Don't mess with Garson. Turns out that while I was correct when using the modern tuning of equal temperment, back in the day of musical geniuses like Bach, instrument tuning was not so crude and was specific to the key in which it was being played. Intervals in musical scales are defined by frequency ratios, and they aren't always so pretty. C# is not Dflat according to that definition.
Ken has done some fine research on this subject in order to point out my infiroirity. Equal temperment is used so that an instrument like the piano can be played in any key. However, from a great summary on the history of tuning and temperment:
* Our first written instructions for setting equal temperament come from Giovanni
Maria Lanfranco in 1533:
* "The 5ths are tuned so flat that the ear is not well pleased with them; and the
3rds are as sharp as can be endured."
Equal temperament has had its share of critics. Very few composers or organists
preferred equal temperament until the French Romantic school.
* In 1879, William Pole wrote in his book The Philosophy of Music, "The modern
practice of tuning all organs to equal temperament has been a fearful detriment to
their quality of tone. Under the old tuning, an organ made harmonious and
attractive music. Now, the harsh 3rds give it a cacophonous and repulsive effect."
So is there a audible difference to those of us who aren't musical geniuses or Ken Garson?
Check out this youtube link of a guy playing the same piece in using different temperments.
I think I can tell the difference but maybe the guy is just playing it better.
A computer simulation would probably be best.