The general theory.
We experience frequencies in many varieties and forms. When we hear a tone or note that is pulsating at a frequency twice that of a lower pitch, it has such a similar quality about it that we call it the same note name. (e.g. A1 and A2)
This is a very basic fundamental of music theory or physics of sound. We call it an octave, Why? Well, best as I can figure, it comes from the number of distinctly different tones which occur between the 8th and 16th overtones in the natural harmonic series. Basically creating a natural harmonic 8-tone diatonic scale.
Though I don’t want to get too carried away on tangents here, I think it is worth reiterating that we experience vibrations in many ways and I find it interesting that the visual spectrum of light all happens within what I would consider an octave from the lowest wavelengths to the highest wavelengths. Meaning that the highest wavelength visible is not more than twice as fast as the lowest.
Similarly to how an octave is frequently considered the “same” note as the root tone, a tempo divided or multiplied by 2 is easily understood as a half-time or double-time feel. Easy to do, easy to feel.
Tempo tuning treats rhythm as the extension below the audible range. In that respect, a tempo can be treated as having a corresponding counterpart in the audible range. So, for instance the note A=440 (440 Hertz or cycles-per-second[cps]) has a corresponding tempo at 103.125 beats per minute.
Let’s do that math! 440/sec @ 60sec/minute = 26,400 cycles per minute (this is why I prefer using cps to Hertz, it is a more accurate title). Now, because we can consider any division or multiplication of a frequency times 2 to a given power as an octave we just need to divide by 2, eight times: 26,400/28=103.125. See, 103.125 beats per minute is truly 8 octaves below A440. Furthermore, it’s only about a pulsating 32nd note below the audible range.
I feel like it’s pretty straight-forward as a concept and I haven’t actually heard of anyone else doing this. Quite likely just because I haven’t researched it beyond coming up with the idea and working out the details. And maybe it’s not worth it, maybe there is no real-world benefit other than for me to have something to nerd on, but when I recorded the album “Tune to the Beat” and used this treatment for every song, I noticed an effortlessness to maintaining intonation, and a cohesiveness to the overall feel.
But I’m nearly certain that is all psychosomatic. 😉
If you’re interested in trying some of this out for some of your own projects, I built spreadsheets to run all these calculations for different keys and tempos and make the process a whole lot more streamlined. I intend to post those here in the future, but for the meantime, I could email it to you. Just hit me up.