a natural scale?

About a year ago, while writing some piano exercises, I noticed myself
consistently singing the "re" in "do-re-me" flatter in minor than in major
keys. Has anybody noticed this? Try it!

I thought, "Gee, maybe that's 10/9->6/5 vs. 9/8-5/4..." I took a look at
it a few months ago and found to my horror that I wasn't singing "me" as
6/5 either. I was much closer to 19/16. I thought maybe I was leaning
toward 32/27, for chain-of-fifth reasons (or perhaps 19/16 for harmonic
reasons --- maybe even 300 cents, for cultural reasons).

I fiddled some more yesterday, and found I liked the minor third even
flatter than 32/27. In fact that ratio seemed to be the upper limit of a
range of desirable minor thirds (7/6 being the lower limit). I fiddled
with all the notes in the major and minor do-re-me's, and finally came up
with this (in cents, because I couldn't find a rational explanation)...

tone do re me
major 0 210 390
minor 0 182 285

Here are the ranges...

tone re me
major 200-215 385-400
minor 180-200 270-295

I used one timbre for the entire thing; a wavetable reed organ patch. I
would play "do", sing do-re-me, and then play re and me to compare. This
is where the ranges came from. Then, I made a scala file with a bunch of
notes in every range, and played around until I got the specific notes
above. Would anybody care to try this? What are your preferences?

It is worthwhile mentioning that if I first played the dyad me/do, and then
sang do-re-me, "me" would always come out where I had heard it in the dyad,
and would sound natural, even if outside the range.

-C.