Answering the Dirty Projectors’ “Impregnable Question”

T he first seconds of the Dirty Projectors’ newest album speak volumes about what’s to follow. Dave Longstreth’s trembly hums at the open of “Offspring Are Blank” lay out the first of many “challenging harmonies” to follow (as various reviews delicately put it). The rhythmic puzzler “About to Die” follows, and next is the incomparably weird “Gun Has No Trigger”; it’s not until the fourth track that there’s some relief.

So Swing Lo Magellan isn’t lacking for things to talk about here. But for this first post in a long while (sorry!!!), I’ve just got a (comparatively) quick note about one of the simplest, most accessible songs on the whole record: “Impregnable Question.”

This album’s got a bit of a positive correlation between track length and musical complexity – and “Impregnable Question” is the second shortest tune. It’s very conventional, with none of the metric or harmonic twists that permeate the other songs. Instead, what’s interesting lies on a more subtle level: the relationship between the harmonies and the lyrics.

The structure of “Impregnable Question” is very simple, with just a twelve-measure progression repeated four times. That’s plenty of time, though, to establish one major musical theme: the denial of any traditional authentic cadence — that is, a sequence where the V chord resolves to the tonic. That’s the cornerstone of traditional “functional harmony,” the theory that each chord in any given key has a purpose, a “function.” The idea is that there are three basic major chords in every key: the tonic, or I, which is the starting and ending point for progressions; the sub- or predominant, or IV, which usually leads to the dominant; and the dominant, or V, which resolves back to I. V-I is the most common and traditional cadence there is.

But there’s no V-I motion anywhere in this song. Every V (here, E-flat major) instead steps down to D-flat, the IV. This thematic denial of any expected resolution is taken even further in the melody. Longstreth never even sings the leading tone, the seventh note of the scale that so yearns to resolve upward to the tonic. It’s the one scale degree that calls that strongly for resolution — but we never hear it.

Take a listen:

The chords:

   Ab                               | Db         Cm
01 If there is                      | ever the impregnable ques-
   Ab             Bbm               | Db            Eb
03 -tion of "Why?    What           | did or didn't pass?"
   Db            Ab                 | (Ab)
05 It would help to seek            |
   Db         Ab                    | (Ab)
07 comfort in destiny,              |
   Db        Ab        Bbm          | Dø7       Db
09 but I really don't. We don't see | eye to eye.    But I
   Ab        Eb7add4                | Db           Ab
11 need you,   and you're           | always on my mind

This expected-resolution-denial theme is driven home at the most dramatic point in the melody, right at the start of the tenth measure. Take another listen to the video – the first time is right at 0:29 (then again at 1:07, 1:42, and 2:16).

Longstreth sets it up by systematically lulling us with two slow-moving D-flat/A-flat pairings. “It would help to seek…” [pause] “…comfort in destiny…” then another pause.

But then he finishes that sentence with “but I really don’t,” and the melody suddenly moves on through a minor chord and down to the crucial moment. There’s no pause this time as he reaches down to the low F and swings back up to the high A-flat for “We don’t see eye to eye.”

The chord that hits on the first “eye” is called a “secondary dominant” – in functional harmony terms, it’s a dominant chord poised to resolve to something besides the tonic (most often the V or vi). Here, it’s a half-diminished seven chord rooted on D, the tritone, one of the most most conspicuous notes he could choose in the key of A-flat major (noted above as Dø7). In most worlds, you could expect this chord would resolve to E-flat. But in “Impregnable Question,” nothing resolves the way it “should.” Just like all the other dominant chords, this one moves to IV instead.

I should note here that it is not at all uncommon for a V chord to resolve to a IV, or even for a V or vii/V (a secondary dominant of V) to resolve to IV. It’s such a common device that there’s a term for it, based on the whole functional harmony theory mentioned earlier, and the standard progression I-IV-V-I. That progression’s reversal — I-V-IV-I, or a retrogression — appears in probably thousands of pop songs.

In this case, however, it’s notable because of a great marriage of music to lyrics. The opening lines are a direct call to disregarding the seemingly inevitable: “If there is ever the impregnable question… it would help to seek comfort in destiny, but I really don’t.” And immediately after that, Longstreth sets up the song’s central tension: “We don’t see eye to eye, but I need you, and you’re always on my mind.” The second verse repeats that line, driving the refrain home.

