For a 22 inch scale, the precise distance between fret 1 and 2 would be "x", but on a 22.5 inch, it would be different value. And the distances would change again for a 23, 24.5, 25, and 26 scale...there would be a different fret alignment all the way up the neck.

The simple answer to the question (especially for those of us who hate math), would probably be to just go buy a pre-made fret board. But how did that guy figure out where to draw the little lines? It's interesting to look at a T-Logo neck...it looks like the frets are part of the bakelite mold...one piece, possibly?

And, could factors such as string spacing and a tapered neck have an effect on fret spacing; or, is fret placement solely determined by the location of the nut and bridge (say if 7 or 8 strings are crammed on a 6 string neck, would the fret location stay same because it's still the same scale length)?

[This message was edited by Jeff Strouse on 12 July 2004 at 04:49 PM.]

DGB Studios

Scroll down on the right and you will see what you're lookin fpr.

Ignore the Japanese "installation" stuff ... just choose English

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www.horseshoemagnets.com

[This message was edited by Rick Aiello on 12 July 2004 at 05:21 PM.]

You can buy rulers that are marked to the 1/100th of an inch for when it's time to execute those calculations on a real live fretboard.

1.05946

As an example on a 23 inch scale the 1st fret would be at 21.71 inches. The second fret would be at 20.49 inches. How did I arrive at this? I simply divided 23 by the constant, then divided that number by the constant, etc, etc, etc, for as many frets as you want.

For any scale length follow the above procedure. If you do not end up at the 12th fret with EXACTLY half the scale lenth, it is due to rounding off. But you should be very very close. Closer than any steel player would ever need since we do not fret the steel guitar.

Good luck and may Jesus bless you in your quests,

Interesting, huh?

[This message was edited by Jeff Strouse on 12 July 2004 at 07:15 PM.]

The scale length divided by 17.817 gives the distance from the nut to the first fret. Instead of going on with a mess of fractions for each fret do this:
1. On a heavy sheet of paper or a flat piece of aluminum, draw a perpendicular line for the nut and another for the saddle.
2. Draw a baseline between the nut and saddle lines.
3. Set a compass from the perpendicular nut line to the 1st fret distance, that you calculated above, on the baseline. Scribe an arc from the baseline to the perpendicular.
4. Draw a tangent line from where the arc meets the perpendicular to the point at which the baseline meets the saddle line.
5. Draw a perpendicular from the baseline to the tangent at the 1st fret position.
6. Reset the compass to the distance from the 1st fret to the tangent and scribe another arc. Where the arc meets the baseline is the 2nd fret.
7. Continue drawing perpendicular lines at each fret position and scribing arcs to find the next fret position.
8. The 12th fret will be exactly 1/2 the scale length.

[This message was edited by Ron Bednar on 12 July 2004 at 08:57 PM.]

...seems the most expediant way to me.

That's pretty neat - I will have to think about that. One point I'd like to make, though. When you draw that diagonal line, you call it a tangent line. If the line were actually tangent to the circular arc you drew for fret 1, it would intersect the perpendicular nut line slightly above where the circular arc intersects that line. It's not a large amount, but for accurate fret placement it's important to distinguish because it will throw the whole thing off after the first fret. Did you mean tangent to the first circular arc or just the line between the place where the circular arc intersects the perpendicular line and the place where the base line and saddle line intersect?

Thanks.

Oh, on edit, the answer is clear to me. It is not the tangent line, it is the line from where the first circular arc meets the perpendicular nut line and the point where the base line meets the saddle line. Just a minor but important (to me) point.

[This message was edited by Al Sato on 13 July 2004 at 11:43 AM.]

I like this method, it seems to work really well. It was given to me by a old luthier that built classical guitars. He learned his craft in Spain, where he grew up, before coming to the States. This method came from a book he had, but I think he also said it was way old, like from the 1500's or there abouts. Hope you all find it useful.

[This message was edited by Ron Bednar on 13 July 2004 at 01:57 PM.]

I'd be glad to share the drawing file if anybody wants it, just email me. It's for a 23" scale, done in CorelDraw but I can also save it as an Adobe Illustrator document.

