ing the same fundamental tone, are given in the following enumeration : Two at a time: (1, 2), (1, 3), (1, 4), (1, 5), (1, 6). Total 5. Three at a time: (1, 2, 3), (1, 2, 4), (1, 2, 5), (1, 2, 6), (1, 3, 4), (1, 3, 5), (1, 3, 6), (1, 4, 5), (1, 4, 6), (1, 5, 6). Total 10. Four at a time: (1, 2, 3, 4), (1, 2, 3, 5), (1, 2, 3, 6), (1, 2, 4, 5), (1, 2, 4, 6), (1, 2, 5, 6), (1, 3, 4, 5), (1, 3, 4, 6), (1, 3, 5, 6), (1, 4, 5, 6). Total 10. Five at a time: (1, 2, 3. 4, 5), (1, 2, 3, 4, 6), (1, 2, 3, 5, 6), Total 5. Six at a time: Total 1. (1, 2, 3, 4, 5, 6). The whole number of groups is 31, or if we allow the fundamental-tone (1) to count by itself as a sound of separate quality, 32. Let us next examine how many clangs of different quality can be obtained from a single combination of three fixed partial-tones by variations of intensity only, supposing that each tone is capable of but two degrees of loudness. Representing one of these by ƒ, and the other by p, we indicate, e.g., by (ƒ, p, p) a clang in which the fundamental tone is sounded forte, and the two overtones piano. The different cases which present themselves are the following: (p,ƒ, ƒ), (p, p, ƒ), (ƒ,ƒ, p), (ƒ, ƒ,ƒ), (ƒ, p, ƒ), (p, p, p) or seven in all, since (p, p, p) has the same quality as (f,f,f). The number of cases increases very rapidly as we take more partial-tones together. Thus a clang of four tones will produce 15 sounds of different quality; one of five tones 31; one of six tones 63; by variations of intensity only. Altogether we could form, with six partial-tones, each susceptible of only two different degrees of intensity, upwards of four hundred clangs of distinct quality, all having the same fundamental tone. The supposition above made utterly understates, however, the possible variety of quality dependent only on changes of relative intensity. A very slight increase or diminution of loudness, on the part of a single constituent tone, is enough to produce a sensible change of quality in the clang. We should be still far below the mark if we allowed each partial-tone four different degrees of intensity, though even this supposition would bring us more than eight thousand separate cases. Since many more variations of intensity are practically efficacious, and also since the disposable partial-tones need by no means be limited to the first six, the above calculation will probably suffice to convince the reader that the varieties of quality which the theory we are engaged upon is capable of accounting for are almost indefinitely numerous. This is, in fact, no more than we have a right to demand of the theory, when we reflect on the fine shades of quality which the ear is able to distinguish. No two instruments of the same class are exactly alike in this respect. For instance, grand pianofortes by Broadwood and by Erard exhibit unmistakable differences, which we describe as 'Broadwood tone' and 'Erard tone.' Less marked, but still perfectly recognisable, differences exist between individual instruments of the same class and maker, and even between consecutive notes of the same instrument. To these we have to add the variations in quality due to the manner in which the performer handles his instrument. On the pianoforte the kinds of tone elicited by a dull slamming touch, and by a lively elastic one, are clearly distinguishable. With other instruments such distinctions are much more marked. On the violin we perceive endless gradations of quality, from the rasping scrape of the beginner up to the smooth and superb tone of a Joachim. A precisely similar remark applies to wind instruments; the differences, for example, between first-rate 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 simple tones of which all composite sounds are made up. 298849A CHAPTER V. ON THE ESSENTIAL MECHANISM OF THE PRINCIPAL MUSICAL INSTRUMENTS CONSIDERED IN REFERENCE TO QUALITY. 48. When a vibrating tuning-fork is held to the ear, we at once perceive, beside the proper note of the fork, a shrill, ringing and usually rather discordant, sound due to overtones which do not follow the series of such tones set out in § 43. If, however, the fork is mounted on its resonance-box, as in Fig. 24, p. 85, its proper note is so much strengthened that the extraneous sound is by comparison insignificant. Provided the fork be but moderately excited, e.g. by gentle stroking with a resined bow, the sound heard is practically' a simple tone. It is characterised by extreme mildness, without a trace 1 Except with very gentle bowing, however, or unless the fork's note has been allowed to grow faint, examination with resonators shows traces of overtones belonging to the ordinary series. |