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Re: [xml-dev] RE: Seduced by Markup

On 11/19/2013 10:42 AM, Sean McGrath wrote:
On 11/19/2013 08:52 AM, xml-dev-digest-help@lists.xml.org wrote:
[Steve Newcomb]
Actually that's a great metaphor, Len. Why do people complain about big
key signatures?  Because they haven't learned to read the notation,
Yes indeed, but why is it that so many people never learn to read the notation?

In my opinion, because its kind of scary and intimidating in ways that it really should not be, given that the underlying concepts are really very beautiful and quite simple. Basic geometry/modulo-arithmetic is all you really need to grok it.

Because classical music notation started out biased towards C Major and everything else has been added on top over the centuries, we have the completely unnecessary notion that, say, "Phrygian dominant" (and its "strange" key signature) is some sort of hyper-intellectual thing when it reality, its just a different simple formula for selecting from a repeating palette of 12 notes. Basic math with basic modulo arithmetic.
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).

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 :)


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