Angle of bridge: why?

[abarson]

I've noticed that almost all guitar bridges, whether solid or saddle, have an angle, usually with the lower frequency strings being towards the end of the instrument, and the higher frequency strings towards the neck. This is in contrast to other string instruments (violin, cello, etc.) where the bridge is perpendicular to the lay of the strings. Archtop guitars seem to have a perpendicular bridge but the tailpiece adheres to this angling scheme.

I'm guessing that it has something to do with intonation, but I would really appreaciate an informed explanation.

[moro]

Yes, it has to do with intonation.

In theory, the 12th fret should be exactly halfway between the nut and the bridge. In practice, though, the string is pulled slightly sharp as you push it down against the fret. So the distance between the 12th fret and bridge has to be slightly longer than the distance between the 12th fret and the nut. The amount by which it is longer depends on the string, which is why the bridge is angled.

I don't know why violins and cellos have perpendicular bridges, but I'd guess that with a fretless instrument, you can adjust the intonation as you play, so there's no need for the bridge to be at an angle. (Though with fretless basses, they still angle the bridge.)

[Geoff St. Germaine]

Here is pretty much the same question:

Shouldn't the bridge be parallel to the nut?

[fish man]

On a violin, the difference in string gauge relative to the distance between the string's resting position and it's depressed position is so small that it wouldn't be worth trying to compensate for, and it is fretless and therefore the intonation is determined solely by the player anyway.

fm

[abarson]

Okay, so I get the gist about intonation. For my fretless project, I'm using a piezo element that I'll install in the bridge (see picture). As each saddle is already precompensated, should the bridge itself be installed perpendicular to the strings? I was initially planning on using posts to adjust bridge height, but by doing so I would lose the ability to change intonation.