GEOMETRY:

ALPHACUBES

So far we've got three primary coloured squares

and they join in pairs to make secondary colour cubes

Here's the yellow and red squares coming together to make a cube:

This is the orange alpha cube

Yellow + red = orange

We can make three alpha cubes, one for each secondary colour:

Yellow + red = orange

Blue + yellow = green

Red + blue = purple

The three alpha cubes represent the three secondary colours of the colour wheel in full detail

Speaking of detail, let's talk about the note structure of the alpha cubes

We know that the primary squares represent cycles of minor 3rds

In the alpha cubes they are joined by perfect 5th intervals:

What we have here is the orange line representing the perfect 5th interval between C (yellow) and G (red)

Every secondary colour line in the geometries of metaharmony

always represent a perfect 5th

They are always connecting two primary colour notes

Ok, so all four orange lines in the orange alpha cube are perfect 5ths:

Take a moment to identify the four 5ths here:

C and G

A and E

Gb and Db

Eb and Bb

The alpha cubes hold many interesting things

But theres just one more thing I want to touch on here:

What are these squares?

Let's look at this one at the front,

It holds the notes C, E, G and A

This gives us the notes of a C major triad:

And C major's relative minor, an A minor triad:

C maj and A min share the same orange face,

This is part of why we can say "orange chords share function"

Check out the page on functional equivalence for more on this:

But all we need to know now is that C major and A minor live on this orange square

and that there are four orange squares in the alpha cube:

This gives us the cycles of orange major and minor chords that we discussed in the secondary colours page:

When we move a chord by a minor 3rd, we move 90 degrees around the alpha cube

When we move a a chord by a tritone, we move 180 degrees around the alpha cube

The alpha cubes show us families of major and minor chords related by minor 3rds

Scroll back up and look at the chart above and just really process the minor 3rd colour relationships going on

Ok so what are we going to do with these cubes?

Continue on to hypercubes