Bob K. wrote:

>OK, I'm getting closer, this is very helpful.  Essentially you have the
>overtone sequence transposed down to the original octave above fundamental?
>That makes sense.  (Hard to get away from that damn octave no matter what
>system you use...)

Correct.

>I wonder if all of your notes are distinct in the scale once you transpose
>back down to one octave?

Yes they are.  The frequency ratios range from 1.0625 to 1.0323.  In terms
of cents the largest interval between two adjacent notes is 105, the
smallest being 55.  So none are as small as a quartertone.

>Our major scale was derived...

Yes I believe Pythagoras circled in fifths leaving that blasted comma.

And you mentioned the square root of 2 as a tritone.  I worked on another
tuning system based on the square root of "n" from 1-16 arriving at a (get
this) 12 note "scale." In a certain sense, this is more practical than the
harmonic series method because there are fewer retunings necessary.  For
example, the 2nd and 7th notes are 7 cents below "normal" 12-tone chromatic
pitches, and the 3rd and 9th notes are 49 cents below.  So a guitarist
(let's say) could play more than one pitch on 4/6 strings.

Once again, I tried my hardest to confuse everyone.

Kyle Major
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