"Compound Radius" Formula: Conical Profiling for Stringed Instrument Fingerboards / Frets
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- čas přidán 10. 07. 2024
- Chapters:
0:00 The Correct (Conical) Way
1:03 The Formula (Credit to Don Macrostie)
3:26 Executing the Formula in Real Life
4:16 Neck Width vs. String Spread
5:02 Summarization of Concepts
5:39 Understring Leveling - A Side Note
7:26 Demo: 7.25" - 10" Conically Profiled Board
7:51 Ending Notes + Thoughts & Commentary
*NOTES*
1) About the "selective fallaway" leveling that I showed at the beginning of the video: the picture is here:
imgur.com/gallery/BJ90JWe
I provide a very lengthy explanation there for my reasoning behind this "selective fallaway", but the Cliff Notes version is that it only flattens the radius where it's needed to be flattened. i.e., over the fret tops that the E, B, and G strings contact while being bent to a whole step or even beyond.
This avoids leveling the fret tops directly under the high and Low E strings, which allows you to leave the saddles for those strings alone.
It's essentially a modified conical radius. You start conical, then further flatten the radius in a selective way, meaning you don't just blindly level all surface area of the fret tops from the starting point to the end point.
Notice how it's like a miniature cone. Narrow at the top, wide at the bottom. Think of it like you're making another conical profile within the conical profile, on a very, very micro level -- only to the tune of a few thousandths of an inch total (I would not recommend removing more material than a few thousandths total).
Additionally, often I will put a single strip of Scotch tape right on the understring leveling beam, over the sandpaper, to span a couple frets, and create fallaway over the length of this secondary conical profile or "miniature conical profile," after I've leveled it down .001" or .002" normally (without fallaway).
Again, this is all very, very subtle. A single strip of Scotch tape is barely a couple thousandths of an inch thick, and I usually will not level that fallaway in all the way until it touches the earlier frets (e.g. the 7th - 9th frets).
This is all very meticulous work, and not much fret material is removed beyond the initial conical leveling along the string paths under string tension -- or with the strings off in the traditional manner. Understring leveling always has the final say when it comes to how much fallaway is required and where exactly that fallaway is needed.
2) Understring Leveling in general: check out rectifymaster.com. I'm not affiliated with Davide Bissoli / Rectify Master in any way, shape or form. But it would be a great help and service to support the original patent holder of these understring leveling tools. I plan on making more videos about my understring leveling methods at some point.
The gist of it is: you can either do it with the guitar face up on a bench, or in the playing position. I use a digital neck relief gauge to check the relief. It spans the 1st and 17th frets, while the probe descends to check the relief at the 7th fret.
The relief will be less with the guitar face up on the bench, as gravity will tend to press down on the neck, causing it to straighten more or even bow backwards. The relief will be greater in the playing position. Always keep this in mind when you're leveling.
The Rectify Master Katana series of tools has the advantage of matching the neck relief if you desire. I personally test the Katana with the same digital neck relief gauge to see how much curvature I have in it, and match it to the neck that way. Davide uses proprietary standoffs made out of brass that fit over the 1st fret, 7th fret, and last frets, and you can stand up the Katana on top of them. You adjust the Katana until it sits perfectly on all three standoffs.
I haven't 100% settled on a method yet, but I find myself leveling with the guitar face up on the bench more often than not. Make sure the neck is straight in that position before proceeding, assuming you're using a flat leveling beam.
I'm not sure if leveling in the playing position is required for the greatest accuracy. Even with gravity in play, the string tension pulling on the neck seems to provide the necessary accuracy for precision fretwork. I reserve judgment to change my opinion on this in the future, and I hope to make a video going over understring leveling in great detail at some point.
I'd love to find a shop that could help me check my beams for level. You're only as good as your tools. That's a story for another day.
3) Compound Radius Geometry. Coming soon. The gist of it is that with a narrower width at the start and a greater width at the end -- of a shape with a radius (curvature) -- to be perfectly level along its length, it needs to be conical. Very simple concept once you understand it.
The narrower width is a section of a smaller radius circle. The wider width is a section of a wider radius circle. My video about this will be coming soon...or, eventually.
