My rant on why EVERY fingerboard should have a compound radius

[cmjohnson]

A long read but if you can understand my reasoning, I think you'll agree with me by the end.




Here's a "pro tip" for you concerning how the neck thickness should change as you go up the neck.

It should follow the same ratio of thicknesses as the ratio of widths on the fingerboard.

So, just pulling numbers out of my head, let's imagine that the neck width changes by 10 percent from the nut to the last fret before the heel starts.

In that case, the thickness of the neck should also then change by 10 percent from the location of the nut to the start of the heel carve.

This way you retain a proportionate neck shape and the shape of the carve can remain constant. Most players will find this to be a consistently comfortable neck.

More neck and fingerboard trivia: Assuming a scale length of ABOUT 25 inches, and using a standard nut width and fingerboard taper, to wit, 1 and 11/16" width at the nut and 2.25" where the body and neck join, then if you were to put a compound radius on your fingerboard which is a 12" radius at the nut and a 16" radius at the end of the fingerboard, then you will have made a theoretically ideal fingerboard.

By theoretically ideal, I mean, visualize this: The two defined radii (12 and 16 inches) define two points on a truncated cone, 24 inches in diameter at the skinny end, 32 inches in diameter at the fatter end. (And right about 18 inches long.)

The surface of this imaginary cone is the surface of the fingerboard. If you were to extend it, to the length of the scale of the guitar, it would represent the entire string path from nut to bridge.

Following these radii, this length, and this fingerboard taper, the width of the board increases at exactly the same rate that the radius becomes flatter.

If you were to set this imaginary big fat truncated cone/barrel on its big end, on a level surface, and start drawing perfect vertical lines down it, as seen from the perspective of someone standing with the cone centered at eye level right in front of him, and you were to draw two of these vertical lines from the top of the cone to the bottom, with the lines spaced 1 and 11/16" apart at the top end, then those two lines create your perfect fingerboard.

What is interesting about this is that the edges of the fingerboard (and the frets) would be perfectly straight if you laid a straightedge across them, like if you were to string a high or low E string across them. The centerline of the fingerboard would also be a perfectly straight line according to the straightedge.

Now, if that fingerboard was NOT made with a compound radius, but only had a single radius on it (let's say 12 inches) then something interesting happens.

The center of the board remains exactly the same.

But THIS board doesn't fit into the conical profile. It's cylindrical.

And thus there is an error in the shape of the edge of the board. The board gets wider but it doesn't get flatter.

Imagine you've removed the compound radius board from our theoretical barrel, and installed the single radius board in the barrel instead. And imagine there are strings running over it.

What happened at the edges of the board? The radius doesn't get flatter toward the bottom of the barrel. If we assume that we installed this board in the barrel with the centerline of the board in exactly the same position as the original radiused board, then you will see that by comparison, the ends of the higher numbered frets are HIGHER than they would be on the surface of the barrel if the board was the original compound radiused board.

What this says is that for a single radiused board, the outer edges of the frets need to be dressed down lower than the centers of the frets. Actually the ideal line of the tops of the frets at the outer edges should be a very shallow gradual curve downward.


It is only with a compound radius board where the ratio of the radius change is the same as the ratio of the change in board width, where the ideal lines (before adding relief) made by the tops of the frets at the center and both edges of the fingerboards are exactly straight lines.

Read that paragraph again. It is vitally important to helping any builder or guitar tech to deliver consistently better fretwork with lower action. Because sometimes, straight topped fretwork is WRONG.

If the fingerboard's radius were to go too flat, too fast, then the problem is accentuated. You'd have to grind down the outer parts of the frets even more to achieve ideal action height. Imagine the board on the cone again. Flatter frets won't wrap around the barrel, they'll go straight instead and would be too high.

If the radius of the board were to get too tight, which is not something you are likely to encounter, then you'd have to grind down the middle of the frets instead.

