MATHEMATICS OF MUSIC—INSTRUCTIONS TO MY DAUGHTER FOR PLAYING ON THE
HARMONIC GUITAR."`
THE titlepage of this work led us to expect something above an in- struction-book for the Guitar; but we were not prepared to find a treatise displaying, an intimate knowledge oft he mat heretics dies of music, and still less to find that knowledge imparted in language so lucid and " Priestley," our author observes, " is understood to have said, ' I wanted to know something of Electricity, so I wrote a hook:' This course may not always be for the advantage of the reader; but all books that are not mere compilations, are in reality studies upon such a plan. That what follows was begun without acquaintance on the subject beyond having heard of the ex.• istence of musical proportions, cannot, it is true, make anything good that is not so. But it may be a reason why anything useful that is found in it should he received with allowances by the adepts, and rather be illustrated by their improvements than condemned by a reference to its defects. The writer's being himself but a student, was favourable to clearness. It obliged him to say, like Funtenelle, En e.erirant, ai tajoers t:ielle de neentendre. if he should; be told that the subject after all is a trifling one, he would reply, that nothing is little, which throws light on what is wonderfully made, and that whoever has estimated human pursuits in the complex ratio of the labour and the reward, will admit, that any man may have found more unthankful occupations than trying to tune his daughter's guitar."
Of all the subjects connected with music, the science of acoustics is the most difficult, and at first view, the most repulsive. The mathe- matician sees its beauty, and delieditain disentangling its labyrinths: but to the practical musician, that principles on which his art is 'founded are most commonly unknown, and seldom mentioned but with de- rision. He is accustomed to refer every thin, connected with music to his ear, and will tell you that he can tune his violin without the assistance of mathematics. And it is true, that if his ear will not be a sure guide to him, no treatise in the world will supply its place. Nevertheless, the theory of musical sounds, like other branches of mathematical science, is so beautiful in all its parts, so perfect in its symmetry, so satisfactory in its results, that any attempt to present it in an accessible form to musical students is a service conferred upon the art. The treatises of SMITH, HOLDER, KEEBLE, and TURNER, will scarcely attract the readers of the present day ; and however great their excellence, they want that which is so preeminently pos- sessed by the present work—the art of imparting instruction in a re- gular, systematic, intelligible form ab incipio. Nor ought we to omit noticing, that the price of this treatise is such as to place it within the reach of everybody : it forms a complete contrast to another book of instructions that we were lately called on to notice—we never saw so much information conveyed at so small a price.
On one chapter of the book—that of temperament—we are tempted to offer a few remarks.
* Instructions to my -Daughter for Playing on the Harmonic Guitar ; being on at- tempt to effect the execution of Correct Harmony, on principles analagous to those of the ancient Enharmonic. By a Member of ,the University of Cambridge. (Name in the Preface, T. Perronet Thompson, Queen's Cull.) Goulding and D'Altuaine. " Temperament is a barbarous invention for saving trouble by playing out of tune ; for playing in many keys, by playing in no key at all ;—for trying how much discordance the ear can be induced to bear, instead of how much harmony it can be accustomed to demand. If men have not musical instru- ments that will play in tune in a variety of keys, they should he content to play in one, or else improve their instruments. But they ought not to play out of tune and call it music.'