Great info !
Insane quality video
Thank you so much!
Great video! How did you refinish the fretboard on the Tele after re-radiusing? The shellac method you've outlined before?
I actually didn't refinish it -- my friend and mentor Steve did. After I was done with the refret, he just sprayed it with nitrocellulose lacquer.
I've sprayed a few nitro finishes in my time, both bodies and necks -- it's great, but just takes forever. If this weren't a vintage Telecaster I would have suggested a shellac finish.
It's all I personally use anymore. Aerosol finishes in general are extremely toxic and I've preferred to use freshly mixed shellac -- dissolved in grain alcohol -- whenever possible.
And it is my favorite finish on necks, for sure. The problem with spraying a finish after a refret is the finish tends to pool up around the frets, and you lose a bit of fret height. Finishing the neck *before* installing the frets totally averts this.
I will say, nitro is great, and looks great...but a royal pain to wait for.
Shellac and a simple paper towel, or even better, a lint-free cloth. That's my favorite way to go.
I've been meaning to make a video going over my Telecaster build/assembly. I did a whole bunch of work to that. I did an ebony grain fill with Timbermate wood filler, and then did a shellac finish. The shellac finish took forever. I think I used olive oil at some points as a lubricant.
But it came out very glossy. Just brilliant. I think shellac is just an excellent finish all around, and it's non-toxic, so you can use it indoors all day long with no issues, don't need to wear gloves, a mask, or anything. It also dries very quickly.
I do think the fresh shellac is best. I've heard of one other guitar tech who complained to me personally that when he's used shellac, it got gummy after a while. Like it never fully set up. He was using store bought stuff though, like the Zinsser Shellac from Home Depot.
You get your own flakes and mix up small jars, and you'll be good to go. I've actually been meaning to get some better quality bottles, like chemical grade, as the alcohol does tend to evaporate when in those little glass dropper bottles. The droppers are convenient but they're not airtight and any solvents or liquids you store in them will evaporate eventually, and totally screw up your carefully calculated ratios.
I have some Paraloid B72 that I dissolved in acetone that's suffering a similar fate. That might be a future video -- store your mixed finishes in chemical / lab grade bottles. Amazon has a good selection. I have quite an obsession with glass bottles in general and those fit the bill! 100ml should be a good size for most applications. I'm not sure how long the shelf life on shellac is but it may be around 6 months or so.
Very interesting video thank you!
Sure thing! Thanks so much!
great video !!!!
Sounds like a good job for a CNC system. Interesting video. Thanks for sharing.
For sure. I wouldn't hesitate to use modern technology if I knew how to.
This guy had a very interesting project using a DIY router setup:
czcams.com/users/shortsXTmFlZFpkFs?si=-UbATXDewN1P-ptR
Hand tools do take forever, and it's very meticulous work. Would love to speed it up, and I'd love to know if someone has a CNC setup for doing so.
Thanks for sharing!
You're welcome. Thanks for the support!
GREAT VIDEO
Thank you!
So nice…
Thank you so much! So glad you appreciated it!
If we use 10" radius block at the end of the fretoard we'll don't get the correct radius formula at the bridge, maybe better go with 9.5 to the end and after let the sand beam do the job, sanding EXACLY thru the strings line. I see it's very easy go over radius formula at the last frets if you don't sanding in the right pattern.
Question: can I use the Rd formula to derive the radius at the bridge?
Yes, that would work. So on the example around 2:42, you'd just plug in, for example, 25.5" on a Strat, as the bridge is about 25.5" from the nut.
In that example, 7.25" ( 51" + 25.5" ) / 51", you'd get 10.87" for the bridge. You could round that up to 11", so your bridge will be set at 11".
The bridge should be a mere extension of the formula, as it's just another section of a cone.
I haven't personally tested this, but mathematically it makes perfect sense that you could use this formula to determine the proper radius at the bridge.
Excellent point! So when doing a build this would be particularly helpful if selecting a bridge with a fixed radius, like locking tremolos with non-adjustable, non-shimmable saddles.
how would you normally go about setting the bridge radius on, say, a strat with a compound radius? is there a more common method than mathematically extending the cone out to the bridge?
