fibres of the ear were employed in hearing each separate series of vibrations, then, in order to distinguish between two or more series conveyed to the ear together, it would be requisite to imagine that the nervous organ of the ear should keep separate the different series of uniform pulses, yet without hearing separately the separate pulses of each series. This difficulty is removed by supposing an appropriation of separate nerve fibres to separate series of pulses, that is, to separate pitches; which is in fact to refer the work of distinguishing pitches to the structure instead of to the function of the organ. The phenomenon of distinguishing differently pitched sounds is as follows: when two or more sounds are heard together, the ear has distinct perceptions varying distinctly according as their respective periods of vibration vary. If these are the same, no difference of pitch is heard; if one is double of the other, we hear the octave; if one is four times the other, the second octave; when they are as three to two, the fifth; as four to three, the fourth; and so on. These distinct perceptions of the relation between sounds of different pitch, perceptions which are invariable whatever may be the intensity of the sounds, or whatever their quality, show that there is some definite relation between the form and the matter of every single sound, though it is a relation which is not perceived in the perception of the sound itself, the duration of it being unanalysed in perception; but still a relation which makes it capable of definite comparison with other single sounds in point of pitch. The accurate perception of pitch is the first requisite for what is called an ear for music. According as the periods of vibration of two notes more

BOOK I.
CH. II.
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§ 11. Hearing.

BOOK I.
CH. II.
PART I.

§ 11. Hearing.

or less accurately coincide, the two notes together are a concord or a discord. Two discordant notes have comparatively few vibrations which coincide, or the beats of which occur at the same instant; concordant notes are those the beats of which coincide frequently, so that the two series of pulses can proceed together without disturbing each other, while the difference between the times of their other beats makes them distinguishable as notes of different pitch. The accurate perception by the ear of these differences of pitch, and the concords and discords which they produce, is a perception caused by differences in the formal element, the time or duration of the sounds, while its object, or the perception itself, is a mode of the material element, the feeling of sound; since it is only different compositions and arrangements of the periods of vibration which make differences of pitch. Pitch in short is nothing but an infinitesimal elaboration or articulation of sound into time portions. The perception of pitch, of concord, and of discord, is therefore an intellectual perception, since intellect is distinguished from feeling only by the greater predominance of the formal element in consciousness; and the pleasure and pain arising from these perceptions are pleasure and pain of admiration, not of enjoyment.

6. The third mode is that of quality, colour of sound, Klangfarbe. It is perhaps the greatest service of Prof. Helmholtz that he has shown the origin of this from the partial tones which are heard together with their ground tone in almost every musical sound which is heard. When these harmonic notes, as they are called, are by artificial means prevented from coming to the ear, the sound heard, that of the

ground tone alone, is comparatively characterless, and the same from whatever instrument it may arise. The vowel sounds of the human voice give the colour to the sounds uttered; and in this respect the organs of voice are of precisely similar nature to other musical instruments, only of a very perfect construction, admitting of far greater variability in the colour. The difference between musical instruments consists in the difference of colour which they produce, and the range or power which they have in producing variations within that colour. The colour of sound corresponds to the specific quality in other senses, to the different odours in smell, sapours in taste, and so on; but, as already remarked, these specific qualities of sound excel those of the other senses in this, that they depend upon and have their roots in differences of pitch, an intellectual sensation, since it is only from the composition of differently pitched sounds, in the harmonic notes, that the colours of musical sound arise. The colours of unmusical sounds, grating, rolling, hissing, rustling and so on, depending as they do upon vibrations so irregular as to be incapable of distinct measurement, correspond more accurately to the specific qualities of the senses of touch, taste, and smell; and it is only because, in hearing and sight, a domain of regular or periodic sensations, involving or containing a minute elaboration of the formal element, is added to the domain of their less regular sensations, which they have in common with the other senses, that hearing and sight are the source of pleasures and pains of admiration, and of the æsthetic perceptions of the fine arts.

7. The perception of pitch depends on a minute

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§ 11.

Hearing.

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§ 11.

Hearing.

analysis of sound, by the nerve organism of the ear, that of colour upon a synthesis of various pitches heard together; in both cases the ear is unconscious of what it is doing, perceiving only the result, the pitch in one case, the colour in the other. Yet the synthesis which results in colour is less abstruse than the analysis which results in pitch; by attention the ear can be brought to perceive the harmonic notes, out of the combination of which with the ground note the colour has arisen; whereas no attention will enable us to perceive the separate moments of sound which together produce a perceived pitch; these are entirely below consciousness, and the pitch itself is the first and only thing heard. For, if the ear heard the separate beats in the periodic vibrations which determine the pitch, and composed the pitch out of them as heard pulses, we ought by an effort of attention to be able to hear the several beats in one pitch, just as we are to hear the harmonies which compose the colour. This attentive perception however destroys the pleasure of perceiving colour. The combination must be perceived unanalysed, in order to the pleasurable effect of colour on the ear. This gives the colour a less intellectual character than the pitch; for greater differences are combined together, the act of combination being equally unperceived. Yet the different pitches which are combined into colour give the possibility of an intellectual measurement when two colours are heard together, the ground tones of which may be either concordant or discordant with each other. This gives a second kind of harmony, founded on the comparison of colours, in addition to that founded on the comparison of pitches. Notes of the same pitch have different har

monics in different instruments; and thus, harmony

of pitch being laid at the basis, colour harmony arises within or upon it, having its pleasure dependent upon more complicated relations of form and matter.

§ 12. 1. The sense of sight remains to be examined. It is in several ways the most perfect of the senses; the pleasure and pain peculiar to it are perhaps less intense than in any other sense, as those of hearing are less than those of touch, those of touch than those of taste and smell, and these than the pleasures and pains of the systemic sensations. Again it is in sight first that we come to single words as names for single specific sensations, the names of colours, whereas in other senses descriptive phrases or letters of the alphabet are used for this purpose; the reason of which is, that sight contains the element of space more clearly than any other sense, and, though it does not contribute more than touch to the perception of space in three dimensions, yet contributes far more than touch to the interpretation of the perceptions common to both. (See this whole subject discussed in Mr. Abbott's Sight and Touch, especially Chap. iii.) We judge of almost everything by its visible marks: they are the signs by which we interpret it, as to its size, its distance, its shape, as well as its colour; and the visible marks of everything are that to which we chiefly attach our associations of its inner or moral qualities, according to which its effects will be. Sight then is the most closely allied to space; and space is the form which, as already remarked in the § on hearing, serves as the logic of all phenomena whatever, in virtue of its completeness and the complexity of its three dimen

sions.

BOOK I. CH. II. PART I.

§ 12.

Sight.