" If it is urged that the differences are small,—the answer is, that it is upon small differences that all excellence depends ; and that the differences are quite sufficient to make the distinction between what strikes the hearers as perfectly harmonious, and what dues not. There are nations that think statues with fingers of equal length are admirable performances, and contemn the difference as small. Tee tenth of an inch may in sonic senses be called small ; but if the question is of the smoothness of a mirror, or the edge of a cutting instrument, it is a mountain.—But it is nut true that the differences ace small. As a rough statement, if what is called a whole note on the piano- forte is divided into nine parts, then three, tour, five, or six of these parts are represented on the instrument by one and the same sound ; the difference of the extremes being as great or greater than the true difference between a note and its sharp or flat.. It is probable that few of those who say the dif- ferences are small, ever suspected they were anything like this. " Should it be replied, that if people are pleased as they are, it is no charity to make them discontented,—the same argument would apply to the lingers of the statue, and to all kinds of improvement. A child is delighted with a hand-organ, and struck with a sense of sublimity from the paintings of an exhibition of wild beasts ; and it may be doubted whether any of its impres- sions in after life are stronger or so strong as these early ones. But it does not follow, that men ought always to be content with such music or such painting, or that it should be a point of economy to husband their progress in perceiving its detects. Nature seems to be in a plot, to force man to be progressive; to oblige him to he continually forgettino-° what he has left behind, and pressing forward to that which is before. It is the salt of the earth ; and there is no more use in quarrelling with the fact, than in reproving grown gentlemen for liking claret and forswearing sugar-candy. " A sophism advanced in favour of temperalomt, is, that the different keys have peculiar qualities in consequence of it ;—that one key is lively, another grave, &c., in consequence of the differences arising out of temperament, or in other words from the keys, or sonic of them, being more or less out of tune. The misetke has probably arisen from confounding the characters of the Major and Minor series, with same supposed quality of the key in which they are found written. As it is easier to play in a moderate number of sharps or fiats than in a great one, the keys which on tempered instruments are made to have the nearest approach to being in tune, arc naturally those which present a moderate number of either. I fence, as the Minor series has always three more fiats, or three fewer sharps, than the Major, the tendency will be for airs in the Major series to be played in a number of sharps, and in the Miner, of lists. And from this the hearers arc led to say how plaintive are the keys with flats, and how lively the others. For it
is observable that their opinion always ?lows in this direction ; and that no- hody is found attributing a lively character to a multitude of fiats, or a plain- tive one to sharps. But in all this there is not an atom of proof, that the particular merits of any key come by being out of tune. It is easy to imagine that either the liveliness of the Major series, or the plaintiveness of the Minor, will be increased by being perfectly in tune ; and if any keys on the organ or pianoforte possess peculiar power in either of these expressions, the I robability is, that being in tune is the cause. Rut that improvement of any kind is to be effected by being out of tune, is certainly nut to be believed without proof."
The whole of this reasoning is founded upon the assumption that the temperament of dilllo-ent keys in common use is a fault. To the eye of the matimmatieian, it is unquestionably, nay demonstrably so. He will prove it to you, by principles, the abstract truth of which you must admit ; and hence lie treats such a deviation from mathematical correetness as an ine.eifection not to be tolerated. We admit his pre- mises, as mathematicians, and assent: to his cmclusion : but: speaking Os practical musicians, we regard this very imperfection as a beauty. We have not specie now to enter into an elaborate inquiry how it is that even instrumeets which are capable of perfect tune, as well as voices, do, in point of awl, give a different temperament 10 diff.Tant keys. Per- haps the most natural solution of the question is, that singers being usually taught by keyed instruments, aequire the habit of accommo- dating their temperament to an imperfect scale, and carry this imper- fection into general use. They insensibly learn to affix to each separate key its own distinctive character; and they impart that character to it whether singing alone, or to file accompaniment of a piano-forte. Our author calls this " a barbarous invention ; " and, like a true ma- thematician, refuses to believe it to be otherwise " without proof." We have conceded that the " proof" which he requires is not to be had; but we cannot consent to abandon the charm which arises from this barbarism, because on ;r.:ir it is a demonstrable imperfection. Still less can WC advocate the ;tit emotive which lie suggests--viz. that instrtunents should be rendered perfect in one key, from which they should never wander. In this case we must allow our ears to decide, rather than our eyes. Take, for instance, the divine air " Bide me from day's garish eye," and will any one contend that a change of its key into one in which the temperament was different would be an im- provement ? Or will it be asserted that the triumphant and cheerful expression of " From mighty kings" does not suffer by having its key transposed into that of A It. We have frequently heard the expe- riment tried ; and the air lets uniformly suffered by the change. Why should not one key mosses a character of plaintive sweetness, and another of brilliant animation ? To the eye it may be proved to be wrong, but the ear will refuse its assent to the demonstration. Notwithstanding this difference between us—which we merely indi cate, without discussine. it—we repeat, that We bear our sincere testi- mony to the general excellence of the kat ritrawm to my Daughter. If musical students will give the work their patient and close atten-
tion, they will assuredly " find their information usefully extended, upon what are apt to be considered as abstruse and unapproachable branches of the history of musical sounds."
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