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.
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?