Monday, July 8, 2013

Guitar Fret Position Calculator

I've been using the googles a lot to get hints, tips and plans for my lutherie. One weak spot seems to be fret position calculators and/or templates. The few I found wanted to give me inches in a decimal representation, and that's not so useful unless I can find a ruler that will let me measure 1.3470 inches. I haven't found one yet. What I really need is a calculator with the ability to get inches as a fraction, or convert those inches to millimeters. So I wrote my own.

Calculating the positions of the frets was historically done with a technique called the rule of 18, whereby you successively divide the scale length minus the offset to the previous fret by 18. This could be done with a pencil and paper. Calculators and computers allow us to easily use a more accurate constant, and so the rule of 18 became the rule of 17.817.

Even with the more accurate constant of 17.817, there is a bit of cumulative error, as you add layers of approximation with each successive calculation. Calculators and computers to the rescue again, we can use a different calculation. The pitch of an ideal string goes up one octave if the length of the string is halved, and that midway point is coincidentally the position of the 12th fret. Thus, fret position offset will be a function of the twelfth root of two and the offset of any fret from the nut can therefore be calculated with the following formula:
    d = s – (s / (2 ^ (n / 12)))
That is the algorithm I use for my calculator. I convert to a fractional amount using a conventional formula with the default JavaScript rounding, and I convert to millimeters by multiplying the decimal inches by 25.4.

To use the calculator, enter the scale length you want in inches and hit the Calculate button. Typical scale length values are 24.75 for a Les Paul and 25.5 for a Stratocaster. You can adjust the precision, so that the fractional amounts are calculated as 16ths, 32nds, or 64ths. If your computer is slow give it a second, there is a lot of number crunching going on.

Calculate Fret Offsets from the Nut

Fret# Inches (Decimal) Inches (Fractional) Millimeters

Thursday, July 4, 2013

Getting Started: Table Saw Repair, Part II

I might as well admit it right now, when I got an old table saw for free, I didn't give any thought to maintenance. It worked, and worked better than the crappy circular saw I had at the time, so I figured that was a win. I wasn't until I started to consider my need to do more precise work than cutting 2x4's and trim molding for home remodels that I started to think about the idea that a table saw might need maintenance.

Getting a pulley reinstalled was just the first step. When I mentioned it to a friend at work, he got me pointed in the right direction for tuning up my saw. I started with a good cleanup. I hit the rusted cast iron top with 500 grit wet or dry sandpaper, then Bar Keeper's Friend and a green scratchpad, and finally Naval Jelly. The change was pretty impressive. It actually had a bit of luster. I gave the whole thing a shot of rust inhibitor.

Working my way down, I hit the undercarriage with a dry parts brush and a shop vac. After things looked respectable again, I gave it several liberal shots of dry spray lubricant.

Then I started truing things up. The throat plate (that red part that the blade sticks through) was visibly out of place due to decades of fine sawdust built up under it. I cleared out that mess an reset the adjustment screws. Next was the pulleys. I laid s straight edge across the face of the motor pulley and drive pulley, and immediately noticed that while they were more or less in the same plane, the motor pulley was at a cockeyed angle. Hmmm... this is not good. A bit of investigation revealed that the motor mount was bent.

Adjusting the motor mount consisted of clamping it down in the vise and whacking on it with a sledge hammer until it seemed straight-ish. I had to fine tune it a bit more by putting two washers under the the side of the motor mount nearest the pulleys, then measured and straightened and measured and straightened until everything lined up.

Finally, I tightened everything down and turned it on. The saw immediately seemed quieter. The rumble and vibration were largely gone. It looks like I might have a working table saw again!