# Intonation

I am a little confused about adjusting intonation: Some teachers say the 12th fret should right on with the open string (Erelewine), other say due to string vibration, etc. it should be set a little flat (Kent Everett). Any insight on this would be appreciated.

Larry

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What's the rationale behind setting up an instrument so it plays flat?
I'll get Kent's exact wording on that before I reply. Here what Frank said:

"As a rule, we set it to be exact when fretted at the 12th, but for some instruments and players it can work a bit better if set a tiny bit flat. It's almost always better to be flat when out of tune rather than sharp, so if there are seriously sharp notes in other places or if the player tends to stretch the string sideways a bit, then it may be simplest to set the bridge flat on one or more strings."
Most very serious rigorous attempts at defining methods to get great intonation up and down the neck have the 12th fret harmonic matching the fretted note as a primary objective. One of the most rigorous analyses has been done by Greg Byers, a classical builder in Willits, CA. A tome describing his analysis and intonation method can be found at http://www.byersguitars.com/research/Intonation.pdf. One feature of his intonation scheme is a variable set back or set forward of the nut depending on the string. A tough read but well worth it. Larry Schultz recently reminded me of the work and passed the link along.

Bob

P.S. The method of tuning a bit flat, of course, has a natural limitation. After all, one can't tune all of the notes flat. You're left with an instrument that plays flat and still has intonation problems. The key piece of information becomes which strings to flat and by how much.
The height of the string at the 12 th fret if you use the harmonic can be different then a fretted string and since you are playing in only fretted strings why would you need it to be in tune with a Harmonic?

Ron
Yeah, Ron, I know what you're getting at. All you need is for the fretted note to be perceived to have the right pitch, period, wherever you're fretting it. Apparently, however, for strings that require heavy compensation like the G string on a classical, the harmonic doesn't necessarily play fair.

Bob
Some times I find it difficult to arrive at an acceptable intonation
at the nut on classical guitars with the old type nylon trebles.

I usually set the entire nut forward 1/2 mm and add
for the g-string another 1/2. Then I back off the hi e-string 1/4 mm.

This is a fairly good compromise, but what if the first four - five frets
are moved successively backwards a bit.

Would you say this is a way to improve the compensation
for the more pronounced sharpening in this area?
It really would be worthwhile for you to check out the Byers article or at least go to his website and look at his generic starting points for both nut and saddle compensation. For the nut, he cuts that end of the fingerboard short by 1mm and then applies varying back set to the individual strings. At the saddle, he also does individual compensation that looks alot like what one would normally do with a steel string guitar.

Bob
I set mine as close as I can get it .I could see doing it another way if sideways finger pressure is a player problem but really don't understand some opinions as others seem to.I think
Thanks Bob!
Unfortunately my english is nearly as bad as my math, but Buyers study
did really inspire me to experiment with intonation some years ago.

A good nut/saddle intonation makes a lot difference, and
I can't live without it now, but there still are some sharp tones,
mostly at the early frets.

There is also the back buzz with nylon strings,
requiering a bit higher nut position,
resulting in more stretching closer to the nut.

This can't be entierly compensated for in the nut, so maybe
it is a way to set the first frets a little flat, compared to the 18-rule?
You clearly have more hands-on experience in dealing with classical intonation than I do. I've just kind of sat by on the sidelines, watched newer and "better" schemes fly by, and listened to the complaints erupt once other people try them. The idea of stretching the intervals among the first few frets is actually a rather decent one but I haven't a clue to how one could get them set by some relatively simple calculation or procedure.

There is one other angle on this that I ran into recently. A friend with a famous maker's classical guitar complained to me that it didn't seem to do a very good job of intonation and that some of the frets seemed to be off. Turns out the fret positions were just fine for the nominal scale length. I then tuned the high E string with a Korgh tuner and recorded an Emaj scale. I used software to determine the actual frequencies of the plucked tonics and, holy cow, there were some pretty large differences from the published nominal frequencies. For example, measured vs ref frequencies were: for open E, 332 vs329.6, f# 374 vs 370, g# 416 vs 415.3, a 440 vs 440, b 490 vvs 493.9.

Turns out, if you measure the first ten frequencies for each note and use that data to calculate a consensus tonic frequency, the numbers compare almost perfectly with the reference values. Apparently that's how the Korg tuner works and they also warn that high harmonics can sometimes confuse the tuner. Further, that's pretty much how our ear and brain work together to determine pitch.

The reason I tell all this, if you've had the stomach to read this far, is that the ear is the final arbiter of proper pitch. Establishing fret positions according to some fretting rule that attempts to position the tonic appropriately could easily lead to the perception that pitches are incorrect.

Whew

Bob
Thanks for the warning Bob, and for the details.

I will try to place those frets by ear,
- and maybe I have to mix in a bit of intuition...
Risky thing.
I did leave one piece of information out and it really kind of spells doom for getting perfect intonation at all frets for all strings from all makers of strings and for all of the same string from a single maker.

The reason that a tonic value doesn't match up with the value obtained from the harmonic data is because the harmonics display inharmonicity. That is to say that their frequencies deviate from a perfect linear relationship; a graph of frequency vs harmonic number is slightly curved. The amount of inharmonicity is related to the stiffness of the string, which is in turn related to intrinsic material properties and, importantly for fretted notes, uniformity of diameter. So, inharmonicity would be expected to differ from the bass strings through the treble strings. It follows from this that perfect fret positions would different for each of the six strings. Who needs that?

Lute makers solved the problem, sort of, by using moveable gut frets tied around the neck and fingerboard. This might not be a bad experimental approach to determine exact fret positions for a particular make of string, where one would just use either one's ear or some average of N harmonic frequencies as arbiter of pitch. In fact, this would be real interesting to do.

Bob