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The part in bold isn't true. The taper of the fretboard is independent of the radii at either end. If you like, I can draw up a fretboard with a 16" radius 1.75" nut and a 7.5" radius x 2.25" wide end.

When designing a compound radius fretboard, the things you need to know are the radius at the nut and the radius at the saddle. Taper (profile in drafting terms) can be whatever you want. With the first two parameters (radius at the nut, radius at the saddle) everything else falls out.

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Indeed you can , Andy, but I think the quote was in connection with a conical fret board ... the fretboard you draw up with these parameters is not going to be conical, even though it will be a very efficient compound radius.

I think I see the confusion now. The surface of the fretboard is indeed still part of a cone. However, the line described by a fret (section at the fret location ) will actually be elliptical instead of an arc. So long as you're using two arcs to define the start and end radii, you end up with a conical surface.

I modified the 3D drawing I made so it's a bit more obvious what I'm talking about. In the first one, the radii are 7.5" at the nut and 16" at the end. The profile (taper) of the board is projected on to the cone and voila! A conical surface compound radius board with a nut of 1.75 and an end of 2.25.

In the second drawing, I changed the nut to a 4" radius and it still works with the same profile (taper).

p.s. I'll be happy to stand corrected but I'm pretty sure I'm right on this one.

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p.s. I think I might be picking up what you're laying down now - I drew my cone so that the circles are concentric. When I'm actually making fretboards the arcs are tangent to one another but not necessarily concentric (I don't check). This could indeed lead to something like a hyperbolic or parabolic surface rather than a conical surface. In any event, they're all ruled surfaces and the deviation from a conical surface would be very minimal.

One could force it to be a conical surface by adjusting the planes on which the arcs are drawn such the center point of the arcs are concentric and the arcs are tangent but it really wouldn't get you anything (but I think I just came up with a fantastic marketing feature - True conical compound radius fretboards!)

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Andy, if your software allows it, try this.

Extend the lines defining the outside of the section back so that they meet at the apex of the cone. They will meet at the apex , by definition. Now, divide the 1.75 into 5 equal spaces and divide the 2.25 into 5 equal spaces. This defines the 6 string paths. Extend these lines back and see if they also intersect at the apex. If they do, then you have a conical surface ... if they don't (and they won't !) then you do not have a conical surface.

You probably didn't read my second message before you wrote this response but - in my examples, I started with a cone and then carved a fretboard out of it. Because I started with a cone, it will always end up with a cone because it's a cone. What might happen though is that my extended lines won't converge in the same place because I'm cutting the fretboard shape from the conical surface.

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Let me see if I've got this correct....
Andy, seems you are talking only about the surface as manufactured
Murray is talking about the string paths.
A straight edge laid along the string paths on your (Andy's) conical surface would rock because it would see the FB surface as convex, because they would be skewed across the surface of the conical section.
Hence the need for flattening the FBs along the string paths, changing it's geometry.

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The name catgut is confusing. There are two explanations for the mix up.

Catgut is an abbreviation of the word cattle gut. Gut strings are made from sheep or goat intestines, in the past even from horse, mule or donkey intestines.

Otherwise it could be from the word kitgut or kitstring. Kit meant fiddle, not kitten.

None of this conical vs compound discussion is of much use to the OP in the construction of a fingerboard. If money is of no object I can see where a CNC machine can handle the initial shaping most accurately but will have to ultimately be cleaned up. The problem with evening things out with a sanding beam is that you have to remove more material from the end of the fretboard than at the nut. Also it's hard to sand in an absolute straight line with a beam. As soon as you go off line you are sanding across some radius no matter how slight. Also you are trying to create a curved surface with a flat beam. Not easy. So you can clean up by sanding across the fingerboard with your beam with more travel at the end than at the nut. Of course then you run the risk of rounding off the edges. And then none of this discussion addresses fall-off or the desirability of having more relief on the bass side of the fretborad from the second to the fifth fret.

Since money is an object for me I use various sanding blocks with aggressive grit to establish the basic compound radii. I add some scrap wood to the sides so I won't round the edges. Then I use beams to initially establish a more exact string path. Then I sand across the board with a beam with more travel at the end than the nut. I mark the board continuously throughout the process and work through the grits to 400. When the board is on the guitar I sand in some relief on the bass side an give it .005 fall off from the body to the end of the board. Then I fret the board.

