Tying my new scale experiments to the deriving of C-major and 12TET

This is one way to get the C-Major scale...that looks profoundly
like the method I used to get my "two harmonic series" scale.

Only, it has a "reverse harmonic series" trick where it takes 10/8
and converts it into 4/3 (same value) and starts working backward
through the harmonic series (from 5/4 to 4/3 to 3/2).

Here is how you can explain C-major:

8/8 = 1 (root note: start of first harmonic series)

9/8 = 1.125
10/8 = 1.25 5/4 (NOTE 10/8 = 5/4: start of "reverse
harmonic series")
1.3333= 4/3
1.5 = >>3/2<< (start of second harmonic series!!!)

>>3/2<<*9/8 = 1.6875
>>3/2<<*10/8 = 1.875
= 2 (>>3/2<<< * 4/3: second reverse harmonic series)

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Now, if you want to create a clearer 12-note 12TET-like tuning and
"derive 12TET", try this

17/17 = 1 (start of first harmonic series)
17/16 1.0625
18/16 = 1.125
19/16 = 1.1875
1.25 20/16 = 5/4 (start of reverse series)

1.3333 4/3 = 8/6 = 16/12
1.41666666666667 17/12(second series)

1.5 3/2 (start third series)
17/16*1.5 1.59375
18/16*1.5 1.6875
19/16*1.5 1.78125
1.875 5/4 * 1.5 (start second rev series)
2 4/3 * 1.5 (octave)

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So, when you think of it, I swear it's fair to say that all 12TET
and all the scales under it are...is combinations of harmonic series
in forwards "major" and backward "minor".

And, perhaps most importantly...
For sure, someone with a good mathematical mind could find out ways
to create much more flexible tunings than 12-tone ones (think 14 maybe
even 16-tone) with this method. :-)

-Michael

You could definitely use 12-tet notes to "substitute" for those
harmonics in a certain chord and get pretty good results. You could
also use those notes to substitute for other harmonics and get pretty
good results.

Even pure harmonics can substitute for other harmonics. If you took
that entire harmonic series and substituted 17/16 for 18/17, for
example, it might not make such a huge difference. 16:20:24 often
passes for 10:12:15, for example. Although there are some that would
say that 10:12:15 also passes for 16:20:24...

-Mike