How chords fit to a space

Let’s look at a grid based on Balzano’s space. If we draw a major chord in that space, it will have a horizontally mirrored L-shape:

This is easy to see if you look at the offsets of the three notes within a major chord, which are [0 4 7]. So, starting the chord from middle C (midi 60) we get midi notes 60+0, 60+4 and 60+7. These offsets we also call intervals.

If we draw a minor chord (with intervals [0 3 7]) , it will have a vertically mirrored L-shape:

What’s so useful about this, is that compact shapes in the space (shapes consisting of cells close to eachother) apparently correlate with interesting chords. We can now turn this around : if you would draw a compact shape at random in the space, there is a good chance that this shape turns out to be a useful chord. This is one of things the tonespace chord fitting algorithm is based on. More about that later.