Applied some concepts in my gesture synthesizer to and older project of mine called seqvm, which is like if a sequencer wanted to also be a virtual machine. Now it can also create gestures: continuous breakpoint line segments running at audio rate with arbitrary slope and relative time, clocked by an external audio signal.

It's actually pretty neat how simple this algorithm can end up being.

The secret sauce here is the clock signal used: a phasor, or signal that is a periodic linear ramp going from 0-1.

Any unit generator can take a phasor as input and analyze and resynthesize a new phasor without knowing anything about the frequency. The cost of this is (only) a unit sample delay, which is constant.

This resynthesized phasor can be scaled by some factor. This allows the phasor to be twice as fast, or twice as slow etc. This will dynamically adapt to any tempo changes in the phasor signal. The factor that controls this is called the scaling modifier, or modifier.

A phasor signal can be used as an alpha value to interpolate between 2 discrete points. If you don't do anything to the phasor signal, this produces a linear line. But you can apply all sorts of functions on this signal to change the slope.

Coordinating the current/next points with the scaling modifier gets you a sequencer line generator controlled by a phasor clock signal. Aka a gesture.

And that's all you need.

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