Or, if the middle of the board was aligned to be perfect to the cone surface then the ends of the frets would just fall away too fast at the bottom of the board. They'd describe a circle INSIDE the body of the barrel. Fortunately you're not likely to encounter a compound radius board where the bottom end has a tighter radius than the nut end.

The last piece of the puzzle is the bridge saddle heights. To be ideal, they have to describe an arc that also fits perfectly into our truncated cone/barrel if it were to be extended to meet the bridge location. You can figure the desired bridge ratio by simple math, already knowing the ratios involved and the distance from nut to last fret and the scale length.

Understanding the truncated cone that defines the compound radius, and how it is natural and correct for a fingerboard that gets wider toward the bottom, will help you to deliver perfect action in guitars you make.

In simplest terms, the nut, every fret, and the bridge saddles should all be proportionate to each other and all form part of that perfect theoretical truncated cone.

Since the nut and last fret may be assumed to have 12 and 16 inch radiuses, and the span between them is about 2/3 of the way to the bridge, then you should be albe to calculate the idea bridge saddle radius now.

Answer: The bridge saddles should form about a 18" radius. A bit flatter but not much.

It's the taper of the fingerboard that dictates, even demands, that the radius of the frets should change proportionately to the fingerboard taper. That demands that the bridge saddle heights should also change according to the same proportions. And being able to visualize the truncated conical barrel is very helpful to understand why this is so.

This also indicates that if your fingerboard has a taper, then a single radius on the fingerboard is ALWAYS wrong. I was surprised when I realized this, because I've always been a fan of the 12" Gibson radius. I'd never really given much thought to it. I just like the way Gibson builds guitars. Critical thinking was not taking place.

Now I know. A tapered fingerboard (narrower at the nut end) demands a compound radius if you want potentially perfect action without having to do a lot of extra fret sculpturing.


But the compound radius has to extend to the bridge saddles, too, or it won't work perfectly.

 

[Mattsta]

Your theory is sound

In reality, I don't believe it makes much difference for a lot of people and their style of playing.

A lot of other criteria also effect the way an instrument plays, no?

 

[DrASATele]

Very interesting... I'm still processing...
I feel as though you are not alone in this point of view A while ago I read another's post similar to this on TDPRI.
The type of neck you describe sounds awesome but it also sounds more suited to a CNC in terms of practice.
I always start with facets when sculpting a neck but I think this would be difficult for someone like me to replicate successfully given the tools, rasps, files and sand paper. Could I approximate it? Probably using detailed facets but even then a little too much or there and this no longer strikes the balance mentioned.

It's a good read... a few well placed images demonstrating your discussion would only enhance your point...just a thought

 

[Ripthorn]

As a physicist specializing in acoustics, I agree with the theory and appreciate the developments on a theoretical basis. However, after years of doing research and comparing theory to experimental data, I have found that in many cases the improvements from some theoretical developments, while an improvement, are not necessarily on such a scale as to warrant all the additional effort.

My personal approach to neck carving is to do it purely by feel. Granted, I don't have a cnc that could handle a neck carve. There is a whole movement in certain woodworking circles that eliminates measurements in units and is done purely by eye and ratios. I sort of do themsame thing when carving a neck, checking it as I go along to make sure the feel is right instead of worrying about a "C" shape or whatever. Now, I don't really build for other people, so I can do that.

As for a compound radius, I've never felt the need to do one, but I can appreciate the mathematical justification for it. I also greatly appreciate the time and effort put into the post here and all that you contribute to the forum.

 

[leocuellar]

Hello cmjohnson, your theory makes perfect sense only if we start with the premise that the neck must fit the shape of a truncated cone, which is not necesarily so.

You can have a tapered neck with a radiused fingerboard with a consistent radius and if the nut and bridge saddles are radiused the same way, then the action will also be consistent and perfect and the guitar will play perfectly. It doesn't matter the degree of the taper, actually the taper has something to do with the radius ONLY if you want it to have the shape of a truncated cone, which is, for the sake of playing music, not a rule or a necessity.

