I checked it out (not read the _whole_ thread to the end) but, In what way can the current tabread4~ interpolation, which is discontinuous even in its 1st derivative, be superior to true cubic interpolation? Even at transpositions near to zero, I can't see what's the advantage, nor what it is supposed to minimize.
both are truly cubic interpolations.
IIRC, one kind of cubic interpolation is designed to go through all four points, and the other kind is designed to be pieced with other cubic interpolations, and Miller confused the two and left the bug there.
Miller's is a true implementation of the former -- his is a Lagrange interpolator which goes through all points -- it's algebraically identical to the cubic interpolator in csound, and so it should have a similar "sound" as any of the table-reading opcodes in csound that also employ cubic interpolation.
The latter is an Hermite interpolator which uses the outside points to approximate the first derivative -- the resulting curve only passes through the middle two points, but doesn't go through the outside two; this ensures that as it's pieced together the first derivative will be continuous at the junctions. It's algebraically identical to the cubic interpolator in supercollider.
They're two different approaches -- each has its own frequency response, but both are true cubics. If you want to match all four points AND the first derivatives, you have to use a 5th-order polynomial. The formulas are easily derivable using the Gaussian method, and it's easy to implement all these as a library of functions that can be accessed by the relevant objects, where the user can choose which type of interpolation he/she wants to use.
Matt