Boredom from Covid-19

[Kevina]

Sick of being in lockdown, I decided to exercise my grey matter in intonation and fretboard radius.


I am not a guitar technician, I am a retired electronics technician; so it is pointless to ask me about the technicalities of guitar construction. I just wanted to exercise my brain as follows:


How do you measure the fretboard radius without a set of radius gauges, the attached PDF tells you how to measure it with the tools you already have.



Intonation stems from something that happened years ago, when I had to work for a living. A supplier had produced a nice looking 3/4 guitar, which could not be set up to play in tune. It transpires that they had simply taken a full size guitar, and scaled it down to 3/4. No one knew what was wrong, so I was given the job.


After a couple of evenings thinking the problem over, I realised what the problem was, and how to calculate the correct bridge position. The next day, after asking a guitar tech what the correct action should be at the twelth fret, I e-mailed the corrected dimensions to the manufacturer, and a new sample showed they had corrected it. The attached PDF shows my calculations



Kevin

[bbsailor]

Sick of being in lockdown, I decided to exercise my grey matter in intonation and fretboard radius.


I am not a guitar technician, I am a retired electronics technician; so it is pointless to ask me about the technicalities of guitar construction. I just wanted to exercise my brain as follows:


How do you measure the fretboard radius without a set of radius gauges, the attached PDF tells you how to measure it with the tools you already have.



Intonation stems from something that happened years ago, when I had to work for a living. A supplier had produced a nice looking 3/4 guitar, which could not be set up to play in tune. It transpires that they had simply taken a full size guitar, and scaled it down to 3/4. No one knew what was wrong, so I was given the job.


After a couple of evenings thinking the problem over, I realised what the problem was, and how to calculate the correct bridge position. The next day, after asking a guitar tech what the correct action should be at the twelth fret, I e-mailed the corrected dimensions to the manufacturer, and a new sample showed they had corrected it. The attached PDF shows my calculations



Kevin

Kevin and all MEF members,

I have been tinkering with guitars for over 50 years and this is what I discovered about your question/topic. This thought will help you create an accurate mental model about the relationship between string thickness and string physical length.

Strings have two lengths.
1."Physical length" is the distance between its two resting points being the nut and bridge for an open string and the fret contact point and the bridge for a fretted note. This is 25.5 inches for a Fender Guitar.
2. "Speaking length" of the string based on the point from where it starts vibrating; typically forward of the resting points for thicker strings due to their mass, core thickness, and overall diameter.

Look at guitar bridge slants and see that thicker strings are longer. Look at the Gibson Tune-o-matic bridge to see how each string length can be adjusted to best match the string gauge being used.

Higher action also affects the accuracy of where the string vibrating frequency at the 12th fret is exactly twice the frequency of the open string. As you press the string down to meet the fret, the string is being stretched slightly and becomes a little sharp and needs the length to be increased to compensate for this effect.

This is why thicker strings tend to be longer than thinner strings. The G string can be either plain or wound and this string many have the most variable differences in length due to its core thickness or overall diameter if it is wound.

Keeping the neck straight (truss rod adjustment), action low (bridge height), and using a thinner gauge set of strings will minimize the offsets from a normal bridge slant. However, string height and string gauge are trade off points for what you feel is comfortable action and ultimately the most accurately adjusted string length called intonation.

I hope this helps?

Joseph J. Rogowski

[Chuck H]

"Speaking length" of the string based on the point from where it starts vibrating; typically forward of the resting points for thicker strings due to their mass, core thickness, and overall diameter.

This is new to me, but the concept seems reasonable to my mechanical mind. So why is it that compensated nuts all seem to move the thicker strings further shortened from the standard starting point?

Higher action also affects the accuracy of where the string vibrating frequency at the 12th fret is exactly twice the frequency of the open string. As you press the string down to meet the fret, the string is being stretched slightly and becomes a little sharp and needs the length to be increased to compensate for this effect.

This has always been my understanding. Which is another reason I don't get the idea of compensated nuts.

