I used the information in this book pretty much exclusively to guide the designing of the stringing schedule for my bentside spinet. I found it very helpful and have been happy with the result. Btw, my few twangy strings seem to have lost some of their twanginess.
I bought it and read thoroughly Louchet’s “The Keyboard Stringing Guide book” years ago to find help for the following:
Writing my webpage re Taskin (and replicas) harpsichord stringing.
Writing my webpage re Hubbard kit restringing.
Restringing my own Hubbard kit.
I have to say that I did NOT find it particularly useful.
First, he follows some ideas by Grant O’Brien I do not agree with.
On p. 22 Louchet lists the typical tensions of a 18th century harpsichord of the “French-Flemish school”.
His curve has a different shape than the one I carefully deduced and published on my “Taskin stringing” webpage. On p. 22 his values 3-4 kgs for the treble and 4-7 kgs in the bass differ significantly from the historical values I have deduced, which are significantly stronger: 3.5-5.6 kgs for the treble and 5.5-7.5 in the bass. Se Fig. 3 in my Taskin Stringing webpage and also the 8’ chart in my Hubbard restringing webpage . I am among those who believe that following ancient pull curves (or at least not exceeding the historical minima and maxima shown in my Hubbard Restringing curves) is paramount to achieve the effect historical harpsichords were designed for.
An evidence of the very approximative way Louchet has worked about harpsichords is the very rounded and approximative harpsichord tension curve on p. 23, Fig. 41.
He also asserts, on p. 41, that “inharmonicity in the treble is hardly perceptible on a well-designed harpsichord.” That the treble inharmonicity does not bother harpsichord tuners is well known, but this is because many of those inharmonic high partials are hardly audible anyway. But a signficant inharmonicity is there in the extreme treble, and is inevitable due to the very short strings relative to their diameter. It is particularly bad in the 4’ foot of course.
Louchet devotes a significant part of this book to the problem of inharmonicity on pianos and on how to make and install overspun piano strings. In this sense, I believe it is a useful book for piano tuners and repairers, much less so for the harpsichord world.
I seem to remember GoB advocates for relatively heavy stringing for Ruckers (in his Ruckers book), 0.27 mm iron for the last note of 8’. I don’t know the tension but this should be some strong tension. Or am I temembering wrongly?
Suppose we’re using Malcom Rose Iron Type A. I then give you 2 types of information (the numbers I give are randomly chosen, they’re just there to prove my point):
The a1 string will have tension of 4.235 kg using a diameter of 0.23 mm, a tension of 5,75 kg using a diameter of 0.25 mm and finally a tenison of 6 kg using 0.27 mm.
a diameter of 0.23 mm will be 3 semitones from its breaking point, a diameter 0.25 mm is 2 semitones from its breaking point and a diameter of 0.27 mm will definitely break before you can tune it to that pitch.
Which info do you deem most useful?
The kg thingy is only of interest to avoid putting unnecessary tension on the instrument when e.g. using West-Fälisches Eisen or steel (instruments before the ’80). With these quasi unbreakable materials one could in theory string the whole instrument in iron using 0.364 mm. However ending up with 8 kg in the treble is not what you want.
And of course let’s not forget the 3th important factor: the string should sound good. That’s what your ears are for
Hi Chris,
You are possibly missing one point. The 0.23, 0.25 and 0.27 diameters are all at the same distance from the breaking point. Same for 0.19, 0.15 … 0.30, 0.36 and so on, provided they are the same material. Other friends with more physics knowledge than me will chime in for providing the details.
(very thin strings can have a farther breaking point due to the surface hardening when producong the wire)
So you can surely string a harpsichord too heavily, say with 0.36 iron at the last note. It will play badly woth overtones etc but it will stay there. The tension will be much higher of course.
D
I did read and did use Louchet’s book, although not the latest extended version. It’s a bit theoretical indeed, still useful and valuable for those who want to better understand string calculations. I do not consider it an important source of historical information. For me the most worthwile chapter was the one about formulas calculating wound strings. Formulas for massive strings can be found everywhere, those for wound strings are more rare and seldomly well explained. Louchet does.
I would not recommend anybody to buy a string calculation model. The risk of errors to be made is substantial for those who do not feel at ease with such calculations. In that case it would be better to ask external advice. Those who feel at ease could easily make and use their own model in excel instead.
Not so often for harpsichords, but many times for pianofortes I did advice restorers about proper stringing options. For this I am most grateful to the late Malcolm Rose. His book on historical stringing is an essential and unique contribution to the field.