As was typical of Leo, he always did the right things -- although not always for the right reasons.

Hey, who can criticize success?

[This message was edited by Roy Ayres on 13 July 2004 at 03:31 PM.]

This is the best I could do with MS Paint ...

Ron, I think Al was discussing the use of the term tangent in #4 in your description.

The two points on each circle that would generate a common tangent line ... would not be at 12 o'clock position ...

Therefore when it (common tangent) crossed the perpendicular ... it would have a greater positive value than a tangent line drawn from the 12 o'clock point on the first circle.

At least that's what I gathered from his post ...

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www.horseshoemagnets.com

[This message was edited by Rick Aiello on 13 July 2004 at 04:36 PM.]

If you want to double OR halve ANY number; but you want to do it in 12 equal "log" steps, the formula is the 12th root of the digit 2.

If you want to triple or cut any number by 1/3 in 17 steps the formula is the 17th root of the digit 3 and so on.

In our western style of music our octaves are doubled (or halved) in 12 equal log steps. Therefore we use the "constant" 12th root of the digit 2 to calculate not only all of the notes expressed in HZ, but the distance the frets are from the bridge.

Now, in order for it to be as accurate as possible, engineers have determined that the 12th root of the digit 2 must be carried to 12 places to the right of the decimal point.

Most scientific calculators are designed around this by the way; EVEN though the LCD readout may show less.

I said all the above to tell you that the actual constant "divider" to determine extremely accurate placement of frets is:

1.059463094xxx.

Where xxx is I don't know on my 9 place calculator. However the arithmetic chip inside my calculator calculates to full 12 places beyond the decimal point.

So If I store the above number in mem on my calculator, then continue to divide ANY scale length by that number, fret placement on any fretted instrument can be placed extremely close IF one does the following:

1. Round the answers to just 2 decimal points.

2. Use a 1/100th divided ruler.

Here is an example:

Scale=25.5 inches.

Where is the 1st fret?

1. Divide 25.5 by the constant above.

2. It comes to 24.06879997

3. Round this number off to 24.07 ("Round" means, 5 or above add 1; 0-4 leave it alone)

4. Using the ruler divided into 1/100's, locate the first fret at exactly 7 slashmarks above 24 inches from the bridge.

To determine the 2 fret, repeat the above steps. Continue this for every fret you want.

This will place every single fret on a 25.5 inch scale soooooo close, your eyes would not be able to see the error IF it was pointed out to you. IE, less than than the width of a human hair.

Note: The simple test is; if you get to the 12th fret and it is not precisely 1/2 the distance from the bridge to the nut, you have done something wrong. Same thing if you get to the 24th fret and it is not precisely 1/2 the distance from the Bridge and the 12th fret. And so on.

You said:

quote:

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This will place every single fret on a 25.5 inch scale soooooo close, your eyes would not be able to see the error IF it was pointed out to you.

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I agree with you -- and the above statement can also be applied to the fret scales laid out by Leo and his non-technical secretary in the 40's. Although his methods were crude and his knowledge of the physics of vibrating strings was zilch, he nailed it well enough that his axes became the "standard" in the world of solid bodied guitars.

Thanks,

Roy

Seems to me that's exactly what is going on with that line. But then again, I'm no geometry mental giant...

[This message was edited by Ron Bednar on 13 July 2004 at 06:48 PM.]

The drawing with the two circles is misleading. Yes, the two circles share the same tangent line, but the centers of both circles are not on the same perpendicular line to the left side vertical line.

If the two circles had their centers on the same line (perpendicular to the left vertical line), and the radius of each circle was equal to the distance from the center of each circle to the tangent line, then you would have the same drawing that Ron started with. Ron's drawing just doesn't show the complete circles, which would necessarily overlap each adjacent circle.

Al is right, however. The line that is defined by the center of each circle and the point on the circle where it intersects the tangent line is perpendicular to the tangent line, not the horizontal base line. So the tangent line would intersect the vertical line slightly above the first circle.

Where the initial vertical line intersects the circle or the tangent line is not important. We are only concerned with the points on the horizontal base line that are defined by the length of each successive radius to the tangent line.

Now I need a donut...D'oh!

