Pigeons

What is the Pigeonhole Principle?

This applet generates two Pitch CV values at the Outputs, quantized using a given Scale and Root Note. The core mathematical concept is related to the Fibonacci Sequence, based on this most excellent video. Something about the way numbers behave in modular arithmetic being akin to a limited number of pigeonholes for an infinite number of pigeons...

How does the applet work?

There are two Pigeons (channels), independently triggered. They are each singing a note (a number representing scale degree) and have a certain number of holes they can visit (the modulus). When triggered, each one adds the current and previous notes together, divides by the modulus value, and uses the remainder for the next note. The pair of notes represents the coordinates of the current hole; your Pigeon is guaranteed to revisit the same holes eventually.

Pigeons are easily triggered - by the physical trigger inputs, internal clock pulses, or neighboring trigger sequencer applets (like ProbDiv).

The CV inputs change the modulus value for each channel, affecting the range of the generated melodic sequence. It is possible to cause both note values to drop to 0 (the root note), and your Pigeon will take a nap there. If that happens, you'll have to nudge it with the encoder, or maybe load a Preset with a MIDI PC message...