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IS ELEMENTS OF A MUSICAL SOUND. [II. § 25.
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-