Is there actually a quantitative measure to know if a temperament is "good" or not? The motivation for my question is that there are quite a few temperament for the 12-tone systems (which may vary according to which piece one wants to play). For other tonal systems (notably 19 and 31), I could not find anything deviating from the equal temperament (or EDO: equal division of the octave).
Here are two aspects which are more focused.
(1) 19-EDO gives a much better approximation for the perfect third (especially the minor third). Still it seems 12-tone is still much preferred. 12-EDO has a much better approximation of the fifth (than 19-EDO or 31-EDO). It seems that when measuring how "good" a temperament is, fifths are much more important than thirds.
The perception of the perfect fifths, fourth, etc. is due to the fact that even from a pure sound (with only one frequency), the harmonics of this frequency are also excited in our ears. A first question is then: say an ear (approximated by a set of [damped] harmonic oscillators?) are excited by a pure sound wave (approximated by a perfect sinusoidal driving wave), how much of this wave is absorbed by the various receptors for the harmonic frequencies? (i.e. compared to the oscillator which has the frequency of the driving force, how much energy do the oscillators with harmonic frequency absorb)?
(2) the classical ratios are the fifth (3/2), the fourth (4/3), the major third (5/4), the minor third (6/5), the tone (9/8) and the semitone (10/9). Why are the ratios 7/6 and 8/7 not perceived as important?