Musical Idea 29: Rhythmic Circularity

04.19.2014 § 1 Comment

This idea is the partner of pitch circularity. The horizontal to the vertical. Where in pitch circularity the illusion of an infinitely rising or lowering pitch is achieved, in rhythmic circularity the illusion of an infinitely speeding or slowing tempo is achieved.

And I’m not just talking about stuff like what I did in my song M’Aidez, where I metrically modulated repeatedly until I reached a quarter note 256/243rds the length of my original, masking that with a gradual tempo change. That’s a thing, too, but it’s not rhythmic circularity.

It is achieved using the same basic mechanism of sneakily fading out some things while sameltimeously sneakily fading in others. In the case of pitches, it was sneaking in a lower version of whatever was getting too high, or vice versa. In the case of tempo, it is sneaking in a faster version of whatever is getting too slow, or vice versa.

For example, start with a waltz: one downbeat, two upbeats. It’s slowing down. Observe that a waltz four times faster in speed aligns such that downbeats and upbeats match:


Therefore, if by the time the waltz is moving four times slower, if these silences have faded in to become the new up and downbeats, we’ll be right back where we started.

More fun and advanced possibilities are certainly there. Suppose we have a pulse following this pattern: strikes once for duration one, then twice for duration two each, then thrice for duration three each, etc. (Credit due to Deftones for their song Poltergeist, which inspired this idea with a 7/4 riff x–x–x–xx-x-). It would look something like this:


There’s nothing necessarily distinct about the sounds of the strikes labeled “1” and those labeled “2”, “3”, etc. — I’m just labeling them by their group for clarity.

Now suppose that once we reach the 5’s, we layer another version of the same thing on top, five times slower, like so:


Now let’s add a subtle twist. We’re going to consider the durations underneath, even though they’re changing, getting bigger and bigger, bigger than 6 even, through 7, 8, 9 — yes, we’re going to consider these to be the units for the numbers on top. Like:


Originally our 3’s were three halves as long as our 2’s (naturally), but now they’re even longer — they’re 3/2 * 6/5ths longer, 9/5ths.

Except that actually that’s just the first 2 3’s, which use up the 6’s. The third 3 uses 7’s as its resolution, so it’s 7/6ths as long as the other two 3’s. The other four 7’s get used up by the first 4, the 8’s get used up evenly by two 4’s, the 9’s evenly by the final 4 and the first 5, and the 10’s evenly by the next two 5’s. The pattern ceases lining up conveniently at 11 (next time it’ll match up is 17 on the 6th 7, then 20 on the 6th 8… not sure after that!), so that’s where we’ll end it, at 10. Like so:


In other words, if we look back at our very first pattern, we realize that our 2 was not exactly twice the length of our 1, even though both were inside the 5’s resolution, because the 5 was itself subject to a deeper layer’s resolution, so the first 1 is actually 45 long while the first 2 is 100 long. As for the second 2, I suppose that’s up to you whether you’d prefer to stay in 10 or move to 11 to stay; I think I’d like the second 2 to be 11/10ths the length of the first, myself.

Well, now for the circularity, huh? If during each time you make it from 1 to 5 you’ve sped up 5x in tempo, you’ll be right back where you started. Simple as that. It should somewhat remind you of things we saw back with tonal movement — while the first 5 will be the same length as the first 1, even without the counting process helping us out, we’d still understand it as a 5 just because of our ability to feel the ratio of the duration to the 4 previous to it.

I’d recommend fading out as you approached the 9 and 10 so that those sneak out nicely. To compliment this, you might want to add some extra stress to the first number in each set. Heck, you could even keep going past 10 if you wanted to continue at least until you hit the next 1, that is, if you wanted three layers at once and didn’t mind the dis-alignment of these extra-stressed strikes from their upper layers.


§ One Response to Musical Idea 29: Rhythmic Circularity

  • the idea that you’ve done the same illusion with both pitch and tempo is eminently cool, these two are just different modes of detecting frequency, for pitch we detect frequency in the continuous classical physics mode, the summation of the waves, while for tempo we detect frequency in the discontinuous quantum mode, the segregation of each wave. if you can will you make a sound clip of the tempo effect, I’d love to hear it!

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