On 11/19/2013 10:42 AM, Sean McGrath wrote:
> On 11/19/2013 08:52 AM, 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 :)
-Mike
