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Hello Mr. Truitt -
Not ignoring your other informative post above, nor trying to detract from your question to BDB, this text is the perfect setup, for simple and clear illustrative purposes.

Here, I believe you are proposing that you are changing the wire model/type , especially with respect to the physical property of PBL which, in this illustrative case, is a function of the wire alloy and processing only. Diameter, length, and real physical tension in the wire has stayed the same. The only thing that has changed is the magnitude in the difference between the stress it is at and the stress at which the string breaks.

Will those three wires sound different? why?

Regarding your post #2321423 above.
Paragraph 1 deals with reducing breakage and rescaling (thinner wire) with XM, fair enough, no questions there.
Paragraph 2 deals with wires that are too loose, so changing the scale (possibly different diameter, different tension, different alloy to accommodate it) will help. No questions there.

Paragraph 3 is absolutely on issue. You wrote "If you substitute the same size XM wire for the original, the tensions won't change, but the BP% will be even lower than the original - it is going to sound lousier there. "

This is the question of interest. Why is going to the wire with lower BP% (or in other language, going to higher yield stress wire, higher elastic limit wire, and higher ultimate tensile strength wire) going to sound worst, keeping diameter, lengths, and tensile stress at tune in the scale the same?
-I'm making all these assumptions about keeping diameter, lengths, and tensile stress all the same because the elastic regime behavior of all these plain (unwrapped) wires are the same, considering Fig. 1 in the link in my post #2320943.

Many thanks-

...but 110% accurate...

Regards
Chris

The same thing could have been said when Bosendorfer added extra notes a century ago, but still, most pianos only have 88 notes, and few pieces even take advantage of all those. I don't see the 88 note paradigm becoming obsolete any time in the next century

Hi Phacke:

Let me address your thoughtful questions.

First, let me make a correction. I had read from the wrong cell for the speaking length yesterday - the correct speaking length is 1477 mm. The calculations arrived at were based on that stable 1477 mm. figure, so they are still correct.

Your second paragraph is correct in its entirety. All three calculations are based on Paulello wire types, starting with the M type, the closest equivalent to modern Mapes or Roslau wire. Paulello doesn't tell us the makeup of his wire, but the differing breaking strengths are achieved by varying the carbon content of the steel, along with whatever else he is doing in terms of the alloy content. For all three wire type calculations, the diameter, speaking length, and pitch of the particular note remain the same. Since the pitch does not change, the tension does not either. The tension is not affected by the substitution of wire type. Since each of the wire types has a differing breaking point - M has the highest of the 3 example, O is in the middle, and 1 is the lowest - then the breaking percentage (for our use, the practical breaking limit (PBL) will vary. With everything else remaining constant in our 3 examples, the M type will have the lowest PBL, the O is in the middle, and the 1 has the highest PBL. Of the three, the 1 wire is very close to the target window of roughly 50% in this area of the scale. Of the three, the 1 is the softest and most flexible, the O is in the middle, and the M is the hardest and stiffest.

Within the parameters of our example, yes, the three wire types will sound different. My own experience tells me the 1 type sounds the best, the O in the middle, and the M type the least well. And it is because of the particular PBL that the wire is at.

If you have ever restrung a piano and begun tuning the wire to pitch, you will encounter the following: As you increase the tension by raising the pitch, you will hear the wire start to come alive at a certain point as you near the correct pitch. You will hear an increase in volume, the tone will become more focused, and you will hear the wire gain sustain. I would be challenged to fill a thimble with my knowledge of physics and metallurgy pertaining to piano wire, so I don't have all the answers. But I think that one thing that we are hearing as the wire comes into the target zone is greater efficiency - more energy is conserved by the wire. And the internal damping changes to something we find more fitting to good piano tone.

Where we have substituted a wire type best suited to a note in particular scale along with the appropriate other particulars, it will sound better. Make the best choices for each of the 88 notes, and you will have an audibly improved piano, even as it may largely otherwise respect the previous existing scale - it will still sound like a Steinway in our example, but one with greater clarity, focus, balance, blending, tone color, and so on.

That's the best I can do to somewhat answer your question.

I'll try to answer your question as pertains to the XM wire. I tried to throw an XM into F21 to see what value it would give me, but the spreadsheet calculation only gives me a "false" reading. I take that to mean that it is so far outside useful parameters that the spreadsheet is instructed to offer no calculation at all. Substitution of much smaller diameter wire along with the change to XM wire type gave me the same "false" reading. So I am flying blind as far as a calculated answer to your question. Suffice it to say that the PBL is going to be lower than the M type, which is already too low to give the best tone.