Finally: it is a given that 17th and 18th century builders did not use string tension calculations. However most builders had the opportunity to learn from building hundreds of instrument. We have not. Today string scheme calculations are easily done and very valuable for restorers.
it provides a range of feasible stringing options, possibilities and impossibilities;
within this range it can suggest options to adapt the instrument towards a desired endgoal: eg some areas could be made stronger or clearer by adapting stringing;
an instrument always is a unique unity of all components, such as soundboard, mechanics, quills (or hammers and leather for pianos) and indeed strings. A good stringing contributes to make an instrument an excellent one.
Here he recommends the practical maximum tension for each diameter. As you see they differ greatly:
0.19: 3.1 kg
0.21: 3.7 kg
0.23: 4.3 kg
0.25: 4.9 kg
0.27: 5.5 kg
0.30: 6.4 kg
0.33: 7.3 kg
0.36: 8.2 kg
Maybe I should have been more precise in my previous mail. Here is an example:
If the following parameters stay the same: pitch, sounding length and material, then the tension will be greater on a 0.25 mm string than on a 0.23 mm string. Comparing these tensions with the maximum tension for the given diameter, we can calculate how many semitones we’re from the breaking point.
Consider a1 with the following characteristics: pitch = 415 Hz, sounding length = 435 mm, material = Rose Iron Type A.
The tension will be as follows:
0,19: 2,927034868
0,21: 3,575685255
0,23: 4,28920068
0,25: 5,067581143
0,27: 5,910826645
0,30: 7,297316846
0,33: 8,829753384
0,36: 10,50813626
The number of semitones from the breaking point will be:
0,19: 0,496969701
0,21: 0,295833121
0,23: 0,021767056
0,25: -0,291093212
0,27: -0,623569745
0,30: -1,135765147
0,33: -1,646860079
0,36: -2,146865989
Negative numbers mean the string will break, so in this example only the first 3 diameters are possible.
For me these numbers mean that this type of wire is too risky for this note. We’re uncomfortably close to the breaking point of the string. A change in humidity/temperature would probably result in a broken string when the tensions mounts up.
Hi @Chris415 speaking from my background in physics, you can’t quote computed string tension to 9 decimal places. This is the illusion of false accuracy that calculators give. It’s actually a type of error. You couldn’t measure that with any instrument or device, and it’s effectively meaningless. It’s better scientifically to quote to say 2 decimal places at most in this context.
Good engineering calculators such as the HP 48GX of mine still going strong in daily use allow internal calculations to 15 places but configurable display to the desired number of places. Also, of course Excel can do this too. It’s nice that we have high precision calculating devices to avoid rounding errors as much as possible, but one needs to consider the purpose of the output.
When I did a course in Numerical Analysis so may years ago, our textbook by Hamming had a quote from him before the preface:
“The purpose of (scientific) computing is insight, not numbers”
Sorry to be a curmudgeon, but this happens to be one of my hobby horses!
There’s a page that covers some of the issues of the matter here:
Don’t get me started on people who quote musical pitch to four or five decimal places.
Hi every body. When Malcolm and I produced the stringing handbook, (published 1991 and still in print), the work, Malcolm collating and collecting all the raw information from his and many other restorers’ work , and I calculating and plotting the results we didn’t have computing power available since most of the work took place in period 1975 to 1985. Golf ball typewriters and early scientific calculators. The calculations and graphs were done using a radio shack programmable calculator the size of a thin wallet which let us get past entering so many figures into a calculator so encouraging some sort of accuracy, and Letraset dots onto preprinted graph sheets at A4 size, after a long and eventually abortive attempt by Peter and Anne McTaggart to use their ancient DTP programme.
When finally we got computers, we could do page layouts (Pagemaker) and when i finally learnt Excel 2 I made a spreadsheet for the calculations, which I use t this day. Claire Hammett and her husband made a spreadsheet to infer all string lengths from just f and c measurements and kindle allowed us to use it.
My eldest son showed my completed spreadsheet to hid maths PhD tutor at Manchester Uni, who said it was clever; so My son decided to correct the big problem with it which was that I hadn’t applied any sort of protection, so it is very easy to corrupt things. However although this basically worked he didn’t
complete it. So it is of very limited use.Malcolm and I were fixed on the notion that we were being practical and so all results can be queried as they were by one Manchester expert on stringing; but he then dismissed these things as irrelevant as all our work was comparative and so had value.
There has been much discussion recently on the forum regarding this so I thought I should make available all three of these spreadsheets , in the hope that some-one can maybe complete the work that my so did to produce a spreadsheet that can’t be corrupted by user error.Excel2 was lovely, and its’ formatting allowed for production of graphs rather close to this in the book. The programme ha exploded so much that even on my 27” iMac it is confusing for me.