But in the third and final verse, Longstreth answers the tension: Rather than the conflicted “we don’t see eye to eye,” instead he sings “What is mine is yours in happiness and in strife. You’re my love, and I want you in my life.” In other words, there may always be tension, be it in music or relationships. But Longstreth’s narrator refuses to let the tension control him; his dominant chords obstinately resolve to IV, and he’ll dedicate himself to his love regardless of any discord. Most rewarding to us, the listeners — the music cued us in to that response well before Longstreth states it outright.

Just one enjoyable moment of many on this excellent album. More to come!

Becky Sullivan, with special thanks to Nick Curry

Songs cited: The Dirty Projectors, “Impregnable Question,”  Swing Lo Magellan, © 2012 by Domino Records, WIGLP272.


Cassette Theory gets the official thumbs-up

By the way: no, thank you! “Source Decay” is one of my favorites of all time.  All the best, Mr. Darnielle.  (You can read that post here.)

– Becky Sullivan

Expectation and surprise: a primer from the Mountain Goats and the Flaming Lips

T he way we hear music is defined entirely by what we expect to hear.  These expectations can come from anywhere, including before music even begins – if it’s a late Romantic opera, my ears are primed for something a lot more harmonically complex than a mid-80s pop song.  That’s a no-brainer; Richard Wagner’s disparate tonalities would be way more surprising in a Journey tune than they are in Tristan und Isolde.

More simply, though, our ears create expectations based on what they’re already hearing.  So, when a song starts in one key, you can reasonably expect it to continue in that key.  When you hear a certain four-chord progression a few times, you expect that progression to continue.  When your brain hears a downbeat every four notes, it expects the song to stay in 4/4.

But when one of those expectations goes bust – say an F-sharp appears in the key of C major, or the chord progression abruptly changes – well, we notice it.  That’s the reason it sounds weird to hear that F-sharp, or for a measure to suddenly add a beat.  There’s some research out there that posits that this expectative setup and subsequent surprise could be a reason why some music seems more interesting than others.  In other words, our brains are pros at being efficient; they pay less attention to things they expected to happen, so that when something unexpected occurs, it sticks out much more.  And because of that, we actually pay more attention to challenging music than we do extremely simple songs.1

I n other words, the setup-and-surprise shtick is rewarding to hear.  And it appears often in pop music, much to my enjoyment, and hopefully yours too.  Let’s start with the chorus of the Mountain Goats’ “No Children” – but be sure to listen to the first 1:10 or so, so that you’re properly primed when the good stuff hits.

A chord/lyric transcription:

01 (Dbm)   (Gb)        
02 (Dbm)   (Gb)
03 (Gb)    (Ab)        
04 (Db)
05 (Db) I hope that our few re- (Ab) maining friends
06 (Gb) give up on trying to (Db) save us.  I
07 (Db) hope we come out with a (Ab) failsafe plot to piss
08 (Gb) off the dumb few that for- (Db) gave us
09 (Db) I hope the fences we (Ab) mended
10 (Gb) fall down beneath their own (Ab) weight... and I
11 (Db) hope we hang on past the (Bbm) last (Ab) exit.  I
12 (Gb) hope it's already too (Ab) late... and
13 (Db) I hope the junkyard a few blocks from here
14 (Bbm) someday burns down... and
15 (Gb) I hope the rising black smoke carries me far a-
16 (Gb) way, and I never come (Ab) back to this town a-
17 (Gb) gain. In my
18 (Ab) life, I hope I
19 (Db) lie, and
20 (Bbm) tell everyone you were a good wife, and I hope you die,
21 (Db) I hope we
22 (Ab) both die.
23 (Db)
24 (Dbm)   (Gb), etc., return to verse..

Hopefully you had a moment of surprise at the end of that chorus.  It’s really a clever bit of songwriting on John Darnielle’s part.  The lyric, obviously, is a bit shocking.  “I hope I lie and tell everyone you were a good wife” is frank enough, but “I hope you die, I hope we both die” is, well, a very strongly-worded statement.  That alone would probably grab a listener’s attention.

