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.
‘Now if you touch the string gently with the finger at the distance of any aliquot part from the bridge, (mind I said from the bridge, not at any of the divisions into aliquot parts, but at the distance of one of them from the bridge,) and at the same time pull the string or draw the bow across between this point and the bridge, you will see a curious thing. The string will divide itself into all the aliquot parts of which the point touched by the finger makes one,—into two, or into three, or into four, as the case may be,—and every one of them will move by itself, as if it was a little string held fast at the two ends; the sound produced being the same that would be made by pressing the string down to the neck at the point touched, in the common way. If the divisions are few, as two or three, this may be seen distinctly enough by the eye: but where this is not the case, it may be shown to be the fact by laying a little bit of paper on the string while it is sounded; and if this is laid on any of the points of division into aliquot parts, whether on the one nearest the bridge or any of its fellows, it will lie still and not be thrown off, but if it is laid anywhere else, it will be thrown off directly, which shows that the points of division are at rest, and the others are not.
‘If you want to know how or why this curious thing takes place, I will tell you as nearly as I can; but remember I do not pledge myself that this is the reason, but only that I think it very likely to be the reason, and this principally because I know no other way in which it can be brought about. And this way is, that when one portion of the string is moving in one direction, as for instance from me towards you, the next portion of the string is moving at the same time in the contrary direction, or from you to me; and so with the other portions, whatever their number may be. In this manner it seems possible that the points of division should be kept at rest, and in any other manner it seems to be not possible; and therefore, since the fact is before us that the points of division remain at rest, I conclude that it is in this way it takes place. This is what the feelosofers would call a syllogism. And because this sort of balance can only be kept up by the portions of the string moving backwards and forwards (which the same sort of people call vibrating) in equal times or with equal quickness, and this again cannot take place unless the moving portions of the string are of equal length,—it follows that this sort of motion in parts or portions of the string can only take place when those parts or portions are of equal length, which seems to be the reason why the experiment will only answer when the point touched is one that divides the string into aliquot parts.
‘But this is not all; for there is a more curious thing still. And that is, that if you touch the string at any other of the points of division into aliquot parts, (by which I mean any other than the point of division nearest to the bridge,) the string will divide itself in the self-same way,—always with the exception (now mind the exception) of the cases in which the point touched falls in with a point in some simpler mode of division that has gone before. For instance, you remember observing, that when the string was divided into four equal parts, one of the points marked 4 fell on the same place as the division into 2. Touching the string therefore in this place must make the same sound it did before; which is a different sound from that which it makes when touched at the other two points of division into 4. And in like manner in other cases. But when this agreement with some simpler mode of division does not interfere, all the points of division on being touched produce the same sound. For example, if the division be into five equal parts, inasmuch as none of these will coincide with any of the simpler modes of division, there must be four points in the string, any one of which being touched will produce the same harmonic sound.
‘But if you want to know how and why this still more curious thing takes place, I can only tell you in a roundabout sort of way as before. If you divide the string, for example, into five equal parts, and touch any of the four points of division you choose, you check and finally prevent the continuance of any motion at the point touched, though at the same time it would appear that the touching (which, to make the experiment answer, must be very light) is not enough to hinder the shaking, or, as the learned people call it, the vibration, given at one end, from being communicated past the point of touch. If, instead of touching the string lightly, you were to lay hold of it with a pair of pincers, then the experiment would fail altogether; the reason of which may be concluded to be, because the motion is presented from being at all communicated beyond the point laid hold of. In fact the art,—for there is an art in everything, from scraping the grains off a cob of Indian corn to sounding a musical string, whatever the difference in importance and dignity of the two things may be,—appears to consist in touching the string in such a manner, and with such a degree of pressure, as shall allow the motion given by pulling or bowing to be communicated past the finger, and yet shall check and finally prevent the continuance of all motion, or, as it was called before, vibration, that is not consistent with the point which is touched remaining at rest. Now if you consider carefully, you will see that the only way in which motion can go on and this point remain at rest, is by the string’s dividing itself into the five equal portions, the movements of which shall balance each other as before described. It does not indeed follow, that because the motion could go on no other way, it must necessarily go on in this; but we have the evidence of the fact that it does go on in this; and the knowledge of the reasons why it could not go on in any other is at all events very useful to make us remember what the effect is that is produced, and how.
