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Actually, according to Mike Doolin, each key would require a different temperament and thus fret spacing even when the frets are staggered. Which I have seen done a few times. Here's a link to part of his article on intonation with the explanation of the staggered frets http://www.doolinguitars.com/intonation ... tion4.html

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Brian

You never know what you are capable of until you actually try.

https://www.howardguitarsdelaware.com/

Just came across this thread. I've been compensating the zero fret for a couple of years now on all my guitars. This was inspired partly by the articles written by Mr Doolin and Mr Byers and partly by a very insistant friend and customer who was obsessed with intonation.

If you want to accurately achieve the compromise of equal temperament then the string must be compensated at both ends. This is how I do it:



nigel

http://www.nkforsterguitars.com/nkforst ... _book.html

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nigel

http://www.theluthierblog.com

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Mike

(MH)===:::

You bring up an interesting point here, Alan, because it is where a lot of guitar players get confused. The table below shows the difference (cents error) between the simple Just temperament which is based on the note intervals being the ratio of small whole numbers, and the equally tempered scale. The significant differences between the two are that Just sounds better to most people than Equal, but in Just the interval between semitones is not constant; whereas it is in Equal. The consequence of this is that in Equal as you modulate through key changes, all the keys sound similar, whereas if an instrument is tuned in the key of A, Just temperament, then you play in a different key, it will sound wrong.

So I guess you're playing your lap steel in Just and comparing your slide position to the frets, which mark the notes of Equal temperament. The difference is quite significant, as you've found. For example, an Equal major 3rd is 13.96cents sharp of a Just major 3rd. Which frets seem most "wrong" depends on the key and your tuning. So if you are playing in standard tuning in E major (unlikely on a lap steel, but bear with me) the frets that will appear to be most badly positioned will be frets 4, 9 and 11 and the most accurate will be the 5th.

How much better alignment you get by "pulling the string towards the saddle" will depend on keys and tunings.

On a "normal" guitar, one is stuck with the relative out-of-tuness (compared to Just) of the Equal temperament compromise, with the benefit that you can play different chord shapes and still be reasonably in tune, provided that your guitar will play Equal temperament reasonably accurately. We then get a debate about what is "reasonably accurately". A lot of players strive for Just, which they just aren't going to get, hence the common complaint of "my guitar won't play in tune". Well, it never will play in tune to Just. The best compromise is accurate Equal temperament, which is what I aim for with my approach to nut and saddle compensation and it's all about correcting for, as best you can, the consequences of string stretch when fretting. Of course, some players "spot tune" to improve certain intervals for certain songs and some players, classical guitarists in particular, pull and push notes into tune as they play, performing their own intonation "on the fly". However, the guitarists able to do that still appreciate well intonated guitars, because it means they don't have to work so hard to get things to sound "right".


At least 3 of the other methods are pretty simple, but some accuracy is lost. But, Grumpy, please don't feel you have to call me a genius!

If you want complicated, there's all the intonation errors caused by resonance coupling, which this thread hasn't even considered yet, and which can be up to 20 odd cents, which Doolin talks about in his last section (though the reason is body resonances, not neck resonances, as Doolin suggests). And that's one reason why modal tuning is important, because it helps you avoid this source of intonation problem.

BTW, the problem with Fretwave solutions, like in some of the pics above, is that they provide a fix for just one string set and set-up. Changing them for another string set or set-up is a lot harder than just swapping out the nut and saddle.

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Trevor Gore, Luthier. Australian hand made acoustic guitars, classical guitars; custom guitar design and build; guitar design instruction.

http://www.goreguitars.com.au

But, Grumpy, please don't feel you have to call me a genius!

Not to worry...

From Wikopedia
The viol (also known as the viola da gamba) is any one of a family of bowed, fretted and stringed musical instruments developed in the mid-late 15th century and used primarily in the Renaissance and Baroque periods. The viol family is related to and descends primarily from the Renaissance vihuela, a plucked instrument that preceded the guitar. Viols are different in several respects from instruments of the violin family.

