The 2 diagrams are 2 views of the same layout.
Worst case error of any white ratio is 7.2 cents.
Frequency of a button is determined by:
`f=c0*c1^x*c2^y`
where:
c0=arbitrary
c1=1.170626
c2=1.095445
x and y are not perpendicular but aligned to the hexagonal lattice like this italic L:
y
*L*x
c1 and c2 were chosen to meet the following goals:
Include every frequency ratio from 1/2 to 2/1 which contains only integers less than 12.
Pack them into the smallest possible circle without conflating any.
I wrote a search program to find it.
The logarithmic spacing in the top diagram is a consequence of the formula.
In the top diagram, you can see 2 "axes" of false equivalences:
10/11 = 11/12
14/15 = 15/16
13 is missing, it would be exactly between 2 buttons or far away.
If diagram 1 is continued based on the location of primes, the first "collision" is 98=99.
Its an easy layout to remember because 5678 is in a symmetric shape that fingers naturally rest in.
I'm sure this is just repeating someone else's work (whose?)