Special types of noble numbers

I found something odd and perhaps quite useful...

     Apparently, there are many noble numbers (including most of those from Erv Wilson's fames Mt. Meru scales aside from PHI) which do not conform to the following condition (which PHI and the Silver Ratio http://en.wikipedia.org/wiki/Silver_ratio) do.

X = 1/X - a whole number

     Note that for x = 1/x - 1, the result is PHI and for x = 1/x - 2 the result is the Silver Ratio.  And you can solve the equation for x = 1/x - 3, x = 1/x - 4...for every single whole number.

  Personally, I've found using 1/x for such numbers as a generator makes it very easy to makes scales which intersect perfectly with the
octave...and I am very convinced these "special" noble numbers are musically
(and in other arts as well) likely significant.

For example, look at 0.618034
(1/PHI)
0.618034^3 = .2360679 + 1
= 1.2360679 * 1.618034 ("the PHI-tave"/period)
= the standard octave, 2/1

Or the silver ratio equivalent of 1/(2.414214) = 0.414214
0.414214^1 + 1 = 1.414214 * 1.414214 ("the Silver-tave"/period) = the standard octave, 2/1

   Has this coincidence already been discovered...and/or can the rest of you think of any uses for it?

>Michael