Sorry dude, just razzing you.

By the way, ever hear a high school orchestra string player warming up, likely all out of tune then when the orchestra plays it is like magic when they all play together and it sounds wonderful.

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Ken

Not to mention that from one set of strings to the next the stretching characteristics vary.

That's been mentioned. Different brands also will have different core to wrap ratios, which will also change the intonation. Then we add the different types, various wrap material(80-20, 15-85, phos. brz., nickel, SS, coated strings, etc...!). There's no end to the variables!

Here's a nut we experimented with some 10-12 years ago. I had cut the fretboard approx. 1/8" short on a guitar that otherwise intonated very nicely(but of course, not perfectly, as that is impossible), and made an extra-wide nut, then proceeded to compensate each string. I had to dig around my scrap nut pile to find it, but here's a photo of it, with some pencil added highlights to show the amount of compensation. Appears to resemble Nigel's results. But this is the nut that also clearly showed me that the closer I got to "perfect", the farther out I was in some keys. While it made some keys much sweeter, it made others rather sour. As Trevor alludes to, there's a lot happening, and that includes partials and overtones, and while the soundbox itself has an affect on these, so does intonation. We can study this stuff 'til the cows give up and leave home, and completely confuse ourselves in the math and physics yet we'll never account for all the variables. Never. Ever. At some point, a human ear needs to make the final decision, via the tuning of the beast...

Oh, and back to the point of compensating the nut, just make it so that it is "correct" as a fret, as that is all it asks for. Again, normal frets will like about .020" off the end, and fat frets may need as much as .030". Do that, then intonate nicely at the saddle, and you'll be golden.

By the way, ever hear a high school orchestra string player warming up, likely all out of tune then when the orchestra plays it is like magic when they all play together and it sounds wonderful.

Exactly! Also note that string players don't tune their open notes perfectly, but rather tune one string open, perfectly, then the rest of them to perfect fifths off of that one open string. The ear takes care of the rest.

I play upright bass, and sometimes someone will ask how we play these things in tune, since they have no frets. Truth is, I really don't know the answer. It just happens. Sometimes I'll be on a stage with bad monitors(or none at all!) and at times have to go by feel; I'll feel the notes more than I hear them. Knowing that, it makes sense that even a high school orchestra magically plays in tune once they all begin to play; it's pretty well impossible to play out of tune with all the other instruments around you.

One thing one will notice is, just about every compensated nut is different. Therefore it's showing that there are other factors that are individually guitar specific coming into play.

We can get into differences in just/equal/ temperament all we want. This has nothing to do with compensating nuts directly. More directly, nut compensation has to do with a compromise to make the nut behave more like a regular fret that the string is stretched to be used.

Does this affect equal/just temperament, to some degree, yes, but no more than any other fret, approached correctly. I'm not trying to quash discussion about temperament or modal tuning or body/neck resonance these things are cool too. But again bang/buck next to saddle compensation, nut compensation helps a lot in tuning and dealing with string tones one to the other.

I believe when one frets or strikes a harmonic and one sees modulation in that note showing up in a electronic tuner one is seeing evidence of resonance, not just in the string but the whole guitar, neck/body/bridge/braces/saddle/nut/candy bar one keeps inside the guitar when one feels a bit peckish.


Guitar is one of the few multi-tonal instruments that has to do with the association of numerous notes one to another and the dynamics of strings themselves, being what they are. Being fretted, creates it's own special conditions.

I've played guitars that have not had individually compensated saddle and even more without compensated nuts, and they were fine. Not great. But many people have played guitars that had compensated nut and didn't know they were.

I'll be honest, I've only knowingly, played one instrument that had an individually compensated nut. Most are compensated with a shortened fretboard. The one I did play was a real cheap guitar that was set up as a test bed for nut compensation. Once one got past the plywood top and incredibly dull response, one could hear, tonally, the guitar was excellent in playing in tune up and down the neck. One of the best I've ever played, all that for $250.00 bucks.

