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In another intonation thread I mentioned my use of calculators for quick
figuring of compensation, and after some inquiries thought it may be
worth it's own topic. My calculator is such an everyday tool it my shop
that I may take it for granted that many don't realize how much time and
headache some simple button pushing can save you.
In the intonation example specifically, this is a brief summary of my
procedure. For routing a saddle slot for a typical scale length I don't
usually go too wild for specific intonation. I use a piece of 1/8" brazing
rod as a dummy saddle. It is slightly flattened on the bottom and bent to
match the radius of the bridge to set the initial line. At this point I
generally nudge it around to set the high E slightly flat and the low E
slightly sharp (The brazing rod is of course round on top, so the string's
end is at the center – on actual saddles the high E will normally be
shaped forward and the low E set back). In doing this I know that I can
shape the saddle to bring the high E forward while making sure that I will
have enough room to move the B back to where it needs to be. The same
idea for the bass side, as the low E typically needs to be further back than
a straight line from the G, D, and A would point to. This typically gives a
line at roughly .075" back at the high E and .125" at the low E when
measured from the actual scale length. If I were building guitars using the
same scale length, fret board, etc., I would just be using a template to set
the line.
For fine tuning the saddle after the slot is cut I keep some bone dummy
saddles around, with the peak beveled to the front (all the strings will be
a little sharp) and shim it to the correct height. Of course all this is done
after the nut height and truss rod adjustment are good. Then I use my
Peterson VSAM to check how far out each string is. Tune the open string
or octave harmonic, then as you play the fretted 12th you can dial in the
tuner until it is stable. That will tell you how many cents sharp that note
is. Jot it down, and check the others and it goes quite quickly.
To figure out how much compensation you need, all you need is a
calculator that can figure specific roots and powers. I use the TI 35XII,
because it's under $20 and does everything I need. You don't need a
$100 fancy graphing calculator for any of this. The numbers that I keep
stored in my memory are the 12th root of 2, the 1200th root of 2, and
(12th root of 2) / ((12 root of 2) -1). This last one is the 17.81715....
that’s where the actual number used for the "rule of eighteen" comes
from, and is actually the one I use least. The 1200th root of 2 is the one
used for calculating cents.
So now let’s say you have a 25.34” scale guitar, and the E reads 3 cents
sharp fretted at the 12th. Raise the 1200th root of 2 to the 3rd power and
multiply that by 1/2 the scale length – 12.67 in this case. Then subtract
that 12.67 from the answer, and there you have how far back from the
front edge of the saddle it needs to be compensated. 3 cents would come
out to just under .022”. Perhaps the B reads 11 cents sharp. 1200th root
of two, to the 11th power, multiplied by 12.67, minus 12.67 comes out to
just under .081” set back from the front of the saddle. It may sound
complicated at first, but I in practice it probably takes me as much time to
lay out compensation for all the strings as it’s taken you to read this
posting. If you didn’t want to deal with the calculator at all you could even
make a quick chart to keep handy for compensation needed per cent. I
think it pays to become fluent with your calculator though.
I’m sure some may have noticed a flaw in my numbers above. Rather use
half the scale length for my calculations it would be correct to use the
actual measurement. Since the saddle slot is already set back at an angle I
should be using 12.745 for the high E down to 12.795 at the low E. I
usually do add a rounded .1” to the half scale length for my calculations,
but it really isn’t enough to make a difference in the real world results.
For example the difference between calculating 6 cents compensation
using ? scale length vs. the actual measurement of .1” greater would be a
whopping .000347”. If you can control your file well enough to reach
those tolerances then great for you, but for the rest of us it won’t really
matter. I didn’t throw it in to the formula above because it could probably
be seen as intimidating enough already for many.
Like I said before though, it’s really quite simple. My personal methods
for adjusting intonation vary in little details from what I described above
in method and philosophy I guess, but that’s another topic all together
and the math is all the same. You can also use this for figuring out nut
compensation just as quickly if you juggle the numbers around a little.
The same idea covers fret placement or compensating frets if you prefer
to do that. There are certainly other methods that work quicker or better
for others as well. Some prefer tools, some numbers, and some just
trained listening or even intuition. I myself like to keep a healthy mix of
all of the above. David Collins39053.8277662037
_________________
Eschew obfuscation, espouse elucidation.
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