One of claims of the wire that I still am mystified about is inharmonicity. That does not change as we change wire types, although that is calculated along with everything else in the spreadsheet. But the wires sound different. One would think that the inharmonicity of the differing wire types would vary if we get different sounding wire. A spectrum analyzer would be a useful tool here.

As to why the XM wire would sound the worst, it is because the PBL is so low. The PBL would be the lowest of the 4 wire types spoken of here.

I suspect (but don't know and may be wrong) that when Stuart restrung the concert grand with the XM wire, he did not use it throughout the entire scale. The top third of the scale, likely. Perhaps in the monochords in the bass if it is a very high tension scale. It may not be as well suited to the rest of the scale, but I am not privy to the scaling data that would allow to determine whether that may be the most effective substitution.

Wire stiffness is not necessarily the most desirable attribute. Why is there a tonal ceiling for effective substitution of a thicker wire in the low tenor of a smaller piano? At a certain point, the wire gets too stiff and begins to function more like a rod. Same for the low bass.

I think this was directed to me, although you did not indicate it in your post. It should have been directed to Steinway. I can only speculate that:
1. Steinway decided by trial and error
2. Tension makes a difference.
3. Weight makes a difference.



If you change the characteristics of the wire, particularly the breaking strength, you will change the percentage. Not by much, as your figures show. But you did not show how you arrived at those figures, nor what the error analysis for them would be.

I haven't been able to get a direct answer on the question of Paulello wire chemistry, but I think the alloy is the same for all wire types and it is the annealing process that is varied. So the carbon content is the same but different annealing rates change the form of the carbon in the wire.

I believe the inharmonicity is similar among the Paulello wire types because the modulus of elasticity is the same and MOE is a big part of the derivation of stiffness as a portion of the restoring force acting upon the string.

I do think I notice the beat rates of the thirds and sixths are slightly faster than what regular wire would produce at the break and I don't hear that 6-4 beat in the fifths as fast either. Which is what you would expect with a reduction in inharmonicity.

If you look at the derivation for the inharmonicity formula of Schuck and Young and the one by Fletcher you will see that the termination types affect the amount of IH. Could be the softer wire would produce a different constant for the same termination conditions.

Hi BDB:

I had indicated in my further correspondence that the means by which I calculated the PBL was through the use of a dedicated spreadsheet written by Arno Patin (the importer of Paulello wire)to perform a multitude of calculations which allow the user to define the parameters of rescaling. Among other things, it calculates plain wire inharmonicity, bass inharmonicity, tension, Practical Breaking Limit, stretch, loudness, longitudinal vibration, transverse stiffness, and the effect of the various Paulello wire types on the various calculations.

As for your questions about the how exactly those figures are arrived at or the error analysis, I'm afraid I'm going to have to
disappoint you. The spreadsheet is the intellectual property of Arno which he sells to the trade. The formulas he has written to perform the calculations are hidden from our view - they do not show up in the destination cell as they would in an unprotected spreadsheet. As such, I can't offer you a meaningful explanation. I can only say that what the spreadsheets show when a good scale is drawn are consistently borne out in the finished piano.

The whole point of having many wire types where the breaking points vary is to allow one to target the breaking percentage to have the most desirable value for each note, and a smooth progression through the scale. Once you hear the results of scaling by this method, you will begin to understand the power that it brings to rescaling. You say not by much when talking about the changes in PBL for the various wire types. But the changes are quite audible, nonetheless. And please remember that we have not abandoned scaling referencing to inharmonicity, tension, and other parameters, they come into play also. It's just that breaking percentage is given first priority. Fortunately, the choices for PBL mostly operate in harmony with the other values.

Piano scaling in general has been arrived at empirically for most of the history of the piano. Only in the past 30 or 40 years have we had computers and other scientific means that allow us to arrive at a deeper understanding and greater precision.

BDB, you had said that the speaking length " is not merely a strong influence on the percentage of breaking strength; it is the only influence." My comments were directed to you because it is not true that the speaking length is the only influence on PBL. Wire diameter has an obvious influence and that is under our control in scaling. And now the wire type is another way.

Well, you could use my spreadsheet which I offer freely.

The fact remains: Increasing wire diameter increases breaking strength. Increasing wire diameter increases tension proportionally. Therefore, percentage of breaking strength remains the same.

