I suppose like many folks, I've always located compensated bridges using a rule-of-thumb that I learned way back. In my case, 3 mm saddle slots are routed in a jig with an angle formed by 1/4" slope over 6", then locate the bridge square to the centre line and with the middle of the slot at the high E string position 2 mm back from the true scale length (2 times the nut to 12th fret, regardless of whatever nut compensation I might have created by shortening the nut to 1st-fret interval). Sorry about the mix of Imperial and metric measurements, but as a baby-boomer that's the way I tend to build.
Now, that rule has always allowed me to do a pretty good job with final intonation, even on a 3 mm saddle, but being a scientifically trained person, I thought I could incorporate proper compensation specs into my fingerboard calculator http://www.luthiersforum.com/forum/viewtopic.php?f=10101&t=30835, and I thought I would specify a compensated measurement to the saddle (either leading edge or mid-point) at both the high and low E string positions. So I've started some research on how various sources specify saddle compensation, and I've been a little surprised how much they seem to vary!
Take, for example, the often-cited Stewmac calculator http://www.stewmac.com/freeinfo/Reference/Calculators/i-fretcalc.html. Let's consider a hypothetical acoustic guitar with a 25" scale. The Stewmac calculator gives the measurement to the high and low E-string break points as 25.087" and 25.210", respectively. Now have a look at the instructions for the Stewmac saddlematic http://www.stewmac.com/shop/Tools/Special_tools_for_Bridges/Saddlematic.html?tab=Instructions#details. If we use that device as decribed in the instructions, the middle of the saddle slot will be located at 25.109" and 25.203", respectively. Break point and middle of the saddle slot are, of course, not necessarily the same thing, but I expect most builders would interpret them the same way. The calculator would locate the saddle at the high E about 0.5 mm closer to the nut and the low E about 0.2 mm further back -- i.e., a steeper angle.
Ideally, the optimum compensation angle is likely to vary with the saddle thickness, to maximise room for individual string intonation. I'm likely to start putting much thicker saddles in future guitars, as 3 mm doesn't give that much room for intonation and some strings can be a problem (particularly on 12-string saddles), even if most are just fine and I don't get complaints. If one could calculate the correct compensation for ALL strings individually, one could locate the saddle at the best possible position, regardless of its thickness.
Am I being a bit anal? Probably, but a spreadsheet can make complicated calculations dead easy, assuming you can find reasonable estimates of the various string parameters. I've not seen any formulae for calculating "theoretical" compensation -- perhaps these exist in the Gore and Gilet books, which is great, 'cause I'm expecting to order those in a month or so anyway. But perhaps someone knows a web source that has a proper mathematical treament of the subject, with formulae, rather than "rules"? Frankly, I've not yet found what I'm looking for with Google. Let's gather up relevant sources in this thread, as I'm sure there are many who'd like to sort through this issue on their own.
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