Fretboard layout question - assymetrical neck

[roberthabraken]

I have a question about the space from the outer side of the two outer strings to the edge of the fretboard. On my previous build, I used equal string-to-string spacing and a fixed space from the strings to the edge of the board (3.15 mm). I took the nut width (38.49 mm), extracted 3.15 on both sides, layed my bass and treble string next to that and divided the other two strings with equal spacing in between them.

But now.. I've heard that this type of spacing can ruin your intonation on a multi-scale fb. So I'm looking at center-to-center string spacing. My middle string (5-string) lies perfectly on the center line of the neck, other two strings with equal center-to-center spacing from there. This approach is different, because I calculate from the center, instead of from the outer edges of the fb. Now I got to the edges and figured out that an equal measurement from the outer strings centers to the edge of the fb, let's say 4.5 mm, gave me more space from the treble string to the edge (4.24 mm) than for the bass string (2.82 mm). I do not really like this, since there's a difference of almost 1.5 mm.

This brings me to my question: if I take the same space from the outer edge of the outer strings to the edge of the fb, this problem is solved, but I will have a slightly assymetrical board (center line not centered). Is this okay to go with?

[pilotjones]

Aha! Your discovering one of the further properties of multiscale boards: the centerline is not the centerline, so to speak.

Imagine it this way: if you start witha "centerline", then draw two perpendicular, centered lines at either end for the bridge and nut; the swing the lines as if for a fan. Now connect the lines to represent the outer strings. You will find that these lines are not symmetrical about the "center." thus is because the tips if, say, the bridge line are equidistant from the center, but at different longitudinal positions, so they result In different angles.


I've been through this. There is no way around basic geometry. I suggest you go to fretfind, go to the multiscale page, and enter an extreme layout, to investigate the various effects.

When you lay out the multiscale in the basis of the outer strings, you will get a proper board. Then after that's laid out, you can figure a centerline. It will not lie on your middle string.

[iamlowsound]

Originally Posted by pilotjones

Aha! Your discovering one of the further properties of multiscale boards: the centerline is not the centerline, so to speak.

Imagine it this way: if you start witha "centerline", then draw two perpendicular, centered lines at either end for the bridge and nut; the swing the lines as if for a fan. Now connect the lines to represent the outer strings. You will find that these lines are not symmetrical about the "center." thus is because the tips if, say, the bridge line are equidistant from the center, but at different longitudinal positions, so they result In different angles.


I've been through this. There is no way around basic geometry. I suggest you go to fretfind, go to the multiscale page, and enter an extreme layout, to investigate the various effects.

When you lay out the multiscale in the basis of the outer strings, you will get a proper board. Then after that's laid out, you can figure a centerline. It will not lie on your middle string.

Couldn't you lay out a multiscale board using the middle string as a centreline? What I mean is, take a five string bass for example. You could figure out the scale of the B string and the A string and lay the A string on the centreline, then extrapolate the D and G strings from that? So basically doing the same thing as laying out the outside strings, only you are using an outside string and an inside string so you can put the centreline on the middle string.

Now this all works in my head, but I haven't laid anything out or done any of the math, but it seems like it should work.

lowsound

[roberthabraken]

Thanks, but I think I'm confused even more right now . Specially because of this part:

Imagine it this way: if you start witha "centerline", then draw two perpendicular, centered lines at either end for the bridge and nut; the swing the lines as if for a fan. Now connect the lines to represent the outer strings. You will find that these lines are not symmetrical about the "center." thus is because the tips if, say, the bridge line are equidistant from the center, but at different longitudinal positions, so they result In different angles.

I stated that the board is not symmetrical because of the edges that could differ (doesn't necessarily have to be a fanned board). But apart from the edges, my middle string is the centerline of all other strings! You said it isn't, so now I'm a bit confused. The fact that the bridge line is equidistant from the center, but at different longitudinal positions, makes me think I did it the wrong way. Let me explain:

I drew a centerline, determined the perpendicular fret and the length from there to the nut for the middle string, thus being my nut. Did the same for the bridge. Then I determined the distance from string center-to-center at the nut (9 mm) and at the bridge (18 mm). This gave me the angles of all strings. Then I calculated the distance from the 7th (perpendicular) fret to the nut for all strings and corrected the nut line. From there, I measured the scale length along each string, going from 32" to 30.5" in steps of 0.5" (I have 7 strings on this drawing). This gave me my bridge line. Then, I measured the fret positions on the outer strings and connected those for the fret lines.

