"Pain" is the word I use to describe the feeling from less-than-ideal tuning; it is therefore the thing to be minimized for the closest possible approach to ideal tuning in a given piece.
I model three sources for pain when doing adaptive-tuning work:
I hypothesize that pain is proportional to the square of deviation from ideal; thus a major third tuned 14 cents sharp, as in 12-tET, is modeled as four times as painful as one tuned 7 cents sharp (or flat).
My tuning model uses an analog to a physical model of nodes connected by springs. In this model, deviation from JI is equivalent to deflection of a spring from rest position, and pain is equivalent to energy stored by a single spring, or by the summation over the entire matrix of springs. Such a model is very amenable to relaxation to minimum energy, thus minimum "pain", thus best possible tuning.
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