Hi fellow musician, welcome here,
are all those strings made of metal? On some instruments (harp, bowed strings...) the core is polyamide, catgut or some more recent material, spun with a metal wire, sometimes two.
Alloys have a "composition" rather than a "formula". Some alloy elements are miscible in any proportion, for instance Cu and Ni, so we couldn't give a chemical formula like CuNi2
like we do for H2
O. Other elements do make compounds in fixed proportions, for instance Fe3
C, and these compounds can precipitate in the alloy, but the crystals they form are dispersed in a matrix of different composition. Exceptionally, the matrix can have nearly-fixed proportions like TiAl, but then it dissolves alloying elements or contains precipitates, in variable amount.
All together, the composition of an alloy varies continuously, so we don't give a formula for it, with integer coefficients on the numbers of atoms, but a composition, with decimal proportions of the mass of the elements.
If you search the Web for "high carbon steel" or "phosphor bronze", some designations suggest a composition, like XC90 or 42CrMo4, while other don't. Each economic zone has (several) different systems of naming, and the alloys are not fully equivalent. When you know a designation, the manufacturer's data gives a range of alloy composition. Many "high carbon steel" and "phosphor bronze" alloys exist, and usually the string manufacturer doesn't tell which one he uses.
The processing history of the string is as important as its composition. Musical strings must be extremely resistant, because usually they shall propagate the sound faster than air does, and when the instrument doesn't need that, the string's core is overspun with metal wire so the core is extremely stressed nevertheless. For steel, 342m/s means 920MPa tensile stress, but 1.3*342m/s is better, and the string needs margins, so well over 2000MPa is desired. This is obtained by cold-drawing the wire extremely. The process was invented for music instruments, especially pianos, and later aeroplanes and other activities used the "piano wire" too.
One manufacturer herehttps://www.roeslau-draht.com/en/products/data-sheets/
guaranteed 2790MPa, wooooooow.
My ramblings about music strings therehttps://www.scienceforums.net/topic/117420-string-instruments/http://www.chemicalforums.com/index.php?topic=98904.0