On the same note (see what I did there ) it always seemed to me that the useful length between the starting point at the nut and the first fret is just plain too short to be a good place for compensation without real detriment to accuracy in the first position. Not to mention that once a string is fretted, which they are nearly all of the time, any string length compensation at the nut becomes moot.

Am I missing something? Or are compensated nuts really just something people do because it seemed like a neat idea and they don't know any better?

Not trying to derail the thread. The subject is a little sideways but still related to intonation.

[Helmholtz]

So why is it that compensated nuts all seem to move the thicker strings further shortened from the standard starting point?

Maybe this helps: If you use a capo at the first fret and adjust string intonation/length compensation at the octave (fret #13), all fretted notes will play in tune, but the open strings will sound flat to different degrees. Reason is that open strings do not need to be depressed.
To get the open strings in tune, the individual distances between nut edge and first fret have to be shortened.
The sharpening effect by depressing is strongest at the stiffest strings, typically g and low E.

[Chuck H]

Ok. That makes sense, BUT, it still seems that the interval between the first fret and the open string is too small to allow for useful compensation without an equal or greater detriment to accuracy in the first position. I guess I remain skeptical. That said, I've seen guitars with compensated frets. Which looks ridiculous, but makes more sense. Unless you like to bend strings I suppose.

[Helmholtz]

BUT, it still seems that the interval between the first fret and the open string is too small to allow for useful compensation without an equal or greater detriment to accuracy in the first position.

Why this? A 2mm shorter string makes a lot of difference.
Remember that nut compensation is only required for the open strings. Problem is that most players tune to open strings, which can't give perfect intonation with an uncompensated nut.

That said, my guitars don't have compensated nuts. Seems I adapted to the imperfection.

[bbsailor]

This is new to me, but the concept seems reasonable to my mechanical mind. So why is it that compensated nuts all seem to move the thicker strings further shortened from the standard starting point?



This has always been my understanding. Which is another reason I don't get the idea of compensated nuts.

On the same note (see what I did there ) it always seemed to me that the useful length between the starting point at the nut and the first fret is just plain too short to be a good place for compensation without real detriment to accuracy in the first position. Not to mention that once a string is fretted, which they are nearly all of the time, any string length compensation at the nut becomes moot.

Am I missing something? Or are compensated nuts really just something people do because it seemed like a neat idea and they don't know any better?

Not trying to derail the thread. The subject is a little sideways but still related to intonation.

Chuck H,

Physics tells us that the length of a vibrating string at exactly half its length must be exactly twice the frequency of the open string length. Thus, open string E is also E at the 12th fret but an octave higher. The formula of the 12th root of 2 is used to calculate the interval and the frequency of each note. In Western music there are 12 tones to an octave, thus the 12th root of 2. Each note in a scale is about 6 percent higher than the previous note. I said about because the exact value of the 12th root of 2 is: 1.059 463 094 359 295 2646 which I will call 6 percent for ease of discussion. For fret spacing, multiply the physical open string length by 6 percent (.059463) to get the space to the first fret. Now subtract this length from the total string length and get the remaining string length and now multiply this remaining length by 6 percent to get the next fret spacing. Repeat 12 times and you will get or should get to the middle of the string at the 12th fret.

Since all compensation occurs after the strings are pressed to frets but there is little to no compensation for the notes closer to the nut. Human hearing note accuracy varies by individual hearing capabilities but nut compensation attempts to make the notes between the 12th fret and the nut compensated as well as the notes between the 12th fret and the bridge. However, since the stretch of the strings between the nut and the 12th fret is less than the string stretch between the 12th fret and the last fret, the compensated nut might provide better compensation on the lower (frequency) half of the neck. Only your ears can tell you! After all, a guitar is not a precise tonal instrument but there are things you can do (described above) to make it better.

Joseph J. Rogowski

[Leo_Gnardo]

Some 25ish years ago when I became aware of (Buzzy) Feiten compensated tuning, not only was the nut altered, but the bridge position was too. Apparently compensating at the nut only is not enough, at least according to Mr. Feiten. He was holding classes for those wishing to learn his method. Two requirements to attend, besides putting up the $$$$ cash, was to bring an acoustic guitar you intended to alter to his spec, and bring tools and have the ability/skill to move the saddle on that guitar.