I played other guitars that did not have the same nut compensation of the same brand and you could hear the difference it made especially above the 5th fret and really started to shine in the octave position. Very easy to tune the guitar in the first place. I was sold.

I thought "I" was the problem I was having in tuning guitars. As I believe now, I was hearing all kinds of harmonics/overtones that were interfering with me finding the right tune on a guitar. Even the guitar being just plain wrong.

Even though I use a electronic tuner to compensate my saddles I use my own sense of hearing when I come up with the final adjustments. Not just for the 12th fret but taking into consideration all frets. Just like in tuning the guitar in general. The electric tuner gets one close to the way a human ear works, but not that close.

As I see it, primarily, compensated nuts allows one to tune that much accurately without much work.

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Billy Dean Thomas
Covina, CA

"Multi famam, conscientiam, pauci verentur."
(Many fear their reputation, few their conscience)

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http://www.birkonium.com CNC Products for Luthiers
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Thanks man, I did not know that. A dear old friend of mine is a classically trained bass player who often filled in as a cellist or violinist, he always referred to these instruments as Viols. Wait till I see him again............

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Brian

You never know what you are capable of until you actually try.

https://www.howardguitarsdelaware.com/

So I got a Pederson Virtual strobe, which purports to be as accurate as the analog strobe, acccording to the web site.
Indeed, even when every note reads correct according to my old tuner and sounds good to me, according to the Pederson, the pitches are not exact.
So the question I have to Trevor: Are you saying that by compensating the nut and saddle in the manner you describe in your book, can I get the notes to be more accurate to the Pederson when the Pederson is set to equal temperment? Is the ear sensitive enough to really tell the difference? Does it work for electric guitars?
I can get my guitars to sound pretty good, but if any improvement is possible, then I must improve.
How close to in tune can you get to the Pederson? What is reasonable?

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Old growth, shmold growth!

I'm not Trevor, but...

Using a tuner as sensitive and precise as the Peterson is a learned skill in itself. You want the instrument in playing position, not laying on the bench with the neck propped up in a support. When you fret a note, fret it only as hard as necessary to get a clean note, no further. Do not fret a note on a guitar laying on the bench with its neck propped up and pushing down at the fret; that will give you a sharp note, every time.

Make sure the strings are high quality, and very fresh. If the strings have more than an hour of playing time on them, change them.

When checking your intonation, tune one string open, perfectly. Then carefully fret that strings at each fret, taking note if it is sharp, flat, or perfect, and at which fret. Some -will- be sharp and -will- be flat, slightly, even with the best intonation we can achieve. Do this for each and every string. Check the open tuning often, to be sure the string didn't stretch a bit, as you go up the neck. Now, look at your notes, and if, on the average, most notes are very near perfect, yet you have a more or less equal number of slightly sharp and slightly flat notes, you're dead-on! But if you have more sharp notes than flats, or no flats, a few perfect, and the rest a bit sharp, then you have room for improvement. Same for the opposite.

In short, check the entire fretboard, and look for a "trend" toward fretting slightly sharp or slightly flat. As you'll now see, using a very sensitive tuner, there is no magic trick that we can do to the nut or saddle to make each fretted note perfect. Your goal is to attain the best average possible. Once you've found this happy place, take a length of steel rod, flat bar, or something similar(not wood!), and very accurately scribe the nut location, 12th fret, and saddle center for the 1st and 6th strings. From here forward, use this to set your bridge/saddle location for all instruments using that same scale. No need to ever go through the whole exercise again....

B.Howard wrote:
" A dear old friend of mine is a classically trained bass player who often filled in as a cellist or violinist, he always referred to these instruments as Viols."

Well, as a bass player he is playing a viol! The modern orchestral bass is the last surviving member of the viol da gamba family, as attested by the sloped shoulders and flat 'cranked' back (at least on most of them). They've left out the frets in the interest of playing in tune.

