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There has been some mention before of frets that are not straight across the board, to account for compensation. I'm not sure if pictures of Tom Ward's guitars have been posted.

http://www.youtube.com/watch?v=H-wG6kO9B1M

You can find out more about it here

http://www.truetemperament.com/site/index.php

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Josh House

Canadian Luthier Supply
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House Guitars - Custom Built Acoustic Instruments.
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I saw something like that in the 70's.
Seems strange that intonation would be that far off on a straight-fret board.
I'm not sure I could ever get used to playing with wiggly frets.
Very interesting.

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wah
Wah-wah-wah-wah
Wah

Straight fretted instruments are NOT in tune with themselves.
Part of the problem is tapering string placements from the bridge to the nut.
We measure fret placement at exactly 90 degrees from the centerline, and then we taper the string spacing. We are literally adding more string length between frets than is called for by our math.

It's simple trig, folks. The fret placement measurement is A to C. When we taper the neck, we are increasing B - thus making c - the hypotenuse longer. The hypotenuse is literally how we slant the strings across the frets.

That's why Strats always sound more out of tune than a Les Paul.
They are wider at the bridge, and narrower at the neck - of course it will play out of tune!


I once explained this to a local jazzer who played with a Strat. I ended up building him a guitar with no string taper at all from bridge to nut. Immediately, all the keyboardists he played with commended him for playing more in tune. Bonus? No one wants to sit in with his guitar because the neck is SO wide.

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"Act your age, not your shoe size" - Prince

That's generally true, and for a number of reasons.

That's not one of them.

If the nut and frets are laid out accurately with respect to each other, you can run a string over them at any angle (as well as the obvious 90 degrees) and still get them to play in tune. What changes is the scale length as the angle varies, so if the saddle is in the right place for the particular scale length of a particular string, there isn't a problem.

Now, the way the majority of people set up guitars, making the 12th fret harmonic play in tune with the fretted note at the 12th, the scale length change due to the "tapering string placement" is automatically compensated.

There's lot's of other reasons why guitars play out of tune, but I'll not go into them in detail here. The first question to ask is "in tune with what?" If one is chasing Just temperament rather than equal, which is what the "fretwave" designs attempt to address, some keys are going to be a lot more out of tune than others. So the best compromise is to get the guitar to play equal temperament accurately and then stretch the tuning a little if required. The easiest way to get accurate equal temperament (that I've found) is by using good nut and saddle compensation.

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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

True. But just to be sure everyone knows, multiscale/fan frets are different. Those have to be laid out along the exact paths of the outer strings, and all strings inbetween must fan out evenly. If you cut across a multiscale board at an angle, the fret intersection points will not make a proper scale. It will get progressively sharp or flat as you move up the board.

I pitty the fool who has to recrown those frets in the future

I beg to differ, sir.

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"Act your age, not your shoe size" - Prince

No, he's correct. The tapered fretboard makes a trapezoid. The length of the sides of a trapezoid are proportional to the length of the center of the trapezoid. The distance between the frets increases proportionally as well, so that even though the outer strings are longer than the center ones scale wise, the fretscale has ALSO increased prooportionally as well. It's self correcting in a way.

I'm sure a geometry expert would have the terminology to explain it better.

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Old growth, shmold growth!

Ok, you got me curious so I had to verify. Took my scale template graphic, stretched it horizontally into lines, darkened those, pasted a fresh template, rotated it (a lot, to amplify any error) and stretched it length-wise until the nut and saddle marks lined up with the lines... perfect match.


And here's my diagram of what happens with fan frets when you run the strings across at the wrong angle. All the nut and saddle marks are placed on their proper lines, but when the angle is wrong, the string's correct fret positions don't match up with the actual fret lines.



The beauty of geometry is that you don't need words

So...I guess that a standard single scale fretboard is self correcting but a fan fret is not?

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Old growth, shmold growth!

Nice demos, Dennis.

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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

Dennis, I think you are making a common mistake with your trig - you are looking at your triangle wrong.

Please note:


The line from A to C is the distance between the frets as determined by the Rule of 18.
Line c is the string between the frets as the string spacing narrows from the bridge to the nut.

Of course, intonation does change some of this effect.

Further - my previous statement comparing the out-of-tuneness (if you will) between a Strat and a Les Paul is true.

If your statements were absolutely true, fretting in true temperament would not be necessary - would it?

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"Act your age, not your shoe size" - Prince

Chris the problem is the interval relationship in equal tempering, not the fret placement alone. Even if a standard guitar had no relief or string stretch issues and produced perfectly correct equal tempered notes it would still sound slightly out with certain chords.

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Old growth, shmold growth!

Good one, Kevin.

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Wah

I would note that the difference in fret placement on the guitars featured in Josh's post are certainly more than .002, would you not agree?

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"Act your age, not your shoe size" - Prince

So ummm lets just yank the frets...smear in some bondo and learn how to caress the fingerboard like the Oudist and violinists do. Simple eh. Right!

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Chris:
If you strike a line parallel to the opposite, and half way between A and C, it will bisect the hypotenuse. Any other proportion works similarly. So long as the frets are parallel the strings can fan out at any angle you want and the proportional distances will remain the same. This is, of course, a version of the old draftsman's trick for scaling to an odd factor. If, for example, you have the layout for a 25.4"scale, need a 26" scale, and don't have a fret calculator, you can just strike parallel lines for the frets on a piece of paper using the scale you have and lay a stick across such that the nut and saddle locations come out 26" apart. Mark the fret locations (carefully!) on the stick, and you've got it.

No matter how perfect my scale length, fretting skills, string tension etc are I am still crap at playing!

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Martin Taylor
http://martintaylorguitars.com.au

I will say this on the subject , I don't think fan fretting is really needed. The variables are
1 scale length
2 action height
3 neck relief
4 string gauge.
5 String alloy
As pointed out the variance due to string angle is very slight under .003 and the fret is usually plenty wide . The human variable is much more into play , hand pressure finger placement etc. The variable on the outer strings is more than the inner. I can get very good intonation under 2 cents on my set ups over all frets , and most humans can't hear anything near 3 cents. If you want you can also adjust the crown on the frets.
Lets face it , no one's hearing is that good and if it was so much better we would see a lot more fan fretted instruments. Having the ability to compensate both the nut and saddle will solve most intonation issues . As a string ages it will change its reaction. It is more important to set up the guitar for the player that uses it. A cowboy chorder won't need the upper register like a lead guitarist would .

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John Hall
blues creek guitars
Authorized CF Martin Repair
Co President of ASIA
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Not actually needed in standard tuning at concert pitch, admittedly. But then again , fan fretting isn't designed to improve intonation so much as to improve tone and playability.

Having your treble e at 24.9 and your bass E at 25.4 does actually make for a very perceptible difference both in tone and in playability.

For anyone venturing into the murky depths of Open C tuning, fan fretting becomes almost a necessity.