Reverse you're thirst

I was thinking about something.

The msical scale is, for equal temperaments, both EQUALLY spaced, and
logarithmic.

Thus, between say, 2*frequency and 4*frequency, if there were 12 divisions,
effectively this would come to:

[(2^(1/12))^n] , where n=12-------24, veiwed on a linear scale, this would
appear stretched-with the higher values of n, as in n=19, 20, 21.... being
relatively larger than n's lower values, as in 13, 14, 15.....

However, there is, in saying this a very interesting property to be
exploited here.

How would we, and what would be the mathematical technique for "mapping"
intervals between 23----->24 to intervals 12------>13, intervals 22---->23
to intervals 13---->14, intervals 21---->22 to intervals 14---->15 etc....?

I have noticed that, interestingly, the superpower temperaments, which are
all now calculated, actually do not grow exponentionally above n=12, for a
12 superpower temperament, -rather they converge to 2 at the octave, getting
smaller and smaller in intervals.

The opposite is true for the reverse superpower tempermanets, these grow,
exponentionally when veiwed in an exponentional scale, and this is why I
have made the distinction between hyper-powers and super-powers.

So, effectively, what would we do, mathematically speaking to make:

-- -- ^ n
| |
| ----- |
| 12/ | to pallendromic intervals, thus:
| \/ 2 |
| |
-- --

1 2 3..... 12 13 14.......24 25 26....
12 11 10 1 24 23 13 36 35..

Any thoughts??

--Sarn.

P.S. The square root of two in a superpower stack converges!!!!

Guess to what?