Since I just discovered it, perhaps "amazing" is immodest, but that is

how it struck me. This is a transformation which transforms from the

64/63 planar temperament to the

126/125 planar temperament and back!

It works as follows: using the approximations 64/63~1 or 126/125~1

respectively, the

7-limit music can be pulled back to a 5-limit preimage in a canonical

way, since

7~64/9 in the first instance, and 7~125/18 in the second instance. We

then apply a standard triad preserving mapping of order 2, namely

2-->2

3-->10/3

5-->5

While sending triads to triads, it also sends tetrads in 64/63~1 to

tetrads in 126/125~1, and tetrads in 126/125~1 to tetrads in 64/63~1; for

instance 1-5/4-3/2-7/4 in 64/63~1 becomes 1-5/4-5/3-10/7 in 126/25~1, and

vice-versa.