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Unlike Simpson's first article, this article only has two figures - a most florid title ON BELL TONES incorporating a deluge of bells and several cherubs (omitted), and a figure showing the profile of a bell and tuning points, incorporated below.
The text of the paper is reproduced in its entirety.
The Pall Mall Magazine
SEPTEMBER TO DECEMBER 1896
pp. 150 - 155
ON BELL TONES No. II
The object of my former paper (vide P. M. M., October 1895) was to place on record certain facts concerning bells as they are, and to call the attention of the musical public to them. And I did so not merely in order to offer an explanation of the want of harmony observable in peals, - and still more still more in carillons, - but also in order to bring public opinion to bear on founders and tuners, so as to induce them to bring their bells into a more perfect agreement with the (presumed) intentions of the original designers of the present form of bell than has been thought necessary in the past.
But I did something more than this. I ventured on a pretty confident opinion that existing bells and peals might (generally) be so rectified as to be much more completely in tune, both with themselves and with each other, than we have yet found them.
And here I desire to say at the outset, that I am not a bell-founder. Had I been such, no doubt I should have kept any special knowledge to myself, and have made use of it for my own advantage. But, having no personal interests to serve, and believing it to be for the best interests of the art that knowledge - which I hold to be essential to any real progress - should be at the command equally of all the profession, I have preferred to make a clean breast of all that I think I have learned, and let bell-founders take it or leave it as they may think best.
If, as I venture to hope, my account of things should prove correct and of value, I shall feel amply repaid if this is acknowledged (as no doubt it would be) by those to whom it may prove an important assistance in what is now a very obscure department of the bell-founders' art. It will be remembered that the main point insisted on in the former article was that the tones which 1 have there designated as the nominal and the fundamental should in each bell be brought into unison with each other. According to theory the nominal should, be an exact octave above the fundamental, But, as a matter of fact, we rarely find it so, the nominal being very generally about a quarter of a tone (more or less) sharper than the fundamental; and the question is, "How to bring them together?"
In order to explain my answer to this satisfactorily I must direct attention to the figure.
This figure represents a half-section of a normal English bell. (Foreign bells (which probably represent an earlier type) differ from English in having the line C D straight instead of curved.). The line A B C D represents the inner surface of the bell, and forms a continuous curve, the curvature of which becomes more acute as we approach the lip at D.
The line of the outer surface is more complicated, but is so ordered that the thickness of the bell shall be uniform from A to B, then gradually increase up to a point C, and then rapidly diminish until the bell terminates in a sharp "cusp" at D.
The points E and F indicate the position of certain "bead lines," which may be observed running all round a bell, which mark the boundaries of what is called the "sound-bow," or principal zone of the bell; and the points H and G are the corresponding points respectively on the inner surface.
We are now in a position to explain how to tune a bell - i.e., how to alter its tones so as to bring them into harmony with each other, or with the corresponding tones in other bells.
It would evidently be inconsistent with the character of this Magazine to enter into a detailed description of the various processes, and of the effect of each; but here is the whole matter "in a nutshell" :-
The point H is the "turning-point" for tuning the nominal.
The point C is the "turning-point" for tuning the fundamental.
To be a little more particular :-
1. To sharpen the nominal, metal must be taken away (of course, all round the bell) from the little triangular portion H D E; by this means the nominal may be safely sharpened about 1/8th of a tone. But the process rather spoils the look of a bell, and, for that and other reasons, is not popular with tuners. Nevertheless it is effective, and, within reasonable limits, quite allowable.
2. To flatten the nominal, metal must be taken off, all round the bell, from H to C, or to G, or even to B if necessary, thus thinning the main part of the bell; by this means the note may well be lowered as much as half a tone if required.
Now, these two processes are well known to all English experts, and 1 have never met with one who used any other; which shows, as I said before, that (consciously or unconsciously) English experts tune their bells to each other by the nominals, and by no other note.
And now for the fundamentals :-
1. To sharpen the fundamental, take off metal along the line C D; this may be continued until the line C E is reached.
2. To flatten the fundamental, take off metal from C to G, or even to B if necessary.
And these are the processes used by foreign experts in tuning their carillons or peals; which, again, shows (as I said before) that the main object which they have in view, is to tune their bells to each other by the fundamentals, and not by the nominals.
If, now, the above rules are carefully studied, in connection with the figure, the following Possibilities, or Impossibilities - which I am unable to establish at length - will, I think, be sufficiently apparent:-
1. That the fundamental cannot be flattened without also flattening, to some extent, the nominal.
2. That the nominal can be flattened considerably without altering the fundamental - viz., by taking off metal, on both sides of C.
3. That the nominal can be flattened a little, while by the same process the fundamental will be a little sharpened, thus bringing the two towards each other - viz., by reducing the rounded surface C E to a flat surface.
4. That the fundamental can be sharpened considerably, while leaving the nominal nearly, if not quite, unaltered.
5. That although the process of sharpening the nominal will also raise the fundamental, it will not do so in the same degree; and would tend, therefore, to bring the two together, in the unusual (and very objectionable) case of the fundamental being originally the sharper note.
