I solved it. And oh man is it beautiful.
Now look at this part. This is what's got make all of you guys laugh your asses off.
Here's the full range laid out from the diagram above.
Note___Freq. Hz._Difference
C____256.00_____N/A
C#___273.38____17.38
D____288.00____14.63
D#___307.55____19.55
E____324.00____16.45
F____345.99____21.99
F#___364.50____18.51
G____384.00____19.5
G#___410.06____26.06
A____432.00____21.94
A#___461.32____29.32
B____486.00____24.68
All the differences are irrational numbers except for the difference between F# and G, and it's a solid 19.5. Go Hoagland.
Beauty.