Not sure how many people will read this post but here goes...
Just how accurate does fret placement need to be for there to be a perceptible difference to the accuracy of a note to the human ear?
I'm looking at using a cnc router to mark the fret positions. When using mm scale it rounds the 3 decimal value of the fret position calculator to 1 decimal place. If you change to imperial it gives 3 decimals, and 0.001inch is less than 0.1mm. Do you think I should use the imperial scale or 0.1mm is accurate enough? This is assuming there isn't major inaccuracies to the mechanical precision of the router.
The more accurate you can get, the better. You'll notice any variation a lot more on the high frets as 0.1mm becomes a much greater proportion of the string length.
0.001" is about 0.026mm, so I'd use inches for the scale length if I was doing it.
There is the accuracy/tolerance of the cnc router to consider as well. If that's say +/- 0.05mm, then the slot could end up further out than you think, so the closer the cnc can get to the ideal position, the better.
However, the software may still be using the mm figure you typed in, but is just displaying it to one decimal place.
If you have a chance, you could do a couple of test cuts on a piece of pine, and measure with callipers how accurate the cuts are.
Don't forget that the ultimate position will be decided by how well you centre the fret crown when you profile it!
I just ran some math, and a .1mm error at the 24th fret on the high E string results in about a 1 cent pitch error. That's your absolute worse case note, 1st fret low E the error is about .2 cents.
Exactly how fine people can hear pitch error appears to be debated, but the average person can consistently hear 25 cents and really good ears gets you somewhere in the single figures. If your frets are within .1mm my bet is you'll be introducing a bigger pitch error by playing the guitar. So I don't think you'll have anything to worry about.
±1 cent error is about what the majority of guitar tuners are accurate to. A lot of older tuners are accurate to ±3 cents.
Yes, I agree, on the changes for 0.1mm. About 0.26 cents for an open string, 0.54 cents at the 12th fret and 1.08 cents at the 24th.
Obviously the worst case is playing high up the neck, where one fret being played is -0.1mm out and the next is +0.1mm out. You could then be 2 cents out, which can be quite noticeable if playing chords.
It's probably best if the error is on the negative side, at least for single notes, so if you are a bit low, you can then compensate by bending the string slightly to raise the pitch. If high, you can't do anything to compensate.
Your playing style can also affect the note pitch. The harder you fret, the sharper the note will be. To some extent this is compensated for by your intonation settings (provided you fret like normal when setting the intonation and don't use a much lighter touch).
You need to be a bit careful in describing peoples pitch error discrimination. There's a difference in a) people being being able to hear the difference between two similar notes played one after the other and telling whether they are the same or different and b) when you are playing two or more notes on a guitar together to form a chord, and hearing whether the notes are in tune with each other. It's a lot easier to tell if a note is out if you have two or more notes played together. Plus if you are a musician, you are always training your ear for out of tune notes (especially if you are into recording), so you tend to have a much better pitch discrimination that the non-musician.
About 12 years ago I was a test subject in some pitch discrimination hearing tests as part of a research project run by a university, and my discrimination was better than 3 cents for single tones played sequentially (the test tones didn't go less that that - except when they used the same note). Which I was told is a lot better than the average.
Anyway, I still think it pays to be as accurate about fret positioning as you can, but there's not too much to fret about (see what I did there?) if they do end up very slightly out. They'll still probably be positioned a lot better than on any Pit Bull neck!
I'd still do some test cuts with the CNC machine just to see how accurate it really is. If it is consistently a bit under or over, you could compensate for that in the entered slot positions.
The Stewmac fret calculator gives the imperial positions to 3 decimal places, so I willl just go with that. I have already created a cut image ready to convert to file.It's a bass scale, so the frets are spread further apart than a 6 string. I think that affords a greater margin. As for using pine, umm... no. I will be doing test pieces with ironbarkto get the settings right. The 0.58mm fret slotting bit was expensive and I was able to get 10 x 0.5mm bits for about half the price, so I can afford to sacrifice a few of those. I have some Indian rosewood coming, since I couldn't get bubinga...won't wast that till I get it working on something slightly harder.
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