Two simple things

[ted]

[rachfan]

Despite the implication for precision of the term "equal temperament", if you discount  eletronic tuning machines, it is a theoretical concept residing mainly in the ear of the beholder (and tuner), despite the fact that it can probably be reduced to a simple and rigorous mathematical representation as you correctly assert.  

Moreover, equal temperament in practice is uneven temperament.  That is, if one is attempting to equalize or temper the different tones within the octave to imbue each with an equal degree of purity of interval with any resulting imperfection being divided among the whole of the octave, it begs subjectivity, not objectivity.  You'll find subtle differences in the way different tuners tune to the ideal of 12 semitones.  The ideal pitches in their minds' ears  for equalizing intervals is often a different ideal than that of another tuner, nevermind the theorem.  And as they each implement and "test" their tunings throughout the octave with unisons, thirds and  fifths, it remains ever subjective, never objective.  In fact, the way a tuner sets the scale is a primary reason why one would want to continue with that tuner or favor another.  Thus, I believe that while the most simple and straightforward mathematical representation might indeed be elegant and accurate, it will remain only a construct.  A particular tuner, biased toward apportioning much of the imperfection to the fourth rather than dividing it equally across the octave, proceeds in reality to do exactly that--oblivious in the moment to the proof of the theorem.