Here's a little historical background and primer on GMR. https://nationalmaglab.org/education...netoresistance
This reminds me of a friend who wanted to build a pickup that tracked capacitance between the string and a fixed plate. The result was very sterile sounding and it was determined to be a dud. One always wonders if the magic of our primitive transducers is because we heard them first or if they really captured something we couldn't get to any other way.