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Todd.
With the scale of the guitar containing all of the open notes in such a close plain of intonation adjustment, it's an apples and oranges comparison between the guitar and piano as instruments. The scale lengths allow for only a fracion of stiffness variation acroos even the most radical guage parameters on a guitar that the harmonics are effected little in their relative pitch to the open note and note increments afforded by the fret positions.

Equal temperament is practically an impossibility on a guitar due the very short intonation adjustment plain aoffered by the saddle and nut as the origin and termination points of the scale. With a piano's much broader intonation plain, and ability to provide string lengths more condusive to and capable of offering intervals over several octaves that can present equal temperament, it becomes a more attainable achievement even with the typical octave stretching that is applied to piano tuning. The smaller pianos present a much more crowded intonation landing and that has always created problems with the intonation process that aren;t as obvious in a longer or larger piano with the much steeper intonation landing.

   String physic and harmonic behavioral theory can present illusive goals for a builder or player when considering intonation of a guitar so I tend to avoid it and stick to what I hear and what my strobe tuner hears. My feeling on music and intonation has always included as certain amount of the thought.."If it sounds right, it's right", but alot of physical things need to be real and present to make it all work.

   There's still a lot of intuition that must be applied to any instrument's intonation and the alignment of the note and harmonic plains and much of it just comes with time and the number of instruments that pass across our benches as we pay attention to the subtle differences between them. Ultimately, though, my goal is to have a 12th fret note that is identical to my open note when it is fretted without any undue string deflection caused by poor technique or excessive pressure. That is always attained once my harmonic blanket is aligned with the note plain using the very slight adjustment palette that is provided by the saddle along with good solid and sure contact and exit surface interfaces between the strings at both the nut and saddle ends. All tuing steps are performed using a very minimal excitement of each string whether activating notes or harmonics to minimize the deflection and broadening of the vibration path that will crate the increased stiffness that Al mentions in his post above. I've wtached guys intonate while plunking deeply on the string for notes and harmonics and they struggle with the process since there is a level of inconsistency in the force with which it is all done. They read notes and harmonics while trying to work over the sound...and pitches generated by, humidifiers, vacuums, fans, traffic and other outside audio forces and it can just make things more difficult and frustrating for them.

   These are just my findings concerning intonation, string physics and the theories that pop up regularly around them. Al is an exceptionally bright guy who really has a grasp of the theories and still is able to build a great guitar that plays in tune. We all need to apply what has proven itself to work for us and on our guitars since there are so many variables that can be present from one instrument to another.

Regards,
Kevin Gallagher/Omega GuitarsKevin Gallagher38797.6612962963

Kevin,

I appreciate you sharing your thoughts and experience. Thanks for taking the time.

If I may hopefully clarify one thing I said, about equal temperament on the guitar. It was not my intent there to make a statement that is necessarily technically correct. I could have said "equal temperament, for all intents and purposes". The point is really, as you said, if it sounds right, it's right. I think it's fair to refer to a guitar that has good intonation and is well-tuned so that the chords all sound good as having equal temperament, perhaps using the term a bit loosely, because the bottom line of equal temperament is that all the chords (and scales) in all keys sound good. My experience bears out that when I've tuned a guitar by my "make-little-adjustments-until-all-the-chords-sound-good" method (that may sound a bit casual or haphazard, but I actually have a systematic way that I do it), it not only sounds in tune with itself, it sounds in tune with other instruments, from pianos to flutes to what have you. Tuning is inherently imprecise, but, even with a guitar, it can be precisely imprecise, and sound good.

I don't mean to be in argument with you - I'm content to agree to see things somewhat differently and let it rest. I truly appreciate your perspective and insight. I also hope that some have gained some insight from the points made about the inherent imperfectness of overtones on strings, even if that was a somewhat tangential discussion.

_________________
Todd Rose
Ithaca, NY

https://www.dreamingrosesecobnb.com/todds-art-music

https://www.facebook.com/ToddRoseGuitars/

Todd,
No problem here. I appreciated your input as well...good points. More input means more info to pull from so it never hurts.

Thanks,
Kevin Gallagher/Omega Guitars

For the rest of us. Especially us newbies, we love to see those more
knowledgeable than us have good discusssions about details such as
intonation. So don't feel like you are arguing back and forth.   I personally
love to see the back and forth discussions....as long as they are civilized
Andy

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Andy Z.
http://www.lazydogguitars.com

L. Presnall asked:
"What's the deal if, in setting intonation, your 12th fret harmonic strobes different from your open note? I have an A string that dead on at A440 open comes up -.03Cents off at the harmonic...is this a nut problem? TIA."