With these possibilities within our reach, it is surely evident that bells can, as regards these two principal tones, be put into tune with themselves and with each other. And if so, they can be so cast in the first instance.
Of course, in all this I am speaking generally. There are many bells so radically wrong that there is nothing to be done with them except "put up with" them, or send them to the melting-pot. And there are numberless cases of treble bells which, in order to make their leading tones powerful enough, have been made of a disproportionate thickness, with the inevitable result that their tones have been thrown very far out of due relation to each other. I fear that there is no help for this, and no effective method of dealing with such cases. There must be a compromise somewhere, and we have a tolerably clear idea as to what had best be sacrificed in order to effect it. All that I care to say here is, that the compromise must not be at the expense of the nominal. Whatever else has to give way, the nominals of these treble bells must be in tune with those of the rest of the peal.
And now, with due allowance for exceptional cases, I hope I have made out at least a very strong case to justify my appeal to the musical public - and especially to such as are incumbents or churchwardens - to demand from bell-founders a more perfect harmony in the bells supplied to them or tuned for them.
Why are we to submit to listen all our lives to a church peal which gives out two (not to say three) series of sounds, which ought to be in octaves, but which, all through the peal, are about a quarter of a tone apart? And I emphasise that word "about" because, if the error were constant, each of the series would be at least true in itself, though false to the others.
Are we to be told: "Oh ! never mind the fundamentals, - the nominals are all right, and that is all that is necessary"?
Well, but here is all Europe (practically) telling us to "never mind the nominals if the fundamentals are in tune."
They may be wrong in bidding us be indifferent to the nominals, but surely it savours of ignorance, or of "insular arrogance," to dismiss in this summary fashion the consensus of European opinion on the value of the fundamentals.
If the result of doing so were satisfactory, we might be content. But it is not so. No one who pays any intelligent attention to English peals can be satisfied with them as they are.
If the dissonance were unavoidable, we might submit to it. But it is not so. I am certain - and I think I have justified my opinion - that in most cases, probably in all important cases, it might be corrected.
Let incumbents and churchwardens, in particular, insist on a greater accuracy of tuning, and in time they will get it. Tuners will find out how to alter bells, if necessary, so as to bring about this unison between nominals and fundamentals; and then founders will learn experimentally how to alter their designs, so that bells should "come out" more nearly right at first.
Of course, this means a good deal of intelligent painstaking, and some little expense. But is not the object worth it? We may be sure of this, that the founder who first has the courage to grapple with, and the perseverance to solve, this problem, will get a name and reap a harvest which will amply repay him, and he will, further, earn the gratitude of all true lovers of music.
And here I must add a word in justice to myself, as well as to foreign professors of bell-tuning. I should be sorry to be thought ignorant of the intelligence and pains which many of them have bestowed on the regulation of the subordinate tones in their bells, and especially in the larger ones. I believe that they know a great deal that I am ignorant of. But 1 am certain that they make a great mistake in underrating, the importance of the tone which I have called the nominal, especially in the case (so common with us) where it is sharper than the fundamental.
I believe that if they would only recognise the conspicuous importance of this tone - in such cases especially - even at the expense of the comparative neglect of some other tone, they would leave little to be desired in the carillons which are their peculiar pride.
It was no part of my original intention to enter upon the consideration of "thirds" and "fifths.". But I may just say, in passing, that the "third" is far too important a tone to be ignored in the tuning, at least, of a large bell. When once its strident sound has caught the ear, it almost obliterates the other tones, and is sometimes, indeed, mistaken for the principal tone.
All that I can say about it here is -
1. That some bells are cast with major "thirds" (more or less imperfect), and some with minor.
2. That a "third" cannot be sharpened; but may be flattened, by thinning the bell all round, from G towards B.
3. That in a peal of (say) eight bells, the " thirds " should be all major or all minor. This is considered correct; but we should rather like to hear a peal in which the "thirds" of the treble 4th, 5th and tenor bells are "major," and those of the rest "minor."
The "fifth," in like manner, cannot be sharpened; but may be flattened by thinning the bell all round, from B towards G.
And now a word about the tone which we have called the "hum" note - the deepest and most persistent of all the tones in a bell.
I have stated that this tone should be a true octave below the fundamental, and a double octave, therefore, below the nominal, thus forming the Bass note of the whole system. That it was really intended so to be, is surely manifest from the fact that it is found nearly to fulfil these conditions, in almost any bell; and that, in most cases, it is not more than half a tone sharper than the fundamental and a quarter of a tone sharper than the nominal.
I believe also that I shall be supported in my contention by Belgian experts, and moreover we have the authority of Helmholtz for the following statement: "According to the observations of the organist Gleitz, the bell cast for the Cathedral at Erfurt in 1477 has the following proper tones - E, e, g#, b, e', g'#, b', c'#." And "Hemony of Zutphen, a master in the seventeenth century, required a good bell to have three octaves, two 'fifths,' one major and one minor 'third.' "
This I think should settle the question, not only of the hum-note, but of the whole theory of bell tones as set forth in these papers.