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Ken Franklin
clumsy yet persistent
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Murry your talent seems to be criticism after the fact, lets see some shavings in the floor and show us with a piece of wood exactly what you mean? Compound radius works for me Easily executed, and very nice to play.

Well, my talent certainly doesn't appear to be the ability to explain geometrical concepts. I think I would have to make a Youtube video to make it easily comprehensible.

Sure , no argument there from me ... you can make a compound radius from any two radii ... the fact that it is not technically a conical surface is immaterial from a practical point of view.

to make them is not that hard. I have a jig that is used with my thickness sander. I can make about any compound radius I want. To do it by hand is a simple process. Make the radius templates you want say a 16 and 18
I use double sided tape on a flat board and you attach the templates at the proper ends. Then using a hand sanding block you set it up to ride the templates. You can do one fairly easy and accurate.

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John Hall
blues creek guitars
Authorized CF Martin Repair
Co President of ASIA
You Don't know what you don't know until you know it

"To get the string paths normal to the surface requires an alteration to the surface which makes the surface non-conical."

That depends on how the frets wrap the "cone." The radius of the fret is fixed only at the center of the fret when the frets don't wrap the cone parallel to the base of the cone, but wrap the cone at an angle, starting from the centerline and then move closer to the base of the cone as they extend out from their midpoints. So the surface of the fretboard is conical, it's just at an angle. You can see this in action if you watch Chris Paulick https://www.youtube.com/watch?v=qgfEM71sja0 sand a fretboard using his jig; not only does he rock the jig back and forth on the radius blocks on either end of his fixture, but he also swings the wide end of the fretboard in sweeping arcs across the sander from side to side, and less so on the nut side of the fretboard. This produces a fixed size cone, and strings can be made to follow the fretboard, normal and equidistant to it at all locations, it's just that at each fret the radius of the fret gets larger as it moves away from its own centerline. But it's still conical.

If you wanted a fretboard where the frets were a constant radius, an oblique cone
can give you what you want. If you can imagine a cone made up of a series of rings hanging on a rod, starting with a large ring and progressing down to a ring no bigger than the rod, then you can imagine the focal point that is 90 deg from a point on the outer edge of the base. A focal point that has been moved from the center of the cone to line up with the base on one side.

You've almost got it right , Todd ... the frets won't be a constant radius, however ... the only form that will produce constantly radiused frets is a cylinder.

Nonetheless, the "oblique cone" you have drawn is in fact the only surface whereby you can take any two radii and any two fretboard widths (nut and wide end) and any fretboard length, and get a surface where the string paths will all converge at an apex. The variable, of course, will be the included angle at the apex.

Many years ago, while exploring this very subject, I contacted various mathematical bodies to see if this particular type of "oblique cone " had a special name ... it would seem that it doesn't, so "oblique cone " is as good a nomenclature as any, although "right angled oblique cone " would differentiate it from all the other oblique cones.

You've got the string spread at the bridge and the string spread at the nut. If you extend (for example on a plan very long piece of paper) the first and sixth string paths past the nut, past the peghead, the lines will meet at a point a certain distance from the bridge. Call that the zero point. Then the nut spread divided by the nut's distance from the zero point will equal the bridge spread divided by the bridges distance from the zero point.
To be a true cone, the radius at the nut divided by its distance to the zero point must equal the radius at the bridge divided by the bridges distance from the zero point.
Another way of expressing the same relationship is to say that the radius at the bridge divided by the radius at the nut must be equal to the spread at the bridge divided by the spread at the nut.

The stewmac compound radius boards have a nice practical rate of radius change to work with normal string spreads. They go from 10 at the nut to 16 at the bridge. The original posters desire to go from 7.5 to 16 inch radius is too radical. With those numbers the strings would have to be too close together at the nut and/or too far apart at the bridge.

So with all this discussion I've been doing some thinkin' and.... I think the ideal compound radius fretboard surface would be a ruled surface with the radius set at the nut and the saddle (using the nut width as the chord for the radius at the nut and string spacing at the saddle as the chord of the radius at the saddle). This surface may or may not end up conical but, it would provide the surface we're looking for as guitar players. This is very easy to do it CAD (using the ruled surface feature) and easy to machine with CNC.

It will also allow any radius at the nut and any radius at the saddle and still provide a constant string height over the fretboard irrespective of what radii you choose.

This will definitely be added to the products offered at Birkonium and should provide the ideal compound radius irrespective of the radius at the nut and saddle.