I wanted to come back with some supplimental information. I had based most of my prior response on various studies I'd read, including a fairly recent one by Prof. Woodhouse, published in the Journal of the European Acoustics Association, in which he detailed some measurements he'd made of string vibrations on one of his son's guitars. But, as has been said: "A good scientist would as soon use another man's data as use his toothbrush", so I figured I'd get my own.

I mounted a new Thomastic 'Spectrum' series .044 string on the rig I built last year for checking the forces the string puts on the bridge, and tuned it to A=110 (more or less) using a handheld tuner. The output of the pickup that measures the 'transverse' component of the force was put through a Fishman endpin pre-amp, and then into my computer soundcard. I plucked the string by looping a length of #36 magnet wire under it close to the bridge end, and pulling it upward until it broke. This gives a very repeatable and controllable pluck. The rig itself is made of a good sized piece of persimmon wood, and can be clamped to the bench top, so there's very little motion of the ends. The signal can be heard on the computer speakers for more than a minute after plucking the string, and contiues innaudibly after that for much longer, as shown by the level indicator in 'Cool Wave'. The signal was 'deconstructed' by an FFT program to determine how much energy there was in the various partials, and the exact frequencies of them.

Basically, the output of this test was as one would expect: relative to the fundamental each higher partial was displaced upward in frequency by a greater amount. The second partial ('octave harmonic') was about .07 Hz higher in pitch than than it 'should' have been. This would give rise to a beating once every 14 seconds or so, which would be very hard to hear. The 12th partial, OTOH, was more than 5 Hz sharp, so you'd hear that for sure.

I then took the same string and mounted it on a guitar; my #60, which is a 12-fret 000 in BRW/cedar. It has a Baggs 'Hex' pickup in the bridge, so I recorded the output of that in the same way as I did for the test rig, plucking at the same point, and I also recorded the sound using a microphone. The two agreed in frequencies for all partials. The sound of the string was quite good, as I would expect for this brand: if it's a bad string it sure doesn't sound it. The test rig is such that it does not 'kink' the string anyplace but at the tuner shaft, and that part of the string was, in fact, above the tuner on the guitar.

The results here were interesting. The 2nd partial of the string pluck was actually .339 Hz sharp; higher than it had been on the test rig. However, the next 5 partials were _flat_ relative to the fundamental, and from there up the pitches rose along the expected curve. The 12th partial was about 3.5 Hz sharp.

The explanation for this has to do with the resonant behavior of the top. The 'main top' resonance on this guitar is at 209 Hz, somewhat lower than the expected string partial at 220 Hz. Because the string is driving the top at a pitch higher than the top's resonance the two are out of phase: the top moves downward when the string is pulling up. This moves the stationary point of the string a little bit toward the nut, and renders the pitch sharp. In his case the deviation might be audible, at one beat every three seconds. It would show up on a strobe tuner, I'm sure. The higher partials are coupling to other top modes, and so work differently.

So it's possible that the problem stated above could be linked to the way the top works; either the 'main air' resonance is a little lower than the string's fundamental, and pulls it sharp, thus making the octave hamonic look flat, or else the 'main top' resonance is a bit higher than the string's second partial.

Or you could have a bad string.....

Al,
That's all great stuff and makes alot of sense. I'd like to read those studies.

I'm glad you included the possibility of the bad string, too.

Good stuff,
Kevin Gallagher/Omega Guitars

Way cool, Al. Thanks. Indeed, when you pluck a string, you're not really plucking a string, you're plucking the whole guitar. Beautiful, isn't it?

_________________
Todd Rose
Ithaca, NY

https://www.dreamingrosesecobnb.com/todds-art-music

https://www.facebook.com/ToddRoseGuitars/

[QUOTE=L. Presnall] I have an A string that dead on at A440 open comes up -.03Cents off at the harmonic...is this a nut problem? TIA.[/QUOTE]

I'm curious, Was the difference really -.03 Cents? Can you hear this? I'm assuming that the string is strobing flat because you used the minus sign. Al's model predict that he pitch would be sharp in the ideal case but top harmonics may make it flat.

Just to round things out, I took the string off the guitar this morning and put it back on the test rig. Another pluck gave a graph of inharmonicity that was practically the same as the first one, so the difference between the 'rig' and 'guitar' results was not from swapping the string.


Kevin Gallagher wrote:
"I'm glad you included the possibility of the bad string, too. "

Ockham's Razor holds here, as it does everywhere else: the simplest explaination that fits all the data is usually the correct one. But, for those times when the simple one just doesn't work (and they're more common than you might think!) it's nice to know about the tricky stuff.

Oh, my achin' head!

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http://www.presnallguitars.com