Ken LeVan - Posted - 01/25/2014:  15:45:22

There has been a thread going on about fret slot cutting and I think WAY too much emphasis is being placed on multi decimal point accuracy, for which I may be guilty of talking about in terms of process and material, just to make a point about a way to do it -  not intonation. I apologize.  Someone just wrote me a private email about how their caliper is more accurate than mine, and I realized this is a topic that ought to be discussed because I think there might be some compulsiveness at play.

These formulas have been developed over the years - Did anyone think Andres Segovia's guitar was out of tune despite an earlier fret spacing formula and gut strings?

Back in the Day, Gibson used a unique fret spacing based on someone playing the banjo and determining fret intervals based on their ear.  Apparently some people like this spacing and a few Gibson Mavens have used the spacing for conversion necks and jealously guard the intervals.

Then there are the non-believers in tempered scales, who go in another direction with fret spacing.

Then there are the digital tuner folks who look at the number and don't listen.

So what's right?  Being able to calculate fret intervals to 4 decimal points and program that into a CNC is meaningless if the formula is wrong or if it doesn't sound right.

Here's a quote from another website:

"Calculating the positions of the frets requires the simplest bit of math. The (really) historical technique is called the rule of 18, and it involves successively dividing the scale length minus the offset to the previous fret by 18. This was easy enough to do using pencil and paper, although way back in the day they probably didn't even do that, instead relying on a mechanical device called a proportional divider to do the work. The invention of the pocket calculator made it possible to make use of a more accurate constant, and so these days we conventionally calculate fret positions for equal temperament by successively dividing the scale length minus the offset to the previous fret by 17.817. This series of calculations puts the 12^th fret (octave) at exactly half the scale length, and we know from the physics of vibrating strings that halving the vibrating string length of a theoretically perfect string doubles the frequency. Those interested can read about the derivation of this constant below. Interestingly enough, the historical technique yielded good results for gut strings, as it included built in compensation, something that we do now by moving the bridge saddle so that the actual scale length is a bit longer than the nominal length. It is also interesting that the amount of compensation we add is empirically derived, as calculating it is a bit of a chore.

Some references specify a constant of 17.835, which is mathematically untenable but which will likely yield good results nonetheless. The reason that all these seemingly disparate systems can be used to good effect is that even the mathematically accurate equal temperament constant assumes a theoretically perfect string which both exhibits no inharmonicity in its vibration and doesn't need to be stretched to be fretted. Since real strings don't behave that way even the equal temperament system is just an approximation of the way real strings need to be fretted. See Gregory Byers nice paper on classic guitar intonation for more on this subject (see the Links section). Which constant should you use? Unless you are building or repairing historical instruments use the equal temperament constant of 17.817. It is the currently accepted standard."

So, my question is how far off can you get before anyone can hear the difference?

How much does action height and fret height enter into the picture?

What would the tolerances of fret placement be?

Zachary Hoyt - Posted - 01/25/2014:  15:54:14

While I see that this is an important topic it seems to me that it is likely to also be an infinite can of worms.  I do the best I can with fret placement and hope it will be good enough and so far neither I nor any of my customers have had a problem with intonation as far as I know.  The trouble for me is that I can't measure the fret positions to 4 decimal places and I also can't measure or calculate the tolerance for error on my instruments.  I think your questions are good ones and I look forward to following the discussion, but for me it will all likely remain fairly theoretical.

Zach

Dan Drabek - Posted - 01/25/2014:  16:29:18

quote:

---

Originally posted by Ken LeVan

Then there are the digital tuner folks who look at the number and don't listen.

So what's right?  Being able to calculate fret intervals to 4 decimal points and program that into a CNC is meaningless if the formula is wrong or if it doesn't sound right.

---

That's an interesting point Ken. Back when I was a graphic artist--back in the stone age when we still did paste-ups sans computer, I quickly discovered that if you wanted to center a headline on a page, there was a difference between measured centering and visual centering. If you centered a line of type with a ruler, it would often look off-centered to the eye. So, like most designers, I learned to drop a line of type into the page at a position where it looked centered. 