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http://www.birkonium.com CNC Products for Luthiers
http://banduramaker.blogspot.com

Sounds like a plan Mr Birko

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The name catgut is confusing. There are two explanations for the mix up.

Catgut is an abbreviation of the word cattle gut. Gut strings are made from sheep or goat intestines, in the past even from horse, mule or donkey intestines.

Otherwise it could be from the word kitgut or kitstring. Kit meant fiddle, not kitten.

I totally agree with Colin .. that is the way forward.

Just out of interest, Andy, would your CNC be able to machine a fretboard with :

1) a specified nut width and specified nut radius,
2) specified string spacing at saddle and specified radius at saddle , and
3) a proviso that the fretboard taper should be such that the the width of the fretboard at the 12th fret should be the same as the string spacing at the saddle?

If you can do that I will be ordering three such boards in the very near future.

No, you are missing the point ... it is perfectly possible to have a ruled surface fretboard with any defined nut width and any defined string spacing at the saddle, with a nut radius of 7.5" and a saddle radius of 15". The resultant surface will not be a section of a *standard* cone, but the string paths will all lie straight on the board. The is no reason why the strings would be too close at the nut or too far apart at the bridge.... you define your own widths, and hence your own string spacings.

My model needs a little bit of updating to do so with a ruled surface but yes it can. Right now I set the radius at the nut and the radius at the end of the fretboard rather than the saddle (it's a really old model!) and use a "loft" feature to generate the surface. It could very well be that in the case of such simple geometry the loft generates a ruled surface but I'd have to check it to make sure. If the loft isn't a strictly "ruled surface", it would be really close anyway. To use the "ruled surface" feature is probably a big change to the model (like almost a total re-do) due to the way the software I use operates.

I'll play with what I have next week and let you know. Moving the end radius to the saddle instead of the end of the fretboard is something that could be done quickly (just set the length of the fretboard to scale length). I already allow the selection of the width fret so it would work out how you like.

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http://banduramaker.blogspot.com

Update: The ruled surface feature of SolidWorks works differently then I thought it would so I checked the lofted feature I'm using for compound radius fretboards right now and it is in fact a ruled surface. As I suspected before, because of the simple geometry of a fretboard, it makes sense that it's a ruled surface. I did this by projecting lines on the fretboard at various angles and the ones that should result in straight lines indeed to.

summary - it will be very easy to update the model to do what Murray's asking for.

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http://www.birkonium.com CNC Products for Luthiers
http://banduramaker.blogspot.com

Great news, Andy ...I will be contacting you very soon via your website to place an order for three boards. Just out of interest, ( and I am putting this here instead of PM because it might be of interest to others) ... would you undertake fretboard cutting in material supplied by customer? The reason I ask is because I had originally intended to make these fretboards out of Rocklite Ebano ...(NOT "Richlite" !!! ). Rocklite Ebano fretboards are available from LMI so it might be just as easy for you to get the material from them. Or I could ship you three boards ... whatever is easiest.

Yes, I run parts with client supplied materials all the time. I just ask that they're planed/sanded flat and oversized in width by at least 1/4". I'll run the concave side over the jointer for nothing (they often cup during shipping) before I run them but I have to charge extra if there's pin holes to be filled, major flattening etc.

Usually if someone is ordering from the usual suspects, they'll just have them shipped straight to me. I find that simplest as well and it's a little bit cheaper as I mark stuff up a tiny bit to cover my time.

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http://www.birkonium.com CNC Products for Luthiers
http://banduramaker.blogspot.com

I've been pondering some of this threads points, not raining on anyone's parade...... But Today I'm fretting a Birkonium CNC board, compound radius. Neck glued on the guitar. Martin style D-28 neck, big mother, very straight. As I was taught at the Ann Arbor Guitars fretting class got out the white crayon Xed up the fingerboard and started sanding with my sanding beam, dead straight on the treble side, just a hint more relief on the bass side and fall away from the 14th fret on. Still a compound radius but its a different fingerboard than what I started with, not much but it is different. So if were going to modify the allegedly perfect compound radius to hit our target of the best possible set up..................it would be a little more work but I could start with a constant radius board and hit the same target.

I was thinking the same thing, Greg. I made a compound radius jig, so any FB's that I do should go a bit quicker. Any extra time reworking a constant radius board is more than made up in how we learned to do fret installation, levelling, bevelling, crowning, and especially polishing.

Alex

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