@@EduardoVelezIII I *always* set the action/radius by each individual string, whenever possible.
On one Strat I'm working on right now, for example, I have the action at around .052" Low E, .046" A, .039" D, then .030" for the G, B and E, all at the 12th fret.
Generally speaking I get the G, B and E strings to the same height, then get the D a bit higher, the A a bit higher than the D, and the Low E the highest of all.
1st fret action is around .018 for EAD, and around .012 for GBE.
.000" relief measured at the 7th fret.
I do this the same exact way every time: set the action for each individual string whenever possible.
I don't worry about what radius a board is or isn't, and I never have to know -- all that matters is the action for each individual string.
4/64" bass - 3/64" treble is generally considered the "lowest reasonable action," though I usually shoot lower than that. Just keep in mind: GBE the same, D a little higher, then A a little higher than D, Low E the highest. This is how I do all my setups and I find it works beautifully.
And it will vary guitar to guitar. It is true that a flatter radius will generally allow for more string bending without issues, so you can get a lower radius.
Sometimes you need a little more height on the Low E to avoid buzzing, etc.
My standard is around .000" to .002" relief at the 7th fret, with around .018" EAD / .011" GBE at the 1st fret, and .046" Low E / .030" High E for "crazy low action." I think this is just about as reasonably low as any guitar can be expected to go with excellent fretwork. I have seen flatter radius boards get to .025" at the 12th fret on the treble strings but this is really pushing it to the limit.
I've been planning on doing a video about this for quite a while. Out of everything I do, setups are probably the one thing I have the most experience with, and I'm *very* adamant about setting string heights individually *whenever possible.*
I also am a huge advocate for the digital action gauge, which Davide Bissoli of Rectify Master invented, though other companies like LMI have made their own version.
Keep in mind if you use a digital gauge, you *must* measure in the playing position, and be very careful not to accidentally depress the string with the probe of the gauge when you go to test it -- before you mean to press it down, of course.
If the guitar isn't in the playing position, the probe will almost certainly depress the string before taking your reading, which will give you massively inaccurate results.
The one exception here is action at the 1st fret, as the strings are usually so tight/stiff there that they can resist the light weight of the probe pressing down on them. Even with the guitar face up on the work bench. So I usually will measure action at the 1st fret with the guitar lying down and will adjust the nut slots accordingly.
Also make sure the neck is as close to dead straight as possible when filing the nut slots. More relief = higher action at the 1st fret. You want the nut slots cut to their lowest depth with the neck straight. If you cut them to their lowest depth while the neck has some relief in it, you'll be stuck at that relief, and if you try to straighten the neck beyond that, the strings might buzz open at the first fret.
Anyway. I could keep going. I know your original question had nothing to do with any of this, but I couldn't help myself. I just love talking guitar!
So yes: don't worry about the radius, and just focus on individual string heights.
You may see varying opinions on optimal action. You might want to get the G a bit higher than the B and the high E for example. Or have the Low E closer in action to the rest of the strings.
But as a guideline, your Low E string should be somewhere around .020" higher than your High E string. So the Low E at .050" if your High E is at .030".
Again, generally speaking. I'm a stickler for precision setups and do extensive understring leveling to get things where I want. And use a digital gauge.
For just a machinist ruler, try 3/64" treble - 4/64" bass. You can set it up the way I do or have a very gradual increase in action as you progress from High E to Low E. But that kind of variation in action is a general guideline.
Go with single strings and you'll never have to worry about radius again. You can measure it for your own information, but you'll be able to set up any guitar without having a clue what the radius is and be OK every single time, as long as you follow those tips.
Looks like I can go lower on my treble string setups. your 0.76mm action at the 12th beats my 0.933mm. But I just set all the strings to the same action - so basically, I set them all to what the 6th string needs. And I never use falloff. Also, I'm running Ernie Ball Extra Slinkeys - 8's thru 36w's. So I don't need as much flopping room as you do with that 46 gauge string.
Lately I've been running .008, .011, .0135, .022, .030, .042.
