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I found a very interesing PDF on scaling from Tallinn Pianos made in Estonia. If I could put a link to it I would but I do not know how - sorry!
My interest is in the diameters of the trichords as I have thought of replacing these on my 51" = 1300mm Brock upright.
y piano must have been made around 1930 or perhaps after WW2.
In the grand under discussion the longest bass string is 1415mm = 55,5" the corresponding string in my piano is 1050mm = 41,25". So roughly their piano is 1,35 times the length of mine - at a calculated guess !!
As I read the article: their piano starts the trichords on note 21.
My piano starts the trichords on note 31 with plain wire of 1,2mm diameter, and the speaking length of this D sharp No3 is 880mm.
Now if I look at their wire diameter for for the same note it is 1mm and the string llength is 1030mm.
They point out that the string tension throughout their treble is 620N . From their graph it does seem to rise for the last eight or so notes.
My point is - "why did Mr Bernard Brock choose 1,2mm wire if it can be done with thiner and with less tension ? ).
Their string, for the identical note in my piano, is both longer (= tighter than mine) and thinner (= does not have to be so tight).

Having looked at all the various wire gauges and thinking about the time that my piano was made - I'll answer my own question!
Probably it was the best that he could lay his hands on in Great Britain or the Continent at that time.
If I was feeling very energetic I would change all the treble strings to a lesser diameter: might even start with those where the hitch pins are not below the bass strings.

You could use my spreadsheet to decide what wire gauges to use on the basis of some science, rather than just doing something that you think might do something.

If you lower the tensions chances are that the soundboard will like it, but there are some drawbacks, less power, more supple strings that absorb more hammer impact. more variations with seasonal changes , lower stress factor.

It have to be compute to see what are the effects.

Even with pianos of the same size there are "long" scales and "short scales", and the soundboard is compliant with that.

I would not underestimate 1930 makers, some may have setup a good progression of tensions and stretches within the scale.

But often the mediums are long compared with the melodic part, that makes a hop in power an presence and the treble have trouble to compete with.
Often also, the first wires on the long bridge have a too low stress factor to sound good, while the last bichords have a too high one.

You cannot lower the diameter of that first plain wire that is yet with a low tension and too low stress factor (662N 35% BS).
The last wound seem to be OK not overly tense if not too thick.
The solution in that case is to raise the stress factor by using softer wire.

Interesting: and thanks.
BDB I can not get your spread sheet to open something to do with not having the correct program to open it.
Oleck on my piano the firstof the trichords (2mm dia) are on the start of the long bridge and have more power than the last six bichords which are on the bass bridge, their steel inners are also 2mm dia.

It is Excel. Just about any modern spreadsheet application should open it.

Hi I am a little lost, you mean 1.2 mm probably , or you have trichords with wound strings on the long bridge ?
Or the 1.2 is the core of those strings, the first one is 880 mm and the last on the bass bridge is 1050 mm ? that is a huge difference . that is the other way usually I did not notice.

Of course you need to measure and input in a spreadsheet, then you can look at the tensions, the stress factor, inharmonicity , stretch eventually.

The A's only plus the break and first last strings of each section gie yet a view on the scale.
The A49 is the "pivot" of scaling in German methods, may be also elsewhere. So the lenght of the diapason and last treble note is giving yet a clue. See also the bridge shape when passing the plate breaks...

I assume you are referring to this article:
www.cs.ioc.ee/~stulov/lisboa.pdf
Stulov has published several papers on string scaling and modeling but this is the most basic.



There is no simple answer to the questions you pose. The best way to go at this will be to analyze the whole scale. There is a fairly good (free) scale analysis program available at:
www.scaleripper.com

It is not good scaling practice to look at just a few notes in one part of the scale. To do the job properly you’ll need to measure the speaking lengths and diameters of all of the strings and plug all of those numbers into some kind of a program that can tell you what you have to start with.

But even before you do this you might give some thought to just what it is that you want to accomplish. Is there some particular timbral problem that you are trying to correct? What is it? Is string scaling really the problem?

The notes you are discussing are located at, or near, the bass/tenor transition where there is frequently a significant impedance mismatch in the soundboard assembly between the ends of the two bridges. If this is the case “fixing” the scaling may not offer much, if any, improvement.

ddf

But in any case you will get a better tonal output but attaining more than 40% for the first plain wire - preferably 50% -

the method is simple as going up to 60% for the A49 note, then allow the stress factor to raise until high treble, with about 80% at the last treble wire.
(that can go along with a lowering of tension up to the treble, often the last octave or a little more have been enlarged, for better tone and stability, with a C88 at 52 mm
Then the tension may stop lowering and can even raise in the upper end of the piano.

It may be a good practice, depending of the age and condition of the soundboard, to lower the whole tension to give the panel some "air" . For an upright taller than 120 cm 750 N (mean) is considered good. (a grand less than 180cm long would use 700N, so you cannot compare both)

I only work in mm so I cannot use softwares with imperial measurements unfortunately.
The computation rules may differ here, particularly the real breaking strain of the wire is lowered 20% at last (25% are commonly used too) so to take in account the fragility induce by the bends, the eyelet, the coils etc.

So all stress factor numbers I gave relate to that computation method.

With softer wire the stress factor is raised, so the wire is more reactive, have a lower iH and does not sound "under solicited" as often the first plain wire. This is getting a very common way to proceed, thanks to paulello that provioded us those wire quality.

Yes sorry, I did mean 1.2 mm for the first note on the long bridge which is a trichord for D sharp 3. It sounds very good compared to the precceding note D3 on the bass brige. I have tried replacing the D3 , same size as original. Plus the next lower five - this made a fair difference ! My C0 string is 1050mm long, od 6,5mm and inner wire 1,8mm. Generally the sound is stronger as one goes down the base. I suppose what I should first do is replace the hammers. Also I could, for practice, first rewire my daughter's straight srung 1890 Broad; specially as it appears to have had a hammer replacement and it's strings look really grotty!
I am no great pianist but I DO HEAR THINGS WHICH JUST DO NOT SOUND "RIGHT".
I found a discussion By Del and others from a few years back it was very informative.
From what I read you Del are in the project to produce a USA piano which will have a carbon fiber sound board - I have made my small $ contribution!
In the correspondence you write of the "cost and the demand", did the group think of first producing a quality upright where the demand would probably be greater?