[pilotjones]

You are using equal center spacing along an arbitrary perpendicular line that happens to attach to the end of your "centerline." This does not work to produce perfect string-fret crossings. To achieve this you must have equal (or proportional) spacing along the nut line itself, and likewise at the bridge.

If you take your current layout and measure the spacings on the nut line itself, you will find that they are not equal. This is fine, as long as you do the following: measure them, measure the overall nut length on the nut line (just to the outer string centers, of course), measure the overall bridge length on the bridge line, and then scale the nut spacings by the ratio of bridge length to nut length, and place your bridges at those points, and redraw the strings.


You can also bypass all of this by using fretfind.

[roberthabraken]

Originally Posted by pilotjones

You are using equal center spacing along an arbitrary perpendicular line that happens to attach to the end of your "centerline." This does not work to produce perfect string-fret crossings. To achieve this you must have equal (or proportional) spacing along the nut line itself, and likewise at the bridge.

If you take your current layout and measure the spacings on the nut line itself, you will find that they are not equal. This is fine, as long as you do the following: measure them, measure the overall nut length on the nut line (just to the outer string centers, of course), measure the overall bridge length on the bridge line, and then scale the nut spacings by the ratio of bridge length to nut length, and place your bridges at those points, and redraw the strings.


You can also bypass all of this by using fretfind.

So it felt not okay and it indeed turns out it isn't. I will check out FretFind, but I really would like to figure it out myself too, just to understand! By the way, I now do understand your point and think you are right, but I don't know how to achieve this while drawing the layout yet... I will do some more study tonight, I will not rest before I fully understand this and I'm able to reproduce a perfect layout .....

[roberthabraken]

Thanks for pointing me to fretfind, it's a wonderful tool to toy around with, try some things, see what happens.. and it sure does take a long time to figure this all out in CAD. But anyway, I entered the exact same parameters as I used making my own layout and exported it to DXF. I made an overlay on my original drawing, turns out the angles of the frets were okay, but all were off by just 0.05 mm or less. And the two outer strings where not exactly in the right place. I can see my method was slightly wrong, but the deviation was far less than I thought. In the next few days I will refine my method and drawing to come up with a nice fretboard layout as a base for my new design.

Back to the original question of this thread: FretFind kinda answers my question if it's okay to use a different edge measurement on treble and bass side of the fb, because it let's you enter them separately. So, basically, the answer is yes .

[pilotjones]

Right. And, the greater the difference between the sizes of the two fretboard margins, the more your centerline is not a centerline.



BTW, since you said that you're trying to be as exact as possible - you shouldn't do the bridges like that.

[Beej]

Originally Posted by pilotjones

BTW, since you said that ou're trying to be as exact as possible - you shouldn't do the bridges like that.

Durn you pilotjones, just when I was so enthralled. Why shouldn't he do the bridges like that? I can't figure it out and its driving me crazy!

[pilotjones]

Originally Posted by Beej

Durn you pilotjones, just when I was so enthralled. Why shouldn't he do the bridges like that? I can't figure it out and its driving me crazy!

Because they should have their axes aligned with the string paths. Being parallel to each other as they are, the outer bridges are at increasingly large angles to the strings, so that as you pull the saddle back for intonation, the string path changes.

The effect may or may not be negligible. I haven't done the math to figure the discrepancies, I'm just fanning them with the strings on mine.

[roberthabraken]

Originally Posted by pilotjones

Because they should have their axes aligned with the string paths. Being parallel to each other as they are, the outer bridges are at increasingly large angles to the strings, so that as you pull the saddle back for intonation, the string path changes.

Damn you're sharp, dude... why didn't I think of this?

On the other hand, lucky to have you around on TB, I now know so much more than just a week ago...

