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).