I think the purpose of compound radius is to fit the style of the one playing the instrument, because usually one use the upper part of the fingerboard (lower notes) to play chords and the lower part (higher notes) to play solos and individual notes, with more bends etc, but that is not necesarily so, it depends on the player.

So, my conclussion is, if you want to make a neck that matches mathematically with a truncated cone, then yes, your theory is perfect and correct, but, our hands are not mathematically perfect or consistent from one player to another and the music styles we play are also not consistent to one another so, ¿why is the figure of a perfect truncated cone the base of the shape?

These are my opinions only, nothing more.

 

[kissTheApex]

Very interesting... I'm still processing...
I feel as though you are not alone in this point of view A while ago I read another's post similar to this on TDPRI.
The type of neck you describe sounds awesome but it also sounds more suited to a CNC in terms of practice.
I always start with facets when sculpting a neck but I think this would be difficult for someone like me to replicate successfully given the tools, rasps, files and sand paper. Could I approximate it? Probably using detailed facets but even then a little too much or there and this no longer strikes the balance mentioned.

It's a good read... a few well placed images demonstrating your discussion would only enhance your point...just a thought

Chris,

I think it was either NickJD's or Mojotron's post from a couple of years back in which he took the formula on StewMac to come up with the optimum compound radius sets. For a 25.5" scale I believe the optimal compound radii sets were 9.5"-12", 10"-16" and 7.5"-10" (Not 100% sure on the last one).

I think facets method would still apply as the use of optimal compound radii sets lets you have an "almost" constant thickness of fretboard edge on the neck.

 

[Stephmon]

Hello cmjohnson, your theory makes perfect sense only if we start with the premise that the neck must fit the shape of a truncated cone, which is not necesarily so.

You can have a tapered neck with a radiused fingerboard with a consistent radius and if the nut and bridge saddles are radiused the same way, then the action will also be consistent and perfect and the guitar will play perfectly. It doesn't matter the degree of the taper, actually the taper has something to do with the radius ONLY if you want it to have the shape of a truncated cone, which is, for the sake of playing music, not a rule or a necessity.

Consider the possibility that you are looking at this the wrong way around.
The assumption isn't that you have to start with a fretboard that is shaped like a truncated cone (like a lamp shade). What you start with, in almost every guitar built today, is a 'fanned' set of strings. If the bridge is larger than the nut, even slightly, the strings will 'fan' wider as you move from the 1st fret, to the 22nd. A cylindrical fretboard is only 'ideal', if your nut and bridge E to E spacing are both 1.5" (for example) and both have 12" radius (for example).

On the vast majority (all?) guitars, the strings themselves describe that cone, not a cylinder. The compound radius simply imitates the geometry of the strings more closely.

And, it doesn't take CnC to realize the cone (or maintain it). The swing arm (made with one long and one short arm) on my long belt sander allows me to compound radius a neck, in about 30 seconds.

To maintain a compound radius, you simply use a long, narrow, flatbar and sandpaper. Sand straight down the center and adjust your angle, to mirror the string paths, as you move to the sides.

 

[cmjohnson]

The big thing about making everything match up to the theoretical cone section radii is that if you closely conform the nut, fretwork, and bridge to the compound radius surface model. then you are starting your fretjob from the most geometrically correct foundation possible. This will result in you having to expend minimal effort to get the best possible fretjob and action.

If you have a compound radius board, say 12" at one end, 16" at the last fret, and the bridge saddles follow a 12" radius, then you will not get the benefits that the compound radius board promises. The bridge radius needs to be flattened, in this case to 18 inches or thereabouts. Now you'll get the full benefits of a compound radius setup.

 

[DrASATele]

Chris,

I think it was either NickJD's or Mojotron's post from a couple of years back in which he took the formula on StewMac to come up with the optimum compound radius sets. For a 25.5" scale I believe the optimal compound radii sets were 9.5"-12", 10"-16" and 7.5"-10" (Not 100% sure on the last one).

I think facets method would still apply as the use of optimal compound radii sets lets you have an "almost" constant thickness of fretboard edge on the neck.

