Accurate Fret-board design

Al Sato · Post by **Al Sato** » 13 Jul 2004 8:31 pm

Hi, everybody. I seem to have made matters more confusing. It is important to draw the first diagonal line properly. Once you do that, Ron's process produces fret distances for equal temperament. His process is so good that it's worth getting the starting point exactly right. The line you want to draw is the line connecting the following two points:

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.]

Jim Smith · Post by **Jim Smith** » 13 Jul 2004 8:36 pm

The tangent line from the arc to the saddle would be slightly to the right of the perpendicular line. The axiom for lines tangent to a circle states that all tangent lines are perpendicular to the center of the circle. Thus, it would be at a right angle to the line from where the arc meets the perpendicular to the point at which the baseline meets the saddle line. This would make each successive arc smaller.

Loni Specter · Post by **Loni Specter** » 14 Jul 2004 12:56 am

Isn't a tangent just a guy who stood out in the sum too long?

Bobby Lee · Post by **Bobby Lee** » 14 Jul 2004 8:54 am

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

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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<img align=right src="http://b0b.com/Hotb0b.gif" width="96 height="96">Bobby Lee - email: quasar@b0b.com - gigs - CDs, Open Hearts
Sierra Session 12 (E9), Sierra Olympic 12 (C6add9),
Sierra Laptop 8 (E6add9), Fender Stringmaster (E13, A6)

Al Sato · Post by **Al Sato** » 14 Jul 2004 9:34 am

Hey Bobby,

You asked:

<BLOCKQUOTE>quote:<HR>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?<HR></BLOCKQUOTE>

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.

Al

Ron Bednar · Post by **Ron Bednar** » 14 Jul 2004 10:08 am

Bobby Lee, I was told, by the old guitar builder that gave the method to me, that it is the refined number rounded off in "The rule of eighteenth's" that many guitar builders used, including Leo Fender, as mentioned by Roy Ayres. The guy told me he first learned it when he was learning his craft in Spain. He said he was told the formula and method was calculated way back by monk's who built classical guitars in southern Spain. Kinda interesting how things get around ain't it?

Al, thanks for the technical explanation.

Bruce Clarke · Post by **Bruce Clarke** » 14 Jul 2004 12:20 pm

I came across the geometric method in a book about guitar building that was published sometime in the 30s, or 40s. but I can't remember the name. I was doing a lot of technical drawing at the time, and I would never have been able to work out the maths in those pre calculator times anyway. So with that knowledge, and after several previous failed attempts, I was finally able to make a lap steel that worked. With a sharp pencil and good eyesight there is no cumulative error.

Recluse · Post by **Recluse** » 17 Jul 2004 6:03 am

Consider the first fret construction. A proper tangent to the circle through the intersection of the nut perpendicular and the circle would be a line paralell to the base line. What is called the "tangent line" is better named a "construction line". The construction will leave a chord in each circle(touch the circle at two places). Try a construction of two frets with a very steep construction line and the chord will be apparent.
An interesting case where the mis-use of a word is perfectly clear.
As it is Saturday morning I must stop thinking now.
Steve Bailey

Roy Ayres · Post by **Roy Ayres** » 17 Jul 2004 7:10 am

Anyone here who can divide by 18?

C Dixon · Post by **C Dixon** » 17 Jul 2004 7:18 am

not me

Jennings Ward · Post by **Jennings Ward** » 19 Jul 2004 4:52 pm

Hello Carl and ROY, and everyone. Have any of you had a chance to inspect the computer program that Ron Lashley Sr. wrote for fretboards< then put it on a floppy?? As you know, Ron designed and built Emmons Guitars....... very interesting....Jennings

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EMMONS D10 10-10 profex 2 deltafex ne1000 pv1000, pv 31 bd eq, +

C Dixon · Post by **C Dixon** » 19 Jul 2004 5:16 pm

Jennings,

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

carl

Jennings Ward · Post by **Jennings Ward** » 19 Jul 2004 5:28 pm

Ron was quite proud of it...we discussed it on ocasion. It [the program] may be available from Emmins Guitars, Burlington , N.C. Ron Lashley Jr. was heading up the company the last I have heard,havent stayed in touch... Jennings

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EMMONS D10 10-10 profex 2 deltafex ne1000 pv1000, pv 31 bd eq, +

Bob Stone · Post by **Bob Stone** » 20 Jul 2004 5:14 am

Hi Jeff,

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.

Dick Sanft, who lives in Palm Harbor, FL, has a 26 in scale Stringmaster quad he fitted with similar spacers. His, I believe, are aluminum and just drop in. Anyhow, he said the 26 in scale was just too long for Hawaiian music--hard to do slants and the string tension was too high. He's been playing professionally for about 60 years.

Jeff Strouse · Post by **Jeff Strouse** » 21 Jul 2004 7:45 am

Hi Bob!

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.]

RON PRESTON · Post by **RON PRESTON** » 24 Jul 2004 6:01 am

WOW......
I have The FORMULA(S) that a Friend had "DRAWN OUT" YEARS AGO on this very subject, but, I Have NO CLUE as to HOW to go into the "PAINT" program to post it. I'll get into the cumputer to LEARN HOW, and, with a little LUCK and some Cool Directions from our Fellow Formite, WAYNE COX, Who, BTW, is EXTREAMLY KNOWLAGABLE in the computer world, Just maybe I can post the EQUASIONS and ANSWERS.
REAL INTERSTING STUFF....

[This message was edited by RON PRESTON on 24 July 2004 at 09:23 AM.][This message was edited by RON PRESTON on 24 July 2004 at 09:26 AM.]

Todd Weger · Post by **Todd Weger** » 28 Jul 2004 6:26 am

Bob Stone said:

Dick Sanft, who lives in Palm Harbor, FL, has a 26 in scale Stringmaster quad he fitted with similar spacers. His, I believe, are aluminum and just drop in. Anyhow, he said the 26 in scale was just too long for Hawaiian music--hard to do slants and the string tension was too high. He's been playing professionally for about 60 years.

My, what a co-inky-dink... Dick was just over to my house yesterday, and we were talking about this very thing! Weird...

He told me that he left one neck of his 26" quad full length, just to play on certain songs for certain effects, but I believe he said he found another shortscale quad, and should be getting it soon. He and I got to jam for a couple hours, with me playing upright bass, and he playing my D-8 shortscale Stringmaster. Man, I just love his playing! He was also playing this mongrel looking steel my drummer had that he wanted me to clean up, etc. Dick and I both agree that it appears to be a Supro, but it was obviously refinished or something, because there's no label on it anywhere. SOUNDS AMAZING, though. I'll post a pic in another thread.

BTW, that was a great program, Bob! Hope all is well up there in Gainesville.

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Todd James Weger/RD/RTD
1956 Fender Stringmaster T-8 (C6, E13, B11); 1960 Fender Stringmaster D-8 (C6, E13); Melobar SLS lapsteel (open D); Chandler RH-4 Koa semi-hollow lapsteel (open G); Regal resonator (open D or G)