Friday, April 29, 2011

Isomorphic Keyboards

One of the first obstacles an aspiring musician will face is trying to understand the relationships between the different notes they can make with their instrument of choice: a piano looks like it's missing every third or fourth black key; a guitar in standard tuning starts repeating pitches five frets along the next string, except for one string where it's only four; a saxophone plays different notes depending on which combinations of keys are held down; and fretless instruments like a violin or sliding instruments like a trombone offer practically no guidance to the desired positions on their own.

Chords make it all even more confusing; the same chord shape can get twisted into all sorts of arrangements depending on which note is the root. Playing a basic major chord on a piano can end up on all white keys, all black keys, or some combination of both. On a guitar, a major chord might involve all six strings or only five or four, and a player's fingers need to learn their own form of gymnastics to switch from one shape to another in time with the music.

Fortunately, there is a better way. Not only is it easier to learn, but it opens up a whole range of new possibilities unavailable on many traditional instruments.

This interface is called an isomorphic keyboard, so named because one hand shape plays the same type of chord no matter what the root pitch is. The pitches are arranged on a hexagonal grid in such a way that each direction represents movement by one certain interval. Such a layout is achieved by selecting any two intervals to define the pattern.

G Ab A Bb B
E F Gb G
C Db D Eb E
A Bb B C
F Gb G Ab A
D Eb E F
Bb B C Db D
G Ab A Bb
Eb E F Gb G
C Db D Eb
Ab A Bb B C
F Gb G Ab
Db D Eb E F

For example, in the above diagram, upward movement represents an ascending perfect fifth (C to G to D to A), so therefore downward movement is by a descending perfect fifth (C to F to Bb to Eb). Movement to the "northeast" is an ascending major third (C to E to Ab to C), so "southwest" is descending (C to Ab to E to C). Such motion is universal across the entire grid; starting on C and moving northeast to E and then moving upward from there will yield a perfect fifth above E, which is B. Given this arrangement, it is clear that motion along the "northwest"/"southeast" axis is by minor thirds.


To play a basic major chord in such an arrangement, the shape is a triangle: a cluster of two hexes on the left bordering one hex on the right (such as C-major, C-E-G). This shape can be moved to any position on the grid and it will yield a major chord built on whatever pitch is in the lower-left hex; for example, look for B-Eb-Gb (B-major) or D-Gb-A (D-major). A minor chord is merely flipped around: the lone hex on the right is instead moved to the left (C-Eb-G).

Additionally, since the physical pattern between pitches does not change regardless of position, compositions can be played in a different key without any need to change the relative hand movements; exactly the same motions are made around a different tonic hex.

Again, an isomorphic arrangement is not limited to the one given in this example, but can instead be built from any two intervals, including those not available in standard Western twelve-tone tuning. An axis could be defined by the 7:4 harmonic (or "barbershop") seventh, or by the 352.9-cent neutral third of 17-EDO, or any other exotic interval your music might demand. As such, tunings that are completely unattainable on a traditional instrument can be accommodated with ease.

Is such a keyboard actually practical? Absolutely. Various isomorphic layouts have been in use for real instruments since the 1800s. Early on, these were unique, custom-built acoustic instruments, though by the late 20th century technology allowed the development of several electronic interfaces that could be automatically retuned to an entirely different layout at the whim of the performer. These specialized devices have typically been as costly as many other instruments, though there are now inexpensive apps for mobile touchscreen devices that make isomorphic keyboards easily accessible and widely available, and there are even free resources online that let visitors use their computer keyboards as isomorphic instruments!


  1. Personally, I find the Jankó layout to be the most practical for general use and piano performance. Though not as flexible with microtonal tunings, it was designed for the 12-tone system and carries all the learning benefits of any layouts designed since its creation. Alas, with the handful of janko pianos and even swappable standard/janko keyboards available, people didn't easily give up tradition for innovation and the same still seems to apply in the music world.

  2. The Jankó layout was actually my own introduction to the idea of different key systems. I agree it's a shame it never caught on!

    The layout I used as the example is the Harmonic Table, and the link I gave uses the Wicki-Hayden layout. There are also isomorphic layouts called Park and Gerhard that I haven't had the opportunity to play, though I think Gerhard looks very interesting.

  3. We will be unveiling our commercially available chromatic keyboard at the next NAMM show. Our website is: