Silence Kid
New member
Spoiler alert/TLDR: Use a radius gauge larger than your neck radius for optimal action. The "tech approved," method of matching the bridge radius to the neck radius works well enough in practice, but will never produce an ideal result and thus bugs me. A couple steps to visualize:
-Your neck radius is a circle. For the sake of this example you have tiny hands and hate bending, so this circle is a toilet paper tube. The guitar came with a fixed-radius tune-o-matic bridge the same radius as the tube. Your string spacing is (humor me) slightly less than the total diameter of the toilet paper tube.
To represent this, trace one toilet paper tube circle for your neck, with another intersecting tracing above it representing the bridge. Both circles are separated by a distance equal to the string action (again, you're a masochist: let's do .5 cm separating the top of each circle.) Look at the resulting shape formed by both circles. It's a crescent moon. The outer strings of the guitar will always be closer to the fretboard than the inner strings. If you choose an acceptable action for the outer strings, the inner strings will be higher than necessary. If you lower the inner strings to the appropriate action, the outer strings will buzz.
-Now you're a tech engineering a guitar for a person with a larger build; this time, the guitar's neck radius is equal to the curve of the planet earth, and the person/diety playing this guitar wants the string spacing which covers about a 90 deg. section of that circle. God likes his action one mile high. So you set up mile-high saddles (bent steel for tone) starting with a low E in the Atlantic Ocean off the coast of Ghana, moving east to set up additional saddles 15 degrees apart until you wind up at the high E string somewhere near the border of the Australian and Southwest Indian Ocean tropical cyclone basins. You fly a helicopter from one saddle to the next to thread the strings through, and measure the radius of that flight; turns out, this is equal to the radius of the Earth plus one mile rather than simply the radius of the Earth.
Going back to the toilet paper tube example, you can visualize the action of the guitar as the remaining toilet paper on a part-full roll; the radius on the outside is greater than the radius of the tube.
...
So while it's not possible to know the correct overall radius without knowing what average string action you prefer, it'll always be somewhat greater than the radius of the neck, usually by only one to three percent but perhaps greater when you take into account these other aspects (not) to forget:
-If you're not using a compound/conical fretboard (per the above examples,) by necessity the outer strings will have to be even higher still, to account for the peculiar aspects of the string spacing at the bridge being greater than the string spacing at the nut, on top of a constant radius cylinder (Stewmac has a good explanation of how on a compound, or ideally a conical neck, the frets "rise up" to maintain more consistent action toward the high frets.) So the actual effective radius will probably be even higher than the radius + action. But in practice, this is more like squashing down the higher radius to a flatter ellipsoid section.
-With a compound/"conical" fretboard, the radius of the bridge should be somewhat flatter than the highest radius of the neck, before you even add the additional radius on to account for the action; you can do a projection to approximate this.
-Sliding a saddle forward for intonation increases the action of that string, so that affects the radius as well
...So what's the end result? Of course very little of the above matters in practice. But for me, I just say **** it when I set up my action, set each string as low as it will go without buzzing (or simply to my preference,) and never use a guage.
-Your neck radius is a circle. For the sake of this example you have tiny hands and hate bending, so this circle is a toilet paper tube. The guitar came with a fixed-radius tune-o-matic bridge the same radius as the tube. Your string spacing is (humor me) slightly less than the total diameter of the toilet paper tube.
To represent this, trace one toilet paper tube circle for your neck, with another intersecting tracing above it representing the bridge. Both circles are separated by a distance equal to the string action (again, you're a masochist: let's do .5 cm separating the top of each circle.) Look at the resulting shape formed by both circles. It's a crescent moon. The outer strings of the guitar will always be closer to the fretboard than the inner strings. If you choose an acceptable action for the outer strings, the inner strings will be higher than necessary. If you lower the inner strings to the appropriate action, the outer strings will buzz.
-Now you're a tech engineering a guitar for a person with a larger build; this time, the guitar's neck radius is equal to the curve of the planet earth, and the person/diety playing this guitar wants the string spacing which covers about a 90 deg. section of that circle. God likes his action one mile high. So you set up mile-high saddles (bent steel for tone) starting with a low E in the Atlantic Ocean off the coast of Ghana, moving east to set up additional saddles 15 degrees apart until you wind up at the high E string somewhere near the border of the Australian and Southwest Indian Ocean tropical cyclone basins. You fly a helicopter from one saddle to the next to thread the strings through, and measure the radius of that flight; turns out, this is equal to the radius of the Earth plus one mile rather than simply the radius of the Earth.
Going back to the toilet paper tube example, you can visualize the action of the guitar as the remaining toilet paper on a part-full roll; the radius on the outside is greater than the radius of the tube.
...
So while it's not possible to know the correct overall radius without knowing what average string action you prefer, it'll always be somewhat greater than the radius of the neck, usually by only one to three percent but perhaps greater when you take into account these other aspects (not) to forget:
-If you're not using a compound/conical fretboard (per the above examples,) by necessity the outer strings will have to be even higher still, to account for the peculiar aspects of the string spacing at the bridge being greater than the string spacing at the nut, on top of a constant radius cylinder (Stewmac has a good explanation of how on a compound, or ideally a conical neck, the frets "rise up" to maintain more consistent action toward the high frets.) So the actual effective radius will probably be even higher than the radius + action. But in practice, this is more like squashing down the higher radius to a flatter ellipsoid section.
-With a compound/"conical" fretboard, the radius of the bridge should be somewhat flatter than the highest radius of the neck, before you even add the additional radius on to account for the action; you can do a projection to approximate this.
-Sliding a saddle forward for intonation increases the action of that string, so that affects the radius as well
...So what's the end result? Of course very little of the above matters in practice. But for me, I just say **** it when I set up my action, set each string as low as it will go without buzzing (or simply to my preference,) and never use a guage.
