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Intonation question

This is my first post, so sorry for sounding extremely basic, but I had a question about intonation.

I am trying to understand intonation a bit. I have heard that the distance from the nut to the 12th fret, should equal to the distance from the 12th fret to the bridge saddle, but does that vary based on note that the string is tuned to, or string size, etc?


I've been playing bass for about 22 years and have finally decided to build my own bass, but wanted to make a custom hardwood bridge as part of the build.

Thanks for the help!
 
In a perfect situation half the wave length will be double the frequency and therfore sound an octave above. This is a simple physical principle. However there are things that change the way a string acts and therefor there is a SLIGHT deviation from the 12th fret being exactly in the middle of the saddle and the nut.
 
In a perfect situation half the wave length will be double the frequency and therfore sound an octave above. This is a simple physical principle. However there are things that change the way a string acts and therefor there is a SLIGHT deviation from the 12th fret being exactly in the middle of the saddle and the nut.


Is there some way to calculate the proper distance of the saddle from the nut for each string? I wanted to make a bridge that was non-adjustable, somewhat like an acoustic guitar bridge, but a bit different, with string through.
 
I know I've seen basses on here that were built with a wood fixed bridge... Does anyone have any input on how I would determine what the proper spacing of the saddle for each string would be?

Pretty please?!?