"Piano wire"

[minhogang]

One of my high treble strings just broke so I read a book and some tutorials on how to replace them. I understand how they work but I have trouble finding a vendor online. Most labeled as piano wire are expensive, but I am wondering whether a wire like this https://www.amazon.com/Carbon-Smooth-Diameter-Precision-Tolerance/dp/B000VYHKO4/ref=sr_1_1?ie=UTF8&qid=1485668537&sr=8-1&keywords=piano+wire could do. (of course finding the right diameter)

[hardy_practice]

If you insist on doing it yourself take or send a sample to a piano parts supplier.  I'd leave it to the tuner (it's what they do).

[indianajo]

I've used this "music wire" from mcmaster.com industrial supply.
https://www.mcmaster.com/#9666K57
The .033" diameter size fit both my 1982 Sohmer and a fifties Baldwin Hamilton.
That .051" diameter wire on Amazon most probably is the wrong size.  Also ductile tie wire and spring temper wire look similar in pictures.  Mcmaster sells both kinds, with ample description to keep you away from the tie wire used for hanging pictures or affixing re-bar in concrete.  
You may want to measure with a micrometer or dial calipers whatever piano you are repairing.
This was a thousandth off from what measurement I got, but sounds original when installed.
You can also buy wire in cut lengths from stevespianoservice.com with an end already affixed to it.  They sell the same parts as American piano supply but don't have the adversion of the latter to talking to amateurs.  
I built a special tool to radius the end nicely.  It was a 3/8" diameter grade 2 bolt with a 9/64"  hole drilled through it near the head. Then I took a tree bit on a die grinder and radiused the hole to one side so the music wire would bend to a nice radius when the bolt was twisted with the wire through it.
Be sure to not wiggle the pin in the pin block too much from side to side when twisting it.  Same hand motion as inserting a bolt in soft material.  All motion must be in the twist dimension.