I recently saw a picture of a type of lyre in a magazine. I thought it might be fun to play with, so I got a board and built one. When I went to string it (using some old autoharp strings) I found that there was a very small tone range between when a string was tight enough to make a decent tone and when it broke.

The thing has seven strings. I know the free length of each string, the hertz value of the note I want each string to play, and can find out the tension needed for the string. Does anyone have a formula I can plug these variables into to find out the gauge of string I need for each note?