I'm never sure what to expect from the Low E. "Buzz" seems to be an undefined variable, that can't be objectively measured -- just heard, and most people have a threshold for what counts as buzz, and how much of it they can live with.
What's your relief? Generally the E and the A are the only ones I get a bit higher -- the 0.76mmm seems to work fine for DGBE.
I've tried every which way. Old fashioned leveling with the strings off, neck straight, flat steel beam. And the other methods I talk about here.
0.933mm on the Low E is definitely very low. If you're getting that, I'm curious how you'd define it -- any light buzzing or clear as a bell? And what method do you use?
Generally I only use fallaway if necessary -- but I may have to redefine what "necessary" means.
0.933mm on the Low E. That and 0.76mm on the GBE, and the D and A just a touch above that, would be ideal. The last frontier for me is the Low E and A -- and again, part of the problem is not having a standard for "buzz."
I have played a couple guitars that were clear as a bell on the Low E around that measurement. Maybe once or twice. Exceptionally rare on a stock guitar. Now if I could master that, I'd really be in business. 4 out of 6 strings ain't bad but I need to get that E and A.
One thing I've wondered is how flat my tools really are. It is possible some of my beams aren't perfectly flat and I'm not sure how to check them. That could certainly be a major thing here.
Sometimes I've found higher tension strings to vibrate in a smaller arc as well -- if you're getting less buzz with a lighter gauge string then I'll rethink and re-test this. I do tune down to Eb with the strings I use and often go to drop D from there, so even that .042 gets pretty slinky.
@@guitar_md I run zero relief on Fender scale lengths. For Gibsons, I'll start with zero and add a bit of relief if needed. "Clear as a bell" is the only REAL definition of "no buzz". I start by setting the fret plane level - not the neck. So, I skip the notched straightedge and go directly to the flat straightedge on the tops of the frets. After all, it's the tops of the frets that we want level. If the fingerboard waves a bit, it doesn't really matter as long as the fret crowns are level. For the nut, I usually fit a locknut. I use a fret pulling guard in the nut slot and across the first and second frets. I then shim the nut until the fret pulling guard just clears the number 1 fret when resting on the 2nd fret and in the nut slot. So, my action at the 1st fret is on the order of 0.005" - almost at the fret plane. Technically, you can go all the way down to the fret plane, but1/1000th lower and your screwed. So, I shoot for just above the fret plane. Then I set the action at the 24th to about 1.4mm and I'm done. I could probably go a little lower across the board if I wanted to be OCD about things.
They make what are known as "machinist's surfaces" (or a similar name). The are dead flat surfaces suitable for checking the accuracy of tools, but they are expensive. A machinist's square or straightedge is a possible alternative:
www.amazon.com/Granite-Surface-Plate-18-Grade/dp/B006JYKIVC/ref=sr_1_5?keywords=machinist+surface&qid=1700163886&sr=8-5
www.amazon.com/Granite-Surface-Plate-12-Grade/dp/B006JYKIE4/ref=sr_1_16?keywords=machinist+surface&qid=1700163886&sr=8-16&ufe=app_do%3Aamzn1.fos.17d9e15d-4e43-4581-b373-0e5c1a776d5d
www.amazon.com/0-0002-10-Straightness-Parallelism-Machinists/dp/B0CGDLKP7P/ref=sr_1_10?keywords=machinist%2Bsurface&qid=1700163886&sr=8-10&th=1
www.amazon.com/Anodized-Tolerance-Straightness-Machinery-38/dp/B07H3DQQHS/ref=sr_1_20?keywords=machinist+surface&qid=1700163886&sr=8-20
Use Stringjoy.com's tension calculator to find out exactly what's what with your string tensions: tension.stringjoy.com/
It will tell you the effect of changes in scale length, tuning, and string gauge on the tension required to bring a string to pitch. And more tension = less floppy. Generally speaking, shorter scale lengths, fatter strings, and lower tunings will all make the strings floppier. That's why multiscale is superior for fat strings and drop tunings. The longer scale lengths help counteract the floppiness from the fat strings and drop tunings.
