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CHAPTER IX.

Harmony of Notes-Consonance and Dissonance-Production of Beats -Dissonance to be attributed to the existence of Beats-Influence of Harmonics upon Harmony-Resultant Tones-Chords-Noises.

IN music we not only enjoy the impression produced by a succession of melodious tones, but also experience great pleasure from an agreeable combination of several' tones. We are best able to judge of the sensation produced if only two notes are sounded together. The pleasant combinations of tones are termed 'consonance,' and the unpleasant dissonance.'

An octave, c, and c', will be consonant. Also a fifth, c and g, and the third, c and e, is also called consonant. If, however, we strike two approximate notes on the piano, as c and d, or two which are still nearer, as c and c sharp, they produce a distinct feeling of an unpleasant sound, which we, therefore, call dissonant. Although there are other intervals which are dissonant besides that between two approximate notes, we will first proceed to examine the approximate notes more closely.

If two tones are dissonant which are separated by the interval of a tone or a semitone, we must suppose that the sensation of dissonance would be increased if the

difference between the pitch of the two notes were still further diminished. This is, in fact, the case. By means of two tuning-forks, which differ but little from each other, we can produce a combination of tones, which will be in the highest degree dissonant. Now, disregarding the æsthetic impression, we make the acoustic observation that the note is produced by separate shocks, which are less frequent the nearer the tones are together. These shocks are called beats.

Two approximate tones may be observed to beat with one another in all musical instruments, but most clearly in those in which the pitch of the tone can be easily altered. If we sound the same tone in two open organ pipes, the tone of one may be slightly lowered, by covering part of the upper opening with the hand. The tones will immediately begin to beat, at first slowly, but increasing in velocity as the hand is advanced. If the beats become still quicker, a buzzing, whirring sound is produced. This may be observed upon the piano when two deep tones at the interval of 'a semitone are struck together.

These beats are no subjective phenomena, but really interfere with, or weaken the tone. They are caused by interference of the sound-waves.

By interference of the waves is meant the coincidence of the elevations of one series of waves with the depressions of the other. Whenever this happens the motion. of each is arrested, for every depression is filled up by an elevation, and the elevations levelled by the depressions. These interferences may be observed in a tuningfork, by holding it close to the ear and turning it round on its longitudinal axis. The tone is most intense when

it is held upright, with the two prongs in a straight line with the ear. As soon as the tuning-fork is turned through 45° the tone becomes weaker, but, upon being turned further, again increases in strength. Thus in one revolution the tone is weakened in four symmetrical positions. A series of waves proceeds from each prong which to a certain extent interfere with each other. The prongs vibrate in such a manner, that they both move simultaneously either outwards or inwards. They, therefore, impart to the surrounding air a motion in opposite directions, for when they both vibrate inwards they throw the particles of air, with which they come in contact, against each other, and when they vibrate outwards the particles of air move in the opposite direction.

There is, therefore, one position of the two prongs with regard to the ear, in which an interference of the two series of waves is distinctly perceptible.

If, instead of two perfectly similar series of waves, we have two with unequal periods of vibration, but still very nearly equal, interference will again take place. Let us suppose the first two elevations of a wave to begin at the same time, then the second elevation of the tone, the vibrations of which are slower, will commence a little later, the third twice, and the fourth three times as late, and so on. At length the lower tone will be the length of a whole elevation behind the other, and we shall now have reached a moment when the elevation of one wave will coincide with the depression of the other, and an interference is the result. But this condition is not constant; the waves of the higher tone hasten onwards, so that another moment is soon reached when the elevations of both waves coincide, and the tone is strengthened.

The result of this is, the tone is alternately strengthened and weakened.

The nearer the tones are together, the slower will be the beats, because it will take longer for the higher tone to get an entire elevation in advance of the lower. The greater the interval the more rapid will be the beats, and when the tones are removed a certain distance from each other, the beats will be imperceptible to our ear.

Helmholtz has attributed the cause of dissonance to the existence of beats. The rapid changes in the strength of the tone produced by beats make an unpleasant impression upon the ear, just as the flickering of a light is so extremely troublesome to the eye. When the two tones are very near together, we are conscious of the cause of the unpleasant sensation, because we perceive the beats separately. But at the interval of a semitone or of a whole tone, when we can no longer perceive the beats separately, their presence is only recognised by a feeling of dissonance. Helmholtz shows that the note possesses a certain amount of roughness which is produced by the beats.

The unpleasantness in this sensation may be attributed to a perception common to all the regions of nervous activity. Every intermittent excitement of a sensitive nerve-fibre is more tiring than a continuous one. The flickering of a light is so unpleasant because, between every two luminous excitements, the retina increases in sensitiveness, and will be more strongly affected by each excitement. If, on the contrary, the light is continuous, the sensitiveness of the retina becomes gradually blunted, and will be less excited with its duration. In coming out of the dark into a bright light,

we are for a moment quite blinded, because the excitement is here very strong; by the gradual decrease of the excitement the eye becomes accustomed to the light. Flickering may, therefore, be compared to a rapidly repeated transition from darkness to light, and therefore powerfully excites the eye.

The case seems to be the same with the ear, or rather with the auditory nerve. Dissonance is an interrupted note, which excites the ear to an unpleasant degree. A refined musical ear will be extremely sensitive to this excitement, just as the flickering of a light is much more unpleasant to the eye of a sensitive, educated man, than it is to the uneducated.

From the comparison of colours and musical sounds it has become general in cominon conversation to speak of a harmony in colours, and, therefore, a discordant arrangement of colours has been compared to dissonance. From the stand-point of natural science this comparison is very imperfect. Two discordant colours, such as green and blue, are unpleasant to us because they weaken rather than strengthen each other by both strongly irritating, and therefore fatiguing, the same kind of nerve fibres, whilst yellow and blue appear harmonious because the fibres sensitive to yellow remain at rest while we are looking at the blue colour, and vice versa. The common physiological point of comparison between discordant musical sounds and colours therefore consists in the fatiguing of the sensory nerve, which, however, is accomplished in different ways, through an intermittent irritation in the case of the auditory nerve, and in the case of the optic nerve by the irritation being concentrated on a certain kind of nerve.

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