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thru-neck bass guitar neck angle

don't get it :/
out of my league with the math; i just make a drawing for each style of bridge :)

Easy trig. Imagine a flat plane, with your bridge and nut sitting on it. Let's say the bridge saddles are .5" higher than the nut. Then you slide bridge away from the nut a distance that corresponds to your scale length; say 34" (34" would actually be the length of the hypotenuse, but it will be close enough.) Now you have two sides of a right triangle, so you can figure out the angle at the nut. From the nut, the bridge height is the Opposite, and the length from the nut is the Adjacent, so using your trusty mnemonic SOHCAHTOA, you know that this is a tangent function. You're trying to get an angle though, not the length of a side, so you use the inverse tangent (or arctan, or tan^-1, they mean the same thing.) So divide .5 by 34 on your scientific calculator and hit the tan^-1 key, and you get .84252..... about one degree.

When you change the neck angle though, you change the height of the bridge from the nut, which changes the angle...this could be a calculus problem, and I suck at that. The trig solution is close enough.
 
Not the nut. The end of the fingerboard. This calculation if to find the cant of the neck. If you measure to the nut then this equation is useless.

so your finding the angle to cut in the body portion that gives you perfect action height on the last fret; and the 'string' would represent the longest line of the triangle?
those arnt techy terms; but im tired and already over my head :/
 
Easy trig. Imagine a flat plane, with your bridge and nut sitting on it. Let's say the bridge saddles are .5" higher than the nut. Then you slide bridge away from the nut a distance that corresponds to your scale length; say 34" (34" would actually be the length of the hypotenuse, but it will be close enough.) Now you have two sides of a right triangle, so you can figure out the angle at the nut. From the nut, the bridge height is the Opposite, and the length from the nut is the Adjacent, so using your trusty mnemonic SOHCAHTOA, you know that this is a tangent function. You're trying to get an angle though, not the length of a side, so you use the inverse tangent (or arctan, or tan^-1, they mean the same thing.) So divide .5 by 34 on your scientific calculator and hit the tan^-1 key, and you get .84252..... about one degree.

When you change the neck angle though, you change the height of the bridge from the nut, which changes the angle...this could be a calculus problem, and I suck at that. The trig solution is close enough.
But does one degree make a difference?
 
so your finding the angle to cut in the body portion that gives you perfect action height on the last fret; and the 'string' would represent the longest line of the triangle?
those arnt techy terms; but im tired and already over my head :/

No. You are finding the angle to cant the neck so that the strings are even all along the neck giving the player the option to set their action. Ignore the string in this triangle it's irrelevant.
 
Not to the nut; to the end of the fingerboard. This calculation is to find the cant of the neck. If you measure to the nut this equation is useless.

Actually, Mikey's right... you'll end up with high action in the upper frets if you measure from the nut. Here's a quick sketch of the triangle you're solving:


Screenshot2011-02-01at14110.png


Same math, just measure from different places. The hypotenuse becomes a line level with the frets, that extends below the adjacent. Stay up late on TB, learn something.
 
All of my instruments I have made are neck thru construction and I have not needed to use an angle on any of them. I use the hipshot A type bridge that is pretty low profile and I make sure the fingerboard has enough clearance from the body to allow for a straight shot from the bridge across the top of the frets. I can see that a tall bridge might require an angled neck but I would either recess the bridge into the body or put a wooden shim under it to level it with the fingerboard before I would do an angled neck thru.

Is neck relief something that you guys take into account when angling the neck? I personally like my neck as straight as possible with very low action but certainly not everyone is into that.