I broke my A string once in the middle of a song where MASSIVE improvisation was required. It was not a good time, but managed to make it through. Turns out I had a tiny burr in the saddle of the bridge. Other than that, I've only had one string break, and that was as I was putting on the new set...defective string. The core wire was broken by the ball.

Also...I've yet to see a music store that won't sell you an individual bass string, (unless it's a high-C string, which most of them don't seem to carry...alas)

Cheers.

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