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[This message was edited by Mark Herrick on 13 July 2004 at 08:37 PM.]

quote:

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4. Draw a tangent line from where the arc meets the perpendicular to the point at which the baseline meets the saddle line.

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from where the arc meets the perpendicular.

If you drew a tangent line as described here ... it would be parallel to the base-line .

Your line certainly is a tangent line ... and a marvelous way to map a fretboard ...

But that particular tangent line ... isn't the one described in #4 ...

quote:

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So the tangent line would intersect the vertical line slightly above the first circle.

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Mark, that was what I hoped to show in my MS Paint .gif ...

I certainly was not trying to mislead anyone by using an inaccurate model ... simply thout a visual might help.

Definitley a long scale (26), turned into a short. I'd be curious to hear the sound of that paricular instument..."before" and "after"...

You guys know more about this stuff than I do anyway!

Seems I remember the old luthier telling me that Leo Fender invented this method...

[This message was edited by Ron Bednar on 13 July 2004 at 09:09 PM.]

1. The point where the first circle intersects the vertical line representing the nut

2. The point where the base line intersects the vertical line representing the saddle.

If you take a line that is in fact tangent to the first circle, it will intersect the vertical line representing the nut at too high a point, as Rick showed. That means that the second fret will be too far from the first fret because the diagonal line will be too high at that point. In practice, given the widths of lines you can draw, the two may seem to be the same. The fact that they are mathematically different but look very similar will be the source of some error in the fret layout. The error is probably small enough that it won't matter for a lap steel guitar because players only use the frets as visual guides.

At one time, I wrote up a description of the way equal temperament worked for a luthiers group. I also used that description to write a computer program to control a CNC milling machine to produce templates for any scale length. It would have been nice to have the process Ron described in the article I wrote. It would have made my article clearer.

Added in edit: after you draw your diagonal line, you then proceed as Ron said to draw a perpendicular line up from the first fret to the diagonal line. The next radius you want is the length of that perpendicular line. Make your circular arc and the place where it touches the base line is the location of the second fret. Continue until you have enough frets...

[This message was edited by Al Sato on 13 July 2004 at 09:43 PM.]

Added in edit again: at the risk of confusing things further, I've thought about it some more and the following procedure also works:

1. Draw the first circle as before, but draw the line that is tangent to that circle that also passes through the point where the base line meets the perpendicular line representing the saddle.

2. Starting from the point where that circle hits the base line (the position of the first fret) draw the circle that is tangent to the diagonal line. It will hit the base line at the location of the second fret.

3. Continue in this fashion, always drawing a circle that is tangent to the diagonal line.

This procedure is harder to do than Ron's procedure but it uses tangents. The best thing is to use Ron's procedure as I described above. I will shut up now and let us all recover.

[This message was edited by Al Sato on 13 July 2004 at 10:22 PM.]

Hey Ron, that's a really cool geometric method. I like it! One question, though. You wrote:

quote:

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The scale length divided by 17.817 gives the distance from the nut to the first fret.

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You asked:

quote:

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Hey Ron, that's a really cool geometric method. I like it! One question, though. You wrote:

quote:
--------------------------------------------------------------------------------
The scale length divided by 17.817 gives the distance from the nut to the first fret.
--------------------------------------------------------------------------------

Where does that magic number come from?

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That number is actually 1/(1-r), where r is the 12th root of 1/2, rounded to 3 decimal places. It's what is used in equal temperament. I could email you the article (assuming I still have it) if you are interested enough but it's all math.

I have never seen it. Didn't know it existed.

I haven't taken the time to read all the posts in this thread, so hope I am not repeating what's already been said.

I first heard Dick Sanft on the Florida Folk Series you did some time back. He is an awesome player! Does he perform in Palm Harbor?

I'd love to take a 26 inch scale for a test drive someday...I've never played one. But my acoustic resonator is 25 and I can definitely tell a difference from the short scale steels that I have.

It's an interesting concept...changing the scale length. It would be fun to compare it to a "natural" short scale quad, to see if there's any tone or sustain difference.

[This message was edited by Jeff Strouse on 21 July 2004 at 08:45 AM.]