# Fretboard Geometry

Discussion in 'Tele-Technical' started by Nick JD, Apr 22, 2011.

1. ### piece of ashFriend of Leo's

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I'm not fishing for an argument. Perhaps one of your posts was deleted. I see 2 questions and 3 statements.

I had no specific knowledge of how a compound fretboard might work with arthritic fingers. Assuming that those arthritic fingers were yours, and respecting your right to preference, I simply advised where you might easily try one of these necks out.

If I'm reading between the lines correctly at this point, it is clear that you have tried these fretboards and your 2 questions were simply a rhetorical way of expressing your dislike for them. I was just taking you seriously.

Follow what Nick is saying here... it is perfectly clear that any fretboard that has been beam leveled has inescapably acquired a compound radius in the process.

2. ### Miopic ChitlinTDPRI Member

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This is why I don't do necks. The lottery is for people who don't know math, and I play the lottery...a lot.

3. ### BolideFriend of Leo's

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I also drank way too much coffee today, but this is a great thread.
I'm onboard with almost everything, and will do some cogitationinizoning before asking the question that is not quite fully formed within my shiny ovoid cranium.

4. ### genesiospinolaTele-Meister

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Hi Nick! How are you my friend?! Great thread! But, one question...The strings radius at the nut is not 9,5" to put in the formula. Do you know what i mean. The slots heights at the nut are differents and do not do a 9,5" radius. High "e" to low "E" we have to increase like 0,002" by string. The amplitudes of vibration of the strings are different, had to its thicknesses. BUT, i know that thinking the fretborad as a cone is the correct way! Let's think about this. For me the ideal would be to put the 6 strings heights at the nut in another program to find the correct "radius", or i think that is not yet a radius anymore, i'll be a curve "goin up".
Cheers Nick!

5. ### Keyser SozeTele-Holic

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That is exactly what Ken Parker was getting at in his comments. The fact that the string spread out laterally due to the changing width between nut and bridge means that the frets/fretboard must either be perfectly flat (infinite radius), or must must describe a cone in order to maintain any sort of even relationship between each string and the fret as we move up the fretboard.

6. ### piece of ashFriend of Leo's

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Yes Keyser. It occured to me somewhere along the line that if you wind up with the geometry Nick is talking about because you "beamed the frets" relative to the string paths and fretboard edges, you have effectively cut a compound radius on the frets that is proportional to the string spread.

So compound geometry is cool... but like many things they went to far? I mean a 10-16 radius... a ratio 1/1.6... that's more than the ratio of string spread. I'll have to play with this in AutoCad... I don't know if I want my silly fixture to be 18 feet long!

And I don't want to know what those blue levels cost at that length...

7. ### Keyser SozeTele-Holic

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Actually, I think 10"-16" is not 'too' far. But it is about as far as you can go without the feature descending into irrelevancy.

Like Nick noted, once the starting (nut) radius gets up around 12" or higher the relative changes in ideal shape can rapidly be overwhelmed by the changes necessary due to other issues (amplitude of heavy strings, the inherent flex of an organic hunk of fiber, etc.) Or, again due to the really small actual differences, the feature can be created solely through fret level/dress technique.

To my mind the compound radius is most useful for people (such as me) who like the smaller Fender radius low on the neck (for barre's and thumb over technique) because it is about the only way to get a decently low action up high.

8. ### murrmac123Tele-Meister

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This is indeed a great thread, well done, Nick.

I am going to throw in a piece of trivia which is of absolutely no practical use, but which might provide ammunition for some arcane discussions over a few beers ...or maybe not ...

In a constant radius fret board, the fret slots follow a true arc of a circle, but in a conical fretboard, they cannot follow a true arc of a circle, instead, they follow the arc of an ellipse.

There, I did say it was of no practical use ...

9. ### David CollinsTele-Afflicted

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The formulas there are all great and interesting, but in practice can be greatly simplified.

If you want the board to represent a truly conical section (mostly for ease of machining while keeping a straight line beneath each string), then there is one simple rule to follow.

The radius should remain directly proportional to the string spacing.

That's it. Radius A / Spacing A = Radius B / Spacing B. If your string spacing is 1.5" at the nut with a 10" radius, and spreads to 1.8" at the 12th, then you have 10/1.5 = x/1.8. Solve for x, and you have your 12th fret radius at 12". Simplified formula - (Ra/Sa)*Sb=Rb

Of course you don't need your board to be a section of a true cone. That makes it convenient to shape a board on a pendulum arm, but it's not the only way to get a straight line beneath each string. You can start at 10 and end at 20, or start at 12 and end at 12 if you want, and if you level in line under each string you will still get a straight line beneath each string. If you do this of course you will not have a truly conical section, and there will in theory be no more than 2 points along the board that are shaped to a perfectly true radius, but all this is actually entirely inconsequential in the end setup. You might have to call the shape or any particular profiles a elliptical, parabolic, hyperbolic, or some other proper name for a geometrical form, but beyond that it doesn't really matter. If leveled properly, each string will still see a series of points in a straight line beneath it.

