Beautiful Numbers

So I've been converting a lot of values between cents and hertz, between musical tone and physical frequency. The way the numbers work out is absolutely beautiful.

I've been working with 440Hz as my baseline because modern practice is to tune A=440Hz. It seems that this was a very sensible choice given the biases of modern music. I find the following pattern:
440Hz Tonic
550Hz Major third
660Hz Fifth
(770Hz Septimal)
880Hz Octave
That's really quite beautiful. Is this a product of choosing 440 as the root?

If we pick 330Hz for the tonic, we get:
330Hz Tonic
440Hz Fourth
550Hz Fourth + Major Third
660Hz Octave
So there's different patterns for different starting values. What we are doing here is logarithmically modifying our selected utonal rules.

Or, with 100Hz as the tonic:
100Hz Tonic
110Hz ?
120Hz Minor Third
130Hz ?
140Hz (0.63Hz out from the Super Major Third)
150Hz Fifth
160Hz Fourth + Minor Third
170Hz ?
180Hz Fifth + Minor Third
190Hz ?
200Hz Octave

I could go on picking out different patterns forever. I realise that I am using the same ratio method I have been using but viewed from the opposite angle. Nonetheless, this is a quite different way to think about things, an alternate cognition of tone. Perhaps it will be fruitful.