It has long been my opinion that temperament is only necessary and workable on fixed-pitch instruments of limited resources. Specifically, it is a great work-around for a specific problem. For the rest of us, it is not a temperament that will be important to us (except where a specific composer adhered to a specific temperament, rather than some other system.)
On instruments, like and especially the lute, where the performer's fingers are on the strings and corrections can be made on-the-fly, nothing that fits the definition of temperament is really necessary. Instead, there are adjustments that need to be made for the specific requirements of the instrument. In the case of the lute, the requirements involve things like different string mass/diameter/tension, and nut-grooves vs. saddle triangle shape (i.e., the height of the string and distance from the saddle as determined by the triangle-shaped bit where the string part through the saddle meets the string part over the saddle.) Organs respond well to temperaments, within each rank, and require some kind of resolution between different ranks, which may have pitches perceived differently because of harmonic content. Harpsichords do well, since the density difference between lowest and highest notes is not greatly different and string lengths even of the highest notes and tensions lead to string-behavior throughout the compass. Pianos respond badly to any kind of one-octave temperament-fits-all because the densities and tensions and string lengths cause the upper strings to act more and more like bars than strings. This is affected even more by the length of the piano's harp (most stark between spinets and 12-foot concert grands.) And it is influenced more subtly, but no less significantly, by the piano's scale-design and implementation. So there's no surprise that the purely mathematical solution (immediately available to anyone who has risen in technical acumen to understand the 12th root of 2) to ET12 is not applicable in the real world. The surprise may be that it can be made to work at all, even if the "it" that is being made to work is but a shadow of the mathematical solution! I find the most satisfying surprise in the discussion of tunings and temperaments is how Dowland's tuning, which is described in his nephew's book of lessons, makes his music sound better than any other system I've tried, even under these poorly-trained (and aging) fingers. Holborne doesn't sound so good to me in Dowland's tuning. Unlike Mr. Turovsky, I don't believe in the aphorism that good music doesn't rely on a specific tuning system or temperament. I believe that good composers take into account their available materials without conscious effort and produce music which uses them all to best advantage. After all, much of late 19th C and early 20th C analysis of renaissance music concluded that it was drab, purposeless and aimless, which seems to me to have been predicated on their using the temperament-of-the-day instead of any kind of just intonation. Compare a cylinder recording of an orchestra like Toscannini's, which can be corrected to reproduce all of the sound that was there at the recording, and compare that to the same piece played by one of today's symphonies: the difference in the sound and attractiveness of the music is incredible. I'm saying, here, that temperament/tuning doesn't make bad music interesting, but it can make "GOOD" music more interesting, when properly applied. Which I think says what Roman wanted to say about Harrison. Anyway, from a performance->listener point of view, the ability of untrained folk to not hear bad intonation should be well-known by now. And the ability of critical people to be, or claim to be, highly sensitive to "out of tune" is also well-known. What isn't well-known is a universal rule for how accurate a tuning (or temperament) has to be in order to please everyone. So it is unlikely that math alone is going to be a solution-source for musicians. ray To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