I think I may have to disagree with Ken's interview on one small point. It sounded as though he was placing the blame for fretting out on bends entirely on the lack of having a true conical section. Not sure if I read it exactly how he meant it, but if so this would not be entirely correct. When bending, it is quite simply the severity of the radius and the height of the action that determine how far you can go before fretting out. That's kind of a separate issue from the bulk of what's being discussed here though.

10. ### piece of ashFriend of Leo's

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The key things in my mind are as follows:

1) The realization that a fretboard leveled with a beam will arrive at some shape very near a conic section.

2) Knowing that this will happen would permit the fretboard to be cut to that shape prior to fretting.

I'll be fretting in stainless:

3) I have no belief in the sonic qualities of frets.

4) The best way to refret a neck is not to... use material that will last longer in the first place.

5) The more accurate the fretboard the less metal that needs to be removed. Nick's demonstrated that the amount of material in question is on the order of a sparrow's fart. But it's still stainless.

The real kicker is this:

6) If a neck made with a cyliderical radius will infact become a compound or psuedo compound radius, when beam leveled, with radius proportional to string spread... then that same logic must extend to fretboards made with compounding that exceeds the the relation of radius proportional to string spread.

Strat spread at nut: 1.4 inches

Strat spread at fret 22: 1.898

Ratio = 1.898 / 1.4 = 1.356

This in mind, it would seem that compound radius fretboards on the order of 10 to 16 have gone too far... in a complimentary sense that "normal fretboards did not go far enough.

This also means that my nifty fixture must have "focal point" 51.5 inches behind the nut... and the sanding beam needs to be 72+ inches long... dammit!

11. ### piece of ashFriend of Leo's

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murrmac123,

Perhaps we should be cutting fret slots perpendicular to the conic axis... and ditch all those all elliptical sections altogether?

Where are we going to get curve nut blanks???

And... I won't buying 3 levels and going through yet another 12 step program... thank you.

12. ### Colt W. KnightDoctor of TeleocityAd Free Member

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Who is Ken Parker?

13. ### piece of ashFriend of Leo's

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I think he is Spider Man... right?

14. ### Colt W. KnightDoctor of TeleocityAd Free Member

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Nope thats's Hank Parker, or wait, is he the fishing guy?

15. ### piece of ashFriend of Leo's

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17. ### piece of ashFriend of Leo's

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Pretty interesting approach on those archtops... hope his engineering is as good as his design...

No bridge adjustment... pretty cool if it works and lasts...

18. ### David CollinsTele-Afflicted

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Yup, that's Ken - or at least the company he started. Not sure if he's still actively working with that line, or if he sold it off or still owns it. I believe he's focused on work with archtops now, which though I've not played any have heard marvelous things about. Ken does have a truly brilliant mind, which kind of makes me wonder if the quote from that interview may have come off not sounding exactly how he meant it.

As to the rest, I wouldn't worry about board lengths (all gets factored out) or abstract focal points. Your leveling bar only needs be as long as your board. If you start with whatever radius you want at the nut, and whatever radius you want at the end, you can easily level any errors out of a board by hand before fretting. Whether the board is a straight single radius, or a compound radius that changes too drastically for a theoretical cone section, the results will be the same. If you adjust your neck before fretting to be dead straight on it's center line, you will end up with a very slight backbow in the middle of its length along the edges. Mark the board with pencil, and start sanding with a bar (fanned to keep in line with string path as you move across) being careful not to alter the radii at the ends. The markings should disappear from the center line in a swipe or two, and you'll end up taking a hair from around the middle frets as you approach the edges. When the pencil lines are gone, you have a pretty much perfectly straight board beneath each string.

19. ### piece of ashFriend of Leo's

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Actually... did you see my jig in post #8? I had floundered around for a few hours with a StewMac sanding bean (PoS0) and got no where. Once I made the fixture with the focal point... I was done in 20 minutes... and it was flawless. Keep in mind, this was for a fretless bass... so you have to "get it right" on the wood itself... no frets to make up for this or that.

I had done fretless conversions before and found that getting good "mwah" over the whole board was tough. This guitar (mine) oozes "mwah". So the anal approach paid off.

I suspect it'll be easier to dial it in a guitar... if for no other reason than they're shorter.

20. ### Colt W. KnightDoctor of TeleocityAd Free Member

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Mwah? Are you talking about kisses?

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