‘The next thing is to be able to tell what all the sounds thus produced are. Now you remember that when you were a very little boy, I showed you, that if you stop a string by pressing it down hard in the middle you produce its Octave; where the two sounds (of the original string and its half) are such sounds as are produced by a man and a child when they sing the same tune together, but in very different pitches of voice;—that if, instead of shortening the string in this manner by the half, you shorten it by a third part, you produce the sound which musicians have called the Fifth; if you shorten it by a fourth part, you produce the Fourth; if by the fifth part, the Major Third; if by the sixth part, the Minor Third; with a great deal more which it is not necessary to mention now;—and I told you, too, that the intervals from one of these sounds to another were not the same, or such as to allow of beginning on any you please and making the others serve in the places they happen to fall in, which is attempted to be done by what is called Temperament, a thing that you as a violin player should hold in as much scorn, as an invitation to cut off your two legs for the sake of trying how pleasant it is to hop on wooden ones. If then you want to know what sound any of the harmonics really is, you have only to do this;—double the distance from the bridge to the nearest of the points of division into aliquot parts, over and over, till you get to some length that when pressed down in the common way makes a note which you know, as the Octave, the Fifth, &c.; and then the harmonic will be this note, only raised by as many octaves as there have been doublings. For example, if you touch the thickest or G string of the violin so as to bring out the harmonic at one-fifth of its length from the bridge, and want to know what note this is,—doubling this length once makes two-fifths of the whole string, and doubling it again makes four-fifths, and four-fifths pressed down in the common way make the Major Third or B; therefore the harmonic produced is B two octaves higher than the B on the thickest string, or the same sound as the first B on the thinnest or E string. And in like manner in other cases.
‘The examination of all the different possible harmonic notes might evidently be carried a long way; and it would be very useful to do it if you were intended for a trumpeter, for all the notes on the trumpet or French horn are harmonic notes. But for playing on the violin, as much as is given above appears to be sufficient. It will enable you to trace all the principal harmonic sounds, and in fact all that on the violin are of any practical use; for though there is no absolute end of the number of harmonic notes, inasmuch as you may divide the string into a hundred parts if you please, and then into a hundred-and-one,—yet after the division into five or into six, the sounds on the violin become so feeble as to be of no use except as matters of experiment and curiosity. And it will have this further good effect, that it will make you cease to marvel and to wonder at finding the harmonic sounds on the same string grow sometimes deeper and sometimes shriller, as you move your finger from the bridge towards the head,—as if there was some mystery in it that anybody could not learn in half an hour when they set about it properly.
‘Suppose now you could stop some tune (as for instance “God save the King”) on one string of the violin, as for example the fourth, with your first or second finger, and at the same time always touch the stopped string gently with the little finger of the same hand at one quarter of the way to the bridge so as to bring out the harmonic note;—is it not plain that you would play the tune, only in the Double Octave, or two octaves higher than if played by the simple stopping on the fourth string? There is no doubt that this is very hard, especially for a little boy; it is almost as bad as playing on two violins at once. But still the thing can be done. And if, instead of touching with the little finger at the quarter of the way to the bridge, you should touch at the third, the fifth, or the sixth of the way, you would bring out notes that were not Double Octaves to the sound that would be made by simply pressing down the first finger, but other sounds, which you have it in your power to calculate; all of which might by possibility be very useful, but the other was mentioned as being the simplest. If you asked me what is the use of playing anything in Double Octaves in this manner, or in any other of the harmonic notes,—I should answer, First, because these harmonic notes have a very fine and pure sound,—they do not squall like the sounds made by pressing the strings to the finger-board very near the bridge;—Secondly, because it is much easier to make the sounds in tune in this manner, than by trying to make them by stopping near the bridge,—for where the string is so short, the smallest error in the stopping becomes sensible in proportion;—Thirdly, because (as it is not necessary to be always playing in harmonics) they may be mixed up with the common notes of the violin, and save an immensity of trouble in jumping from one end of the instrument to the other to find the high notes. Look, for instance, at an old-fashioned fiddler playing on the second string, and wanting (suppose) A in alto; and see what a leap he will make to find it on the first string, and what a horrible screech he will bring out after all, when he might produce the note in the most perfect tune and tone by only touching the second open string that he is on already, harmonically at a fourth of the way from the head to the bridge, or at the same place that he would stop D on the second string.’
