Possible method to match a timbre to a PHI scale

Consider a PHI scale derived from the simple formula (1/PHI)^x + 1
1
1.09
1.145
1.23
1.38
1.48
1.54
1.618 (period)

And now consider the timbre 1, 1.38, 1.618, 2 (1.618 + 1.38).....
Note that many of the notes match the timbre almost exactly IE 1.09 + .38 = 1.47, 1.145 + 0.38 = 1.525 and 1.23 + 0.38 = 1.61...again, almost exact matches to notes in the scale!

Hopefully this can solve a good deal of the "sure PHI scales sound interesting, but the timbre conflicts are terrible" issues.

-Michael