even within a single syllable; if it ceases so to vary, it assumes a musical character, witness the epithet sing-song' then commonly applied to it. We may then define a musical sound as a steady sound, a non-musical sound as an unsteady sound. It is true we may often be puzzled to say whether a particular sound is musical or not: this arises, however, from no defect in our definition, but from the fact that such sounds consist of two elements, musical and non-musical, of which the latter may be the more powerful, and therefore absorb our attention until it is specially directed to the former. For instance, a beginner on the violin often produces a sound in which the irregular scratching of the bow predominates over the regular tone of the string. In bad flute-playing an unsteady hissing sound accompanies the naturally sweet tone of the instrument, and may easily surpass it in intensity. In the tones of the more imperfect musical instruments, such as drums and cymbals, the non-musical element is very prominent, while in such sounds as the hammering of metals, or the roar of a water-fall, we may be able to recognise only a trace of the musical element, all but extinguished by its boisterous companion. We have seen that Sound reaches our ears by means of vibrations executed by the particles of the atmosphere. It has also been shown that steadiness is the characteristic feature of musical, as distinguished from non-musical, sounds. We We may infer hence that the motion of the air corresponding to a single musical sound will be itself steady, i.e. that equal numbers of equal vibrations will be executed in precisely equal times. This conception of the physical conditions under which musical sounds are produced will suffice for the present. We proceed to consider in detail the various ways in which such sounds may differ from each other, and to investigate the mechanical cause to which each such difference is to be referred. In what follows, by the word 'sound' will always be meant 'musical sound,' unless the contrary be expressly stated. CHAPTER II. ON LOUDNESS AND PITCH. 24. A musical sound may vary in three different respects. Let a note be played, first by a single violin, then, by two, by three, and so on, until we have all the violins of an orchestra in unison upon it. This is a variation of loudness only. Next let a succession of notes be played on any instrument of uniform power, such as the harmonium without the expression-stop, or on the principal manual of an organ, only one combination of stops being in either case used. Here we have a variation of pitch only. Lastly, let one and the same note be successively struck on a number of pianofortes of the same size, but by different makers. The sounds heard will all have exactly the same pitch, and about the same degree of loudness; nevertheless they will exhibit decided differences of character. The tone of one instrument will be rich and full, of another ringing and metallic, that of a third will be described as 'wiry,' of a fourth as 'tinkling,' and so on. Sounds thus related to each other are said to vary in quality only. The instances just considered have the advantage of simplicity, since they allow of changes in loudness, pitch and quality being exhibited separately. They are, however, less striking than other cases where sounds vary in two, or in all three, of these respects at the same time. A practised ear may be requisite to detect the difference between the tones of two pianofortes, but no one is in danger of mistaking, for instance, a flute for a trumpet. There is here, no doubt, considerable difference of loudness as well as of quality, but let the more powerful instrument be placed at such a distance that it sounds no louder than the weaker one, and the distinction between the two kinds of tone will be still quite decisive. Two assigned musical sounds may differ from each other in loudness or pitch or quality, and agree in the other two or they may differ in any two of these, and agree in the third-or they may differ in all three. There is, however, no other respect in which they can differ, and accordingly we know all about a musical sound as soon as we know its loudness, its pitch and its quality. These three elements determine the sound, just as the lengths of the three sides of a triangle determine the triangle. 25. The loudness of a musical sound depends entirely, as we shall easily see, on the extent of vibratory movement performed by individual par ticles composing the conveying medium. A soundproducing instrument can be readily observed to be in a state of rapid tremor. The vibrations of a tuning-fork are recognisable by the eye in the fuzzy, half-transparent, rim which surrounds its prongs after it has been struck; and by the touch, if we place a finger gently against one of the prongs. The harder we hit the fork the louder is its sound, and the larger, estimated by both the above modes of observation, are its vibrations. The experiment may be tried equally well on any pianoforte whose construction allows the wires to be uncovered. It is natural to infer that a vibration on the part of a sound-producing instrument communicates to the particles of the air in contact with it a corresponding movement. Thus a sound of given loudness is conveyed by vibrations of given extent, and, if the sound increases or diminishes in intensity, the extent of the vibrations which carry it must increase or diminish correspondingly. We conclude, then, that the loudness of a musical sound depends solely on the extent of excursion of the particles which constitute the conveying medium in the neighbourhood of our ears. This limitation is clearly essential, since a sound grows more and more feeble the greater our distance from the point where it is produced. This diminution of intensity |