Limit 21.5 - The Microtonal Arcade Machine

“Limit 21.5” is an arcade game, as well as instrument created to explore my interest in combining complex musical output with simple, game-ified interfaces. In this case, I wanted to create an instrument that allowed me to write music I could never write before, and specifically I sought to create a conduit for my ideas about microtonality and alternate tuning systems that didn’t require extensive theory knowledge or training to play.

The fundamental tuning system at play here is various types of just intonation, in particular, 5 and 7 limit tunings. These systems are each perfected versions of our perpetually out of tune twelve tone equal temperament, and each construct their pitches using various multiples of factors up to 5 and 7, respectively. By arranging these pitches in a lattice, you can create a visual representation of these tuning systems, like this one below for 5-limit tuning:

The arrows are part of what’s called “Helmholtz Ellis Notation”, and indicate a raising or lowering of the base Pythagorean pitch by one “syntonic comma”, which has a size of approximately 21.5 cents, and is where the instrument gets its name.

With this tuning system in place, the musician plays by drawing shapes of 4 blocks onto the screen that represent indices into this lattice, which then get sonified into microtonal chords. I was inspired by a number of visualizations that made comparisons to Tetris in that shapes are appearing on the screen and in this case, being turned into sound.

After each shape is drawn, the musician has a few options for the next shape. Each shape after the first must either share one common block with a previous one, or be one of several transformations that the user has available. These transformations include translation, rotation, mirroring across the center line, as well as the ability to swap between 5 and 7 limit based tunings on the fly with the press of a button. These transformations were chosen for their musical potential: transformations of parallel shapes, for example, is similar to the idea of “planing” or parallel chord structures as commonly found in impressionistic music of the 19th and early 20th century. Similarly, the restriction of forcing one common tone allows the performer to modulate across odd microtonal tonalities while keeping one tone the same in a sort of pivot tone modulation.

As a composer, I wrote and performed a piece for my instrument, entitled, “The Well-tuned Arcade Machine”, paying homage to the American composer La Monte Young, whose microtonal compositions were always a great inspiration to me: