09.22.2016 § Leave a comment

I recently stumbled across the factlet that every even ed2 contains the square root of 2 interval AKA the 600 cent tritone.

It immediately got me thinking about how therefore every multiple of 3 ed2 would contain 2^(1/3) and 2^(2/3) intervals, AKA the 400 cent major third and 800 cent minor sixth, respectively.

And every other even ed2 would contain the 2^(1/4) and 2^(3/4) intervals, AKA the 300 cent minor third and 900 cent major sixth, respectively. And its 2^(2/4) would reduce to 2^(1/2), reinforcing the already existing tone there.

And so forth.

As the count of equal divisions of your octave rose you’d introduce more and more new intervals, and reinforce existing ones. Of course every ed2 contains the root, so that would be the strongest, second only to the tritone. You could keep going further and further up, and your peaks of frequency would grow increasingly washed out, but never disappear. You’d be expressing the texture of divisibility through sound. And it would probably sound like a noisy devil.

Here is what that sounds like:

The root kind of dominates. So here’s an example with the root silenced, leaving the tritone as the strongest interval (though a tritone only through the implicit effects of the other frequencies, mind you):

Another thing that occurred to me you could do is center everything on the root, so everything up to 600 cents is above and everything beyond 600 cents gets shifted down an octave. They’re symmetrical around both 0 and 600 cents, anyway, so doesn’t really matter, just a different texture. (I randomly split the tritone between taking form on the upper end and the lower end):

However you slice it, it seems to come out like a cheesy 50’s sound effect, like a UFO or something. I suppose that’s not surprising because the effect is extremely primitive and would be just the sort of thing an early synthesizer could naturally pull off.

What I didn’t get a chance to do yet is some sort of shimmering of the constituting pitches, either by building them out of an organic sample, or by having waves of amplification flow through (perhaps according to ed in some manner). If you’re interested, here is the Github where I build this:


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