Key drift up the scale

Rather than complicate my previous post too much I have split this part
out. It is a justification or explanation of how I arrived at the idea
that as we move from the bass to the treble we want to change key by
adding a sharp or removing a flat.

In fact, as me move to higher notes the prime indices all want to be
higher so that in the Blues the notes with the 7 ratio (Ebv and Bbv)
should be favoured in the treble only and not in the base. Some
appreciation of what I am on about here can be gained by looking at the
diagrams listed here from my web site which are the result of haronics
calculations which I believe reasonably accurately represent the nature
of the universe ...

In this diagram the pattern of harmonics is presented
http://www.kcbbs.gen.nz/users/rtomes/rt-ha-nm.gif

In these two diagrams the harmonics are labelled with notes (the
notation is NOT consistent with this post and should be ignored).
http://www.kcbbs.gen.nz/users/rtomes/rt-ha-mx.gif
http://www.kcbbs.gen.nz/users/rtomes/rt-ha-my.gif
From this you can see how the key shifts from F around (2) to C around
(48) to G around (288). Then a minor flavour develops around (2880) and
it comes back to a major at (17280).

I believe that all natural music comes from structures that look like
this. The reason is that such a structure has the absolute maximum
amount of harmonic content right to its very core and in as many ways as
possible. This is a bit of a sideline from the main argument, but I
wanted to justify my statement about the drift of all the prime indices
at higher frequencies.

All sorts of things can happen because of this. For example, C might
have relative frequncies of 1, 2, 4, 8 in the lower octaves but
eventually it might become 126, 252, 504 rather than 128 etc in the
higher ocatves. That is always assuming that we are spanning enough
octaves. For example, try the chord C Bb D D F C spanning 3 octaves.
It can be interpreted as 8:14:18:36:42:63 so that the two "C"s are not
in tune according to standard ideas. This is quite unrelated to my main
argument and just a curiosity really.

-- Ray Tomes -- http://www.kcbbs.gen.nz/users/rtomes/rt-home.htm --
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