Note layouts for an alternative piano keyboard

Lately I have been working on rearranging keys of a piano keyboard, as you can see on my song “Galactic Overload”.

The note layout for that piece is the following one:


I call it “555” because it contains 3 groups of 5 keys each.

The tuning system is a 15 note version of
Carlos Alpha (see my article Alpha Compressed Octave).
The numbers on the white keys show their round distance, in cents, from what I consider the root key. The tuning system repeats every 1169.925 cents.

Is that one the best note layout for Carlos Alpha on an alternative piano keyboard?

I started investigating trying to follow the same line of thought that brought to the creation of the
Halberstadt keyboard.
The piano keyboard is not an isomorphic one, so there must be a privileged set of keys (the white ones) representing the main “key” of the system. The (visual) disadvantage of this note layout is its symmetry with 3 equal groups of 5 notes each.
Keeping the same ratio of 6 black for 9 white keys I came up with 2 alternatives:


this one (named “357” ) does not include ratio 3:2 with the root note on a white key


this one (named “375” ) seems better than the 2 previous ones because is more “diatonic” (white keys include a nice approximation of ratio 5:4, ratio 3:2 and the interval close to 6:5, 312 cents, is on a black key).
These 2 layouts share the same mechanical problem: there are no 2 white keys of an Halberstadt keyboard that fit as the first 2 keys of this configuration because these is never, on a regular keyboard, a single black key separating 2 white ones. To fix this problem you need, somehow, to sand those keys to make them thinner, as I will demonstrate on an
upcoming article.

Another layout using the same number of black and white keys would be:


this one (named “771” ) has a main mechanical disadvantage: that full white key (with no indentations) appears on Halberstadt keyboard only once (it is always the top key). If I needed 4 or 5 of those keys I would have to dismember as many keyboards to get them! Of course I could use other, indented, keys but it would be an ugly solution.
Besides that, 2 adjacent small steps (78 cents), compared to the large ones (156 cents), on white keys do not make any sense to me.

Other solutions?
What about a layout using 7 black and 8 white keys?


Compared to the previous ones, this one needs a lot of black keys:
a 61 keys keyboard would require 28 black and 33 white ones.
For comparison, a 61 keys Halberstadt keyboard has 25 black and 36 white ones and those configurations with 6 black and 9 white keys need (for a 61 keys keyboard) 24 of the former and 37 of the latter ones.

If, instead, we consider Carlos Alpha as the ninth root of ratio 3:2, 2 more note layouts come to mind:


this one suffers from the same visual problem as the one called ”555” because of its symmetry. A 61 keys keyboard, using this layout, would require 20 black and 41 white ones.

The other one is:


A 61 keys keyboard, using this layout, would require 27 black and 34 white ones.

After all this thinking I decided to go for the “375” note layout.

To be