[SDB Guitars]

Originally Posted by pilotjones

Because they should have their axes aligned with the string paths. Being parallel to each other as they are, the outer bridges are at increasingly large angles to the strings, so that as you pull the saddle back for intonation, the string path changes.

The effect may or may not be negligible. I haven't done the math to figure the discrepancies, I'm just fanning them with the strings on mine.

Pilot -

You don't have to align the bridges with the string path, you can run them all parallel to the body centerline with no negligible effect. Look at Dingwall basses. The saddles are perpendicular to the body centerline, as they also are on pretty much every factory bass. They are just staggered to accommodate the scale placement.

Placing the bridge saddles that slightly "off axis" isn't going to perceptibly affect intonation or speaking length.

OTOH, placing the bridges radially in line with the strings would *look* really cool.

[roberthabraken]

Originally Posted by SDB Guitars

Pilot -

You don't have to align the bridges with the string path, you can run them all parallel to the body centerline with no negligible effect. Look at Dingwall basses. The saddles are perpendicular to the body centerline, as they also are on pretty much every factory bass. They are just staggered to accommodate the scale placement.

Placing the bridge saddles that slightly "off axis" isn't going to perceptibly affect intonation or speaking length.

OTOH, placing the bridges radially in line with the strings would *look* really cool.

I think you're right, you don't have to.. the effect will be minimal. But if you're looking for perfection it sure is a nice touch. I made a drawing like that and it really looks awesome too. Seems to be one of those unique features to make your bass stand out .

[pilotjones]

Shawn, yeah, I realize the difference is probably negligible, since Dingwall doesn't bother with the correction. Robert had said e wanted everything "perfect," so that's why I mentioned.

I can't say definitively either way since I haven't donea survey of pitch error on Dingwalls and compared it with some other (non-existent) database of pitch errors on other intstruments.

BTW, on a multiscale, there may be a possibility of using a sideways shift (towards the treble direction) as an intonation compensation adjustment. It would have to be tried to see how it works. And even if it is at least as good as the conventional saddle lengthening, you couldn't do it on the highest treble string, unless you built the neck with extra room.

[roberthabraken]

I managed to get the fanned thing right for center-to-center spacing. Now I'm moving to string-to-string spacing, can't let it go... While browsing through my 'inspiration' image library I noticed equal string-to-string spacing on an F-Bass, all the way to the bridge! If I look at the bridge sadles, they are further apart on the bass side, now I'm sure this will be the way to go .

[roberthabraken]

I got my method right!! I first made a layout using FretFind. I did a check on the average deviation of each fret (!) along the strings and found out it was only 0.02 mm. That's something I can work with. Then, I drew all strings with their actual thickness and measured their 'thickness' along the lines of nut and bridge. Then I removed all strings, except the outer two. I measured the space in between, subtracted the sum of all strings that would go in this space, and divided this amount by the number of strings minus one. I did this for both bridge and nut. This gives me a string-to-string spacing, I guess the way pilotjones said and also the way I see F-Bass has done it on his fretless traditional (not fanned) fingerboard.

(What actually happens is that the strings shift to the treble side of the fretboard in total, but they stay at the same angle to the centerline. If you would only correct the spacing at the nut, the strings rotate slightly, thus changes the angle between the string and its frets and thus changing the distance from one fret to the other.. this basically screws up your intonation.)

After redrawing my layout the way I described above, I measured the average deviation (thus the correctness) of the frets and it came out to be 0.068 mm, ranging from a minimum of 0.02 mm and a maximum of 0.1 mm. So that's not as good as the original layout from FretFind, but I think it could be acceptable. I did work very precise, using three decimal places all the time, but I think it could be done better, although I don't know how.

I have not finished my CAD drawing, but I think it will be a very nice and balanced FB like this. I also fanned the individual bridges.. looks neat. I will keep you posted.

[roberthabraken]

Got it !

Finished the layout, a seven string 32" - 30.5" multi-scale fretboard with evenly spaced strings (string-to-string spacing) and fanned bridges. Also the fretboard edges are equal on bass and treble side, thus also incorporating string width. All frets spot on, no intonation or calculation mistakes . Thanks for your help, especially pilotjones!

[pilotjones]

Two mistakes you've got there.

