This bit needs you to concentrate quite hard as it involves thinking about inverted ratios which is a difficult concept for many people. It's easy to imagine "twice as much"; a lot harder to visualise why "3.5 times less" is actually more than "3.8 times less"...
The spreadsheet shown above uses the following data as parameters.
The scale length.
The fret placement factor (12th root of 2)
The measured clearance at first and 12th fret (cells F3 & F4)
A nominal compensation value (hidden cell E2) which has no effect on the final result as it is self cancelling.
The spreadsheet tests the value of the actual compensation needed, based on the incremental strain at first and 12th fret. This is expressed as a percentage increase in cells L3 & L4 and as a ratio in cell M3. Because the resonant frequency of a string is proportional to the square of the applied tension it's necessary
to look at the square root of this figure to have an idea of it's actual effect on pitch and this is expressed in cells M3 & M4 ad the ratio of these figures is shown in cell N3, outlined in red.
The amount of compensation actually delivered at each fret in a real world scenario is obviously going to be an arbitrary figure in a theoretical model but as it happens it is self cancelling.
The figure shown in cell B5 is the ratio of the compensation delivered by a fixed displacement of the saddle based on the percentage lengthening of the string shown in C3 & C4.
It's clear from this that although the string requires just over 4.5 times less compensation at the first fret it is actually receiving just under half as much compensation as the 12th fret. This leads to the inescapable conclusion that the first fret is being over-compensated. This is the exact opposite of the clams made by Buzz Feiten and other proponents of nut-end tension compensation. In fact, in order for the first fret to be under compensated the figure in cell G3 would have to be raised to approximately 0.6mm (by raising the nut height, for example).
Download a copy of the original spreadsheet here
