Banjo bridges - where to position them
In theory, you measure the distance from the 12th fret down to the nut (the ivory looking thingie where the strings sit on, near the peghead) and put your bridge the same distance away from the twelfth fret towards the tail piece, at a ninety degree angle to the third (middle) string. In a perfect world, that's the proper spot for it and putting your bridge there gives you the best sound possible - in theory anyway. Don't touch anything just yet!
Testing the theory
Not all banjos are created equally and most can benefit from a little tweaking. Finding out if you're a candidate for some tinkering is pretty simple: tune your banjo with an electronic tuner and if things sound wrong when you make a chord, especially higher up on the neck - you're it. Match tuning is another tip-off: assuming you're in the regular bluegrass G tuning (G5435, or gDGBD), when you fret the second string at the third fret and it doesn't match the pitch of the open (unfretted) first string - think bridge. Here's some more critical match tuning spots: fret the third string at the seventh, this note should have the same pitch as the open first string. Now fret the second string at the eighth, and this note should be the same as the open fifth string.
More match tuning tricks, play three chimed notes: the first string at the twelfth fret, the third string at the seventh fret and the forth string at the fifth fret - these three notes should all have the same pitch. If they don't, despite the proper theory, your bridge is in the wrong location. Either that and you need fine tuning, or you need a compensated bridge. If they do sound the same you're just about done but check the fine tuning details anyway. You never know, you might come up with additional sound improvement.
Oh, in case you don't know what a chime is: lightly touch the string with one of your left hand fingers directly above the fret - not behind the fret like when you're playing - of the 5th, 7th, 12th or 19th fret, but do not press down on the string. With your right hand pick the string and you'll hear a real pretty bell-type sounding note. Of course, left-handers are smart enough to know the drill here...
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