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I have studied this entire thread and attempted to re-scale a 1949 Lester 6'2" grand using the spreadsheet of BDB and input from Bill Bremmer RPT as they attempted to assist Ryan Marlowe.

In the past, I have replaced many broken wires, and have replaced full sets of wound bass strings, but am now attempting to help a beloved aunt restore her grand piano to "better than new" condition. I am not certain, but believe the piano may have been restrung before. The original wires measured from 18 to 12 1/2.

Using the spreadsheet, I added my measurements and then tried to "tweak" the wire sizes to attain as close to a uniform 160 pounds across the scale. I ended up with a scale ranging from 156 to 165 pounds of tension.

Am I on the right track, or am I missing something here ?
I will appreciate any opinions or criticism !!

Many thanks,
ncpianoman

"Volume range on the first chart (original strings, A435) is from about 260 to 120.

Volume range on the second chart (original strings, A440) is from about 150 to 120."

Any explanation to this counter intuitive fact ?

more tension mean less iH and more elasticity, how does it relates to volume ? I have the Travis book but did not remind the way he compute volume, it should be related to mass and tension, and I see no reason it lower with more tension, unless it is about the harmonic content and that volume is only the first partial (?)

It sounds like you are on the right track. A variation of 9 lb. in the tension is pretty uniform. Many original scales vary more than that much between adjacent notes.

Isaac is wrong. Tension has nothing to do with elasticity and more tension can increase inharmonicity.

Correct about tension variation.

correct about elasticity, but more tension does not increase inharmonicity. Higher tension makes the wire "seem" thinner.

If you have a fixed speaking length, in order to increase the tension, you have to increase the diameter of the string, which increases the inharmonicity. Assuming that you want to tune each note to pitch, of course!

It is a little difficult to get but if you increase the diameter of course, you get more iH
but if you change the pitch your raise the elasticity of the wire then the iH lowers. Call that anything, it seem like elasticity (faster return to original dimension in cas eof deformation)


So assuming you keep the same diameters and you raise the tension, why would the volume lower ? just because of less parsing of the partials ? Is not volume a global energy measure ? is it just for the fundamental ?
In that case I can understand, as more partials mean less fundamental probably (?)

If you want to keep the same diameter and raise the tension, go ahead, but I prefer my pianos tuned to a chromatic scale!

BDB, the link to your spreadsheet seems to be broken (I know its an old thread ). If you would be willing to repost or email me (miscrmsATgmail.com) a copy I would be very interested to play around with it. Probably won't be restringing any pianos any time soon, but its very interesting stuff!

Also noticed the local library has the Travis book mentioned, so I'll have to swing by sometime and pick that up unless there's something better/more recent you all would recommend.

Thanks,
Rob

Many thanks BDB and all!

Just for fun, the original strings amounted to these unisons:
8 @ #18
12 @ #17
17@ #16
7 @ #15
4 @ #14
5 @ #13 1/2
4 @ #13
3 @ #12 1/2

The new scale worked out to this:
9 @ #17
7 @ #16 1/2
9 @ #16
3 @ #15 1/2
1 @ #14 1/2
7 @ #14
3 @ #13 1/2
2 @ #13


I am assuming I will have to tie off a few strings to attain this scale exactly ? Does this seem reasonable ?

One last question.... if the goal is 160 pounds of tension, why does the Excel chart start at 150 pounds ? Just curious ?

Thanks again for sharing the spreadsheet. Any input or criticism from anyone will be appreciated !
ncpianoman

OOPS ! The "new scale" above is NOT correct ! That was the wire size list based on the 150 pounds default on the spreadsheet.

Here is the actual "tweaked" scale I created as I attempted to attain a steady 160 lbs. tension:
4 @ #18
8 @ #17 1/2
8 @ #17
6 @ #16 1/2
7 @ #16
5 @ #15 1/2
7 @ #15
3 @ #14 1/2
3 @ #14
4 @ #13 1/2
5 @ #13

Please excuse my error in the previous post !
ncpianoman

The link is almost the same. I guess I took the space out of the name.

Awesome, thanks!

An un-even number of unisons of any given gauge always calls for a tied off string. In most pianos, tied strings occur only at a few special places. For the vast part, there are even numbers of unisons of a given gauge, which allows for the string to loop around the hitch pin and come back to the next tuning pin.

Unless you begin to pull out hitch pins, and drill holes for new ones, you will not have the luxury of plopping any given spreadsheet-generated scale onto an existing piano plate.

Remember: piano design is all about compromise (in the right spots, of course)

As I see it the stretch of the wire is important too, hence the BS relation hich is not only there as a security, but as a tone quality parameter. But first tension of course (while on old pianos the tension curve (never find a flat tension scheme) is lowering in the high treble, while in modern ones it raise.

We could say that the yeld stretch is raised in the treble region, to compensate for our human ear that hear less good that frequency range. So the raise in tension as well as in stretch seem a good reason. it also fight the iH rise

Hello thanks for chiming in, any reason why the volume should lower with more tension ? (435 to 440 ?)

Older wire could have alower breaking strain and can be tense more in the good constrain one with less tension.
Modern wire oblige to make much compromizing as it is more hard. I have seen numerous old instruments that had definitively lost their original tone because of new strings.
SOme colleagues even keep the old wire find in some old Erards going to dump, so they can keep the original wire. I never heard a modern replacement with such a tone quality.

