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  #1  
Old 02-13-2018, 07:17 AM
hat hat is offline
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Default scale length, cents, and bridge compensation

I'm wondering if there are any direct correlations between cents off of a note, and bridge offset. Let me rephrase that - Lets say you have a guitar that frets a little sharp at the 12th fret. And lets say it is exactly 10 cents sharp. Given a set scale length, lets say 25.4 - is there any sort of formula that says for 10 cents off you need xx/xx inches of extra compensation to correct it?
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Old 02-13-2018, 01:28 PM
Alan Carruth Alan Carruth is offline
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One thing that helps is to remember that there are 100 cents in a tempered semitone. The distance from the nut to the first fret represents 100 cents.

If you're trying to get the fretted note at the 12th fret to be exactly on octave above the open pitch, it would seem to me that you'd look at the distance between the 12th and 13th frets, since what you're trying to do is knock (in your example) 10 cents off the fretted note pitch. If that distance is about 16mm, then 1.6mm will be pretty close to ten cents worth, and that's how far you need to move the saddle. If it's sharp, move the saddle back.

This is an approximation, of course. In such cases I try to do two things. One is to find some way of making a temporary change that you can reverse easily. That may not be possible in this case. When setting a new guitar up you can start with a flat saddle top and put a piece of string across it under the string you're checking as a stop point. Moving the stop back and forth makes it easy to find the right length, and you can then file the saddle top to match.

Another thing to do is remember the 'Rule of Half': make only half the change you think you'll need, and see how that works. Sometimes you get it right the first time that way, and it saves you from going too far. At worst, you just have to go in and make another adjustment.
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Old 02-13-2018, 03:31 PM
Frank Ford Frank Ford is offline
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Here's the text of an article I wrote in 1996:


I check for intonation by the usual method of playing the string fretted at the 12th fret and comparing to the note produced by playing the harmonic at that same position. Most often, I'm reconfiguring a saddle or bridge to correct for a guitar that plays sharp up the neck. Here's a formula I use to save the effort of trial-and-error.

Let's assume I'm working on a guitar that plays SHARP when fretted, and that all other aspects of set up are satisfactory, e.g. string gauge and action. I’ll start with the Low E, and repeat the procedure for all the strings

Compare intonation at 12th fret using an electronic tuner. Observe the NUMBER OF CENTS sharp the fretted note is compared to the open string harmonic. IT PLAYS 8 CENTS SHARP (that's a lot, but I often see worse.)

ONE CENT IS ONE HUNDREDTH OF A SEMITONE. I think of one cent as ONE PERCENT. And, I think of the number of cents error in intonation as the PERCENT ERROR. So my E strings plays 8 PERCENT SHARP.

Therefore, If I know the LENGTH of a semitone, I can calculate the distance I must move the pivot point of the string to correct for intonation.

My guitar has a scale length of 25-1/4” and I can look up the distance from the nut to the center of the first fret on a fret scale chart, or I can simply measure it. A SIMPLE MEASUREMENT IS ALL I NEED, because I’ll round off the decimal places, so I measure 1.43 inches. (For my purposes, a measurement of 1-1/2 inches is probably accurate enough to get reasonable results, but with my dial caliper I don’t have any trouble getting 2 decimal places.)

Here we go then: FIRST FRET DISTANCE times PERCENT ERROR
For my E string, it’s 1.43” x 8% = 0.114” or a little more than 7/64” (a fair distance when you think about it.)

I can now plot my ideal saddle positions for all the strings by starting with the points where the strings cross the saddle. I can choose whether to compensate the existing saddle by carving the top of it fore and aft, or by routing for a wider saddle, or by inlaying the saddle slot and routing to relocate the saddle in the bridge.

The advantage of this method is that it works easily for even the most bizarre instrument, stringing, tuning, and setup combinations.

My biggest source of error in measuring is the intonation measurement with my electronic tuner - you know how the meter wants to move around a bit. . .


Here's a simple explanation of the reasoning, submitted by Greg Neaga of Stuttgart, Germany:

It is easy to think this through if you use a very extreme intonation flaw as an example. Let's assume the pitch at the 12th fret is one complete semitone too flat.

In this case, you would have to move the saddle towards the nut by distance equal to the 1st fret distance.

Assuming the string tension stays the same, this would have the following effects:

1) The open string is raised by one semitone
2) The 12th fret harmonic is raised by one semitone
3) The fretted note at the 12th fret is raised by 2 semitones

Which is exactly what we need in our (admittedly extreme) example.
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Last edited by Kerbie; 02-13-2018 at 03:37 PM. Reason: Edited
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Old 02-14-2018, 12:22 AM
bausin bausin is offline
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>> If you're trying to get the fretted note at the 12th fret to be exactly on octave above the open pitch, it would seem to me that you'd look at the distance between the 12th and 13th frets, since what you're trying to do is knock (in your example) 10 cents off the fretted note pitch. If that distance is about 16mm, then 1.6mm will be pretty close to ten cents worth, and that's how far you need to move the saddle. If it's sharp, move the saddle back.

Alan,

The problem with this reasoning is that while the fretted note will now match the original open string note, the new open string note will have gone flat by half as much as the fretted note.

That's why Frank's method of using the distance from the nut to the 1st fret works; it is twice the distance from the 12th to the 13th fret.

Steve
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  #5  
Old 02-14-2018, 12:15 PM
Alan Carruth Alan Carruth is offline
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That's what I get for posting off the top of my head, rather than actually checking it out on a guitar. Frank's method gives, as you would expect, about twice the compensation I got.

I compare the open string pitch with the fretted note, looking for an exact octave, rather than using the overtone and the fretted note. You will, of course, be tuning the open string to the correct pitch before checking it, right? Assuming Frank got it right his compensation will be right on, and mine will still be a little bit sharp.
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Old 02-14-2018, 03:45 PM
bausin bausin is offline
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>> You will, of course, be tuning the open string to the correct pitch before checking it, right?

Actually, I don't use open strings. I check the notes at the 3rd and 12th frets to set the bridge compensation. Since I rarely play open strings, I'd rather leave the nut out of the picture.

BTW, I think the reason Frank's numbers aren't double yours is that the 12th to 13th fret should be close to 18mm instead of 16mm.
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