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I am interested in the relationship between frequency and tempo, both of which measure the same thing (repetitions per unit time) for different ranges (units of time).

Are there any musical pieces that experiment with this concept?

As an example of what I mean, we can work out the tempos that match A:

A4 = 440Hz
A3 = 220Hz
A2 = 110Hz
A1 = 55Hz
A0 = 27.5Hz
A-1 = 13,75Hz
A-2 = 6.875Hz
A-3 = 3.4375Hz
A-4 = 1.71875Hz
A-5 = 0.859375Hz

A-4 * 60 (seconds per minute) = 103.125 BPM and
A-5 * 60  = 51.5626 BPM

So if we had a sampled A4 and kept transposing down by an octave, 8 octaves later it would be at 103.125BPM.

OR

If we had a sample of something played at 103.125 BPM and we played it on a sampler at increasing octaves, it would eventually be tuned to an A. At least that's what my suspicion is...

Are you aware of any pieces of music that play with this idea?

How does temperament complicate things?

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    Adam Neely did some videos that explore the effect. I think Stockhausen also used it in some compositions, but I forgot which. – leftaroundabout Aug 26 '17 at 9:32
  • @leftroundabout Thanks. I'm surprised you didn't put this as an answer because it was exactly what I was asking for. – Schizomorph Aug 26 '17 at 11:18
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Since you've said this:

If we had a sample of something played at 103.125 BPM and we played it on a sampler at increasing octaves, it would eventually be tuned to an A. At least that's what my suspicion is...

Are you aware of any pieces of music that play with this idea?

There's an entire subgenre of electronic music that plays with the idea of speeding up atonal samples so fast they become musical tones. It's called extratone. It doesn't have its own Wikipedia article, but the Wikipedia article on its super-genre, speedcore, puts it like this:

When a song reaches 1000 bpm, the music is known as extratone. However, when beats are in the range of 1000–1500 bpm the individual beats become indistinguishable, and turn into continuous tones.

You can find some extratone songs on YouTube, and they typically string together and speed up drum beats so fast that they sound like notes with strange timbres.

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