There can be some difference with different materials, even sample to sample differences. But overall, this percentage of breaking strength can only be changed by changing the speaking length.

By the way, since the longest strings proportional to the pitch are the highest notes in the piano, that is where you would expect the highest percentage of breaking strength.

I suppose you mean these go with the square of wire diameter , pi•d^2/4 (as opposed to a linear proportion) , but I understand your point.



Well, what I understand Mr Truitt is writing is that using the various published values of breaking strength of the wire, indeed changed by its physical properties as opposed to the diameter, it is also possible to meaningful change the percent tension from the breaking point. Based on my understanding, it is for sure, technically possible to do that. How that helps you with the sound is in the observation of those testing it, but a mystery to me.

best wishes-

I have no doubt that Mr Paulello and his wire making subcontractor did destructive testing to establish the breaking point for each gauge of wire and corresponding wire types, just as any wire maker would do. I don't see any controversy in that. Mr. Patin's unseen Excel formulas likely reference those values for each gauge and type, as applicable. Since I cannot see them, I cannot comment from direct knowledge and acknowledge that limitation. Moreover, while I have some skills at writing Excel formulas, they are fairly rudimentary. For the complexities of scaling calculations, I have left the chores of writing the formulas to more talented hands. I think Ed McMorrow has more skill in this area than I. Perhaps he can comment.

I have reread BDB's last post several times, and I do not clearly understand where he is trying to go with his statements. I would ask him to clarify and embellish his remarks.

Ed McMorrow has offered that he understands the alloy and carbon content is the same for all wire types, and that the annealing process itself is what creates the differing properties for each wire type. To our hand the stiffness and hardness of each wire type vary, and there are meaningful differences of tonal characteristics for each type. I have also noticed the differences in beat rates of which Ed speaks, and measurements of inharmonicity constants bear this out.

And Phacke, your comment about the physical properties changing the breaking percentage as opposed to changing the diameter is where the rubber meets the road for me. IN PRACTICE, this is non-controversial. The intended change yields the desired result in a predictable manner, when no other variables are introduced. I wish I could flesh this out more for you, Phacke.

Really, the wire types mirror the history of the evolution of piano wire, combined with precise metallurgy and great craftsmanship at every step of the process. Early piano wires have a different voice from modern wires, as did 19th century wire. Paulello even identifies each wire type with a historical equivalent. For some reason, many want to think of this wire as strange and exotic. I think the extraordinary quality of the Paulello wire is what separates it from other wires more than anything else. The advancement of the state of the art comes primarily from the protocol of combining the usage of the various types, less so from the quality of the wire.

Please call me Will, Phacke. You too, BDB

The now deceased and former technical Editor of the Piano Technicians Journal Don S. Galt once wrote that: All sizes (of the same kind), of piano wire break at the same pitch. I added the part in the parentheses because at that time all the wire available was essentially the same.

In other words the same pitch that #13 wire will break at on note 88 is the same pitch that #18 wire will break at. The tension produced by #18 wire will be higher than the #13, but the breaking point as a percent of the tension is the same no matter what size wire is used. (As long as the same wire type is used).

It is my assumption that most of the tonal differences noticed by employing Hybrid Wire String Scales is a result of changes to the volume and pitch of the longitudinal modes. I don't see how any other explanation can be possible. It would be nice to research this with L-mode sensors.

It also would be nice to have independent testing of a few sizes of all current wire types available for break point, elastic limit, young modulus, roundness, surface smoothness, and comparable L-mode strength and frequency. I have tried to interest the PTG Foundation in this but no takers from my verbal suggestions so far.

I have trouble understanding what others do not understand, but my point is what Ed cited from Don Galt: If you hold the pitch steady, it does not matter what the size of the wire is, the percentage of the breaking strength remains the same. The weight of the wire per unit length increases according to the area of the cross-section, as does the breaking strength. The tension rises with the weight at the same rate. So the percentage of the breaking strength is a constant for a given speaking length. Of course there will be minor discrepancies, but they will vary from sample to sample.

So the idea that anything important depends on the percentage of the breaking strength is unlikely. You get significant differences with different gauges of wire, while the percentage remains more or less the same.

The single bass notes are M or O depending on the better response. This is the reason why the bass notes down to C0 (the fundamental is 16hz so you can count the vibrations as they come off the string) are so much cleaner than on the Bosendorfer Imperial, where those notes are so blurred it really doesn't matter how you tune them as long as you're roughly right.

