Equivalency of tempos

Object To Be Destroyed
by Man Ray

A rhythm issue I've been thinking about is the equivalence of tempos and their halves and doubles. I was wondering how small a range of tempos would cover the entire practical range of performance tempos. A mathematically minded individual could probably figure it out in a second, if he knew anything about music. I checked, and he doesn't, so I had to actually think it through myself.

The answer is 52-100, which includes sixteen standard metronome markings:

52 54 56 58 60 63 66 69 72 76 80 84 88 92 96 100


Let's walk through it:

Standard metronome tempo range: 40-208
Before digital metronomes, that's what they used to mark on all metronomes. It's a realistic practical tempo range for most music.


Tempo range in actual performance: 25-400
At least, there are examples of recorded music in approximately that range. Tempos from 200-280 are common in jazz, tempos from 280-400 are increasingly uncommon. Quarter note = 400 is an extreme tempo, and is very rare. Let's consider that the outer limit of what a very ambitious jazz drummer will ever be asked to perform. We can have a conversation another time about whether a 400 bpm pulse can even be considered a “beat” in any meaningful sense.

You can decide for yourself how to approach very slow tempos. Dig into Shirley Horn's recorded works to get an idea of the practical lower tempo limit in jazz.


Traditional standard bpm values for mechanical metronomes: 
40 42 44 46 48
50 52 54 56 58
60 63 66 69
72 76
80 84 88
92 96
100 104 108
112 116
120 126
132 138 144
152 160 168
176 184 192
200 208

A total of 39 markings. Note that if we halve the values from 40-76— 80 and above are doubles of lower values— they increase in single bpm increments from 20-30, then 1.5 beat increments from 30-36, then a two beat increment from 36-38.


That's the answer: 40-76
We can derive all of the values above by doubling the values from 40-76. I've extended that to cover our entire range up to 400 bpm, or 54 markings:

40 / 80 / 160 / 320
42 / 84 / 168 / 336
44 / 88 / 176 / 352
46 / 92 / 184 / 368
48 / 96 / 192 / 384
50 / 100 / 200 / 400
52 / 104 / 208
54 / 108 / 216
56 / 112 / 224
58 / 116 / 232
60 / 120 / 240
63 / 126 / 252
66 / 132 / 264
69 / 138 / 272
72 / 144 / 288
76 / 152 / 304


More practical answer: 52-100
Most of us don't play or listen to a lot of tunes in the 40 bpms— it's not real familiar terrain, musically. The 52-100 range is much more common in day to day usage. Double everything twice, and half-time the tempos from 80-100 to get the metronome range plus the faster jazz tempos.


For slow-click practicers
Working with a slow click, regardless of the actual tempo you are practicing, is an extremely effective way of developing your time, so here are the 40-76 tempos halved.

20-30 (1-bpm increments)
31.5 33 34.5 36 38

Most metronomes won't let you use decimal points, so you'll probably have to get these by using the 40-76 numbers, and setting the device to give you downbeats every two beats, and then silence the quarter note pulse. If you're really sick in the head, you could do the 10-19 gamut by setting it do give you downbeats every four beats, and silencing the quarter notes.


Conclusion
So, the real range of tempos is fairly small, if you think in terms of this matrix-type concept. Being aware of it may help you structure your practice, and improve your concept of time and rhythm overall.