First, when you subtracted the thickness of the inner strings, you should also have subtracted half the thickness of the two outer strings.

Second, if you're still going for accuracy, you can't do what you did at the bridge. Whatever shift you apply to each string at the nut, you cannot apply the same shift at the bridge, keeping the string parallel to its former path. You must multiply that shift by the ratio NOAW/BOAW (bridge overall width, measured along the bridge line, divided by nut overall width, measured along the nut line). The strings do change angles. And this is what keeps your intonation on.

You cannot simply shift a string sideways on a fanned board. For an exaggerated example, imagine if you took your first string, and slid it over to the opposite side of the board, so that it is landing in the nut slot for your last string - but keeping it parallel to its original angle. All your fret crossings would be wrong.

[roberthabraken]

Originally Posted by pilotjones

Two mistakes you've got there.

Originally Posted by pilotjones

First, when you subtracted the thickness of the inner strings, you should also have subtracted half the thickness of the two outer strings.

That doesn't make sense to me. These halves are not physically located in the space that I call 'between the outer strings', but outside. If, measured from the inner edges of the outside strings, you would substract a part of those strings, you would substract too much. And you would end up with a gap when aggregating all distances (space and string thickness) along the nut.

However, I did incorporate half of the thickness of the outer strings when calculating back to center-to-center distances, to make an accurate drawing. If that's what you mean.

Bottomline: as a result (and I did check my measurements) my string thickness is correct and the space inbetween them is exactly the same. If I did it wrong, that wouldn't be the case, would it?

Originally Posted by pilotjones

Second, if you're still going for accuracy, you can't do what you did at the bridge. Whatever shift you apply to each string at the nut, you cannot apply the same shift at the bridge, keeping the string parallel to its former path. You must multiply that shift by the ratio NOAW/BOAW (bridge overall width, measured along the bridge line, divided by nut overall width, measured along the nut line). The strings do change angles. And this is what keeps your intonation on.

You cannot simply shift a string sideways on a fanned board. For an exaggerated example, imagine if you took your first string, and slid it over to the opposite side of the board, so that it is landing in the nut slot for your last string - but keeping it parallel to its original angle. All your fret crossings would be wrong.

I did not simply shift my strings sideways on the board. What I did, is dividing the space on the nut as explained above AND also, using the same method, on the bridge. So I took the space inbetween the outer strings on the bridge line and subtracted the total string thickness (also measured along that line) and divided the space left by six. So I calculated new points on the bridge line as well as on the nut line. I then connected these new dots and got my new string path. With a different angle than before.

But! My CAD software measures these angles with an accuracy of 0.01 degrees (maybe I should change this to 0.001 degrees). Turns out, the new angles of the strings are different, but not that much that you would notice if you use an accuracy of 2 decimal places.

So, my drawing is right, but my explanation wasn't. I meant: I did change the angles of the strings, but the difference is soo minimal, you'd only notice with a caliper .
By the way, I edited my previous post, removing my incorrect statement.

[pilotjones]

On the first point, I can see why this works out for you - as a starting point, you are using the space between the outer strings, rather than the distance between the outer strings' centers, as I was - so there is no need to subtract out the two half strings. So no problem, what you're doing is right, you are using a slightly different method, which I hadn't realized.


On the second issue, though, you may not have simply shifted them sideways, I can see that now. You have made the gaps equal at both - which will not be producing a proper string path on the fan. You can check this: for each string, first measure the overall distance from nut intersection to bridge intersection. (At this point, you must ignore the original data from FretFind, since you have changed things.) Then, for each string measure the distance from bridge to 12th fret crossing and from bridge to 24th fret crossing. If hese are not exactly .500 × the overall string length and .250 × the overall string length, then your intonation will be off. If these are exactly right, then you are OK.

(BTW, you can't use the distance to the 7th fret and compare it to 2/3 the overall length because the 7th fret is not exactly at a 1/3 point - it is only an approximation - 1/(2^(7/12)) ≠ 2/3 . The 12th and 24th fret distances are exact.)

Also, if you are working in CAD, you should use as many decimal places as you have available, and then round off your final answer, if you need to to make it more understandable. Rounding before getting a final answer only introduces veiled inaccuracies.