(Sketching this part out on paper will help you grasp what's going on here.) We're shifting the base of the right triangle up above the top of the front face of the guitar 1/4 of an inch such that it's level with the top of the 16th fret. about what a single cut les paul jr has it. the height you want to the top of the 16th fret above the face of your slab / flat top guitar. The general rule of thumb for bridge height seems to be 9/16ths = 0.5625". We need to define the length of 2 sides of the triangle to find an angle, so we'll also need the opposite side of the triangle (opposite the angle we're looking for) = the bridge height. In trig terms, that 9.9455 is the adjacent side of our right triangle. Subtract the 16th fret's measurement from that to get the 16th fret to the center of the bridge. So the center of the bridge is 24.811 + 0.0625 (1/16th = half of the 1/8th back) = 24.8735 from the inside of the nut. Most people building a gibson style use a 24.5625 or 24.625 scale board) (aside = eventhough gibsons are stated to have a 24.75 scale, it's closer to 24.5625 when calculated by the modern rule of 17.817. Down below, the recommendation for a tom bridge is treble post 24.811" from the nut. The flyers vs friars game isn't all that great, so let's start here: ΔΆ4.75 scale (rule of 17.817 - 12th root of 2) has the 16th fret 14.928" from the inside of the nut.
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