I went and bought this saw just to use for this but I don't see any inherent reason why you couldn't use a bigger saw. This is the Evolution Power Tools 7 1/4" sliding miter saw. After I bought this, I was in Lowes so I looked at the Kobalt saw they have for about the same price ($150 or so) and it does seem a little better-built but this one does fine.
I have a 12" compound slider out in my garage, it's just way too big to fit in my shop and I didn't want to deal with swapping it over every time I needed to cut a fretboard.
These saw blades are 2 3/4" diameter. They are available in 4" sizes too but it seems like most people who try the 4" blade without stiffeners are upset at inconsistencies from the blade warping. This smaller size is so small it doesn't seem to have that problem. The only catch in using this setup on a larger saw would be how much "clearance" you have for such a small blade to reach past the motor housing. Here's a photo shot underneath the motor on this small saw:
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You can see the saw blade just barely peeks out past the housing, so you have to get the fretboard way up high off the saw's table to be within reach of the blade. I measured the distance the blade is sticking out and it's about 3/8". So the clearance from the center of the arbor to the edge of the motor housing on this saw is about 1". If you have much less clearance than that, you won't be able to get the saw blade close enough to your workpiece.
I took a photo of the raised table I made, it's two layers of 3/4" mdf and one 1/2" mdf at 18" long by 4.5" wide mdf with a 1/4" thick by 1" wide mdf strip as a fence. I determined the total thickness of 2" just by measuring the from the saw's table to about where the blade is with the blade depth stop all the way down. Then I can turn the blade depth stop up as appropriate for a given fretboard blank thickness. After making it, I screwed this table to the saw and used the saw to cut a slot in it, then I put a .023 feeler gauge in that slot to use for indexing the templates.
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The templates are 1/2" thick mdf that I put a paper template on and cut the slots with the saw, just holding the mdf on the table and lining up each cut manually. I made a 24.75" template and a 34" template. I can use the 24.75" for 23.3" (tenor guitar) or 20.8" (uke bass, 1/2 scale guitar) and the 34" for 32.1" or 30.3" by skipping down the first few frets as appropriate.
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To use the template, I turn it slot-side-down, screw the fretboard blank on top with the nut lined up to the double cut (or the appropriate starting fret for smaller scales) and then index the slots onto the feeler gauge. So, you make a cut across the blank, lift the template up off the feeler gauge and move it over a slot, make a cut, move it over, and so on. By my 4th board I was moving pretty fast, probably two or three minutes to make all the cuts.
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That's a finished fretboard on there, I just set it in place for the photo.