Often we find intervals that don’t fit how we think they should fit. This is because there may be a conflict between two ideal interval sizes.
One approach is to compromise. Another approach is to prioritize which intervals are more important.
Often it is the M3’s around the tenor break that end up not changing speed evenly. If evenly beating M3’s in this area cause other more obvious intervals to suffer, then the M3’s should lose their priority. This is obvious when we consider the musical quality evenly beating M3’s bring us compared to pure 12ths for example; none.
For example;
If when tuning E3, the E3G#3 does not change speed evenly with its neighbours, but the E3B4 (P12) is pure and sounds nice, and changing E3 would make the E3G#3 beat evenly with its neighbours, but destroy the P12, the conclusion is clear – Drop the evenly beating M3 priority.
This document lists some of the interval priorities possible, their checks, and the areas where they should take priority: