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A simple formula for any instrument
Calculating Intonation Correction
© Frank Ford, 2/28/96
Fairly often, I'm asked to correct intonation on an acoustic guitar.I believe this is rightly done at the bridge in the form of a compensated saddle,where each string’s vibrating length can be set to achieve reasonable intonation.There are much more sophisticated methods of achieving intonation correction; thereis more than one system of tempering the fretted scale. My interest is in simplyachieving the reasonable intonation that's found on a well-made conventional guitar,without undue modification.
At this time, we generally accept modifications at the bridge because bridges arerelatively easy to replace. Some systems for correcting intonation require shorteningthe fingerboard at the nut. This is not currently a generally accepted modification,although it has merit from an engineering standpoint.
I check for intonation by the usual method of playing the string fretted at the 12thfret 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 playssharp 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 allother aspects of set up are satisfactory, e.g. string gauge and action. I’ll startwith the Low E, and repeat the procedure for all the strings
Wolf website designer 2 30 100. Compare intonation at 12th fret using an electronic tuner. Observe the NUMBER OFCENTS sharp the fretted note is compared to the open string harmonic. IT PLAYS 8CENTS 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 Estrings plays 8 PERCENT SHARP.
Therefore, If I know the LENGTH of a semitone, I can calculate the distance I mustmove 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 nutto 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, soI measure 1.43 inches. (For my purposes, a measurement of 1-1/2 inches is probablyaccurate enough to get reasonable results, but with my dial caliper I don’t haveany 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 distancewhen you think about it.)
I can now plot my ideal saddle positions for all the strings by starting with thepoints where the strings cross the saddle. I can choose whether to compensate theexisting saddle by carving the top of it fore and aft, or by routing for a widersaddle, or by inlaying the saddle slot and routing to relocate the saddle in thebridge.
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 electronictuner - 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:
Pcalc 4 7 Little Elm
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.
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.