As part of Chiptune Chaos, I quite regularly write pieces that play around with key in weird ways. Sometimes they do this thing called modulating, which is when a piece changes from one key signature to another. It’s pretty common in pop music, in which the usual method is a key change up a half- or whole-tone; you can hear it quite clearly if you listen out for it, ‘cos it’s just the part where everything suddenly seems to lift up a bit and the melody’s just ever so slightly higher than it was, giving a feeling of triumph towards the end. That’s possibly the simplest (some might say laziest, but I don’t know that I’m feeling that uncharitable) way of doing it. My own methods have thus far been largely random, since I’m not very good at music.

Recently, I’ve been listening to Muse, a band I really enjoyed a few years ago and haven’t heard much of lately. Just decided to go back and have a gander at the albums I used to love; actually, I wonder if I might do a post ranking all their albums in order of how much I like them, but that’s beside the point for now. I’m finding that some of the songs I used to enjoy are no longer quite as compelling to me, but some others that I might have overlooked before now seem astonishing. In particular, ‘Take a Bow’ from the album Black Holes and Revelations contains perhaps the most ridiculous and impressive use of modulation I think I’ve ever heard.

Before we dive into ‘Take a Bow’, a few notes on key changes in general. As I mentioned, the most common in modern pop music is the ‘Truck Driver’s Gear Change’ (as it’s called by TV Tropes). That’s just hopping up a step or so for dramatic effect and staying there until the end. A more common idea used throughout classical music is the ‘circle of fifths’.

A quick run-down on what a key is might be in order here. Broadly speaking, the key of a scale or piece tells you how many sharp or flat notes are in that scale or piece (the sharp/ flat notes are the black notes on a piano; the white keys are considered ‘natural’). C major has no sharps or flats, so only uses the white keys. G major has one sharp, D major has two sharps, and so on; F major has one flat and B flat major has two. On the circle of fifths, G major is next to C major because it has one more sharp, and D major comes after that for the same reason. It’s called the circle of fifths because G is a ‘fifth’ interval (i.e. five notes in the scale away) from C, and D is a fifth away from G. So moving clockwise around the circle, you get one more sharp each time and move to a key a fifth away from the one before. (Going anticlockwise, you have one more flat each time and move to a key a fourth away. This is because a fourth is kind of the inverse of a fifth, in that G is a fifth up from C and C is a fourth up from G.) Moving to a key that’s adjacent on the circle of fifths to the one you were already in is easier than jumping elsewhere, because most of the notes in that key will be shared with the one before; there’ll only be one more or less sharp or flat, so it’s quite a nice smooth way of transitioning. I think I should probably try to make use of this in my Chiptune Chaos work, since I’m trying to move a little bit away from the overly chromatic jumble of notes that have marked my style so far and maybe get into something a bit more appealing and sensible.

The reason I bring all this up is because ‘Take a Bow’ changes key a total of thirteen times, each time moving to an adjacent key on the circle of fifths. It goes counter-clockwise, so one more flat each time and travelling a fourth (remember that counter-clockwise is an interval of a fourth, the inverse of a fifth), for the most part, with one small section in which the changes reverse direction before heading back the same way again. It’s a really astonishing piece of music in many ways: there isn’t really a verse-chorus structure as such and the song never sounds as if it’s jumping around, but it spends its entire duration slowly and gradually travelling until it reaches a completely different place to where it started. Each shift is almost imperceptible unless you listen out for it, that’s how smooth the transitions are. If the chord sheet I’ve found online is to be believed, it’s achieved by changing a single semitone to take one chord from minor to major and thereby change the entire key of the thing: the smallest possible change, one semitone, drives the song’s whole journey, a journey that takes it the best part of the way around the entire circle.

It’s a really smart song. Not that surprising, really; Muse are known for being pretty well-versed in musical theory and influences, with some of their songs including excerpts from Rachmaninoff and others. I think I’ll be trying to learn from it.