December 10, 2013

Isomorphic Musical Keyboards

When I finished college I had plenty of free time on my hands. Inspired by musette players like Tony Murena and Jo Privat I bought a C-system button accordion to see what I could do. I still have a tough time reading music on the keyboard so I came up with this little quiz to practice sight reading.  I've also added various other isomorphic layouts: a bayan B system, the Jank√≥ piano system, and the Jammer. Press the buttons to practice and get a feel for where the notes are located. When you're ready press 'Start Quiz'. The score is the average number of seconds it takes to answer all five questions.


Some Thoughts

Finding abstractions is one of the pleasures of being a software developer. You begin implementing eight different keyboards in what starts out feeling like it will be eight different ways and you soon discover a pattern and the eight different ways become one. Though the inventors of isomorphic systems worked separately the fascinating thing I found was that all these systems can be built on a brick-like lattice with a simple algorithm. The variation between the eight systems shown above boils down to two parameters: (1) the number of rows required before the pattern repeats and (2) the size of the interval going up one key diagonally.

The earliest example of an isomorphic keyboard I found was from the 1850's, when an Austrian musician, Franz Walther, arranged the buttons on a Schrammel accordion in rows to match the notes of a diminished chord, thus creating what’s known today as the chromatic B-system. (Read more about the Viennese Schrammelharmonika in Andreas Teufel’s thesis.) A few decades later, in 1882, Hungarian engineer Paul von Jank√≥ patented an alternate keyboard for the piano which generated enough attention to result in a few instruments being a built and at least one piano school adopting the keyboard. (Many examples of this keyboard can be seen on the Squeezehead’s page on uniform keyboards.)

Since accordions were much cheaper to build than pianos, experiments with isomorphic keyboards on the squeezebox reached a wider audience. An extended B-system became very popular in Russia and the Balkans, while in France it was the C-system that was the layout of choice for musette players. Some modern concertinas use the Wicki system which keeps all the fingers together in reach of all the diatonic scale notes, catering to that instrument's limitations on hand mobility. Even the Stradella bass system, seen on just about every piano accordion, can be thought of as an isomorphic keyboard if only the roots and the counter rows are considered.

In the 20th century proponents of microtonality employed isomorphic keyboards to build microtonal instruments such as the Fokker 31 tone organ. But like pianos, organs are very expensive to make so there are very few examples of isomorphic organs. MIDI controllers, on the other hand, are the modern day accordions. They’re cheaper to make and can reach a much wider audience willing to try new things. One such controller is the Jammer. Software controllers dispense with the physical keyboard entirely such as Musix.

Source for this keyboard is available on GitHub.