[Chuck H]

Oh I get it. And it's been explained to me a few times just as well. But there's one glaring omission from any of the explanations. Compensating at the nut only changes the interval between the nut and the first fret. I'm going to wait while everything that means sets in...

So the interval between the first fret and the second fret (or the second to the third, etc.) is unaltered. Most of the compensated nuts I've looked at absolutely seem to shorten the interval between the nut and the first fret to the point where it's the same or shorter than the interval between the first fret and the second for the second, fifth and sixth strings. No way that's going to work in the real world and no way you're going to tune up for playing open chords with that S going on. Maybe the open strings are more in tune with notes above the first position, but it's not that damn unacceptable now, so what's it worth if you can't play open chords in (reasonable) tune anymore?

I couldn't find an image showing more than the nut and the first fret to demonstrate my point about the ridiculous shortened interval for the nut to first fret. But I mean it. No way this plays in tune for open chords or anything behind maybe the fifth fret relative to the open string.

[tedmich]

there is simple math for all this



that is, of course, a total simplification...

interesting article here:https://guitargearfinder.com/faq/tru...erament-frets/
apparently Steve Vai now has the squiggly frets on his favorite old Ibanez: FLO.

[Mick Bailey]

My first encounter with a compensated nut was on a Micro Frets guitar in the 70s and they had some nicely engineered features. The one I saw had an adjustable roller nut where you could do your own compensation, and that seems now to be a better idea than a fixed compensated nut.

[minim]

there is simple math for all this

[ATTACH=CONFIG]58259[/ATTACH]

that is, of course, a total simplification...

interesting article here:https://guitargearfinder.com/faq/tru...erament-frets/
apparently Steve Vai now has the squiggly frets on his favorite old Ibanez: FLO.

As I read through the linked article, I considered that making music that is perfectly in tune all the time could make for a lacklustre listening experience. Some of the wildest, spine-tingling guitar I've heard has often been played 'on the edge', so to speak.

The other major consideration, as is pointed out near the end of the article, is if you're playing with a band and they're all still 'out of tune', then what's the point...

[Justin Thomas]

Gee, that looks GREAT for bends!

Jusrin

[Chuck H]

As I read through the linked article, I considered that making music that is perfectly in tune all the time could make for a lacklustre listening experience. Some of the wildest, spine-tingling guitar I've heard has often been played 'on the edge', so to speak.

Most guys that recognize that quality to sonic effect are more outside the box than this, but Alex Lifeson from Rush is a master of border line dissonance working bends a few cents different than other main stream players.

The other major consideration, as is pointed out near the end of the article, is if you're playing with a band and they're all still 'out of tune', then what's the point...

Agree. But when you're NOT with the band on stage in a loud club it all changes. I remember being young and tearing hair out trying to actually tune even a properly setup and intonated guitar. We didn't have articles on line then to clue us into the fact that it can't be done.

[Helmholtz]

Compensating at the nut only changes the interval between the nut and the first fret.

Yes. If you use the first fret capo method for tuning and setting bridge compensation, it gets obvious that only the open strings need correction. The only way to only affect open strings is to change the nut distance.

With a precise chromatic tuner and standard nut position you can see that first frets' notes tend to intonate sharp compared to open strings by a few cent.
Of course a chromatic tuner can also show how well a compensated nut works.

No reason that open chords should sound out of tune with a well compensated nut (the one in the picture looks ridiculous). Rather mixed chords will intonate better.

The amount of nut compensation needed depends on (nut) action. With low action I typically see no need for a compensated nut.

It's all explained in detail (theory, calculations, measurements) in electroacoustics Professor Manfred Zollner's book "Physics of the Electric Guitar". (He enjoys to debunk some of Feiten's claims and statements.)
https://www.gitec-forum-eng.de/the-book/