Part 6B: Compound Radius; Is It Worth The Effort?
After posting Manufacturing Thor Part 6: Compound Radius Fretboard, Tangente Instruments, pointed me to an article by Liutaio Mottola: Lutherie Myth/Science: The Strings of a Stringed Musical Instrument Describe a Conical Section. “So called compound radius fretboards are not worth the additional effort required to make them. The same action and tolerances are achieved by using cylindrical fretboards and normal fret leveling and dressing techniques,” Mottola concludes.
I always keep an open mind, and so I went on to analyze my particular case, from Thor’s actual specifications. I’m using CAD to help me with my analysis. Here are the constraints:
- 43mm width at the Nut.
- 58mm width at the 24th fret.
- The centers are at the same level.
- The outer edges are at the same level.
Here’s the drawing below. You can see two arcs, one with a radius of 304mm (A) and the other with a radius of 522.77mm (B). The latter is derived based on the constraints above.
As you can see in the drawing, if you trace the path of the 304mm arc (A), there is a 0.63mm drop at the edges. The action of the strings are progressively higher towards the sides (low and high E strings in a 6-string guitar) the farther you go from the nut. This is in addition to the normal action, which also follows a certain incline towards the bridge. Proponents of conical fretboard surfaces are right. A cylindrical (single radius) fretboard surface is not optimal.
For Thor, I’ve chosen a Nut radius of 304mm (12″). For smaller radii, the drop increases. For instance, for a Nut radius of 254mm (10″), the drop exceeds 0.7mm.
Now, can this be compensated using normal fret leveling and dressing techniques? Let’s see… Here are the specs of the Jescar Jumbo Stainless Steel Fret wire (57110-S) that we use:
- Crown Height: 1.45mm (0.057″)
- Crown Width: 2.79mm (0.110″)
- Tang Depth: 1.88mm (0.074″
To compensate for the drop, we can file the centers progressively more towards the bridge side of the fretboard. We will be filing away 0.63mm from the center at the 24th fret. Wait! But doing so will leave you with less than 1mm of fret wire (even more for smaller radii). And that’s for a jumbo fret wire!
Eh, I don’t know about you, but to me, that’s too much filing.
I actually played fast and loose with the specs, at least with one parameter. After doing this analysis, I realized that the correct curvature at the 24th fret should be 522.77mm (20.6″), as seen in the drawing above. The current Thor specification has that at 456 mm (18″). Also, it is important to note that the bridge I am using (Schaller) has a fixed 355.6 (14″) radius, which adds up to around 0.4mm discrepancy. I tend to adjust the bridge height a tad bit higher at the bass side, keeping the treble side perfectly constant. It would have been perfect if I chose a 522mm radius at the 24th fret and individually adjustable bridge saddles. Minor adjustment, but a note for the future nonetheless.
But all that being said, I think it is indeed possible to have an optimal, low-action fretboard setup using proper manufacturing methods with tight tolerances. In my opinion, such an optimal setup cannot be achieved by ad-hoc fret leveling and dressing techniques alone.
In any case, the compound radiusing jig we created saves time and ensures consistent results without the need for time-consuming sanding with a sanding block. That alone is worth the extra effort.