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I have been unable to find equations / calculators online for rescaling pianos using alternate string materials. I'd like to experiment with a couple notes on my 1950 Baldwin Hamilton, and see what difference using tungsten winding (19.25g*cm^3 density per Wikipedia) would be compared with copper (8.96g*cm^3 density).
(Tungsten is ~2.15x denser than copper. IMO this would allow for much thinner windings, improving the inharmonicity - as I understand, inharmonicity is directly related to the ratio of string length to its diameter.)
Maybe there's a reason why it's not used though. Why? Cost? It doesn't work? I'd like to find out for myself, but only on a couple notes for starters cause I don't want to waste several hundred $ on the entire bass section just to find out it doesn't work.
Then there's the possible difficulty of getting said strings made. I know some string bass makers make them, but would they be able to make them to my specifications, if I specified the core wire material and diameter, total length, the fact that there's a hitch pin loop (which I could make myself later if necessary), winding material, diameter and length, etc.? Or would I have to make them myself, and possibly scrap the idea? (Then there's the difficulty / impracticality of using tungsten windings on the upper end of the bass - I understand it's difficult to make strings with extremely thin windings.)
Also if I used a string material with radically different density from the original, would that mean I might need to change where the piano switches from unichords to bichords, and from bichords to trichords? (Obviously I'm not moving the bass/tenor break, and I don't want to rescale the bridges on this piano.) And, if I was to end up rescaling the entire bass, up to the tenor, I personally would prefer to keep the plain steel trichords starting at C#3. IMO they sound better than the wound bichords on newer Hamiltons, even though they may not be as easy to tune. (While I may like running plain trichords a bit lower than some designers like, I have heard cases where the designer took it TOO far, like the older 4'11" Yamaha grands, for example.)

Pure tungsten has very low ductility. IOWs, It won't wind worth a darn.

I think you have some misunderstandings concerning inharmonicity. Inharmonicity relates to the flexibility of the wire. In the case of wound wire, the main component is the core diameter. The wrap has some stiffening effect which is far outweighed by the increase in flexibility of the entire unit. IE the core becomes MUCH more flexible because of the increased tension attainable because of the increase in mass from the wrap. \\

The additional stiffness of a non-ductile material would serve to counter the decrease in inharmonicity of the core. You might find that you have a small overall sized bass string, that is less flexible because of the lack of ductility of the wrap.

Tungsten won't wind worth a darn? Then why is it used on some cellos, string basses and electric bass guitars? And what would prevent it from being wound around a steel core and used in a piano? Or would the string designer need to come up with a different core material?

And maybe I do have some misunderstandings about inharmonicity. I was basically trying to figure out how to improve a given string by winding it with a denser material, while keeping flexibility up, speaking length and tension equal, and diameter down.

I assumed you meant pure tungsten. My mistake. Tungsten alloys would have to be used.

I'm not sure it matters what you wind a string with. (Within limits, of course). Inharmonicity of a string is based on the flexibility of the (Core) wire. THe important thing when trying to keep everything the same, (Length, tension and flexibility) is to keep the mass of the wound wire the same. You could (again within limits) wind with most any ductile material. Keeping in mind that not all materials have the same density.

Aluminum has a density of about 27% that of piano wire, Copper about 89%, soft iron as found on many older piano is about 79% as dense. Tungsten has a density almost 3 times that of copper. Based on these densities, one can understand why some American makers used Aluminum windings on small consoles and spinets in the low tenor of their scales. Copper would have been entirely too small a diameter to wind successfully for the small amount of weight needed for these scales. Tungsten would be too dense for most of the higher bass notes on most scales. Unfortunately, the AL wound strings sounded BAD by the time I heard any of them. Perhaps they sounded better when new.

I'm sure other metals have been used. Most likely we keep with copper because it lasts a long time, sounds good when done well and is fairly inexpensive.

Of course the best way to reduce the diameter of the bass string is to make the piano longer.

Good luck with your quest. I'd be interested in hearing if you have any breakthroughs.

Copper is denser than steel or iron. Tungsten is a bit more than twice as dense as copper.

Ok... so is there a way to make calculations for strings taking into account different density materials? I so far haven't found anything online - the few calculators I've tried all assume you're wrapping copper over steel, and if I remember correctly don't account for double wrap.