I'm certain you could reproduce my results and probably even take then a bit farther by switching to 8 thru 36w's and standard tuning. If you're worried about losing fatness on the bottom end with 36's, just give it a notch on volume and a nudge on the lower bands of your EQ pedal. If you're out of headroom - time for a bigger amp. If you have to play something in D instead of E, a pitch shifting pedal is a possible alternative to drop tuning. But if you're really into fat strings and drop tuning, I'd recommend you make yourself a multiscale 6 or 7 string.
FYI, Ken Parker makes his under string fret leveling tools from pickguard material and sandpaper - no handle. They are quick to make, easy to use, disposable, and inexpensive.
So after watching this and a few other vids on compound radius fretboards, I've decided to try something totally insane - a 12" or 16" to infinite (flat) "compound radius" fretboard. Being flat at the heel, it won't be a true cone. If it doesn't work, I can always get another piece of Richlite and do a 12 to 16, or a 16 to 20 or some such thing.
Its just occurred to me that those formulas might be artificially restrictive. Nothing says the cone has to be uniform in both width and height. But the formulas restrict the height to what will fit in the width. Nothing says the cone must be circular on the bottom. An oval bottom (wider than it is tall) would allow more radical changes in radius. So you could do a 9.5 to 16 instead of a 9.5 to 12, for example.
@@normbarrows We have very similar tastes. Zero relief here as well. I also level according to the level of the fret tops, and don't use a notched straightedge anymore. I know exactly what you mean.
With you on the stringjoy tension calculator as well -- actually have been working on a video about it, regarding string tension and preference. A lot of players just go with stock sets when *sometimes* it can make a tremendous difference to swap out even one string.
One of my old friends (one of my mentor's best friends as well), who was a machinist (only relevant because we were talking about that) -- he loved a regular .009-.042 set but with a .015 on the G.
For me, I was using a .014 for a while, and eventually came to .0135. Using the Stringjoy calculator, it puts my GBE strings right around 10 pounds of tension. I'm OK with the .011 B string but a .0105 would actually be closer to equal tension, around 9.8 pounds.
There are some people who prefer progressive tension -- each string successively getting a little higher in tension -- some who prefer balanced, etc. String gauge is a very personal preference yet most people don't know what they like simply because they haven't experimented -- and that's OK! But experimenting with string gauges is a real joy.
String compliance is another factor, or how easily the string bends. Break angle at the nut/saddle will affect this, also whether using a locking nut or not. I tend to like very shallow break angles on my electrics, or at least, as shallow as possible. So with a decked trem on a Strat, I like replacing the saddle screws with shorter iterations (I also prefer 316 stainless steel because it's pretty much 100% rust proof, important when dealing with corrosive sweat), I get the action where I want it while having the saddles as low as possible.
Sometimes that requires shimming the neck at the top, to raise the action a bit. I never used full pocket shims except a handful of times, and the guy who taught me never used them.
However, I do get the concept, and I'd love to make my own. i've had my eye on a Byrnes Model Machines thickness sander for years now, and would love to use it for making pickup bobbin assembly rigs, thicknessing bone nut and saddle blanks, and making tapered full pocket shims, just to start.
Thicknessing is a real pain and the Byrnes is accurate to .003". His machines really are top notch and they have incredible functionality to offer people who like tinkering with small objects in very fine detail.
Also agreed about multiscale instruments. I have a multiscale 7 string and it's a godsend for that reason. The additional scale length adds to the string tension and not only do the fanned frets intonate better, but that added tension goes a long way in preventing buzz.
I used to use a .038 on the bottom. One more note about volume: in my years of winding pickups, I've come to the opinion that magnet stagger is more relevant for string gauge than it is for radius. The string gauge seems to have a much more pronounced effect on volume balance to my ear than the radius does.
Now on my Tele I use a wound G, so it would make sense to have a raised G pole -- plain steel G strings, not so much. In general for standard modern strings I like a stagger of .680, .693, .710-.719 for EAD / GBE. Short medium tall, short medium tall. They balance great. You can tweak it of course for oddball string gauges like a wound G or an extra heavy Low E string, or B string for that matter.
