GEOMETRY:

ARCADES

These are the four arcades:

Arcades connect keys in whole tone families:

Watch above how we start with the C major key cube,

and then extend to include the D major key cube which is whole step above

We continue joining keys by whole tones until we come back to C

How to identify the four arcades?

Firstly let visualise the four keys of the orange hypercube:

Each key cube branches out into a different arcade

Here for example we have the orange key of Eb major branching out into its arcade:

This makes another family of keys related by whole tones

This allows orange keys to associate with green and purple keys

This is how we can start to shift the function rules of the hypercubes (more on this at the end of this page)

Here's the next arcade which is connected to the Gb major key cube in the orange hypercube:

Here's the final fourth arcade coming off the A major key cube in the orange hypercube:

Fact:

When you rotate around the four orange keys, you are switching arcade:

Conversely:

When you rotate around an arcade, you are switching hypercube:

Final thought: Duplicate arcades

The 'inner' and 'outer' arcades have the same six keys, just reversed:

The same goes with the 'front' and 'back' arcades:

Notice the tritone relationships here,

Focus on the key of F and how it swaps with the key of B

Can you see how its jumping 180 degrees across the hypercube?

Let's have some music:

I've simply chosen chords from the arcade and used them acording to their function in the arcade

For example C major to A major in the orange hypercube would be tonic to tonic

but here A major is subdominant in the key of E

This is the beauty of the arcades (and metaprism)

We can shift our colour function rules that exist in the hypercube

There's much more to discuss here, and we'll explore more music in the cook book

But lets move onto the final geometry page which is the atria