Indeed that is the thread I was thinking about. Thank you Sir!

.... it doesn't take CnC to realize the cone (or maintain it). The swing arm (made with one long and one short arm) on my long belt sander allows me to compound radius a neck, in about 30 seconds.

My Bad! I was thinking about the back of the neck in terms of my CNC and facet comments. I was really thinking more about what it take to shape the neck and get that balance that CMJ is talking about. I should have been clearer.
I couldn't imagine using a rasp to do a fret board!
I wish I had a belt sander like that that would rock

 

[cmjohnson]

You can order a belt sander AND fretboard/neck "swing" jig from Grizzly Tools. They're stock items. It's very good for us guitar builders that the President of Grizzly is himself a guitar builder, though his artistic tastes don't do much for me personally. Because of that, Grizzly offers quite a few tools that are specialized specifically for instrument building.

I shape my necks by hand but I establish certain measurements as targets to work to. I've found that if I don't pick a few critical measurements to shoot for, then I don't get the kind of consistency in neck shapes that I really need to achieve.

 

[Stephmon]

I wish I had a belt sander like that that would rock

Build one. Mine was under $100 worth of parts (though I cheated a bit, by starting with a hand-me-down motor).

Here are the basics of the build...
http://www.mylespaul.com/forums/lut...-your-workbench-right-now-99.html#post5801133

 

[kissTheApex]

You can get away without a belt sander actually. My compound radius router sled jig has been one of the most utilized things in my garage.



I used sketch up to setup my nut and 24th fret radii, and then extended the resulting conical surface to form the end plates of the sled.


The rest is cutting them up, finding appropriate length "sled" ( I used 1" galvanized steel pipe), and setting it up.



The trick is to check the "fall away" every time you use the jig and raise body end of the fret board. Since nut end of the jig is a much tighter radius, two parallel pipes sit lower on the tighter radius end than the body end of the jig. That difference is what I call the "fall away". You can better visualize the fall away if you look at the below photo of end plates on top of each other. Think of two points 3" away from the center on the plates, and you'll see how the rails sit lower at one end of the jig. Over three feet, the fall away is roughly 1/16", but I check every time and adjust accordingly.

 

[Adinol]

I think the purpose of compound radius is to fit the style of the one playing the instrument, because usually one use the upper part of the fingerboard (lower notes) to play chords and the lower part (higher notes) to play solos and individual notes, with more bends etc...

These are my opinions only, nothing more.

Actually, your opinion is 100% on the money.

Although everything that cmjohnson explains is correct, I agree with leocuellar about the actual purpose of a compound radius.

Imagine a very extreme fretboard radius, let's say, that you put some frets on a 3" plumbing pipe, put the strings on and started playing. Everything would be fine (although not very comfortable) as soon as you tried bending some notes. As leocuellar said, you would most likely bend notes higher on the fretboard. With an extreme radius you would soon discover that it is impossible to bend any strings, simply because of the geometry of the plumbing pipe neck. The bent string would basically attempt to be a straight diagonal line through the pipe itself, and after a very small bend, let's say on the 10th fret, the string would touch the 11th fret.

On a guitar we are not talking about a 1.5" radius fret board, of course, so the same exact theoretical example does not literally apply. However, if the radius is shallow and the action is low (something many player prefer) then you are more likely to get fret buzz during bends.

So, In my opinion the reason for a deeper radius closer to the guitar body is simply to allow for a lower action and eliminate fret buzz during bends.

 

[Stephmon]

So, In my opinion the reason for a deeper radius closer to the guitar body is simply to allow for a lower action and eliminate fret buzz during bends.

I think we all agree that a compound radius allows for a lower action, on the outer strings and can reduce/eliminate fret buzz during bends. But, the real reason for "a deeper radius closer to the guitar body" is because that better approximates what the strings do naturally.

The alternative (constant radius) is a compromise, that is easier to sand with a radius beam. In order to give a constant radius board the same advantage, you would have to narrow your bridge, to the same string spacing as the nut and radius it to match the fret board. I'm sure it would be playable, but I'm not sure it would have much of a market.