I suspect that a similar effect might be at work in tuning an instrument. I've often tuned my guitars and banjos to a strobe, only to fine-tune them by ear. In other words, the mathematically correct in-tune-ness differed from my auditory impression. Which was correct, and does it really matter?

In response to your second question, I've noticed that luthiers will saw fret slots with extreme precision, and then they will level the frets and round the tops of the frets with little or no thought to how they may be shifting the position of the fret crown. The fact of the matter is that even with a significant shift in the crown of the fret, you can still get perfectly acceptable intonation. I think instrument builders just enjoy a bit of obsessive compulsion, whether or not it makes a difference.

DD

sunburst - Posted - 01/25/2014:  16:32:03

They can be off a lot(!) and still sound in tune. When I built my first guitar 20-some years ago, I measured out the fret scale (rule of 18) and sawed the slots by eye using a radial saw. Later, when I checked the measurements with accurate equipment, I was surprised and distressed to find that some slots were over 1/32" off! When I strung up the guitar and checked the intonation with a strobe tuner, it was in tune. Not perfectly, that's impossible, but closer than some, and close enough that it is well in line with guitars of high quality as far as intonation.
I have my current fret slotting jig set up for +/- .004" accuracy, but I know from experience that that is well within the inherent errors introduced with different strings gauges, action heights, fret shapes and so forth.

MOUNTAIN GOAT - Posted - 01/25/2014:  16:45:51

I was eluding to this in a previous thread a few months ago. The other variable is how hard you fret the string. So, if the fret spacing does not need to be real accurate, then fretting pressure with you finger won't change the note either. You won't stretch a string 1/32 of an inch by fretting it. I too wonder how accurate placement of fret's need to be, and how accurate are they on a bought fret board or manufactured banjo.

banjosam - Posted - 01/25/2014:  18:18:54

I have a number of friends who are excellent musicians. One will tune an instrument and play it a little. If he hands it to another

musician of equal skill he will invariably retune several strings. This seems to occur no matter who the musician is, and I've

encountered this with professional musicians also. It appears to me that we all seem to hear the tuning slightly differently.

beegee - Posted - 01/25/2014:  18:29:34

I think in one of the old Oak repair books, there is a graphic of laying out a fretboard by using a tangent and a series of arcs based on the first fret spacing interval and its intersection with the tangent. I think I'll look it up and check it out.

The Old Timer - Posted - 01/25/2014:  18:48:13

Dave Nichols up in Malone NY once showed me a line up of all the pre war Gibson Mastertone tenor necks he had in his shop, when I visited to get a 5 string neck made for my 1926 TB Granada. No two of them had the same fret spacing!

It's well known that you have to tune a Martin flat top guitar different than a Gibson flat top guitar, especially the B string. To me that has to reflect scale and fret spacing.

I really wonder if there is a "correct" fret spacing, considering the keys we tune and play in, capoing, etc.

In general I find the 1960s better model VEGA 5 strings have the best intonation of any banjos I've tried. Anyone know what system VEGA used?

oldwoodchuckb - Posted - 01/25/2014:  18:53:44

A friend of mine did his fingerboards by the series of arcs and tangent method. His guitars sounded jes'fine. He didn't do it often however. He had each scale he used blueprinted and multiple copies made (it was a long time ago - before most of the modern equipment in use these days.

Another friend just bought fretting diagrams from Stu-Mac or others and his fingerboards came out right on too.

grizzly1 - Posted - 01/25/2014:  19:04:32

Interesting question.

So many variables. how would you set up the test?

To the extent a banjo is tuned to an even tempered scale some of the notes are going to be a few cents out of tune in relation to another note in a cord under the best of circumstances.  To try to control for this could would it help if we specify a G scale banjo tuned to a harmonically perfect G cord, and only play G cords up the neck?  