I recently finished a 12-string on which I used both nut and saddle compensation. I've done just the saddle on them in the past, and goten decent results, but after reading Trevor's book I decided that the nut would be a good target for some effort as well. I took the coward's way out and made a beam rig with a movable first fret (to accommodate different scale lengths in the future), saddle and nut, and ran checks on each string three times, to get an average reading. The result played virtually spot on for every string and fret, without the 'crunchiness' one usually gets between strings within a course on the upper frets. I was a little concerned initially that it might be too sweet: it doesn't have some of the 'character' of most 12-strings, but as soon as the player tried it out I was disabused of that notion. Of course, if it had been too sweet, we could always have backed off a little bit.

Grumpy is right, of course; it's impossible to make a guitar that will play in tune on every fret on every string, even if you specify the strings in advance. On the other hand, you can always get arbitrarily close, if you want to, and it does seem to me that's a good thing to shoot for.

But who really wants a guitar that is perfectly in tune everywhere on the fretboard? One of the things that makes a guitar unique and sound the way it does is the slightly not so perfect notes at various positions. Even the various same note keys on a piano are not exactly in tune with each other.

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Another day, another dollar.

I simply want one as perfectly equal tempered as possible, which is where the character of the guitar lies, I believe. Getting it as close to equal tempered as possible should simply sweeten up the tone, I don't see why it would destroy the character of the guitar. The notes will still be not exactly in tune with each other.

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Old growth, shmold growth!

I would be curious to see the beam setup if you wouldn't mind sharing??

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MK5acoustics.com

Me too

Fred

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Fred Tellier
http://www.fetellierguitars.com
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I'm not Grumpy, but...

Grumpy said pretty much what I would have said about reading sensitive tuners. What you notice pretty quickly is that a played note moves in frequency during its decay and what we tend to focus on as "the note" is what we settle on after about 0.2 seconds. I use an app. called AP tuner and select View/Harmonics Graph, which plots out in real time the frequencies of all the partials, so you can see how they all move with time. Most tuners just show the frequency of the strongest partial which is frequently not the first, because we tend to pluck at the 1/4 length point of the string and thus excite the 2nd partial more. So it takes some practice to correlate what you hear with what you measure.

Grumpy goes on to explain an intonation technique of mapping the fretboard errors, which is similar to one of the methods in the book, which then goes on the explain how you compensate the nut and saddle to minimise the errors you have. However, this technique can be more problematic than Grumpy mentions, because it, too, is guitar specific: a significant component of the intonation errors can be due to the "repulsion effect" of coupled oscillators, where the string frequency (and hence its intonation) is shifted when it couples with a body resonance that is close in frequency to a played note. So unless the body resonances are pitched in the same place for every guitar you build, there won't be a general solution.

If you (or your customer) can't hear it, be grateful and don't obsess about it. The limit of resolution for a good ear is about 3-5 cents. The difference between an equal temperament third and a Just third is 14 cents. It's when the already compromised intervals (compared to Just) have more error stacked on top that you get to hear it and it gets annoying. Thirds and sixths are the worst. Very few people can pick errors of a few cents in a series of single notes. It's the intervals (double stops) that cause the problem.

Sure does. Electric guitars are actually a lot easier to deal with, because you don't get anything like the problems with body resonances that you get on an acoustic. Classicals tend to be the worst for issues with body resonances causing intonation problems.

It's reasonable when you have a satisfied customer! It is player dependant and it takes a very good player not to squeeze strings out of tune when they play.

Here's a story. I had a customer who'd heard about my intonation work and he came to me with a beaten up but good sounding J45, which he said he couldn't get tuned. It had some massive intonation shifts due to resonance coupling. This guy was a lefty. I had him leave the gutiar with me (a righty) and I mapped all the intonation errors, playing the guitar "upside down" and fixed up the intonation. I thought it was pretty good. When the guy came to collect it he said it sounded worse than before, and when he played it, it did! I turned it over and re-did some of the error mapping left handed and got different results. Don't ask, I don't know! So I got him to play all the notes and did the error mapping again, fixed the intonation (again) and he was delighted. When he played it, it sounded fine, when I played it upside down (with reverse chords) it didn't. But he got what he needed.

