Just a note or two on perfect tuning and even temperament:

Until Bach's time, musical instruments were tuned to the scales discovered by Pythagoras 2000 years before when he started experimenting with harmonics on a string under tension. These scales were in so-called "perfect tuning." The problem was that instruments could only be played in the keys in which they were tuned, and if you tried to play in a key that was not closely related (say, the instrument was perfect-tuned to a C and you tried to play in E), the instrument would sound out of tune, which, in that key, it would be. The further away you got on the Circle of Fifths from the key the instrument was tuned in, the further out certain notes would be. It's cumulative.

What Bach did was to very slightly retune his instrument, in this case, the clavier (essentially, a harpsichord). He tweaked the tuning minutely so that the distance between half-steps was even all the way. True, it was a compromise tuning, and it meant that a note or two in each scale would be a tiny hair off—but still so close that it would take a very acute ear to hear the difference and even then, most people would not even notice it. Then, as a demonstration of the advantages of this system of tuning, Bach wrote his preludes and fugues for "Well-Tempered Clavier," showing that one could play in all keys without having to laboriously retune the instrument—and it sounded just fine. Not only was this a mechanical breakthrough in musical instruments opening up a wide range for future composers and musicians, it was musically brilliant as well.

If you want to hear these, there are MIDI files for the whole shebang HERE

This work had far-reaching effects. Among other things, Beethoven could not have written the symphonies, string quartets, and other works that he did had it not been for Bach showing the way by introducing even temperament and making it possible for Beethoven and future composers and musicians to modulate freely to and from keys that were not closely related to each other.

I have a pretty good ear, and frankly, I can't hear much difference between perfect tuning and even temperament. And most long-time musicians that I know, including professional classical musicians and early music buffs can't either. I am deeply suspicious of those who say they can, and insist on making a big deal of it. Those who claim they can hear the difference remind me of the fairy tale about the princess and the pea. I can hear a slight wobble between a couple of notes if you sound them long enough, but if a quarter note lasts for much less than a second (and that's a fairly slow tempo), the discrepancy isn't there long enough for the wobble to manifest itself.

Among other things, pianos and other fixed pitch instruments—including the placement of guitar frets—are tuned to or geared for even temperament. For a guitarist, imagine having to have to retune for different keys. And how would you go about adjusting the position of the frets to accommodate the new tuning? And using a capo? Forget it!

Messy, eh?

Don Firth