The 2 types of tuning used currently are equal tuning, which means each half tone is equal to the next, or, in the cases of strings, winds and voices who are not performing with set pitched instruments, just (natural) tuning, where each note is tuned according to its harmonic neeeds.
Of course, clarinets, and other woodwinds, are both fixed and flexible in tuning; fixed because they must be tunes as equally as possible in design to be adaptable to any type of music, and flexible since the pitch can be altered by fingerings, embouchure and air control.
Though the article linked above and quoted below is a website which sells software to adjust "midi" players to reflect well-tempered scales, it offers some interesting musical perspective on the power of certain chords to "shock" the listener in Monteverdi and Mozart, and the relative loss of that psychological power with equal intonation beginning with Beethoven.
"The patented Justonic innovations not only restore to music the lost harmonies of Monteverdi, Bach, and Mozart, but open up a whole new world of tonal possibilities for modern musicians."
When Claudio Monteverdi introduced the dominant seventh chord, its dissonance was more sharply felt than it is today (with equal temperament). When a modern, tempered orchestra plays Monteverdi, the contrast between true consonance and dissonance is obscured. Inversions, modulations, and other compositional resources have also been dulled by temperament.
In 1685, the year that Bach was born, Andreas Werckmeister applied mathematics to the problem and came up with the entirely contrived equal tempered scale, eventually adopted by piano makers. Bach, however, wrote for meantone and "well" temperament in which the thirds and fifths were sweet and pure in the "near" keys and became more out of tune in the "distant" keys. When played in equal temperament the full radiance of Bach harmony is compromised. Likewise, a Mozart vocal harmony was written to be sung in tune. A tempered version is still music, but it isn't what the composer intended, and it does not reveal the full genius behind the harmony.