Step 6: Tuning the Pipe
After cutting the pipe, use a pencil to mark the nodes, 22.4% in from each end (this need not be very precise--if you get it within a millimeter or two, that's fine). Then measure the frequency, exactly like you did for the test pipe, again allowing the pipe to cool after the cut. Since you cut too long, the frequency should be a bit too low. (If not, measure your cut pipe. If the measurement of the pipe is bigger than per calculation, you mis-measured something with the test pipe. Re-do your calculation of A with your new pipe, and recalculate your pipe lengths.)
Make sure you set yourself a tolerance. Since none of us in the family are very gifted musically, 0.5% or about 5 Hz was satisfactory for our purposes. You might want to set yourself a more exactly tolerance like 2 Hz. Also, if you can get all the pipes with errors on the same side, the errors should be less audible.
If after the cut you're within tolerance of the correct frequency, you're done after a very light sanding to remove jagged edges (very light, because you don't want to de-tune), and just repeat with other pipes. If your frequency is too high, and not within tolerance, you've cut things too short. Just re-cut this pipe for your next note (so, if you're making the C6 note, just re-use this pipe for D6, cutting it a bit shorter), and cut a new one for the present note. (Of course, if this is your highest note, you've just wasted some copper pipe--maybe you can use it for another project.)
If the frequency is too low, you need to trim the pipe a bit. I found a rotary tool with a sanding drum attachment to be the best way to do it. You could also use a sanding block if you're patient, or a bench grinder if you're not. Wear safety goggles and breathing protection.
What you do is trim a tiny bit, check the frequency, if it's still too low and not within tolerance, keep on trimming. But make sure to cool the pipe off before measurements. If you over-trim beyond the tolerance, cut a new pipe, and use this for the next note.
I recommend writing in pencil on each pipe what its note is.