the attributes of the complex feelings which arise with complex clangs (feelings of harmony and discord) see § 12, 9.
 
 

References. Helmholtz, (English trans. by A. J. Ellis) The Sensations of Tone, Pt. I and II. Stumpf, Tonpsychologie, vol. 2. K. L. Schaefer in Nagel's Handbuch der Physiol., vol. 3, pt. 2. Wundt, Grundz., 5th ed., vol. II, Chaps. 10 and 12; Lectures, lecture 5. On tonal Fusion: Lipps, Grundtatsachen des Seelenlebens, chapter 21; Zeitschr. f. Psych., vol. 19. Stumpf, Zeitschr. f. Psych., vol. 15; Beitrage zur Akustik und Musikwissenschaft, Nos. 1—3. R. Schulze, Phil. Stud., vol. 14. On Difference-tones and Beats: R. König, Poggendorff's Ann. der Physik, vols. 157 and 158. Hermann, Pflüger's Archiv, vol. 49 Schäfer, Pflüger's Archiv, vols. 78 and 83. Krüger, Phil. Stud., vols. 16 and 17; Archiv f. Psychol., vols. 1 and 2. Dennert, Arch. f. Ohrenheilkunde, vol. 24. Attempts to develop new theories of Hearing: Hermann, Pflüger's Archiv, vol. 56. Ewald, Pflüger's Archiv, 76.