Where on the neck we are talking about? As the frequencies get higher I think the fret placement tolerances would have more of an effect. in other words, the farther up the neck you go, would a given deviation would have a bigger effect? 

Fretting pressure/downward deflection? Not sure quite how to control for this one. As the strings get shorter finger pressure seems to have more of an effect. Maybe I am imaging things?

Are we talking about the notes fretted on a single string, or a cord and the relative harmonic sweetness of all five strings?  

So is the question: on a banjo that is in perfect harmonic tune to a G cord, and where equal (or relatively equal?) fret pressure is applied, what is the least deviation in fret placement (at the 12th fret? 21st fret?) that would produce a noticeably sharp or flat single note or cord?

I realize I don't have an answer as to how to set this up, but it's a fun question to consider.

Thanks Ken

oldwoodchuckb - Posted - 01/25/2014:  19:13:46

With the equi-space fretting system necessary to play any fret in any key, we give up a certain amount of accuracy in our frets. Add the problems associated with string diameter, core diameter of wound strings, action height and bridge saddle placement, it is a wonder we can tune at all.

I started with classical guitar and went into flamenco. The instruments all sounded jes'fine to me when I was using them daily. At that time classical and flamenco guitars all had a straight saddle, placed mathematically with no allowance for intonation on varied strings.

Later they started using saddles that "compensated" by being angled slightly - as they did with flattop guitars. those sounded jes'fine to me too.

Then I got into playing electrics with six movable saddles. No acoustic guitar has ever sounded really "in tune" to me since. I even thought about building my own bridge, based on the compensation needed for the string set I liked best (LaBella Black & Gold). I never did it though as an injury left me unable to handle 6 strings anyway.

I do use a compensated bridge on my banjos. People tell me my Moon Bridges and Grover Compensated bridges are not correct. But I started using Shubb Compensated bridges in the 1970s and right or not - they sound jes'fine to me.

All this is the long way to say - what we have become accustomed to, is what is going to sound right.

rudy - Posted - 01/25/2014:  20:49:42

I know everybody gets tired of seeing my links, but it's easier than copying and pasting and inserting graphics.  That said, I have an entire section devoted to "Fret Placement Accuracy" included in the "Open Back Banjo Design Primer" here:

bluestemstrings.com/pageBanjoD...n.html#21

Be sure to follow the related link within that section titled "Why can't I get this thing to stay in tune?"

The entire process of mechanical projection and mathematical derivation of fret intervals is covered elsewhere on the website if anyone is so inclined to check it out.

Dave1climber - Posted - 01/26/2014:  06:46:51

quote:

---

Originally posted by rudy

I know everybody gets tired of seeing my links, but it's easier than copying and pasting and inserting graphics.  That said, I have an entire section devoted to "Fret Placement Accuracy" included in the "Open Back Banjo Design Primer" here:

bluestemstrings.com/pageBanjoD...n.html#21

Be sure to follow the related link within that section titled "Why can't I get this thing to stay in tune?"

The entire process of mechanical projection and mathematical derivation of fret intervals is covered elsewhere on the website if anyone is so inclined to check it out.

---

I had followed this link a while ago, thanks for reposting it.

Dave

MOUNTAIN GOAT - Posted - 01/26/2014:  12:49:54

I just did the math on my banjo for string stretch between an open note and the highest fretted note. Not taking into account how hard one presses, the difference in length of the string is .001 inches. Basically nothing. My banjo has a extremely low action. .110 at the 22nd fret.

Ken LeVan - Posted - 01/26/2014:  14:30:37

quote:

---

Originally posted by rudy

I know everybody gets tired of seeing my links, but it's easier than copying and pasting and inserting graphics.  That said, I have an entire section devoted to "Fret Placement Accuracy" included in the "Open Back Banjo Design Primer" here:

bluestemstrings.com/pageBanjoD...n.html#21

Be sure to follow the related link within that section titled "Why can't I get this thing to stay in tune?"

