Pulse to Pitch, Chapter 1

I’m teaching a class for my daughter’s homeschool community in which we explore some of the relationships between music and math. As part of that process, I began making these videos. This set of five “movies” shows the transformation of pulsing single sounds into pitches through the process of repeated acceleration.

Over the next few weeks I’ll be posting as complete a set of the harmonic intervals as I can manage, all derived from polymetric superimpositions of click tracks in various tempi.
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This video starts with a 60 mm click track and accelerates it repeatedly by a factor of 4: 1 beat per second / 4 bps / 16 bps / 64 bps / 256 bps / 1024 bps. The transformation of pulse to pitch is very clear.

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Instead of a click track, this video uses a bilabial fricative to provide a more timbrally complex starting sound. It’s moving at approximately mm60, and I accelerate it repeatedly by a factor of 4: 1 beat per second / 4 bps / 16 bps / 64 bps / 256 bps / 1024 bps. The transformation of pulse to pitch is clear, but the complexity of the original sound makes for a somewhat “fuzzier” pitch identity.

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Instead of a click track, this video uses handclaps to provide a more “organic” starting sound. The claps move at approximately mm60, and I accelerate them repeatedly by a factor of 4, from roughly 1 beat per second to 4 bps, 16 bps, 64 bps, 256 bps, 1024 bps. The transformation of pulse to pitch is clear.

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Instead of a click track, this video uses a low-register piano tone (C#) to provide a tonally complex starting sound. The impulses move at approximately mm60, and I accelerate them repeatedly by a factor of 4, from roughly 1 beat per second to 4 bps, 16 bps, 64 bps, 256 bps, 1024 bps. The transformation of pulsed pitch to pure pitch is clear (by the time the signal is accelerated 3 or 4 times, the relevant portion of the sound is no longer the original pitch, but the “attack” of the piano note).

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Instead of a click track, this video uses a low-register piano tone (C#) to provide a tonally complex starting sound. The impulses come more slowly than the previous default tempo of mm 60. As I accelerate them repeatedly by a factor of 4, the transformation of pulsed pitch to pure pitch is clear. By the time the signal is accelerated 3 or 4 times, the relevant portion of the sound is no longer the original pitch, but the “attack” of the piano note — note that the final pitch at the end of the movie is quite different from that at the end of the previous video!