All of the other notes from the bichords to the high F8 are XM.

Regards
Chris

The Bosendorfer Imperial was and is a half-hearted and half-arsed attempt to extend the ambitus of the piano. Firstly, as explained above, the clarity of the extra notes is abysmal. You may as well hit the piano with a hammer - the sounds would be more musical. Secondly, they provided a cover to make the notes invisible to all except Superman, and even then reversed the colours of the notes to make it clear that these are not to be touched except in cases of extreme emergency and/or life-threatening illness.

The 88-note paradigm is a marketing ploy foisted on us by the Steinway dominance of the piano market. Many French composers of the late 19th and early 20th century were familiar with and wrote music for pianos with a larger ambitus.

I heartily recommend the new CD by the very talented Australian pianist Zubin Kanga, who is very quickly establishing for himself a world-wide reputation in the performance of avant-garde and modern classical piano music. The CD is called 'Not Music Yet' and is recorded on a 2.9m 102-note Stuart & Sons Piano - using the entire keyboard range and the full gamut of the unique Stuart sound and variations. I have had the pleasure of recording Zubin's playing myself and am amazed by the sounds he is able to get out of the Stuart piano. The accepted wisdom is that the Stuart piano is the _only_ piano which is capable of doing justice to the music - a conventional small-keyboard piano such as a Steinway cannot cut the mustard in any way.

These limitations will become more and more apprarent over time and the 88-note paradigm will disappear much as the technology which currently supports it will also disappear.

Regards
Chris

Hello M. BDB,

All that is true, but if you move to a hardened wire (dimensions the kept the same), you are given another factor with which to control percentage of the breaking strength.

Here is an illustration, with two breaking strengths highlighted. The use condition is the same for both because of same dimensions and same stress state in the wire (pitch does not change). However, the percentage of the breaking strength differs for the two highlighted cases because the stress at which they break is different.

Best regards-

From Stephen Paulello's website, these values as the breaking load for each wire type, as measured in Newton by mm2, according to the diameter of the wire:
Type XM - 2600 to 3000
Type M - 2200 to 2550
Type O - 1700 to 2200
Type 1 - 1200 to 1900
Type 2 - 1000 to 1400

It would seem that, unless these values are a complete fiction, breaking percentages for any given note at a defined pitch, diameter, and speaking length would vary depending on the wire type for Paulello wire.

May I offer for reading to all participants in this discussion, Arno Patin's excellent article from his website. http://www.arnopianos.com/#!piano-wire--rescaling/cfm1

In it, he offers that breaking point data is available by class and gauge upon request. I know Arno and will make a request for him to e-mail that data to me. I will share it once I get it.

Phacke, thanks for sharing your chart. What is the source?

Will

If you two want to argue that some obscure measurement is significant against overwhelming evidence that it is not, you are welcome. Since neither of you are likely to rescale a piano, at least you will do no harm.

Au contraire, my dear BDB, I have rescaled many pianos over a period of 20 years or more, using various software programs along the way. And I have done several rescalings using the Abacus software using Paulello wire. I deliberately chose to have Arno Patin do my first two Paulello scalings, since he had already been doing this for about 9 years. I thought I would learn something looking over his shoulder at the beginning and did.

That said, I don't claim to be as sophisticated at rescaling as some fine rebuilders I know. But I'm not a dubber either. My customers are happy so far.

I have no problem conceding your point (confirmed by others)about the percentage of the breaking point remaining the same even as wire sizes increase, it remains a constant. But your comments are based only on wire of one type. Several others agree that this is true within that type wire. This has been a generalized truth where we have had basically one wire type for quite a long time.

But now it is no longer true that we have only one wire type, Pure Sound and Paulello offer other wire types with differing breaking points and attendant breaking percentages. And the same people who agree with you on the one hand are choosing to disagree with you on the other pertaining to these hybrid wires. Several have offered evidence to support their view. But you simply discount it without comment. If you are going to discount the evidence presented, then you have the burden of proving why it is not so.

I leave it to you to argue why the measurements are insignificant. I know that the results are in practice. But you have never actually listened to a piano rescaled and strung with Paulello wire, have you?

Will

Oh, have you had all this experience as an amateur, or are you just ignoring forum rules?

[sigh]...is that really necessary BDB? WilliamTruitt is somewhat new here. He probably didn't know, and besides, he is not hiding anything: he states clearly what he does in his profile!