 

[cmjohnson]

Adinol, thanks for your comments. That's the part I didn't really address much in my diatribe, but I was thinking about it.

All bends on a radiused fretboard will note out if the bend is taken far enough or the board radius is small enough. The flatter the radius, the less of a problem this is.

 

[QReuCk]

Disclaimer: I'm not a luthier.
I think - understand the theoretical point. I even think on extrem radiuses such as some Fenders (7.5), the constant radius could sligghtly mess with intonation as well.
But all my guiatr's'have a constant radius of 12 or more. I believe the flatter you go, the less the imperfection of a constant radius is a problem.
Some of you are stating a compound is difficult to achieve by hand. So lets say you build this and somehow deliver as well a perfect fret job. The player then has a very nice guitar and plays it until some fret wear appears. We all know a fret has a few level and crown in it before needing a refret. So the player wants to do the level and crown himself (actually not very hard with very basic tools on a constant 12 radius). Those who like to do the levelling with a radiused block can't level frets on a compound. Those who do it by hand with simpler flat files can, but have to pay a lot more attention to detail to not screw the compound radius of the top of the frets. My bet is than in most cases, most of the advantages are gone by the first level and crown. To me, who happen to be a heavy picker who likes his action slightly higher than standard, that's'not worth the effort so I sure would'nt pay extra for a compound. I even think at the same price, I would go constant 12 over any compound.

Your opinion may differ.

 

[mudfinger]

I play chords and bend notes from one end of the fretboard to the other. My #1 has a compound radius (12" to 16"). I don't find it any easier or more difficult to work with than a traditional Fender or Gibson.

 

[DrASATele]

You can get away without a belt sander actually. My compound radius router sled jig has been one of the most utilized things in my garage.



I used sketch up to setup my nut and 24th fret radii, and then extended the resulting conical surface to form the end plates of the sled.


The rest is cutting them up, finding appropriate length "sled" ( I used 1" galvanized steel pipe), and setting it up.



The trick is to check the "fall away" every time you use the jig and raise body end of the fret board. Since nut end of the jig is a much tighter radius, two parallel pipes sit lower on the tighter radius end than the body end of the jig. That difference is what I call the "fall away". You can better visualize the fall away if you look at the below photo of end plates on top of each other. Think of two points 3" away from the center on the plates, and you'll see how the rails sit lower at one end of the jig. Over three feet, the fall away is roughly 1/16", but I check every time and adjust accordingly.

Wow thanks, my jig making has improved greatly in the last year or so I might give this a go. How did you go about enlarging the radius for that the router base moves on? Enlarged print outs?

 

[Bill Hicklin]

The type of neck you describe sounds awesome but it also sounds more suited to a CNC in terms of practice.

Not in the least. In fact, you don't even need fancy jigs. All you need to do is keep the fingerboard edges at a constant thickness (just use a marking gauge). The FB center naturally also stays a constant thickness. Draw your nut-end radius, transfer the dimensions, fit a circular segment to your three points at the other end, draw three nogo lines, layout done. Radius with a plane or, if you must, a long sanding block.

--------------------------

(A long time ago I made a simple radius gauge for this and similar jobs. Just a set of concentric circle segments, with radii in 1/2 inch increments from 7.5 to 18, printed out on a sheet of clear acetate.)

 

[Adinol]

...The player then has a very nice guitar and plays it until some fret wear appears. We all know a fret has a few level and crown in it before needing a refret. So the player wants to do the level and crown himself (actually not very hard with very basic tools on a constant 12 radius). Those who like to do the levelling with a radiused block can't level frets on a compound. Those who do it by hand with simpler flat files can, but have to pay a lot more attention to detail to not screw the compound radius of the top of the frets. My bet is than in most cases, most of the advantages are gone by the first level and crown. To me, who happen to be a heavy picker who likes his action slightly higher than standard, that's'not worth the effort ...

You make a very good point.