It’s similar to the Circle of Fifths, and relates to musical tempos, in beats per minute.
Let’s see some examples of metric modulations, using a simple drum beat.
A”3 over 2″ metric modulation moves us approximately 210°, or 7 notches on the circle, to the right. For example, from 60 bpm to 90 bpm, or from 90 bpm to 135 bpm.
The “2 over 3” modulation slows the beat down, for example from 120 bpm to 80 bpm, or from 90 bpm to 60 bpm. It’s the reverse of the “3 over 2” modulation, moving us 210° to the left.
This type of modulation moves us 150°, or 5 notches on the circle, to the right, for example from 60 bpm to 80 bpm, or from 90 bpm to 120 bpm.
The “5 over 4” modulation moves us approximately 4 notches to the right.
There’s math behind it, but I’m not going to bother you with it. You can work it out yourself. But that math tells us that a metric modulation to move just one notch is too complex to be practical. It would have to been something like a “16 over 15” or something silly like that. I can more or less do “3 over something”, and just barely “5 over something”. Similarly with jumping to the opposite side of the circle, 6 notches.
| Type of modulation | Tempo change (approx) |
| groups of 3 (from 4) | 5 notches faster |
| 3 over 2 | 7 notches faster |
| 2 over 3 | 7 notches slower |
| 5 over 4 | 4 notches faster |
| 4 over 5 | 4 notches slower |
| 6 over 5 | 3 notches faster |
| 5 over 6 | 3 notches slower |
Starting a new tune in the tempo you want
Metric modulations can be very useful when playing live. A common problem is when the band gets engrossed in one tempo, and it’s hard to break out of it. If left unchecked, the band might carry over tempo from one tune to the other.
If you’ve just finished a tune in 120 bpm and you want to start the next one in 80 bpm, you can do the “2 over 3” modulation in your mind and you’ll be in the vicinity of the tempo you wanted, without having to consult the metronome.
Maciej Bliziński 
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