Just a guess but using the formula that you found for copper over steel, copper density being 8900 Kg/m3 - would it not be unreasonable to replace the density number with that for the material that you propose to use - like iron would be 7900 or aluminum 2700?? tungsten ??? and arrive at a reasonable tension/ inharmonisity value?

It is a waste of time to speculate about the density of materials that may not be at all suitable for wrapping strings.

Some people have more curiosity than others. Besides, it's our time to waste.

But it would be more fruitful to look into the properties that make a material suitable for winding bass strings other than density. Why does copper work so well? Why does aluminum work so poorly? Why is soft steel somewhere in between? How would you test for longevity, which has turned out to be so important?

I agree. Copper is used because it works so well, lasts so long and can be used for all but the lightest requirements.
In looking for alternatives, I believe that most people will learn something about how the piano functions. In other words, they will become knowledgeable about what they are doing and the theories behind proper function and design. This is usually a good thing as most people choose to remain woefully ignorant about what they are doing for a living.
So I never discourage a theoretical discussion if it isn't based on total lunacy.

The basis for calculating wound string tensions is the Taylor formula which is: Tension= freq.squared times length squared times diameter squared times pi (3.14) times specific weight of the materials all divided by the constant 9.81. The difficulty lies with calculating specific weight, as you will have two different materials, (the core and the wrapping) and small spaces of air, not part of the string, but which you must take into account nevertheless. This works out to 78.5 % wrapping material to 21.5% air. For example the actual specific weight for copper is 8.9, but figuring the air space, the specific weight is reduced to 6.9865 for purposes of the formula. And then of course, there is the steel core which is 7.85. For bass strings, there are guidelines for ratios between core material and winding, depending upon where you are in the scale. I would imagine they would hold true regardless of the winding material, at least used as a guideline. It is 2:1 for the very low strings, 2 of winding to 1 of core, to 4:1 in the highest wound strings. Anyway, maybe you can use this as a jumping off point (but not as in jumping off a building <g>).

I’ve heard something like this before and I keep wondering where it came from. It does not seem to have been followed by piano makers in the real world. For some—though by no means all—single-wrapped low bass strings that 2:1 ratio might be close but for the higher wrapped strings a 4:1 ratio is not even close. For example, in the scale for a new piano that I just happened to have open there is a bi-chord wrapped string up close to the break with a core of 1.0 mm (approx. 0.039”) and a copper wrap of 0.47 mm (approx. 0.019”).

Depending on the length of that string (relative to the length of the lowest strings using plain steel) the diameter of that wrap wire could be more or less on a smaller or larger core and with no consistent ratio between them being discernable.

ddf

I am aware of only very limited experiments being conducted with tungsten wire. The main problem (if memory serves) was that the the wrap wire broke down quickly under repeated hammer blows. And we do expect our wrapped strings (as with every other component of the piano) to last pretty much forever.

I do not know for sure if the wrap wire was pure tungsten or some tungsten-based alloy. I think it was pure tungsten, but here memory does not serve....

ddf

Oops, my mistake. The ratio should be 1:4. Read my notes wrong. Sorry.

Even so...it just doesn't seem to hold true in real life.

I've tried, over the years, to come up with a simplistic, yet reliable, "rule of thumb" like this but they always break down when I start trying to use them to design real strings in real pianos.

ddf

[/QB][/QUOTE]Even so...it just doesn't seem to hold true in real life.

I've tried, over the years, to come up with a simplistic, yet reliable, "rule of thumb" like this but they always break down when I start trying to use them to design real strings in real pianos.

ddf [/QB][/QUOTE]

Not trying to be too pedantic about this, I just want to respond that the 1:4 ratio is taken from "On the Calculation of the Tension of Wound Strings". The author says: "for the note F33 the copper-steel ratio should average 1 to 4, e.g. .2mm copper to .8mm steel." Quoting further, "The two average values of the diameter ratios for A0 and F33 are the two extremes...we can set up an average value for each intermediate note." Since the 1:4 ratio refers to a fairly high note for a wound string, this rule of thumb may be a little closer to reality.

And that's not the only mistake in the book.

ddf