> This system ensures that every key and every note sounds equally good, but it sacrifices the purity of just intonation.

Bach wrote two books of the Well-Tempered Clavier over 300 years ago that explain musically why that sacrifice is worth it:

* Book I: pick a prelude/fugue in any key and it will sound ok on a keyboard that you tuned ahead of time

* Book II: modulate anywhere you want[1] in the middle of a piece and it will sound ok

That same system works all the way through high-Romantic Wagnerian operas and atonal pieces of the 20th century. Use equal temperament and let the singer/violinist/horn player "sweeten" a third by ear where applicable.

Edit: well, anywhere Bach wanted. Hee hee.