Apart from anything else, equal temperament will never let you get it that good!

Exactly right. The guys who really go for the whole intonation thing tend to be the jazzers, because they can hear all the subtle differences between their altered chords, rather than just something vaguely dissonant.

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Trevor Gore, Luthier. Australian hand made acoustic guitars, classical guitars; custom guitar design and build; guitar design instruction.

http://www.goreguitars.com.au

I know I'm over-thinking this, but....When doing this do you just slide the fingerboard towards the nut by .020" after the cut or make the nut that much thicker.

Thanx Trevor!
So far most of my customers have been satisfied with how I've been doing it, even jazz guys.
However, I think some of my customers would notice even a slight improvement, even though they say the guitars I've done for them are the most in tune they've ever heard.
I'm going to experiment with my new tuner and the method described in Trevor's book on some of my own personal instruments. I'll get back and post my results (or ineptitude) on this thread, possibly some sound clips.
I'll start simple on an electric guitar I made YEARS ago that I reserve for experiments of this sort.

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Old growth, shmold growth!

I thought it was pretty good. When the guy came to collect it he said it sounded worse than before, and when he played it, it did! I turned it over and re-did some of the error mapping left handed and got different results. Don't ask, I don't know! So I got him to play all the notes and did the error mapping again, fixed the intonation (again) and he was delighted. When he played it, it sounded fine, when I played it upside down (with reverse chords) it didn't.

That's precisely why I said you need to check the instrument in playing position(in this case, held lefty). Many guitars, and especially those with heavy headstocks and/or thin and/or weak necks noticeably change when checked on their backs, VS in playing position. In this case, you were holding it right handed, so the headstock's mass was pulling the neck toward the floor in exactly the opposite direction that the (left handed) player was going to, thereby doubling the error.

Todd made a excellent point when he said that many, if not very much most, intonation/compensation errors are player-specific. I've "fixed" at least as many "can't get it to play in tune" guitars by teaching the player how to tune his/her guitar specifically for how they play it, than I have by actually working on their guitar. Way too many players think they can tune-up with an electronic tuner(and typically they'll have a cheap unit with near-dead batteries... Ughhh!) and the guitar should be in perfect tune, but it just isn't so. A perfect example is me, myself. My left hand's ring finger is very strong, too strong, and I don't have the fine muscle control necessary to prevent that finger from sharping a fretted note more than my other fingers do. So I compensate for it with how I tune, which changes slightly when I change keys. I won't always bother to tweak the tuning between one key and another, since I'll often just find the happy medium and call it good, and go forward with the whole reason of playing guitar, which is to make music. But if I were to record something, I'll tweak as needed to get myself as "in tune" as I can get.

As a player, I do!
It always bugged me when I used to play a git with frets
when I played a D chord.
Check it out.
Out of tune!

IMO, grumpy's responses have been the most spot on about this rather convoluted subject...

the mathematics required to correctly model the phenomena associated with a fretted string being in tune would be intense to say the least (needing math teachings that the vast majority of humans haven't been exposed to, and are not capable of understanding)...and would require actual measurements of physical properties of both individual instruments and players to be plugged into any derived algorithm...

I will go out on a limb and say that Todd Stock's statement of "but it's usually to correct for his or hers bad habits rather than any issue with the guitar." is treading on very thin ice...anybody care to detail just how many "bad habits" Jimi Hendrix had?...enough said!

I think the best any luthier can do is to set up each instrument for the player that is paying for it...in my eyes that is his/her job!...I don't know how many times in the past I've either had to hold my tongue or actually taken the time to take the head off of a repair tech that tried to defend their "work" by blaming any "errors" on the customer...

I`m not sure if this is a bad habit,But I saw Jimi Hendrix play the guitar with his teeth live in San Diego back in I think it was 1967.Probably had some major dental bills.Hard to forget something like that

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James W Bolan
Nashville Tennessee