“Fond as you are of music, my dear Louisa, I am not surprised at the wish you have just expressed to become acquainted with the nature of musical sounds; I shall, therefore, endeavour to convey, in as simple a manner as possible, the theory which has been proposed for their explanation. I think you will immediately perceive that, if the aërial waves which I have endeavoured to describe, should be irregular, or run into each other, there must arise a confusion of sounds; thus _discords_ may be readily imagined to be produced whenever a second vibration shall commence before the first is finished, so as to meet it half-way on its return, and interrupt it in its course. In like manner may we conceive the general nature of those arrangements upon which _unison_ and _concord_ depend: where the vibrations are performed in equal times, the same tone is produced by both, and they are said to be _in unison_; but _concord_, as you well know, is not confined to unison, for two different tones harmonize in a variety of cases. If, for example the particles of one sonorous body vibrate in double the time of another, the second vibration of the latter will strike the ear at the same instant as the first vibration of the former; and this is the ‘concord of an _octave_.’ When the vibrations are as 2 to 3, the coincidence will be at every third vibration of the quickest, which, therefore, is the next degree of perfection, and is called a ‘_diapente_,’ or ‘fifth;’ while the vibration of 3 to 4 will produce the ‘_diatessaron_,’ or ‘fourth;’ but this, and the next which follow in order, are not so agreeable to the judicious ear, and are therefore called ‘_imperfect concords_.’” Louisa here enquired whether the difference in the acuteness of a sound did not depend upon the nature of the vibrations; and her father, in reply, stated that it depended entirely upon the degree of quickness with which the vibrations were performed: the slower the vibration, the graver the tone; the quicker, the more acute.[55] “But, if I strike any one note of the instrument repeatedly, whether quickly or slowly, it always gives the same tone,” observed Louisa. “To understand that fact,” replied her father, “you must remember that the vibrations of bodies are regulated by laws very similar to those of the pendulum; consequently the duration of the vibrations of strings or chords depends upon their length, and thickness; for if two strings of equal magnitude, but with their lengths as 2 to 1, be equally stretched, their vibrations will be in the same ratio; therefore the shortest will make two vibrations, while the longest makes one: but the vibrations of the same string will always be the same whether it be struck quickly or slowly, upon the principle of the _isochronous_ property of the pendulum, already described.”