Before speaking of the method of altering the hum-note, so as to bring it into line with the other tones, I should like to say a word as to its practical importance.
The fact that it is the bass of the whole system of tones, in any perfectly attuned bell; ought to be sufficient. And though it is not so loud as the fundamental, nor so clear as the nominal, it is impossible that any want of agreement with these should not injure the general effect, especially if in a series of bells these great "booming" tones do not rise and fall fairly evenly with the others. In the case of large slow-striking bells of clocks, or carillons, this want of agreement with the other tones must be specially objectionable, as the hum-notes are, as we have said, the most persistent of all.
But their general importance may be made clearer by the following illustration :-
Sitting in my dining-room, with outer and inner doors shut, I was struck by the singularly sweet sound of our six little Fittleworth bells as heard down the chimney. On opening the doors, so as to hear them directly, I observed with surprise that the scale was different; and I finally discovered that what I had heard down the chimney were the hum-notes, which alone found their way, to me by this devious course.
After this experience, we cannot dismiss the hum-notes as unworthy of careful attention.
How to govern them and bring them into unison with their proper fundamentals and nominals? is a question which I am not prepared to answer with quite the same certainty as in the case of the other tones. To be able to do so, we must first determine on what proportions of the bell its "pitch" mainly depends.
Now, in the case of the other tones this is sufficiently known, and it is from this knowledge that we are able to deduce the rules for altering them, as given above.
But there is a mystery about the production of the hum-note which has not yet been quite cleared up. I give here my own belief, founded on observations which I cannot here describe at length. I believe, then, that whereas each of the other tones may be referred principally to some particular portion, or zone, of the bell, the hum-note is, in a peculiar sense, the tone of the whole mass of the bell. And I have come to the following conclusions as to its government :-
1. That this tone can never be sharpened.
2. That it may be flattened to any reasonable extent by thinning the walls of the bell near to the crown - i.e., near to A in the figure.
3. That, possibly, the proportion of the "length" of the bell to its "width" may have some bearing on the relation of the hum-note to the other tones; any shortening of the length in proportion to the other dimensions having the effect of sharpening the hum-note.
These are points, however, which can be easily settled by any bell-founder; and, should they turn out as I suggest, the whole problem will be solved; and, thenceforward, no founder ought to permit at least any large clock-bell to leave his hands which has not its hum-note, fundamental, nominal, "third" (and perhaps "fifth"), in harmony with each other.
I know of no such bell at present. Who will be "first in the field" to produce it?
But though I do not know of any completely attuned bell, I should wish to do justice to modern founders; and I am bound to say that, as a rule, the bells produced nowadays by our best founders are more nearly in harmony than are the majority of our old church bells; especially is this the case with large bells.
A remarkable instance of this may be heard any day by dwellers in London. I refer to the Great Bell of St. Paul's Cathedral. This bell, weighing nearly seventeen tons, hangs in one of the western towers, and is rung every day at 1 p.m. Its position in the tower, sunk as it is so much below the orifices, is very unfavourable to its "carrying" power, and to the even development of its tone. Nevertheless, it can be heard very well from any point of the space round Queen Anne's Statue.
I have tested this bell, as far as my instruments would permit, with the result that 1 have found all the tones, so far, in perfect accord : i.e., the fundamental and the nominal are in true octave, each being a true Eb. The tone next above the fundamental is also in perfect tune with it, but with this peculiarity - that the note, instead of being a "third" above the fundamental, is a "fourth," i.e., Ab instead of G or Gb. This is a pity; and the more so that, from the position of the bell in its tower, this tone is heard in undue proportion to the others. Nevertheless, the general effect is musical, and very pleasing.
The hum-note of this great bell was too deep for a scientific test by any instrument within my reach, but it appears to be in complete unison with its fundamental. Altogether, this bell is a very noble specimen of modern English bell-founding.
There still remains one very important matter to be considered, which has already, no doubt, suggested itself to those who have had the patience to read these articles. "How," it will be asked, "are we to discriminate, with accurracy, all these various tones, so as to be able to compare them, and note the various degrees of error?"
This is a most pertinent inquiry, for unless this can be done I am confident that any knowledge of the methods of altering these several tones will be practically useless. And more, had I not possessed some method of eliciting each tone, separately, I should never have attained what knowledge I have on this subject.
The method which I have used for about twenty-three years, I have reason to think, is not unknown to foreign experts; but, as far as I am concerned, is my own invention, quite effective, and very simple to those who know how to use it.
But it is not merely a piece of information to be imparted by words, but rather an art to be learnt; and I am unwilling to risk the probability of its being pronounced "a failure " by those who, acting on a mere verbal description, should make nothing of it.
If any of my readers are really desirous of making themselves masters of this "art," a letter addressed to the writer at Fittleworth Rectory, Sussex, shall receive every attention; and I can promise to founders a most valuable help in their difficult work, and to any lover of music a fruitful source of interest and pleasure.
A. B. SIMPSON.
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