I went looking for vals which could be used for approximating the

7-limit miracle canonical map, stepping through divisions of 3 rather

than of 2, and seeing how well the canonical map was approximated. It

turns out that not only does [72, 114, 167, 202] work well, it works

extremely well--vastly better than anything else.

If we do a least squares for (114*x-cents(3))^2+(167*x-cents(5))^2, we

get x=16.68429155 as the size of a step; [7*x, 72*x] gives us

[116.7900408, 1201.268992]

and the difference in cents from the canonical map is inaudible:

[-.6300e-2, -.54236e-1, .37024e-1, -.2922e-2]

We can do the same calculation and get a least squares optimum for

all four images of the primes under the canonical map, with

essentially the same result: x=16.68427953 cents, with generators

[116.7899567, 1201.268126]

and difference from the canonical map of

[-.5434e-2, -.52865e-1, .39031e-1, -.494e-3]