The entire process of mechanical projection and mathematical derivation of fret intervals is covered elsewhere on the website if anyone is so inclined to check it out.

---

Rudy, nobody - NOBODY gets tired of seeing your links. If they get tired of anyone, it would surely be me, not you, and to prove that, I will write another long and boring post.

Back in the day, I had a 36" aluminum yardstick with fret spacings scratched into the back - one side that I got from a friend's Vega Pete Seeger, the other side from another friend's 1944 Martin D-28. Those were my fret spacings for many years and I would transfer them onto my fingerboards.  The Seeger was especially helpful because it worked for a 32" scale longneck or a 27" scale "regular length.

The only times I would get into trouble was when I would try to do a "short scale" and calculate the spacings with a pencil and paper (no digital calculators then).

What I discovered was that there is a fairly wide latitude or tolerance of error that is as we used to say then when we tuned up was "good enough for bluegrass" - kind of what they told us on the rifle range in the Army - "good enough for government work"

We now have digital tuners, which have, sadly, spawned a whole generation of lookers rather than listeners. Earl used a straight bridge with a piece of tape under one of the notches, and he tuned it by ear, as did Ralph Stanley, Pete Seeger, Sonny Osborne, Eric Weissberg, Douglas Dillard, Don Reno, JD Crowe, Bill Keith (uses a moon bridge) etc etc.  and do we think they were playing out of tune? I don't.

My point here is that I think way too much importance is being placed on a few thousandths vis-a-vis fret placement and a slavish dependence on digital tuners.

Dan Drabek's point about the frets is well taken - lots of people want extra wide frets like on a Fender guitar - they look cool - well when they wear flat across the crown, the contact point is not accurate anymore - off by a lot. The old banjos had skinny frets.

Then we have the string stiffness / physics thing that has caused a renaissance in compensated bridges. As you go up the fingerboard, the intonation degrades differently on different strings regardless of fret accuracy.

The banjo is not a digital synthesizer with perfect intonation you can count on - it's a little wonky because of the movable bridge and variable string stiffnesses.

I remember doing this sound file one before for some reason - it's a comparison of harmonics and fretted notes at the second harmonic partial - the octave, with a moon bridge - listen to it.

Honestly, how "digitally" accurate does it have to be before the intonation is offensive?

Ken

Harmonics vs fretted G

rudy - Posted - 01/26/2014:  15:30:25

quote:

---

Originally posted by MOUNTAIN GOAT

I just did the math on my banjo for string stretch between an open note and the highest fretted note. Not taking into account how hard one presses, the difference in length of the string is .001 inches. Basically nothing. My banjo has a extremely low action. .110 at the 22nd fret.

---

It's not the change in length of the string, but rather the change in the amount of tension in the string to arrive at that amount of deflection.  If this was "basically nothing" then there would be no need to compensate string length.  The change in string tension varies with string material, and that's why you find lesser and greater degrees of compensation necessary for synthetic and steel strings.

MOUNTAIN GOAT - Posted - 01/26/2014:  20:56:57

Rudy my point was when you fret a string you are stretching it, and on the worst case note, only .001 inch. Which means nothing, or insignificant. I know the note isn't made by stretching the string.
Not something anyone needs to compensate for. String tension does change with material, heat treat and size, but it still must stretch the same distance. The force required to do so will change when those properties change.
The reason I did the math was to see if the string stretch on worst case mattered for anything. It doesn't.

rudy - Posted - 01/27/2014:  05:31:49

quote:

---

Originally posted by MOUNTAIN GOAT

Rudy my point was when you fret a string you are stretching it, and on the worst case note, only .001 inch. Which means nothing, or insignificant. I know the note isn't made by stretching the string.

Not something anyone needs to compensate for. String tension does change with material, heat treat and size, but it still must stretch the same distance. The force required to do so will change when those properties change.

