Skewed/modified 9-tone 12TET based on square root of fractions

   This scale sounds remarkably "normal" yet still gives the type of tonal flexibility of alternative scales. 
   It is not pure 7-tone Just Intonation, so to speak, but rather based on the square roots
of Just Intonation + some notes from Just Intonation. 
   Try this and let me know what you think:

9-note "12 Roots" Scale

1
1.11803 = sqrt(5/4)
1.224744 = sqrt(3/2)

1.33333 = 4/3       
1.41421 = sqrt(2)
1.5 = 3/2

1.66666 = 5/3
1.7320508 = sqrt(3)
1.87082 = sqrt(3.5) = sqrt(7/2)

Note numerator + denominator is never more than 9.