MELODY AND HARMONY[64].
THE object and end of all music is the expression and excitement of passion, of which its notes are the signs. The practice of music doubtless shows best how powerful are these signs over the production of corresponding passions; but its theory also, in the hands of some writers, has even indicated the precise and simple expressions which respectively belong to some of the passions.
Now we know that two passions cannot coexist in the mind, except at the expense of their respective continuity, depth, and intensity. It follows, of course, that their corresponding signs cannot coexist in the ear without breaking and enfeebling their expression.
But melody consists of a succession of simple sounds, and harmony of coexistant and related or concordant sounds. It is obvious, therefore, that melody is alone adapted to the expression of passion—that is, to musical expression.
A moment’s reflection, indeed, will show that, in language, it would not be more absurd to endeavour to express or excite passion by means of the related terms, emotion, sentiment, &c., or to express and excite any one passion, as that of love, by means of the related terms, friendship, affection, &c., than it would, in music, be to endeavour to excite any passion, in all its purity, simplicity, continuity, depth, and intensity, by means of impure, compound, broken, and feeble notes.
Which, accordingly, are the nations that have excelled in melody?—The Italians, the Scots, the Irish, in whom the passions are intense and powerful; while the Sclavonic and Gothic tribes, in whom the passions are feeble, have practised that play upon related notes which indicates the weakness or absence of passion, and which constitutes harmony. There can, I think, be no more striking illustration than this at once of the intimate nature and of the relative value of melody and harmony.
To the superior value of melody, however, similar homage is paid, whether reluctantly or not, in the highest productions of scientific music. Whenever, in the opera, sentiment, affection, or passion has to be expressed, the simple melody of the airs is indispensable. If anything were wanting to corroborate the preceding train of reasoning, this surely is sufficient.
Let us now, however, from principles which regard the intimate nature of melody and harmony, as well as their precise relation to the great end of all music, descend to the mere practical observance of the relative effects of melody and harmony.
Here one thing will, at the first, strike those who are in the habit of paying any attention to the operation of their own minds, and of endeavouring to analyse it. It is this, that, while there is no end to the variety which the simplest melodies produce, there is but one sentiment excited by harmony.
However varied the melody may be, whatever the succession of emotion and passion which it calls up, it will be found that, with each of these, and always at its expense, the harmony, quoad harmony, associates another, and that always one and the same, feeling. This, if observed, will be found to be a feeling of surprise, and certainly of pleasure, at the display of knowledge in the instant association of related notes; surprise and pleasure at the art and skill, not at the feeling and taste, of the composer[65].
The compositions of Handel, Bach, and others, are admirable in their kinds and perfectly descriptive; but they touch not the most exquisite feelings; they sink not into the heart; they rouse not the passions. They excite, as already said, surprise and pleasure at the art and skill, not at the feeling and taste, of the composer. Let them be compared in this respect with Sarti, Cimarosa, &c., and all doubt on this point will cease.
It is evident, then, that the admiration, however delightful, produced by the instant and unexpected association of related notes, must, precisely in proportion to its degree, weaken and diminish the effect of the melody—must, in fact, destroy its purity, simplicity, continuity, depth, and intensity.
It is, perhaps, scarcely a less fatal objection to the indiscriminate practice of harmony, that even the restricted pleasure which it conveys is, from want of education in this peculiar art, incapable of being at all enjoyed by the vast majority of hearers.
The best practical illustration, indeed, of the relative value of melody and harmony arises from observing their effects on the mind and the expression of the features. The English people, being chiefly of Gothic origin, have a fair capability of apprehending coexisting related sounds, and their conduct while hearing them will furnish this illustration.
Let any one, then, observe the effect of these sounds in the finest harmonies produced at our Opera-house. An affected look of knowingness, an insincere grin, passes from one face to another, and occasionally, when some one who really understands the matter gives a bold and loud rap with his stick,—believing that there must now certainly be something very fine, they very innocently break into a long paroxysm of applause, and they repeat this as often as the courageous fellow with the stick chooses to give them the signal, each secretly thinking how devilish stupid he must be not really to enjoy what everybody else is so highly delighted with.
