My friend, the crackpot inventor sent me the msg below.
I'll mail the MP3 files to which he refers upon request.
As obvious from the header, I'm sending this to musician friends and a
Physics of music expert in addition to the list.
bc
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I've been studying music scales and I've been tabulating some inherent
harmonies not recognized by western music. This came about as a result
of my "Harmonic Visualizer", which is just a fancy Lissajous pattern
generator. See:
My device easily shows many mathematical patterns that are not musical
harmonies in the western scale, but are inherently harmonic because of
the low value integer relationships (like 7:4, 11:8, 13:8, 14:8).
For example, there are ratios of halves (3:2 = perfect fifth), thirds
(4:3 = perfect fourth), quarters (5:4 = major third), fifths (6:5 =
minor third), sixths (see thirds and halves), and eighths (9:8 = major
second, 15:8 = major seventh).
But there are no ratios of sevenths. Even though 8:7, 9:7, 10:7, etc.
are pretty low ratios and, in theory, ought to be pleasant harmonies.
And they are, in fact, relatively soothing harmonies, which you can hear
below:
[nope]
<>Yet none of these notes (outside the root and octave) are in western
music. Furthermore, if you diagram out the notes of our scale and the
ratios that produce them, there are some major harmonies missing. Like
7:4, which falls between A and A#. A is 5:3 and A# is 9:5. But 7:4 is a
pleasant harmony BETWEEN A and A#:
[nope]
It just seems odd. One wonders what sort of music might be possible by
using more of the mathematical harmonies, or by using only (for example)
ratios of 7.
Since there is nothing new under the sun, one wonders if someone has
already made music using these exceptions.
One also wonders if any non-western music explicitly uses these
additional harmonies.