The reason I did the math was to see if the string stretch on worst case mattered for anything. It doesn't.

---

Sure it does.  The stretching of the string raises the intended pitch of the note.  If it didn't there would be no such thing as compensation.

To illustrate how action height affects pitch  and the need for compensation in general all we need to consider is how steel string guitar players produce vibrato and pitch change by deflecting (bending) the string sideways across a fret.  When used as a string bending technique it's fairly easy to raise the pitch of a note by a full step or more.  An 1/8" of sideways displacement will produce a lower but noticeable amount of pitch change, not coincidentally about the same as we compensate for by bridge compensation positioning.

Hopefully that thought exercise makes it clear to anyone who doesn't think the pitch changes when you push the string down to the fret or fingerboard surface.

The change in string length IS insignificant, but it's effect on pitch at the noted position is not.

Edited by - rudy on 01/27/2014 05:43:41

Jonnycake White - Posted - 01/27/2014:  08:51:10

FWIW

Just to smooth an apparent point of contention - Mountain Goat states that his banjo has extremely low action, and that he performed his measurements on this banjo.  The low action accounts for the low amount of string stretch.  No doubt the bridge position on that banjo and resulting compensation is also very low.

Those of us who prefer much higher action (i.e, we frailers) will need to have more compensation at the bridge.

Getting back to the original question, I too have often wondered about this.  I think the answer might be found in asking those who sell handmade banjos to professional players what their fret marking and slotting technique is and how many complaints they've had about poor intonation. It would also help to somehow accurately measure the actual banjos they produce. We might want to guarantee anonymity for the makers in this survey.

mikehalloran - Posted - 01/27/2014:  09:12:55

Certain "Gibson scale" vintage scales sound better in standard bluegrass keys. As one who played in all keys, I needed banjos with more accurate equal tempering. One of the reasons that I liked heavier strings was that they were easier for me to fret in tune. More resistance to stretching behind the fret was better for me. Light strings with tall frets - couldn't play like that.

Edited by - mikehalloran on 01/27/2014 09:14:05

Ken LeVan - Posted - 01/27/2014:  09:56:16

quote:

---

Originally posted by Jonnycake White

FWIW

Just to smooth an apparent point of contention - Mountain Goat states that his banjo has extremely low action, and that he performed his measurements on this banjo.  The low action accounts for the low amount of string stretch.  No doubt the bridge position on that banjo and resulting compensation is also very low.

Those of us who prefer much higher action (i.e, we frailers) will need to have more compensation at the bridge.

Getting back to the original question, I too have often wondered about this.  I think the answer might be found in asking those who sell handmade banjos to professional players what their fret marking and slotting technique is and how many complaints they've had about poor intonation. It would also help to somehow accurately measure the actual banjos they produce. We might want to guarantee anonymity for the makers in this survey.

---

I have sold three banjos to professional players and performers in the past year. One to guitarist John Miller, who is VERY persnickety about intonation, and there have been no problems whatsoever.  John, who frails, put medium strings on his, another person used for fingerpicking and strumming has medium light. the third, also meduim light.  I have NEVER had any problems with intonation due to bad fret spacing.

On the other hand, I re-set the dowel stick an old ODE a few years back with frets lined up improperly, probably due to whatever they were up to in Boulder in the 60s. It still fretted right as long as the bridge was set properly

In order to detect whether there were actual problems, you'd have to do blind testing of some sort using different fret interval calculation systems on similar banjos, with good players, good setups, proper bridge placements, and people with good ears listening. It would be a giant waste of time, in my opinion.

Ken

MOUNTAIN GOAT - Posted - 01/27/2014:  10:22:23

So if the fret spacing can be off more than .001 with no affect, there is no way that string stretching by fretting a note will have a negative affect. I am sure that no banjo exists anywhere in the world that has all its frets located within .001 of absolute position.