See, however, the same faces when a simple melody breaks out from the chaos of the harmony: waiting for no prompter, pleasure instantly beams on every face, and truth and nature have a triumph in that deep and universal sympathy which art and affectation are utterly incapable of achieving.
The practice of harmony has, indeed, been borrowed by us from the boors of Russia, Bohemia, and Swabia, whose broad and flat configuration of head seems to be as much connected with this practice as their coldness and apathy are utterly opposed to musical feeling, which has no existence independent of passion.
So natural and universal is melody, that even many quadrupeds are powerfully affected by it, while not one seems to be influenced by harmony.
Such then is the kind of music which, originally borrowed from these boors, the influence of a few amateurs has rendered fashionable among the half-civilized people of Europe,—for we must call those half-civilized who have no perception of the fundamental necessity and transcendent beauty of simplicity in all the fine arts, those sole tests of the highest civilization.
In Greece, where alone those arts reached the highest perfection, the purest simplicity characterized every one of their productions; and there, accordingly, harmony—as in general a complex and idle decoration, in no way promoting expression, the end of music, but, on the contrary, defeating its purpose, was, we are told, absolutely proscribed.
Even if this fact had not been recorded, the slightest knowledge of the genius of Grecian art would prove that it must have been so; and we might as safely have predicted that they no more loaded their melodies with Gothic or Sclavonic harmonies than their temples with Gothic traceries[66].
The analogy is perfectly strict; for these gingerbread traceries are not more unproductive of great or good effect than harmonies are; nor are the barn-like temples which they cover more ugly in their general form than the meagre airs which harmonies are intended to decorate.
But this is not all. Not only are the airs which harmonies are intended to decorate generally meagre and worthless, it would appear that no other airs than those are fit for conjunction with harmonies. It is certainly true that, whenever the apathetic Germans have attempted to harmonize the impassioned airs and exquisite melodies of Scotland and Ireland, they have ruined them, and disgusted every person of pure and natural taste.
The purpose, then, to which harmony is applicable is not to the expression of pure, simple, continuous, deep, and intense passion—the very highest purpose of musical expression,—but to the expression either of the slightly modified and less definite feelings, or of the more variable, and even jarring sentiments of several persons, purposes far inferior to the former.
It is evident that, where several persons express musically somewhat similar sentiments on the same subject, they may naturally sing in harmony; and where these sentiments occur at intervals of time slightly extended, they may even be supposed to chant in that regulated succession which constitutes fugue. Hence harmony is peculiarly suited to many voices, where deep pathos and passion are impossible; and it is an abuse to apply it to the higher species of music.
It is evident, too, that, in descriptive or epic music, harmony may form the background of the picture—the accompaniment of the narration,—in the front of which some kind of melody appears; and of this the most admirable examples are to be found in the works of Beethoven, the most profound and philosophical of composers. But whoever mistakes this for the highest species of music is not in a condition to understand the present paper.
It is in fact, the absence of pathos and passion among the Gothic races of modern Europe, that has led to the substitution of harmony for melody. At the same time, their excellence in mechanical invention has enabled them greatly to improve instruments, which, however suited to the former, are incapable of the feeling and the meaning, the expression and the delicacy, which essentially belong to the latter. And again, the deficiency of instruments in these most important qualities has led to those strong basses and accompaniments which fill up the vacuity. Music, consequently, has sometimes degenerated into a series of tricks which do not rank above rope-dancing or the ballet.
One word may now properly be added on instrumental accompaniments. They are the natural resource of performers who are destitute either of feeling or of voice. They may be comparatively beautiful when associated with these, but they are absolutely offensive when they interfere with the expression of deep feeling by a beautiful voice.
The best instrumental accompaniment is consequently that which least interferes with the voice—not the continuous sounds of wind or bowed instruments (for their music is rather the poor unfeeling substitute for, than the accompaniment of, fine vocal music), but the light touch of the string of the harp, the guitar, or the lyre, which, while it verifies the accuracy, least interferes with the feeling of vocal expression.
Hence the great masters of art, the Greeks, employed so simple an instrument as the guitar (their κιθαρα being obviously its original), or the lyre, which appears to have been simpler and better still. I rejoice, therefore, to see the former becoming as fashionable in England as it has long been on the Continent.
DONALD WALKER.