What are isomorphic layouts?
Isomorphic layouts are a method of layout for musical keyboards in which the keys repeat in the same pattern in every direction, vs. the irregular "black and white notes" we're used to. Isomorphic keyboards have been invented and reinvented many times over the past few centuries: These three layouts are well known enough to each warrant a Wikipedia entry, and each is interesting and worthy of some exploration.
What makes isomorphic layouts different
They share a useful property: every chord shape can be transposed up and down without learning a new fingering. This makes them very easy to learn, much easier than the standard clavier layout. They also tend to lower distance between notes by making better use of two dimensional space, lending themselves to one-handed play. They are not uniformly better for all tasks, as you may find that a typical beginner's song like "Chopsticks" becomes quite twisty and challenging on these - but in exchange you gain a virtuoso's power to shift chords and keys, and may end up with happy accidents without thinking deeply about it. This might be just the thing if you need to break out of a compositional rut.
How I implemented them
I actually have a harmonic table in hardware(the AXiS-49) but it's rather fragile and a chore to set up. Recently I got interested in using these layouts again and thought it would be fun to try mapping them onto a standard keyboard for some tracking this evening. I was surprised by how effective they came out, so I thought to post them here.
The bindings are the OpenMPT defaults apart from the notes, input on a US 101 laptop layout and using all four rows. Jankó and Wicki-Hayden use the "inverted" lowest octave at the top, starting with "1" = C-0, while the harmonic table starts with "Z" = C-0. In each case I opted for a rotation that would make the most of the three octaves OpenMPT allows for binding. The physical distortion of the keyboard makes them feel a little different from how they're intended, but they are quite usable.