I've gotten a bit less ballsy lately with action at the 1st fret. Usually I'll leave it quite a bit higher than you've mentioned, but now that you bring that up, i might lower my Strat just a bit more. I'm a freak for low action and the 1st fret action is tremendously important, as you obviously know.
Getting it within a whisper of the 1st fret with zero relief really does feel the best. You're probably the only other tech I've ever talked to who does this. Most people's specifications for a setup are *far* higher than what we're talking about here. To me, guitars set up much higher than the way I do them are basically unplayable.
That might sound ridiculous, but once you experience truly low action, the ease of playing it offers -- it's really hard to go back. Of course, I have some customers that despise low action and due to their style, they need it high to "get under the string" for bending and vibrato.
To me, I always felt this was a product of having frets that were too low. I usually prefer .110" x .057" frets. Sometimes I'll deliberately take them down to around .050". I'd say .050" feels great to me, and I don't like it any lower than that.
@@normbarrows @normbarrows RE: Pickguard material for understring leveling. Years ago I made understring levelers out of 1" carbon fiber i-beam from Dragonplate Carbon Fiber in NY.
Expensive, yes -- but it's incredibly thin, around .030", and has the benefit of being re-coatable. You can coat it with epoxy and re-level it if it ever happens to go out of spec. It's so thin that the amount you need to jack the strings up for a full-length leveling is minimal. I do own and use the Rectify Master tools in support of Davide Bissoli who really has been the biggest pioneer with the understring leveling game.
Sadowsky from Warwick was actually Davide's first major sponsor and has been a huge advocate for understring leveling, in particular, Davide's tools from Rectify Master. Anyway, I have to give credit where credit is due. I will say I still think carbon fiber is the best material for understring leveling.
RE: radius. This is where the distinction comes in. Conical profiling, strictly speaking, *is* restrictive -- but that's why we call it conical.
Deviations from a strict geometric cone are no longer a cone. However, they can and do work. I've wondered about this myself, after learning the formula and wondering how places like Warmoth could do a 9.5" - 12" radius, but then do a 9.5" - 14" or 9.5" - 16" if they wanted to.
I'm not sure how I'd recreate this, outside of leveling a 'secondary cone' into the fret tops. Like in that picture I show early in this compound radius video. I'd be really curious how they do it at the factory. It seems you're better at naturally visualizing this stuff than I am.
What I've done for years is level the *middle* of the frets from say, 9 or 10 to the end, to flatten the radius at the top a bit. This deviates from a cone. But really allows for much bigger string bends with little issues, and rock bottom action.
The conical formula I see as the definition of a strict cone -- but not the be-all end-all for guitar fingerboards. I do think they're the best *starting* point. They can also be the finishing point.
Also: as a player, I *vastly* prefer the conical profile/compound radius. The hand naturally forms more of a curve when the neck is narrower. As it widens, it feels more natural to have a bit of a flatter radius. This is my opinion of course but has been 100% true for me as a player. The difference in feel is night and day to me. Ever since I discovered the compound radius, I never looked back.
I do wonder about that older video you commented on. I got just fine results. But didn't really understand what I was doing like I do now. That's the trouble with some of these videos -- you learn a lot more as you go, as every video is a deep dive. I don't want to be throwing anyone off so at some point those videos might get completely re-done, or just put on Private.
i do keep my playlists all updated with only my most recent content. That's the saving grace here.
@@guitar_md Yeah, in the other video I saw that under string leveling tool you made - pretty sweet. Too bad someone else has a patent - could be a nice side gig for you. I tried the Ken Parker style tools but wasn't really impressed. But that probably had more to do with trying to spot level when I should have just gone for a full level. These days, I take a less is more approach to fretwork. Checking the truss rod and rolling fret ends and fretboard edges with sandpaper (if needed) are now the only steps I do on all necks. But I'm mostly modding Ibanez replacement necks. can't remember the last time I had to do a full level crown and polish on a build - last year? maybe 6 builds ago? These days it's just the occasional fret sprout, now that the cold weather is here.
"youre gonna learn how to solve for it" woah woah woah i am here for guitars, not math class.
ignorance is a bliss