>What we have for the situation key sig/tonic/scoring mode is
>practically trivial algebra. [Simple minded Gramm-Schmidt
>procedure to get an orthonormal set of basis vectors that span
>the space.]
I bet that there are some [virtually] present who would regard
Gramm-Schmidt as very highly advanced algebra indeed!
To paraphrase Mark Twain: the difference between the right
syntax and nearly the right syntax is like the difference between
being hit by lightning and being nearly hit by lightning.
There are lots of analogies about coordinate systems. For
instance, if you wanted to drive to this place I could give
you the latitude and longitude. For an American who
wanted to know where I live it would probably be very
good, but to get here you need to know that you head out
of the city and turn left immediately after the footbridge.
A coordinate system which is right for one purpose can be
wrong for another, even if they are trivially related.
To me as a musician knowing the mode tells me a lot about
the character of the tune. (I play a fiddle mainly and it
doesn't have any black or white notes). The next thing
I want to know is the tonic. If the guitarist is struggling
to find where I am, I don't shout to him "one sharp!"
which would be completely silly and send him off
in the direction of {G, D7, C, Em}, I shout "I'm in A
Dorian" which tells him {Am, G}.
> K:<tonic><[scoring] mode><key sig.> puts top priority last
It's a case of horses for courses. To me the priorities are
1. Mode, 2. Tonic, 3. Any corrections/adjustments
This is not to say that your priorites are wrong, it's a case
of relativity. I am not in your frame of reference.
Laurie
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