BobY adds:
...tempered tuning, which became the standard method thanks largely to its championship by J.S. Bach nearly 300 years ago.It gets even more complex than that. The change didn't happen all in one swell foop. There were bunches of partially tempered systems with all kinds weird names like 1/4 comma mean tone that fit in the general category of non-just non-equal temperaments (
http://www.ixpres.com/interval/dict/temp.htm). The system we use today is called equal temperament; the relation between the frequencies of any of the adjacent notes in the 12 tone scale is identical. Thus Freq(E):Freq(F)::Freq(A#):Freq(B). Mozart did not have the benefit of this temperament scheme and some of his music, in my opinion, shows it. I had never been a great fan of Mozart until I went to a Malcolm Bilson concert in which he was showing off his new pianoforte. He had it tuned in the temperament that Mozart would have used and was pretty much restricted to playing in three keys. He played one piece that he had introed by saying that most composers would repeat a motif maybe two or three times but that Mozart had done it 13 times in this piece. Mozart had taken the little three or four note theme and dragged it kicking and screaming around the circle of fifths watching it get more and more discordant until it made it halfway around at which point it slowly came back to harmonious accord. Ever since then I have listened for that sort of thing in Mozart's music (which I am getting more and more appreciative of
Hi E) wondering what it would sound like if they were playing in his temperament.
