Pitched tempos
A pitched tempo is a tempo that happens to be a valid (albeit extremely low) pitch in whichever tuning system the song's using.
Tempo is measured in BPM, beats per minute. Pitch is measured in Hz, cycles per second. There are 60 seconds in a minute. So BPM ÷ 60 = Hz, and Hz × 60 = BPM.
Given that a pitch is simply an audible frequency (in the range of about 20 to 20,000 Hz, or 1,200 to 1,200,000 BPM), and that a beat is simply a much lower frequency (in the range of about 60 to 180 BPM, or 1 to 3 Hz), you could argue that pitches and tempos are measurements of the exact same thing, frequency, just at different scales. By extension, chords and polyrhythms are also the same thing at different scales.
To use a specific example, A4 is 440 Hz. 440 × 60 = 26,400 BPM. Down 8 octaves (halved 8 times), that's 1.719 Hz and 103.125 BPM. So A-4 is 103.125 BPM.
You can similarly infer all the other tempos of ISO standard pitches:
| Name | Frequency (Hz) | Tempo (BPM) |
|---|---|---|
| F-4 | 1.364 | 81.850 |
| F#-4 | 1.445 | 86.717 |
| G-4 | 1.531 | 91.874 |
| G#-4 | 1.622 | 97.337 |
| A-4 | 1.719 | 103.125 |
| A#-4 | 1.821 | 109.257 |
| B-4 | 1.929 | 115.754 |
| C-3 | 2.044 | 122.637 |
| C#-3 | 2.165 | 129.929 |
| D-3 | 2.294 | 137.655 |
| D#-3 | 2.431 | 145.841 |
| E-3 | 2.575 | 154.513 |
| F-3 | 2.728 | 163.701 |
Making drill'n'bass
While such a claim may seem absurd and pointless at first glance, it might well have practical applications in music that blurs the line between rapidly triggering notes and turning that rapid triggering into a sound in its own right.
When you retrigger a sound at 64ths or faster, the rate of each new note becomes the pitch of the sound. This is known as a snare rush, a staple of drill'n'bass. In effect, sufficiently rapid notes become a form of oscillator sync, as they regularly reset the waveform they're drawing. The sound played becomes just the shape of the waveform, and the note length becomes its pitch, manually dictated for each and every cycle.
The sequencer's notes, purely through speed, become DCO clock pulses.
This is generally done at 64ths, 128ths, 256ths of a bar, and so on. Each doubling of frequency is an octave jump. Meanwhile, the beat lasts a quarter of a bar, so the tempo is four octaves down (four halvings) from the 64th's frequency. So whichever pitch the tempo is tuned to, all 64ths and doublings of it will be that root note at different octaves.
Quickly changing a sample's tempo
There's another advantage to using pitched tempos: you could sample a breakbeat, repitch it until it's 103.125 BPM, and tell your sampler its original pitch is A1. (Given that MIDI doesn't go down anywhere near as low as F-4, these can all be mapped out exactly 5 octaves up from their true pitch.)
Then, provided your song is in one of the tempos in the above table, you can make the breakbeat match it exactly simply by playing it at the appropriate pitch, without having to mess around in the menu with fine tuning its playback speed. When playing breakbeats in samplers designed for pitched instruments, this could genuinely save a lot of time.
In effect, you're moving your breakbeat-tuning work from each moment you import a breakbeat into your latest track, to the single moment you sample and save it first. Every time you re-use that breakbeat, even at different tempos, you're saving work and time.
Say, for example, you bought a sample CD of breakbeats. You want to use one that's at 91.941 BPM (maybe it's a sample of "Jimbrowski", in turn a sped-up sample of "Good Old Music"), and your track's at 120 BPM. That involves either figuring out some tedious maths, or doing a lot of fiddly work, finessing its tuning in the sampler while looping the bar in the MIDI sequencer. Either way, it's time away from being creative.
Now let's say you bought a sample CD of breakbeats that had already been tuned to play back at 103.125 BPM when you pressed A1 on your MIDI keyboard. Your track's 122.637 BPM, so you'd simply look up that your tempo is C, and press C2 on your MIDI keyboard. No messing around with fiddly retuning, and no accidental slight gaps in the loop. You can perfectly loop all your breakbeat samples in all your songs, without having to adjust their tuning, simply by sticking to those thirteen tempos.
Even more useful, if a cappellas were sung in the above tempos (even if the key they were sung in didn't match the tempo), they could be transposed to another key, and the song's new tempo would be easy to look up in the above table. These thirteen tempos could be a lingua franca for sampling.
Admittedly, you can start at any tempo and still transpose to a new one proportionally, but then you'd need to tabulate the new tempo from that arbitrary starting point. Using divisions of standard pitches would save a lot of work.
Knowing the sample's key
The above examples exploit the advantage of sticking to one of thirteen set tempos, but there's another advantage to be had if you also match the tempo's pitch with the main pitch in the sample.
If you're creating new samples, then you have the option to tune your snare drum to the tempo's pitch, and sing your a cappella in a key that has the tempo as its root pitch. That way, playing back the samples, whichever note you press on your MIDI keyboard dictates both the tempo and the main pitch.
Just as the standards of twelve-tone equal temperament and A440 ignored the potential complexity of pitches in order to enable musicians to easily co-operate and build upon each other's work, I think they could potentially do the same for tempos.
Electronic music making tables: BPM to milliseconds | DX21 guide | Interval | MicroVerb III guide | Pitched tempos | Pitches | S1000 page map | ST MIDI sequencer timeline | Transposing tempos
Fringe music making ideas: Pitched tempos
Music theory: Arpeggio | Block chord | Broken chord | Circle of fifths | Interval | Music | Pitched tempos | Polymetre and polyrhythm | Rest | Swing | Velocity