Thanks to you asking why it's right to left instead of left to right, I have the opportunity to talk about some interesting design decisions. I agree there should be an organized pattern. For example, 1-30 lexographically. So I'll explain the hidden logic and pattern.
The three necessary primes to represent on the organized lattice are 2, 3, and 5. Given a key like 16, each of these primes should be represented in its adjacent buttons, hopefully in an axis-like manner, because these are the consonant notes to it. Left of 16 is 5/4, right is 3/4, and up-down is 2 and 1/2. But why this way?
Consonant pitches stay within a range - so large leaps in pitch are the least common. That means next to any number, the adjacent keys must have close by numbers. That's why the three primes 2, 3, 5, are converted to 2, 3/4, 5/4 - because these are the closest numbers to 1, after multiplying by a power of 2.
Your hand has a harder time reaching vertically than horizontally. 2 is the largest of these three numbers, which is why 2x is on one of the 4 vertical directions, and 3/4 and 5/4 are on the horizontal directions. Furthermore, it means that 2x must be on the 5/4 side, not the 3/4 side - because this keeps pitch distances the smallest.
There's only one remaining decision - why right to left? Your hand has an easier time turning inward than outward. And, whichever way it turns, the horizontal notes should have pitches as close as possible. Thus, 5/4 must be to the left direction.
Luckily, divisors don't exist, so the fact that the 3/4 axis and 5/4 axis are on the same line - rather than 3/4 turning to 4/3 on the opposite side - is perfectly fine.
So thanks to the above, the keyboard is forced to be this way, and every note is in its logical and rightful place, with no subjective choices. Except not, because there's not enough space. And because 7 and 15 can't be on the lattice, so they are just placed wherever there's room. 2 should really be below 1, and 3 should be where 2 is. 30 should be 40, etc. I tried to maintain the structure as much as possible but had to make things fit.
It'd be interesting to see a fantasy layout: say you were to let go of the computer keyboard layout, how would you set it up? Thumb keys, foot keys, toggles, etc, go wild.
The linked layout editor (http://www.keyboard-layout-editor.com) allows pretty wild layouts. Try loading the ErgoDox layout. While you might want to go farther still, it does nicely showcase rotated thumb clusters.
The plate & case builder tool can then generate some basic CAD files for a sandwich keyboard build to fit your keys. This can then be laser cut or something.
Because most designs use a Teensy with USB connection, you might even be able to make the keyboard output MIDI, so it could easily plug into a DAW, or whatever.
Hex keyboard, purple keys under thumbs. Extra set of temporary purple (blue) keys 1/2-1/7x, not ratios, applying to one copy only. Two copies of the green keys, one for each hand. Added numbers are 36, 40, 48; unsure about 45. 7, 14, 15, and 30 probably moved. The organized core should be continued as much as possible; I share the sentiment that ease of learning is important. The physical buttons should make fat-fingering convenient, because that's useful for fingering (and for playing lots of extra notes).
The musician probably wants his feet for other things like sustain pedal and effect pedals. I won't be too greedy :)
Though, one possible use of foot pedals is to select the instrument timbre. Since with this layout, you can take the role of two musicians, playing two different timbres, and you might as well have the flexibility to change one instrument out while the other is playing. All your fingers are occupied so it'd be hard to ask them to press extra buttons.
The three necessary primes to represent on the organized lattice are 2, 3, and 5. Given a key like 16, each of these primes should be represented in its adjacent buttons, hopefully in an axis-like manner, because these are the consonant notes to it. Left of 16 is 5/4, right is 3/4, and up-down is 2 and 1/2. But why this way?
Consonant pitches stay within a range - so large leaps in pitch are the least common. That means next to any number, the adjacent keys must have close by numbers. That's why the three primes 2, 3, 5, are converted to 2, 3/4, 5/4 - because these are the closest numbers to 1, after multiplying by a power of 2.
Your hand has a harder time reaching vertically than horizontally. 2 is the largest of these three numbers, which is why 2x is on one of the 4 vertical directions, and 3/4 and 5/4 are on the horizontal directions. Furthermore, it means that 2x must be on the 5/4 side, not the 3/4 side - because this keeps pitch distances the smallest.
There's only one remaining decision - why right to left? Your hand has an easier time turning inward than outward. And, whichever way it turns, the horizontal notes should have pitches as close as possible. Thus, 5/4 must be to the left direction.
Luckily, divisors don't exist, so the fact that the 3/4 axis and 5/4 axis are on the same line - rather than 3/4 turning to 4/3 on the opposite side - is perfectly fine.
So thanks to the above, the keyboard is forced to be this way, and every note is in its logical and rightful place, with no subjective choices. Except not, because there's not enough space. And because 7 and 15 can't be on the lattice, so they are just placed wherever there's room. 2 should really be below 1, and 3 should be where 2 is. 30 should be 40, etc. I tried to maintain the structure as much as possible but had to make things fit.