“As I now understand how sound is produced and carried to a distance, I should much like to learn the cause of different tones,” said Louisa.
“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.”
“Upon my word, Mr. Seymour,” cried Mr. Twaddleton, “you are getting out of your depth; pray let us take leave of this subject, for I am quite sure that my young friends have already received more than they can carry away.”
“I submit, my good sir; and in return for my compliance,” said Mr. Seymour, “use your influence over Miss Villers, and induce her to favour us with a practical illustration of our subject upon the piano-forte.”
“Most cheerfully; but my intercession is quite unnecessary, for I am sure that our fair friend is no disciple of Tigellius.”[[56]]
“I am ever ready, sir, to comply with the wishes of those I respect. I consider the caprice which our sex too often displays upon these occasions, as not only a breach of good manners, but an evidence of unpardonable vanity.”
“Pray, Miss Villers, may I be allowed to ask whether you have ever directed your enquiries into the nature of ancient music? it must have been very superior to that of modern ages,” said Mr. Twaddleton.