tions of quality, from the rasping scrape of the beginner up to the smooth and superb tone of a Joachim (or, as I ought rather to say, the Joachim). A precisely similar remark applies to wind instruments; the differences, for example, between firstrate and inferior playing on the hautbois, bassoon, horn, or trumpet, being perfectly obvious to every musical ear.

In the next chapter we will discuss the quality and essential mechanism of the principal musical instruments, among which the pianoforte will receive an amount of attention proportionate to its popularity and general use. We begin with the elementary tones of which all composite sounds are made

up.

CHAPTER V.

ON THE ESSENTIAL MECHANISM OF THE PRINCIPAL MUSICAL INSTRUMENTS, CONSIDERED IN REFERENCE TO QUALITY.

1. Sounds of tuning-forks.

48. When a vibrating tuning-fork is held to the ear, we perceive, beside the proper note of the fork, a shrill, ringing, and usually rather discordant, sound. If however the fork is mounted on its resonance-box, as in Fig. 24, p. 79, the fundamental tone is so much strengthened that the other is by comparison faint, and the sound heard may be regarded as practically a simple tone. It is characterised by extreme mildness, without a trace of anything which could be called harsh or piercing. As compared with a pianoforte note of the same pitch, the fork-tone is wanting in richness and vivacity, and produces an impression of greater depth, so that one is at first inclined to think the pianoforte note corresponding to it must be an octave lower than is actually the case. It follows

immediately from the general theory of the nature of quality, that simple tones can differ only in pitch and intensity. Accordingly, we find that tuningforks of the same pitch, mounted on resonance-boxes and set vibrating by a resined fiddle-bow, exhibit, however various their forms and sizes, differences of loudness only. When made to sound with equal intensity by suitable bowing, their tones are absolutely undistinguishable from each other.

2. Sounds of vibrating strings.

49. Sounding strings vibrate so rapidly that their movements cannot be followed directly by the eye. It will be well, therefore, that we should examine how the slower and more easily controllable vibrations of non-sounding strings are performed, before treating the proper subject of this section. Take a flexible caoutchouc tube, ten or fifteen feet long, and fasten its ends to two fixed objects, so that the tube is loosely stretched between them. The tube can be set in regular vibration by impressing a swaying movement upon it with the fingers near one extremity, in suitable time. According to the rapidity of the motion thus communicated, the tube will take up different forms of vibration. The simplest of these is shown in Fig. 26. A and B being its fixed extremities, the tube vibrates as a

whole, between the two extreme positions AaB and AbB.

The tube may also vibrate in the form shown in Fig. 27, where AabB and AcdB are its extreme positions.

Fig.27

B

A

In this instance the middle point of the tube, C, remains at rest, the loops on either side of it moving independently, as though the tube were fastened at C, as well as at A and B. For this reason the point C is called a node, from the Latin nodus, a knot.

Fig. 28 shows a form of vibration with two nodes,

Fig.28.

at C and D, dividing the distance AB into three equal parts. The portions of the tube AC, CD, DB vibrate independently of each other, forming what are called ventral segments. We may also obtain forms with three, four, five, &c., nodes, dividing the

tube into four, five, six, &c., equal ventral segments, respectively. The stiffness of very short portions of the tube alone imposes a limit on the subdividing process. Let us examine the mechanical causes to which these effects are due.

50. If we unfasten one end of the tube, and, holding it in the hand as in Fig. 29, raise a hump upon it, by moving the hand suddenly through a small

Fig. 29.

B

distance, the hump will run along the tube until it reaches its fixed extremity B; it will then be reflected and run back to A, where it will undergo a second reflection, and so on. At each reflection the hump will have its convexity reversed. Thus, if while travelling from A towards B its form was that of a, Fig. 30, on its return it will have the form b. After

reflection at A, it will resume its first form a, and so on. Now, instead of a single jerk, let the hand holding the free end execute a series of equal continuous