What is an Isomorphic Overlay

To understand what an isomorphic overlay is we need to understand what it means for something to be isomorphic. Using the Greek roots of the word, iso meaning "equal" and "morphosis" meaning to shape, we can say something is isomorphic if it has “equal shape” (source). In the context of a piano overlay, this means the physical distance between musical intervals will always be the same. For example, the distance between the root note and the major third will always be the same for any root note.

Let’s look at how this plays out in practice by looking at major thirds on a standard piano. The second image above shows three major thirds with their root notes labeled.

This should make intuitive sense to seasoned pianists, however, less experienced pianists will likely find themselves counting semitones.

The same three chords are highlighted on an isomorphic layout in the third image above.

Looking at major thirds on an isomorphic layout, we can see that a major third only requires skipping one “tile” in the horizontal direction and the same pattern is applied for every root note. This idea can be applied to any chord like major and minor triads, seventh chords, etc. This means you can learn the shape of a chord once and apply it to any root note/any key making it significantly easier to learn the piano.

It might be easy to assume this is a recent invention to revolutionize the piano, however, this layout is based on a design invented by Paul von Jankó in 1882 (source).

Supplies

3D Printer
2 kg PLA filament
3D model available here

Step 1: 3D Print the Overlay

At the time of writing this article, there were no free 3D models for isomorphic layouts available for my Yamaha P4-5 so I designed one; you can download it here. I have also inserted an image of the model above.

The keys are staggered in the design to make it easier to play on the overlay with your thumb. The thumb needs to be roughly parallel to the hexagonal tiles and will get in the way of other tiles if everything remains on the same level.

There are 4 unique key overlays in this design and the number of copies you need to 3D print for a full 88-key piano is shown below:

Tall black overlay - 21
Short black overlay - 15
Tall white overlay - 22
Short white overlay - 30

The overlays should be printed upright, as shown in the diagram above. I recommend printing with a 0.4mm nozzle and with 0.3mm layer heights using any material of your choice.

Step 2: Assemble

To assemble, stick the overlays onto your piano keys with double-sided tape. I would recommend starting with a small quantity, like an octave if you want to test things out before committing fully.

Here's a link to a video demo.