Six Degrees of Metric Modulation
A beginner's introduction to exploring music's lattice - Part V
Straight to the point today (a video👇):
This is part V of a deep dive into the lattice. What’s the lattice? Jump to the beginning.
Fun! What was that point again?
Prolific and ubiquitous Hollywood icon Kevin Bacon has a band. It’s called “Bacon Band.”
Just as we can find a path from anyone in Hollywood to Kevin Bacon via a series of not more than six films (“Six Degrees of Kevin Bacon”), a composer or DJ can also find a path from any tempo to any other — via a series of proportional tempo changes on the lattice.1
In the video above, we’ve done Tears for Fears’ Everybody Wants to Rule the World, which is at a tempo of 112 BPM…
… which is in a 3:2 ratio with drummer Donovan Miller’s2 cover of same,
… which is in an 8:7 ratio with Bob Marley’s I Shot the Sheriff,
… which is in a 5:4 ratio with John Phillip Sousa’s The Washington Post,
… which is in a 3:2 ratio with Weezer’s Undone (The Sweater Song),
… which is in a 5:4 ratio with The Bee Gees’ Stayin’ Alive,
… which is in a 3:2 ratio with Tom Petty T-Shirt, at 150 BPM, by… Kevin Bacon.
There are surely more direct routes, but this example would give Everybody Wants to Rule the World a “Bacon Number”3 of six.
Sorry, ridiculous. Moving on:
Tempo changes can happen suddenly or gradually, but those aren’t the only two options. One extremely effective and underutilized way to change tempos is via metric modulation.4
Metric modulations are awesome. They also get a seriously bad rap. The idea is not remotely as complicated as people make it out to be5 — it’s simply the technique of changing from one tempo to another via dovetailing them together. One tempo starts before the other stops, and there’s a moment of delicious ambiguity where the listener has the joy of experiencing the sensation of switching teams.
That’s really it. Here’s a freaky one from my own catalog6:
Two tempos transition smoothly via a brief overlap (starting at around :18).
In our Kevin Bacon example I’ve dovetailed the metronome sounds on top of each other, creating metric modulations in the spaces between each song. But when a composer incorporates dovetailed tempo changes intentionally into the fabric of the material, it creates a sensation for the listener that is simultaneously compelling on both an intuitive and intellectual level — it’s something to “feel,” but also something to “figure out.”
For a concrete and beautiful example of just how interesting music can be with more fluid, proportional tempo changes, I turn to the 2015 album Dysnomia by the trio Dawn of Midi:
Dysnomia
This music is a Rorschach test. I would love to connect LEDs to the brains of five different people and compare their internal metronomes over the course of its intense forty-seven minutes. At any given point there are often several interpretations of tempo possible, and several places that might be perceived as the starting points of its small- and large-scale cycles of material.
Dysnomia is meticulously composed, with no role for the type of improvisation found in other music based in repetitive processes (such as Steve Reich’s Music for 18 Musicians, Philip Glass’s Music in 12 Parts, or even the West African Ewe drumming from which Dysnomia draws much of its material). The length and proportion of its form is set in stone. The group toured it for years, playing it note-for-note every time.
And yet, although the group has stated that they are deliberately challenging culturally ingrained instincts with regard to tempo and rhythm perception, it never feels as though there is a “right answer” to be found, but rather many possible subjective personal interpretations.
Below is one example, a visualization of the way my brain hears one of the metric modulations. This isn’t meant to explain or “analyze” anything about the piece itself. Rather, this is an analysis of one person’s perception of the tempos, and where they change:
That there can be different interpretations possible of the same music, and that they each reveal something physically, intellectually, and culturally about the listener is one thing that makes this record so beautiful.
I highly recommend taking a forty-seven minute break from reality and seeing how it affects you.
But why the lattice?
Once you accept metric modulations into your life, the lattice is how to visualize them: a map that can show you the way from one tempo to any other.
You might wonder, why not just arrange tempos from slow to fast on a line, and call it a day? What could be clearer than that? For example, here are a several very nice tempos, in “order:”
They seem organized. That is, until I want to know: how do I change from one to any other? This arrangement implies that changing from 60 to 72 is done by somehow just “adding 12 BPM”… how would I add or subtract beats per minute? Our perception of tempo doesn’t work that way. It would involve perceptual guesswork. Even if I guess, how could I confirm whether I got it right?
What I need is to play tempos A and B together — let them hold hands for a bit. Once tempo B is established, their proportions will sync. Then tempo A can let go and disappear. That’s a metric modulation.
This requires knowing what proportions are involved. And that’s where the lattice comes in — it’s an isomorphic visual map of those proportions:
These tempos map to a simple two-dimensional lattice: all blue lines are 3:2 proportions, all red lines are 5:4. 7
We now see a path from tempo to tempo via proportional relationships, which are what we can actually perceive and work with in real-time.
For example, if we metrically modulate one step “up” and one step “left,” we find our way from 108 bpm to Bacon:
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I’m operating with an assumption of universal familiarity with “Six Degrees of Kevin Bacon,” a parlor game based on the premise that actor Kevin Bacon is so ubiquitous and prolific that you can connect any other actor in Hollywood to him via not more than six movies or commercials.
Check out Donovan Miller’s full incredible take on the #tearsforfearschallenge as well as other awesome drumming videos on his youtube channel.
Also there’s, this guy, who appears to have created the academic urtext on the challenge.
The shortest path to Kevin Bacon is that actor’s “Bacon Number.” Find your favorite star’s Bacon Number at https://www.oracleofbacon.org
Reader Sam reminds me that they are often called “Tempo Modulations,” and do you know what. That’s way better actually. It’s not the meter that’s modulating, it’s the tempo.
Metric modulation as a compositional technique tends to be associated with highly academic music of the twentieth century. Sadly (ironically?), in the midst of highly complex compositions, these moments can be missed unless you are actively following on a score… and they are rarely very groovy.
But I do enjoy the March for solo timpani by Elliott Carter, which cleverly plays with the idea of “march tempo,” via several clearly articulated metric modulations, and is a staple of college percussion auditions everywhere now and forever.
This is The Help You Need from my album Stay the Same, out one year ago today!
If you prefer to think in terms of standard musical notation, a step to the right is a quarter note triplet, and a step up is a quarter note quintuplet… but the important point is that each dimension represents a unique prime number: here we have 3 in blue and 5 in red.
Also, as is the common practice, I’ve “collapsed” the dimension representing 2, because all multiples of 2 could be perceived as the same tempo. But you could easily represent 2 on a third dimension.