‘Dr. Ayrton was an excellent musician, of which his compositions for the church bear indubitable evidence[62]. The performance of these has been chiefly confined to the Royal Chapel, but the publication of them, which has long been expected, would usefully augment the musical resources of our various choirs, and add greatly to the reputation of their author.’ (Dictionary of Musicians.)
HARMONICS OF THE VIOLIN.
IN the Westminster Review for last January, is an article, under the above title, which, judging from its clearness and simplicity, we are inclined to believe must have proceeded from the very able pen of the critic who recently reviewed in that work the scientific and clever treatise on the Enharmonic Guitar[63].
The author, wishing to render the doctrine of harmonics comprehensible to persons of all capacities, has imitated, in a very felicitous manner, the style of a writer who, whatever opinion may be entertained of him in other respects, allowedly has the art of making himself understood by every one, however difficult or intricate the matter on which he treats; and in a letter written as if from Mr. Cobbett to his son, has given an intelligibility to the subject which it never before received, insomuch that we are tempted to exceed the limits of a quotation, and, for the benefit of such of our readers as do not see the Westminster Review, borrow more largely from the pages of that very able periodical than is usual, hoping that the liberal spirit of its proprietors will not accuse us of piracy, and summon us into the awful presence of the Keeper of the King’s Conscience.
‘The whole theory or principle of finding and producing the harmonic notes is in reality very simple, and such as might be communicated to any intelligent child in two or three short lessons. If the author of the Political Register had been born and bred a professional musician, (as among the possible freaks of fortune why should he not?) he would have set the hope of his family before him, and said,
‘My dear little Son,
‘You are to get your bread by playing on the violin. It will therefore be exceedingly useful to you to know all that can be known about the harmonic notes; by which means you may not only get your bread, but be able to secure its being well buttered also. A violin-player is worth a great deal more when he knows all about the harmonic notes; and in fact, since the appearance of Paganini, the chances are, that a player who does not know it will be worth nothing at all.
‘Do you know what an aliquot part is? I am sure you do not. If you have a cake or an apple, and divide it equally among your companions, whether they be two, three, four, or any other number, then the thing is said to be divided into aliquot parts,—“aliquot” being a word in the old Latin language meaning “some certain number or other,” and implying here that the thing is divided into equal parts of “some certain number or other.” But if you were to divide it among the same so that their shares should not be all alike,—or if you were to give each an equal piece, but there should be a piece left after all which was not equal to one of the pieces you had given away, but was greater or less,—then the thing would be divided into parts, but not into aliquot parts. Now then, my dear little son, you know what is meant by dividing a string into aliquot parts.
‘Tell me now, how you would begin to show me the different places in which a string can be divided into aliquot parts. You would first show me the middle point, which divides it into two equal parts. Then you would divide the string, with your eye or with a pair of compasses, into three equal parts, and show me the two points of division between them. Next you would divide it in the same way into four equal parts, and show me the three points of division. And so on, for five, six, seven, eight, and as many more as you liked to continue. These, then, you would say,—both those I have made and those I might make if I liked—are the points that divide the string into aliquot parts. And if you pleased, you might mark them by writing under each point of division the figure which shows how many equal parts the string is divided into,—as for instance a 2 under the point where the string is divided into two, a 3 under each of the points which divide it into three, and so on. And indeed it will be better that you should do this; for then you cannot help observing, that sometimes more figures than one will fall on the same place—as for instance when the string is divided into four, one of the marks 4 will fall on the same place as the division into 2; when it is divided into six, one of the marks 6 will fall on the same place that was previously marked 2, and two more on places that were marked 3; and so on. All of which will be wanted another time.