Jonnycake White - Posted - 01/27/2014:  10:33:37

quote:

---

Originally posted by MOUNTAIN GOAT

So if the fret spacing can be off more than .001 with no affect, there is no way that string stretching by fretting a note will have a negative affect. I am sure that no banjo exists anywhere in the world that has all its frets located within .001 of absolute position.

---

I agree, especially considering that the actual width of the fret that is in contact with the string is probably several times .001 inches.

Jonnycake White - Posted - 01/27/2014:  10:43:36

quote:

---

Originally posted by Ken LeVan

quote:

---

Originally posted by Jonnycake White

FWIW

Just to smooth an apparent point of contention - Mountain Goat states that his banjo has extremely low action, and that he performed his measurements on this banjo.  The low action accounts for the low amount of string stretch.  No doubt the bridge position on that banjo and resulting compensation is also very low.

Those of us who prefer much higher action (i.e, we frailers) will need to have more compensation at the bridge.

Getting back to the original question, I too have often wondered about this.  I think the answer might be found in asking those who sell handmade banjos to professional players what their fret marking and slotting technique is and how many complaints they've had about poor intonation. It would also help to somehow accurately measure the actual banjos they produce. We might want to guarantee anonymity for the makers in this survey.

---

I have sold three banjos to professional players and performers in the past year. One to guitarist John Miller, who is VERY persnickety about intonation, and there have been no problems whatsoever.  John, who frails, put medium strings on his, another person used for fingerpicking and strumming has medium light. the third, also meduim light.  I have NEVER had any problems with intonation due to bad fret spacing.

On the other hand, I re-set the dowel stick an old ODE a few years back with frets lined up improperly, probably due to whatever they were up to in Boulder in the 60s. It still fretted right as long as the bridge was set properly

In order to detect whether there were actual problems, you'd have to do blind testing of some sort using different fret interval calculation systems on similar banjos, with good players, good setups, proper bridge placements, and people with good ears listening. It would be a giant waste of time, in my opinion.

Ken

---

Ken, I double checked your fret slotting procedure as you described it in the ultimate fret slotting machine thread, and it seems to me that what ever deviation from perfection may be in your banjos, is due to placing the saw blade and cutting the slot accurately (or inaccurately) on the lines of the computer generated fretboard layout.  I don't know how to measure this accuracy but I suspect that it is probably worse that .001 inch and better than .02 inches, probably somewhere close to .01 inches.  Is that fair to say?  Your excellent results obviously speak for themselves.

Edited by - Jonnycake White on 01/27/2014 10:45:25

Ken LeVan - Posted - 01/27/2014:  11:42:55

Jon, it's hard to say.

My saw kerf is .023", and I just measured the lines on one of my layout, and they are about .030", so if I get the saw exactly in the middle of the line, I should theoretically have .0035 on either side of the cut.  All I know, is that I cut right in the middle as close as I can, and would notice right away if I was off to one side or the other.

The critical thing in making the layout is that Adobe Illustrator will automatically place an object (in this case, a line) at any specified increment, so I place a fret line at the nut edge, set the keyboard increment at 1.5098", hit the arrow, and the line moves 1.5098" down the fingerboard layout. I make another line, put it at the nut edge, set the keyboard increment at 2.9348", hit the arrow, and that line moves down the layout 2.9348", then 4.2799, 5.5495, 6.7478, etc etc, all the way down.  Each fret line is spaced from the nut edge - never from the previous fret, so there is no error build-up. I have never had any problems with this.

If I used the same kind of layout and had a Stewmac fret-cutting circular saw blade in my Radial arm saw, I don't think I could place the cut any more accurately than I can do it by hand, even with a laser guide.

Doing it on a table saw would be more difficult because the layout would be upside-down

Ken

Dave1climber - Posted - 01/27/2014:  14:26:29

Ken

I do mine upside-down on the table saw, however I make the marks on the side.  When I cut I split the saw blade with the mark.  Is it better?  No, just different, not more difficult with good lighting.