But please understand that Discourse forums are not a file store for arbitrary files. You can upload photos but not Excel and not zip files. See my recent reminder about this a couple of days ago.
Ask people to PM you if they want copies from you.
BREAKING POINT. Sorry to disagree, Chris and a few others, and with very “sound” bases.
Theoretically, using the same material, Mersenne’s laws guarantee that the breaking point depends on the frequency and string length, and is INDEPENDENT from the size or gauge. The misunderstandings we are reading sometimes arise from the word “tension”, that can have different meanings and formulae. I prefer to clearly distinguish between “pull”, i.e. total pull of the string in kgs. from the harpsichord case, which affects sound but not breaking point, and “stress”, i.e. tension of every molecule, measured is in kgs/(mm2 of cross section).
Stress, as per Mersenne’s laws and confirmed ever since, is indeed independent from the gauge. As you increase the gauge, you have to increase by a square the pull to achieve the same pitch, but at the same time the cross-area of the string also increases by a square (area of a circle is in square proportion to its diameter!), so the stress remains absolutely the same, as known by centuries and well clarified by Domenico above. It is the stress that determines the breaking point, NOT the pull! For the details, see my webpage on Taskin stringing, section 4. GAUGES, TENSIONS AND FORMULAE4. Whoever asserts something different is just wrong, and just go to any “sound” book on musical acoustics to verify this.
This said, the breaking point of a material is “theoretically” constant (when applying Mersenne’s formulae). In practice it is not, it very slightly goes up with gauge. A thinner string is slightly more resistant than a thick one, due to superficial tensions: the material is often harder on the surface. This does not depend on formulae, but on the specifications of the maker. Anyway, the difference between gauges in my collections is not very significant.
Some further clarifications. Chris, I re-read your post, you believe that the “pull” in kgs has a relation with the breaking point. It has not. Not at all.
By the way, stating the breaking risk in semitones is not easy to calculate, is a very rough estimate and can produce confusions. I prefer to state the “scientific” value: we measure the string’s stress in Kg/mm2 and have that value for the breaking point. If the stress is 40 and the breaking point is 50, we say that the string is at 80% of the breaking point, thus absolutely safe.
As for variations with gauges, especially extreme bass brass, let me just “stress” what I just posted, copying here some values I got with the red brass wires I got from the late Lutz a decade ago. He measured them with American measures, in thousands of PSI (directly proportional to Kg/mm2 of course):
.026" 80 PSI
.024" 80 PSI
.022" 80 PSI
.020" 110 PSI
.018" 110 PSI
.016" 120 PSI
.013" 120 PSI
In Yellow brass the differences are smaller, varying from 120 PSI for .020" up to 125 PSI for .012". In Iron the differences are again a bit larger. In steel they are virtually nil.
I will not care to check what Malcolm Rose wrote. Chris says that he wrote that, other things (string length and alloy) being equal, breaking risk is proportional to gauge size, i.e. to total string pull: if so Malcolm Rose is dead wrong, and demonstrably so.
I don’t think Chris was quoting Malcolm Rose’s and David Law’s book, but only a short page on Malcolm Rose’s website, which may be unclearly written, probably because of the reason you gave in your first post:
However, David Law is fortunately here so he can clarify what is actually written in the book. I’m sorry I don’t own it so I can’t relate.
‘A Handbook of Historical Stringing Practice’ by Malcolm Rose and David Law nowhere contains the statement attributed to it by Claudio. The book is essentially a compilation of facts about existing old strings found on antique instruments, the great majority of them pianos of some kind. This valuable evidence is very carefully evaluated, and presented in such a way that the user can use his judgment about whether the information is valid. Tension graphs of the instruments considered are indeed presented, based on the (supposedly) original stringing found. Appendices do explain the basic string calculations, and suggest appropriate ‘tension profiles’ for various kinds of instrument. There is some helpful data on densities and Youngs moduli of various wire materials.
Jean Louchet’s book is quite different. It aims to discuss the subject from first principles, and it deals with evidence from surviving antiques only incidentally. In particular, its discussion of overwound stringing – mainly about close-wound overwinding in pianos – is original and valuable. I would have preferred a deeper treatment of inharmonicity calculations, which he touches upon.
I would suggest that any professional who wants to undertand stringing seriously and scientifically really needs both books: this despite the fact that they both have shortcomings.
I attributed the statement to Chris reading Malcolm Rose, not to the latter which, as I clarified, have not read. And indeed Chris has a long list of breaking points varying continuously and very significantly with gauges, which is incorrect.
