CAUTION! THEORETICAL MUMBO-JUMBO AHEAD!

I've been playing around with something that may be mostly useless musically, but is still pretty interesting theoretically. The thought occurred to me that there are thousands of different types of scales, but they all seem to share one thing in common: they repeat every octave. So I started wondering what would happen if they repeated at some interval other than an octave.

Here's on example I've been toying with:

...etc.

At first I was thinking of this as a scale that repeats every minor 7th, but then I started to see that it actually repeated every perfect fourth. There are only five different transpositions of this scale from the perspective of any given octave. But any transposition will match perfectly with the original key if it is placed in the correct higher or lower octave. You might have to play with this to see what I'm talking about.

Harmonizing in this weird scale is something quite mind-boggling. Naturally you'd have to throw all previous notions of harmony out the window. Octave doublings are out. Well, that is unless you do something like this:

In the above example, we hit a perfect octave every third note, and the other notes are major ninths. In the right context, this can actually be a fairly interesting sound.

Here's an alternate way of doubling:

This unusual version contains no octaves at all... only minor 9ths and major 7ths. It's conceptually closer to doubled octaves than the first example (average distance for "incorrect" notes are closer to a perfect octave), yet contains not a single consonance.

Why am I playing with this? I really don't know! It's a whole new world where only tremendous experimentation has yielded anything useable for me. Still, I'm a little obsessed by it at the moment, and thought I'd share the concept.

Has anyone ever worked with anything like this before?

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