GEOMETRY:

METAPRISM

This is the metaprism, it holds all possible harmony in and between all keys:

There's nothing we can do in western harmony that isn't encapsulated by the metaprism

We can start in any key, use any chords in that key, and change into any other key.

Step 1: A ring of Hypercubes

The metaprism simply joins the hypercubes together:

How exactly?

Ok, Here's a familiar hypercube, but we stretch the inner cube like this:

Nothing about the hypercube has been changed

We still have the purple alpha cube and its four chords for example:

The purple cube has just been squished flat.

Same for the green cube below

This allows us to join two hypercubes together:

We can see how the purple cube is part of both hypercubes

This is how the metaprism is constructed

We can see our joined orange and green hypercubes forming part of the metaprism

This is how the hypercubes join around the whole metaprism:

Step 2:

Inside out hypercubes

All the hypercubes we've seen have the tonic cube (green) in the middle,

and the complimentary diminished cube (red) on the outside:

Heres a IV V I with green in the middle:

Heres a IV V I with green on the outside:

Both hypercubes are exactly the same, it's like an inside out tee shirt

In the metaprism, these three hypercubecubes have their tonics in the middle:

and these three hypercubes have their tonics on the outside:

After a bit of study it gets really easy to quickly identify the hypercubes and whether they're innies or outies

A quick tip:

look at a hypercube, what colour is the centre cube?

A secondary colour? then thats your tonic

or is it a primary colour? then thats the complementary colour of your tonic

or do this by looking at the outer cube

Step 3

Final thought, the metaprism has two of each hypercube

We have an innie and an outie of each hypercube

They're duplicated so the meta prism can connect in the proper way and allow for arcades

Congratulations!

We've just built and visualised the metaprism

Stay on this page and meditate on the visualisations for as long as need

and do return to it as often as you feel the need

These pages are meant to be returned to and studied over and over

There's always more to see in these shapes

Let's have some music!

Here's a simple progression turning chord iii (dominant) in C major into chord ii (subdominant) In D major:

Hear how E minor sounds like chord iii in C but retrospectivly sounds like chord ii in D major

We've shifted from the orange hypercube to the green one

Check out the cookbook page on doing more with this specific idea:

This idea stayed within one arcade (see next page)

But we can also traverse the metaprism across multiple arcades like this:

We start in C major, we grab Fm (the minor iv)

This is all in the orange hypercube

But we take that F minor and pivot into the purple hypercube

This makes F minor a dominant chord, which we can resolve to any purple key

So we choose G major, making F minor the minor backdoor

Check out exploring the dominants in the cookbook to hear all these movements:

Our progression has a few layers of complexity to it because we're using strong non diatonic chords between both keys

We use a non diatonic chord in C (Fm)

Turn that into a minor backdoor of G

And we keep using the Fm in G

another thought: this progression could stay in the orange hypercube with G^7 being a dominant chord

We could just resolve that G back to the key of C, this would mean everything would stay in the orange hypercube

But we establish G major as the new tonic, which means we've traversed the metaprism and landed in the purple hypercube

Ok

Once we feel comfortable indentifying the hypercubes in the metaprism we're ready to see the arcades