On the contrary, unless you have along enough scale you are in trouble with older designs.

Some reasearch pretend than the old wire had phosphorous traces and that this is why the tone was so particular. Today no string maker will accept to have phosphorous in their batches so we cannot have that done again.

I believe that the wire sollicitation is taken in account in order to keep the stretch of the wire in correspondence with the frequencies, then the piano cna stay in tune longer.

in the mediums , where the soundboard change are the most noticeable, is suppose that a maximum of tension is also expected so to limit tone changes with the soundboard shape changes.
It does not happen really with old panels so this may not be a problem.

Anyway low level of solicitation provide that flacid tone with proeminent partials and too much iH, that can be noticed on some old pianos stringed with modern wire, it is sensitive with american wire in the treble of a Steinway I have seen lately, that treble is all but elegant (5th octave) . did not check the wire diameters but I can hear the lack of solicitation there, because I am acustomed to that kind of flaws in the tone on old pianos.

Moaning a lot and difficult to make a nice tone with tuning; Harsh, give an impression of power but non musical one, When you voice down the tone get just more accepteable.

too much iH = the spectra is unclear the fundamental is perturbated, pitch refernce is not evident.

Thank you Supply, BDB and Oleg !

This is exactly the information I needed to hear ! SO, if I understand correctly, I should make adjustments to my "tweaked" scale, to a "final" scale using even numbers of unisons while still attempting to retain the most even pounds of tension, right ?

What about the post by Oleg ? Should I attempt to raise the tension in the treble in a smooth curve toward a certain tension in the treble ? What would be that ultimate tension on note 88 ? And, if so, at which note should I begin that upward curve ?

I truly appreciate all this kind and helpful assistance from ALL !!

ncpianoman

I try to keep note 88 close to 160 lb. The problem is the transition from the highest wound note to the lowest plain note. You could plug in the diameter of the highest wound note to get an approximation of the tension on that string. It has to be converted to a gauge. The conversion factor that I use on the spreadsheet is that the diameter in thousands minus 5 divided by 2 is the gauge. So for .031 inch diameter, that is (31 - 5)/2 = 13 gauge. That conversion works for the usual gauges used in pianos, but it is not accurate for much smaller and larger gauges.

Hello NCP, if you have an even tension you cannot really be wrong at the base, what I refer to is the level of solicitation the wire is subjected to. AN accepted rule is to avoid too low levels (the computing in Europe differs from the way it is seen in the Travis book , as a security 25% lowering is used on the real breaking strenght before computing how much % is allowed)

This to take in account "at large" the fragility induced by bends and coils.

Then not less than 40% in the first plain notes, raising to 80% BS in the last treble notes, and you have aneat moderate scale.

Original tension in many old scale make a hop on the first 10 notes then lowers sligthly toward the high treble.
SO if you can raise it possibly you will have a better result in the end, as modern wire ask more tension to tone well than the one availeable at older times (in my opinion)

so in the mediums, the goal is to have around 50-60% solicitation. It is just that the mechanical behaviour of the wire is better in those limits, and can raise with thinner wire. The optimum tone for treble being not far from the end of the elastic zone of the wire.

Recent proposals from Paulelo, that are pplied with good results whatever wire is used. I also know at lat one manufacturer that use more solicitation even in the mediums, and I also have senn thos high levels of BS attained in the mediums by some old high tension scales (Pleyel, 1915)

But for instance Bechstein pianos of today have a little tension in the low mediums that raise toward the treble...

You have differnt types of scale, it should be interesting to determine what kind of scale your instrument had, as it may relate with the resiliency and the weight of your soundboard.

The last being now old, some corrections can be envisaged so you dont ask too much of the panel...

Here is a graf of the plain wire of an old 1860 piano Erard

https://docs.google.com/file/d/0B6GjQDkF_AMQM25FSHpSRmV1bEk/edit?usp=sharing

tensions in the 415-500 N range for the plain wire and 500-360 N for basses. of course soft wire is used here. the strings are not long

AT some point this begin to be a tad complicated. SO at last trying to have tension without jumps is yet a good thing.

Old pianos also had what I consider registers, considering a zone for the treble, another for the mediums, tension wise (if not some of the designs I see are a mystery)

The idea that we need more power and more partials in the treble is from Jean Louchet and seem to corrobore the audition curve, that is less sensitive in that region.

I like to be sure of something :

are more partials giving an impression of more power or no ?

What helps to ascertain the scale is a comparison of the string's lenght progressiveness on a spreadsheet in logarithm display mode :
the original frequency (f) in HZ, multiplied by the string length (speaking length) in meter

(direct display of the lenght give not as much information)

You can see where the lenght reduction begin on the scale, how is the bottom of the long bridge.

here is the original BS% of a 1925 Pleyel 3B (small grand 1.64 m)



https://docs.google.com/file/d/0B6GjQDkF_AMQNmdvWEhJMXNBSTA/edit?usp=sharing

Here are the tensions, that look strange at first sight (but typical on an old scale)

https://docs.google.com/file/d/0B6GjQDkF_AMQRHh2a3J3bnVCSU0/edit?usp=sharing

Compare them with BS% you will notice that 80% is kept as a limit in the high treble.

I believe that the last notes are less tense by fear of blocking the soundboard on its edge , but ther may be another reason