Looking square, sounding hip

Here’s a 3D preview of the cube if you are not quite ready to assemble the paper version.

The Jazz Harmony Cube is a map of the country, continent or dwarf planet that we may call Mixolydia. This is where we find the mixolydian scale and at least seven scales which share essential notes with it. It is where we find the many varieties of dominant chord, with every extension and alteration. It’s where a lot of the difficult – and exciting – stuff in jazz harmony happens.

The geography of Mixolydia is complex, and a good map can help you to find your way around. This knowledge may seem rather abstract, but it is relevant to situations that jazz musicians meet every day, such as seeing ‘G7’ on a lead sheet and trying to decide what to play.

I first mentioned this project in 2017 but it has remained low-key so far. Now, at last, anyone can download the cube design, print it out and assemble it in a matter of minutes.

Our YouTube videos will help you understand how the cube works and what it is for. 

A five-minute introduction to the Jazz Harmony Cube
More about how the cube visually represents relationships between chords and scales
The colours and small print on the cube explained – and why there isn’t a cube face labelled ‘#9’

Much the best way to understand the cube is to have it in your hand. Download the free PDF file, print out the pattern (or ‘net’, as mathematical modellers call it), cut it out, make two glue joints and your cube is ready for use. 

If you have a few craft skills you should have no problem. If you are less confident, watch the cube assembly video.

You could 3D-print it… but we think this way is easier. Watch the entire cube assembly process (less than 9 minutes). Skip through or play back at 2x speed if you are in a hurry.

By the way, let me know if you have any success with cutting machines. Our first experiments did not go too well, but new machines have come on the market since then. It really ought to work.

The PDF file also contains a net for the new Minimalist cube. The concept is the same, but the design is less cluttered and perhaps more visually striking. With only very condensed information printed on the cube faces, the Minimalist cube will be useful to people who already have a Classic cube or a solid knowledge of the relevant theory. 

The new thing is the shading. This provides visual evidence for the idea that musicians and listeners prefer scales which are fairly even. Intuitively, that means no dense clusters of notes or wide gaps. But evenness can be given a more precise mathematical definition, and this is what was used to compute the shading. Three of the eight scales on the cube have notes inserted or deleted to make them more even. You’ll find them at the three darkest corners of the orange cube – where the pressure to make the scale more even is at its strongest.

A full explanation of the Minimalist cube will appear on this blog soon.

❔Questions about the cube? See the cube FAQ.

📥Download cube designs.

📲View 3D model on Sketchfab, or download for offline viewing.

3D model running full-screen on a smartphone. Easily view the cube from any angle, zoom in and out.

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