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On 11/19/2013 10:42 AM, Sean McGrath wrote: The idea these signatures are unnecessary is pure 21st century thinking. When the music notation was invented, *key signatures were not equivalent*. The mathematical uniformity you describe was a new invention in Bach's day - I believe it was called "even" tempering. But the precedent was to tune by the ear, by the so-called "perfect" intervals (3:2 for a 5th, 4:3 for a 4th), but these are *not the same* as 2^(7/12) and 2^(5/12) which are the intervals in even tempering (although very close - what a strange coincidence).On 11/19/2013 08:52 AM, xml-dev-digest-help@l... wrote: [Steve Newcomb]Yes indeed, but why is it that so many people never learn to read the notation?Actually that's a great metaphor, Len. Why do people complain about big key signatures? Because they haven't learned to read the notation, The consequence was that it was a meaningful difference (on the keyboard instruments, I'm not talking about cranky horn players and so on) which key signature you chose. Distant signatures on the circle of fifths sounded more out-of whack, discordant, eerie, imperfect. So there was an emotional reason to shy away from them. Not sure that informs current practice though :) -Mike
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