Scale length

[zeeway]

The scale length of a string is the length of the string available to vibrate, period. Sometimes physics disagrees with guitar lore, and this is one of those times. Yes, the scale length is a bit different on every string, which drives some people crazy.

IMHO, the scale length of a particular guitar is the distance from the saddle side of the nut to the nut side of the saddle, taken at the midpoint of the nut and midpoint of the saddle. It is a reference number.

So, in designing a guitar, you choose the scale length, which is used in the calculation for fret locations. Then somewhere down the line you compensate the saddle, to get the tuning more exact...which alters the scale length of those strings...which means you should recalculate the fret positions, which means you should....keep chasing your tail.

Guitars are not exact instruments in terms of tuning. Capos and even forming chords with your fingers result in pulling strings out of tune.

But like the bumblebee that theoretically cannot fly, some guitars still sound good to our imperfect ears, anyway.

[charles Tauber]

Originally Posted by zeeway

The scale length of a string is the length of the string available to vibrate, period...the scale length is a bit different on every string

You can redefine the term anyway you wish, as Martin has. Most of the world regards the scale length as the theoretical string length, the one used to calculate the position of the frets.

Unless you are making a "multi-scale length" guitar (including a "fan fret"), the scale length is the same for all strings. What differs is the amount of compensation, giving each string its own actual vibrating string length. Regardless, the scale length remains the same for each string.

So, in designing a guitar, you choose the scale length, which is used in the calculation for fret locations. Then somewhere down the line you compensate the saddle, to get the tuning more exact...which alters the scale length of those strings...which means you should recalculate the fret positions, which means you should....keep chasing your tail.

What most guitar makers/designers do is chose a scale length. The scale length is used to calculate the fret positions. Once calculated, the fret positions are never changed, but, perhaps, for the distance from the nut to the first fret (compensation at the nut).

The saddle is then moved away from the nut to make the actual vibrating string length longer than the scale length. Doing so provides compensation for the increase in pitch caused by depressing the strings against the frets and, for some, some correction of inharmonicity. It is, generally, a once-through process with no chasing of one's tail. (There can be some back and forth if one is optimizing intonation using both nut and saddle compensation.) The scale length and fret positions are not changed.

By using agreed-upon terminology, communication is facilitated. The generally agreed upon terms, and their meanings, is as follows:

Scale length is the theoretical length of the vibrating strings and is used to calculate fret positions.

The actual vibrating string length is the "speaking" length of the actual vibrating string. In practice, the actual vibrating string length is always longer than the scale length.

Compensation, at nut and/or saddle is the amount by which the actual vibrating string length differs from the scale length. When nut compensation is used, the nut/zero fret is moved closer to the first fret decreasing the theoretical distance from nut to first fret given by the scale length. When saddle compensation is used - it universally is used - the breaking point of the string over the saddle is moved away from the nut to increase the actual vibrating string length.

[mirwa]

Originally Posted by zeeway

Guitars are not exact instruments in terms of tuning. Capos and even forming chords with your fingers result in pulling strings out of tune.

Just one i did earlier, still a 25.5 inch scale, fret positions are compensated for the string differences, it’s pretty exacting, just to throw a spanner in the thinking.

TT system.

Scale length for me, is simple string length, if it’s a 25.5 inch scale, the length of the string theoretically is 25.5. Bridge and saddle placement is compensated to accomodate string thickness’s and push down of strings when playing

Steve

[MC5C]

For me, scale length is what I used to calculate the fret locations. I do that to .001", measure with a tool that is that accurate, then saw a slot by hand that ain't that accurate, not in my hands... But that is what scale length is. I then compensate the nut by the slot width, as mentioned, so the nut is moved 10 or 15 thou. up the neck. I then compensate the bridge saddle by whatever amount works, I don't calculate it particularly, I just adjust the saddle until it's right (archtop, don't you know). I do know this - manufacturers quoted all sorts of scale lengths that aren't all that accurate, notably Martin putting the bridge in the wrong place and Gibson with 24 3/4" scales that are actually 24 5/8", and so on. As long as their fret slotting jigs are accurate, worrying about scale length and trying to adjust same on an instrument is a waste of time.

[Rodger Knox]

Originally Posted by Alan Carruth

Roger Knox wrote:
"To get the scale length, measure from the nut to the 12th fret and double it."

Unless, of course, the nut has also been compensated. In that case the nut will be closer to the first fret than it 'should' be, and you'll come up with a scale length that's too short.

Ultimately, the scale length is the length used to calculate the fret positions. After that you apply whatever compensation you feel will correct the intonation so the guitar plays in tune, more or less. It's never going to be 'perfect', and even if it is, some folks will still complain about it.

Originally Posted by charles Tauber

I was kidding.

When slotting a fingerboard, if one cuts centred on the zero mark, one shortens the distance from nut to first fret by half the saw kerf, typically about .011". The Buzz Feiten system, for example, advocates 1/32".

I've read Mr. Gore's fine books and his process for optimizing intonation.

I knew that, you've posted your method several times. Mine is virtually the same. I guess irony doesn't come across in print, but I did know that's the way you do it.

Originally Posted by charles Tauber

You can redefine the term anyway you wish, as Martin has. Most of the world regards the scale length as the theoretical string length, the one used to calculate the position of the frets.

Unless you are making a "multi-scale length" guitar (including a "fan fret"), the scale length is the same for all strings. What differs is the amount of compensation, giving each string its own actual vibrating string length. Regardless, the scale length remains the same for each string.