But a major part of what makes that line work so well is the unexpected way the chorus is phrased – that is, the way its melody and harmony are structured.  Up until this point in the song, everything has been in groups of two.  Each line in the verse is two measures long, demarcated by the initializing “I hope”s.  And even the chorus opens up like this – the G-flat measure is paired with an A-flat measure, followed by D-flat/B-flat minor, and D-flat/A-flat.  Each line of the chorus comes in a pair: “In my life / I hope I lie,” “and tell everyone you were a good wife / and I hope you die.”

Until, that is, the stunning “I hope we both die,” which Darnielle declines to pair with a second line.  Instead, it simmers – and that simmering takes place over a single measure, not a pair.  Both antecedents (the lyric, the final chorus measure) come without a satisfactory conclusion, and so the line lingers in your mind for an awkward moment before the song returns to its opening chords.2  And of course, I probably don’t have to draw you the connection between the unsatisfactory conclusions of the music and what we can probably assume was an analogous experience in Darnielle’s life.  [Edit.: John Darnielle tweeted this to me a few hours after I posted this: “No analogous life events tho – all fiction in that song!”]

O n a happier (and less uncomfortably candid) note: “It’s Summertime” by the Flaming Lips.  I don’t want to spoil anything, so without further comment, listen to just the opening just-under-five seconds:

This intro is a great example of how good our brains are at building expectations.  It’s only four seconds, but that’s enough to establish a meter in the mind of the listener.  We hear a group of sixteen notes, the first of which is clearly accented, and then a second group of notes, apparently identical, begins.  There are some fancy terms (namely, “metric projection”) for how our mind hears this.  In effect, the idea is that when our brain hears 1) a unit of time, followed by 2) the beginning of a second unit, it expects the second interval to equal the first, and for repeating identical intervals to continue indefinitely.3  On top of that, sixteen is a very easy number of beats for our Western ears to understand; it’s four groups of four – so usual, in fact, that they even call it the “common time.”  So when the second group begins, there’s little doubt in our minds what the meter is, and more importantly, where the downbeat is (at the beginning of the song, and then there’s another one sixteen sixteenth notes later, of course).

But Wayne Coyne ain’t gonna let us off so easy.  Play on!  The first ten seconds or so is plenty:

Wait, what?  Pause and listen again, if you need to.  Here’s what happened (pretend the Os are the notes):

         band should join here -->|X
band actually joins here ->|X (???)
in retrospect, it was actually this:
  (band joins on downbeat) |X        

WTF, Wayne.  After taking just enough seconds for the bass guitar to create the expectation of a certain meter, the rest of the band crashes the party a beat and a half early.  It’s disorienting!  And the bass even sticks with the misaligned downbeats until the lyrics come in.  It rights itself temporarily at about 0:46, but the misalignment – a form of metrical dissonance called “displacement dissonance” – comes back for good at 2:05.4

This song actually asks a philosophical question about expectation and music that I love to think about.  Which is more important: what you’re experiencing at a specific moment, or what you know about that moment afterward?  Tell me what you think.  I have my own thoughts, of course, but I’ll expound on them later.

Becky Sullivan

1 On the other hand, there’s the fact that your brain gives itself a dopaminergic pat on the back every time its predictions come true, which is why it can be rewarding to hear a song you already know.  In reality, there’s probably a sweet spot between total randomness and bland repetition.  NPR’s blog 13.7 speculated a bit back in February about this “Goldilocks zone,” though it doesn’t delve in very far.

2 The word “antecedent” carries some extra implications when it comes to music theory, but those can largely be ignored in this instance. I’m referring simply to the fact that this is a unit that inherently carries the expectation of a second, complementary unit.

3 This philosophy (and the term “metric projection”) courtesy of Christopher Hasty and his book Meter As Rhythm. A thick but fantastic read.

4 The term “displacement dissonance” comes from an unusual monograph on meter by Harald Krebs called Fantasy Pieces: Metrical Dissonance in the Music of Robert Schumann. Instead of the usual dry music theory fodder, Krebs imagines a lively conversation between Schumann and a friend at a coffee shop where in between cups of joe and mid-afternoon desserts, the two posit a slew of interesting ideas about meter and rhythm.

Songs cited:
  • The Mountain Goats, “No Children,” Tallahassee, © 2002 by 4AD Records, CAD 2215CD. 
  • The Flaming Lips, “It’s Summertime,” Yoshimi Battles the Pink Robots, © 2002 by Warner Bros. Records, 9 48141-2.