The Lydians

The Simpsons’ theme song, by Danny Elfman, isn’t exactly pop, rock, or jazz, but it obviously has a clear connection to pop culture, so here it is. Sorry for all the errors in the transcription, especially in rhythms.

One of the defining characteristics of this piece, in terms of its sound world, is that it is written in the Lydian mode, a major scale with #4 (“fi”). (At the beginning, it’s C Lydian.) And part of the Lydian mode’s characteristic sound, in turn, is the tritone between its “color note,” #4, and its tonic. Elfman embraces this awkward interval and distributes it generously throughout the texture, most obviously in the bass’s alternation between 1 and #4, which is clearly supposed to sound like a warped version of the more common 1-5-1-5-1-etc. bass line. But it’s also highlighted between the first and third notes of the melody in m. 7, as well as between that first note and the lowest note in m. 9, and of course in the opening two notes of m. 2, plus #4 is emphasized in the upper-voice ostinato.

The piece several times modulates to new tonics, always taking the Lydian mode along for the ride. And here’s my favorite aspect of how Elfman uses the tritone/#4/Lydian sound world: the chord that prepares the modulation each time, circled in the score above, is made up of two tritones. In m. 10, for example, at the end of the measure, the right hand has both a C-F# tritone and an E-A# tritone.

In traditional theory, this chord (which incidentally fits in a whole-tone scale) is often called a “French augmented sixth.” It usually works as pictured below in C major, resolving to a dominant chord with very specific voice leading.

In the theme song, instead of the outer voices resolving outward to the dominant, they resolve outward to a new tonic–not an unheard-of resolution. This is a tritone substitution for the dominant seventh chord, since it shares 4 and 7/fa and ti with that chord. In the example below, E and A# are fa and ti in B major. The graphic below shows the resolution in mm. 10–11.

But the modulation, which sounds almost the same in each case, is down a half step in mm. 10–11 and down a perfect fifth in mm. 18–19. What’s going on here? This chord is a symmetrical chord, so it can be rearranged so that a different pair of outer voices emerges.

The way the chord would resolve if it worked just like mm. 10–11 (I know, nobody wants to resolve to A-sharp major):

Here I’ve moved the B and D# up an octave and respelled the other notes enharmonically to allow a resolution to E major:

In m. 19, Elfman just resolves the chord as if it had been rearranged this way, facilitating the different modulation.

A few more interesting aspects–the piece “normalizes” the oom-pah accompaniment in m. 19 to 1-5 instead of 1-#4; briefly in m. 23 the piece moves to a whole tone scale, another one that emphasizes tritones (every 4th in the whole tone scale is a tritone); and in m. 25, two measures after the transcription ends, a direct modulation brings us back to a C tonic, an important formal moment, just as we arrive in the animation at Lisa’s band practice.

All of this contributes to this piece’s quirkiness, cleverness, and maybe even catchiness, and it’s been a fun one to dig into.

Update: Wikipedia, the source of all knowledge, tells me this song is actually in the “Acoustic” scale, major with sharp 4 and flat 7. I suppose–the A# in m. 10, for example, could be respelled as B-flat, C’s flat 7. But it’s hardly emphasized. I like Lydian better.