Musical Idea 31: Reverge
05.10.2014 § Leave a comment
In the Anti-Staticism entry we looked at a situation where two pulses that together — by keeping rates that are in simple ratios with each other — make a polyrhythm, then diverge by gradually changing their rates, finally converging again on a new polyrhythm as their rates stop changing at points in a new, different simple ratio with each other. We could refer to the period during which the two pulses are between these states of polyrhythm as the verge: between divergence and convergence.
The idea of this chapter is that the verge is a blessing in how much flexibility it affords us.
In terms of form, you can take as long or as short as you like with the verge. One pulse stream can arrive at its destination rate far earlier than the other. A pulse stream can even backtrack for a bit, I mean, if it ultimately has to end up faster, going slower than it used to be going at some point during the verge.
However, there’s something even more critical on the level of counterpoint. The verge presents a wonderful opportunity to subtly realign them. That is, you don’t even have to have the two streams end up in a different rate against each other, for this divergence and convergence to allow you to offset them in a different way than they were before. And importantly, because the scale of time within each repetition is nothing compared to the scope of the time it takes for the process to occur over, we can adjust rate of the rate change ever so slightly to get it exactly how we like. And supposing what we’re dealing with here are more complicated than mere pulse streams, then this is even more powerful for reorienting melodies or rhythms complicated in and of themselves.
Verge realignment, then, for short, is reverge.
Here’s our example. Two identical pulse streams, going simultaneously — thus the initial polyrhythm is essentially a monorhythm — but then one begins to speed up while one slows down. They approach the point where the first is going at 3/2 its original speed, and the slower is going 3/4 its original speed. That is, in the second polyrhythm, the now faster pulse stream is going twice as fast as the slower, striking twice as often. We could say that if the pulse streams started out striking every 3 atomic units of time, then now the faster one is striking every 2, and the slower one is striking every 4.
The simplest assumption might be that we would align the new polyrhythm so that the two pulse streams coincide with each other, so that every other of the fast pulse stream’s strikes is doubled by one of the slow pulse stream’s strikes. But in reverge, however, we can align them however we want! Suppose we offset them so that the slow pulse stream’s strikes fall exactly equidistant between two of the faster stream’s onsets (every other space between two of the faster’s strikes would be empty). What we would hear now then would be is — well, let’s come up with a system for describing it first. Let’s count by the aforementioned atomic units of time, refer to one of the faster stream’s onsets as F, one of the slower stream’s onsets as S, and a durational cell containing no onset as a rest and use an underscore for it. So the new polyrhythm would sound like: F, S, F, _, F, S, F, _, F, S, F, _ … and so on. The repeating set of interonset intervals we’ve arrived at is 1, 1, 2, 1, 1, 2, 1, 1, 2 .
On the other hand we can impose structure on the verge. If we aesthetically dislike the looseness of the period of disalignment, we could find a rhythm that works for both the old and the new polyrhythm, and have that persist in the background from the old, through the verge, and into the new. That way, the timing of the verge is constrained ever so slightly: it at least has to conform to a multiple of one of that third bridging rhythm’s pulses.