Hi,
A question about equal temperament for the technical types. Starting with the A440 reference and equal temperament's tuning of the M3rd above the A at +14 cents and the P5 above the A at -2 cents. This would give an E that is 2 cents lower than an exact E. Does this E which is a M3rd above a C work out to be 14 cents above an exact C ?

If an equally-tempered "C" is unaltered and an equally-tempered "E" is adjusted by "x" cents (by whatever convoluted means), the new C-E interval is "13.7+x" cents sharp from the perfect (non-beating or Just) C-E third.

By the way, the equally-tempered P5 interval would normally be adjusted in the opposite direction (i.e., +1.9 cents) to make it beatless. Adjusting A-E in this way would make the C-E interval 13.7+2=15.7 cents sharp from beatless.

-mike