What most guitar makers/designers do is chose a scale length. The scale length is used to calculate the fret positions. Once calculated, the fret positions are never changed, but, perhaps, for the distance from the nut to the first fret (compensation at the nut).

The saddle is then moved away from the nut to make the actual vibrating string length longer than the scale length. Doing so provides compensation for the increase in pitch caused by depressing the strings against the frets and, for some, some correction of inharmonicity. It is, generally, a once-through process with no chasing of one's tail. (There can be some back and forth if one is optimizing intonation using both nut and saddle compensation.) The scale length and fret positions are not changed.

By using agreed-upon terminology, communication is facilitated. The generally agreed upon terms, and their meanings, is as follows:

Scale length is the theoretical length of the vibrating strings and is used to calculate fret positions.

The actual vibrating string length is the "speaking" length of the actual vibrating string. In practice, the actual vibrating string length is always longer than the scale length.
Compensation, at nut and/or saddle is the amount by which the actual vibrating string length differs from the scale length. When nut compensation is used, the nut/zero fret is moved closer to the first fret decreasing the theoretical distance from nut to first fret given by the scale length. When saddle compensation is used - it universally is used - the breaking point of the string over the saddle is moved away from the nut to increase the actual vibrating string length.

What has yet to be mentioned is that the actual vibrating length of the string is less than the distance between the breakpoint on the nut and the breakpoint on the saddle. Strings have some stiffness, so there is some amount near the ends where the string does not flex. That amount depends on the stiffness of the string, and is included in compensation.

My point is that scale length is a theoretical number used to calculate fret locations, and measuring it accurately on a guitar can be problematic.

[MC5C]

You can just say "this guitar has a 25" scale length, and no, you can't borrow my tape measure..."

[brianhejh]

Thanks for all the comments, it has increased my understanding greatly.

Below is a link on the subject I found interesting (below that) is an exert from that same article - it mentions leading edge (Is this the sound hole edge of the saddle or bridge pin hole side.)


http://www.lmii.com/scale-length-intonation


Find the point on the bridge that is double the length of the nut to the 12th fret and add 1/16" where the 1st string will cross the saddle and add 5/32" where the 6th string will cross. Mark a pinpoint on those two points then draw a line between the points. This will be the forward edge (not the center) of a ramped 3/32" saddle slot.

[Rodger Knox]

Originally Posted by brianhejh

Thanks for all the comments, it has increased my understanding greatly.

Below is a link on the subject I found interesting (below that) is an exert from that same article - it mentions leading edge (Is this the sound hole edge of the saddle or bridge pin hole side.)


http://www.lmii.com/scale-length-intonation


Find the point on the bridge that is double the length of the nut to the 12th fret and add 1/16" where the 1st string will cross the saddle and add 5/32" where the 6th string will cross. Mark a pinpoint on those two points then draw a line between the points. This will be the forward edge (not the center) of a ramped 3/32" saddle slot.

Yes, leading edge is soundhole side.
This is a starting point, there is still setting the breakpoints on the top of the saddle. The bold is minimum compensation, the distance from the front of the saddle to the breakpoint is added to that.

[nacluth]

Originally Posted by mirwa

Steve, how did that sound when bending strings? Actually I would be curious to know if there was discernable difference or if it was just a fun science project. Cool nonetheless.

[mirwa]

As much as I disliked doing the job and I have done a few now, it plays pretty good, I’m actually doing another guitar next week with it.

Downsides, all band members must have it done, if you are the only one in the band with it, everyone else sounds out of tune.

Steve

[bausin]

>> There is probably a way to figure out the scale length by measuring from the 1st fret to the 13th or something, but I don't fell like figuring it out right now.

Measure from the 1st to 12th fret and multiply by 2.25289

[Bruce Sexauer]

Originally Posted by bausin

>> There is probably a way to figure out the scale length by measuring from the 1st fret to the 13th or something, but I don't fell like figuring it out right now.

Measure from the 1st to 12th fret and multiply by 2.25289

Measuring from the 1st to the 13th and doubling it will give you the scale length if you are capoed at the first fret. No one cares. You were joking, but I’m not, although I do think I’m funny in a dry way.

Why the scale length as calculated by 0 through 12 doubled matters is that this is how we figure out where the frets are located. This analysis of scale length is what the rule of 18 (not really 18, but what we call it) is applied to. The actual stop to stop length is called string length, and is also valid, but more useful on violin family instruments than on Guitars.

[bausin]

>> Measuring from the 1st to the 13th and doubling it will give you the scale length if you are capoed at the first fret.

That solves a different problem, which is trivial.
The problem was to calculate the scale length in spite of the fact that the nut may be compensated by shortening the distance to the 1st fret.

>> No one cares. You were joking, but I’m not, although I do think I’m funny in a dry way.

I was not joking. The scale length is 2.25289 times the distance from the 1st to 12th fret. Feel free to calculate it yourself:

((2 x K) / (2 - K)) where K is the 12th root of two; 1.0594631...

[Bruce Sexauer]

Double post

[Bruce Sexauer]

My apologies, you are definitely not funny.

Yes, eliminating the first gap and using math can calculate the actual scale length, unless Buzz Feiten is involved. This could be done with the accurate measurement of any single fret gap if one knew which one it was. I do not have accurate enough tools for the precision thus would involve.