The LP method is crucial since it gives

__two__ discrete measurements of a function using the

__same__ variables of known variation.

Without this variation, one ends up with simultaneous equations of dissimilar variables with only one measurement of each, and none with the exact same variable set.

From the other "ugly" thread;

Hmmm, ya know, it seems like there may be some capacitive filtering afoot here.

Is the tone control all the way up/off so that the resistance thereof is at its largest?

Does it settle faster if it's at its full on/lower value (take the tone pot resistance out of its maximum reading settling effect)?I started to run the algebra last night, but my SLU (symbolic logic unit) had already powered down for the night.

The maths are a bit onerous and grow quickly during expansion. Especially at 4 am. Simultaneous linear equations are middle school algebra, simultaneous non-linear ones are not so simple.

I was in no condition to fire up Maple or MathCAD (both of which contain symbolic algebra engines - no numbers required until desired), so cheating was out of the question.

I took another tack and started an iterative interpolating spreadsheet with some seed values. I started with a pickup of 5,000 Ohms and one of 10,000 Ohms, and a volume pot of 500,000 Ohms.

I calculated the measured values of the volume pot in parallel with one pickup, the other pickup, and both in series.

Using these "measured" values I used a differential ratio-metric averaging procedure that after one complete pass came up with 5,002.xxx and 10,011.xxx Ohms for the pickups and around 430,000 and 480,000 Ohms for the volume pot.

This is pretty dang close. These coil values are likely more resolute that one can read with a 3 1/2 digit multi-meter. They are certainly more accurate.

This is why I suggest the use of a multi-meter with enough digits of resolution such that one can use the

__same resistance range for all measurements__. The different ranges are realized with scaling resistors (voltage divider) in the meter, and these are at best +/- 0.1% in accuracy. By using different ranges to gain resolution, one induces a variation of +/- 0.2% or worse in inter-range accuracy.

Using the same range will still be within the meter's absolute (in)accuracy, but at least all readings will be at the same level of ratio-metric accuracy.

If you want to get all of the digits of resolution, for most examples of paralleled pots and coils, you need a 20,000 to 40,000 count meter (4 1/2 to 4 3/4 digit). I use a 6 1/2 digit one of no small cost.

As in the above example, while I got very rapidly very close to the actual coil values, the volume pot values were low. But, so what.

As a bit of insight I tested (in math) the premise that the volume pot resistance span could be ratio-metrically applied to each pickup as a function of its ratio of the total series resistance.

For my test case pickups, I assigned 166,666 Ohms to the 5,000 Ohm coil and 333,333 Ohms to the 10,000 Ohm coil.

As suspected, the parallel values calculated were virtually identical to the "measured" values for my test cases for each pickup selected alone.

This was to be the basis for my second stage interpolation effort, but I haven't done anything with it yet since I'm already close to or better than a +/- 0.1% coil resistance error in my first interpolation stage.

I'll post my spreadsheet later. Let me know if you want me to send it to you after you see the post.