Tag Archives: music theory

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):

|Oooooooooooooooo|Oooooooooooooooo|
         band should join here -->|X
   
|Oooooooooooooooo|Oooooooooooooooo|
band actually joins here ->|X (???)
                            
in retrospect, it was actually this:
Oooooooooo|ooooooOooooooooo|oooooo
  (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. 

The apoplexy over appoggiatura: an explanation

T his weekend, the Wall Street Journal tried its hand at music theory, and it wasn’t pretty.  (NPR ran a similar story on Monday’s episode of All Things Considered.)  In the article, WSJ writer Michaeleen Doucleff claims that “science has found the formula” to why Adele’s ballad “Someone Like You” makes everyone cry, and it’s not that it’s sad or Adele’s a badass or anything like that.  No, Doucleff says, it’s because of a marvelous musical device called an appoggiatura!  The appoggiatura, she claims, is that little ornament of the held-out “you” in Adele’s chorus “never mind, I’ll find someone like you,” where it dips down for a split second mid-note.  Take a listen:

Well, there’s something there, but it ain’t an appoggiatura.

And it wasn’t just me who noticed this error.  I’m not sure about the Wall Street Journal, but NPR received an onslaught of emails from outraged theory nerds like myself.  Yesterday, they aired a correction.  While it’s a step in the right direction, their composer-theorist guest (for various reasons) avoids a precise definition of appoggiatura and confusingly implies that other notes in “Someone Like You” are appoggiaturas when they are, in fact, not.1

An appoggiatura – forgive the cumbersome term – is one very specific kind of “non-chord tone,” or a note in the melody which doesn’t belong to the chord being played behind it.  Yes, Adele’s little dip is a non-chord tone, but it is not an appoggiatura, which has these requirements:2

  1. It must occur on an accented beat, usually the chord change itself.
  2. It must be approached by an interval larger than a step.  (The dip fails on this requirement; it’s approached by only a step.)
  3. It must resolve to a chord tone by a step.
  4. The resolution should be in the opposite direction of the approach – in other words, if the melody leaps up to the appoggiatura, it should resolve down.  And if the melody leaps down to the appoggiatura, it should then resolve up.

The so-called “appoggiatura” in “Someone Like You” fails requirement #2, and is therefore what you could call an accented neighboring tone – that is, a neighbor tone (where the melody goes up/down a step to the “neighboring” non-chord tone, and then back to the chord tone) that occurs on the chord change.  Or, because the note is so short and insignificant, you could even just slap the noncommittal title “ornament” on it and move along.

Later in the NPR follow-up, composer/theorist Rob Kapilow goes on to suggest that some of the melodies in the verse are appoggiaturas.  There are at least two, he says.  First, the song’s third and fourth words: “that you’re,” then the “found a girl.”  (Listen above to the beginning of the song.)  Both of these are also not appoggiaturas.  “That” isn’t approached by a leap (it’s an accented passing tone), and “found a” isn’t even a non-chord tone.

T rue appoggiaturas have a very distinctive sound.  Dissonant notes on the downbeat are often noticeable anyway, but the sound of an appoggiatura is extra accentuated by its arrival by a leap, because the melody leading up to it isn’t smooth.

There’s a great example in one of my favorite songs ever: the Muppets’ “Rainbow Connection.”  In fact, an NPR listener fingered this very tune as an example of the elusive appoggiatura.3  It occurs on the “nec” syllable of “connection” in the line “someday we’ll find it: the rainbow connection.”  Check it out:

Here’s a transcription to help you out – the notes in parentheses are the chords, while above the words are the notes of the melody.

      D   F#  A            G#   A   F#
(Bm7) Someday we'll  | (E) find it, the
       E   G#  B            G# A#    D
(C#m7) rainbow con-  | (F#) nection, the
    D F#    A              C#        B
(D) lovers, the      | (E) dreamers, and
    A
(A) me.4

The bona fide appoggiatura is that G-sharp in the fourth measure, right on “con-NEC-tion.”  It’s clearly a non-chord tone; F-sharp major contains only the notes F-, A-, and C-sharp, so G-sharp doesn’t belong.  Second, the note is accented by its location on the downbeat and chord change.  Third, it’s approached by a leap (an interval of more than one step) – even though it’s only 1.5 steps, it still counts.  And finally, it resolves up to the A-sharp, a chord tone of F-sharp major, in the opposite direction of its approach.  It’s a very weirdly placed note, especially when followed by an accidental.  In effect, it draws the listener’s attention just before an out-of-key A-sharp.

Grizzly Bear’s 2009 hit “Two Weeks” is another example.  This appoggiatura happens in the opposite direction – the melody leaps up to the appoggiatura, then resolves down.  It happens throughout the chorus, on the first syllables of each “always,” “sometimes,” and “easy.”  Take a listen for yourself:

“Two Weeks” is in the key of F major.  The syllables in question are Gs over a B-flat major chord; they’re all approached by an upward fourth and resolve down to the F.  Here’s a transcription:

                               C     D
                 | (Am)    (C) would you
     G F                       C  D
(Bb) always      | (F)     (C) maybe
     G   F                     C    D
(Bb) sometime    | (F)     (C) make it
     G F                       C    D 
(Bb) easy        | (F)     (C) take your
     A  G C
(Bb) ti-i-ime...

This is a prime example of why it’s called the “leaning tone.”  There’s no doubt that the G will resolve to the F.  And in an analogous move, the entire B-flat major chord is similarly expected to resolve down to the F major, and sure enough, it’s the next fall after the G-F move in the melody.  It’s sort of a double lean that starts the downward momentum that carries through each line of the chorus.

On the surface, though, the usage of appoggiatura in “Two Weeks” and “Rainbow Connection” is similar.  They’re both used to delay the arrival of the chord change to the melody.  It’s an effective move; the unexpected non-chord tone draws the listener’s attention, which makes it extra satisfying when it resolves.  That said, the appoggiatura is still pretty rare.  In order to identify even two or three examples beyond “Rainbow Connection,” which I learned in school as an example of appoggiatura, I had to listen to nearly 100 songs.  And even then, a couple were too weak too include.5

R egardless, the major takeaway here should not about the magical power of the elusive appoggiatura.  It’s simply the name given to a very specific form of non-chord tone.  Yes, non-chord tones are effective melodic devices.  By moving off the chord, you create dissonance; dissonance begets tension; tension begets emotional response from the listener.  But they also occur very naturally in songwriting and don’t really warrant this kind of laser-focused analysis in a discussion about a topic as broad as “why music makes me cry.”

It’s true that Wall Street Journal and NPR got their definitions wrong.  But it’s much more important to understand that songs like “Someone Like You” don’t derive their emotional punch from something as simple as a single appoggiatura in the chorus.  What actually makes “Someone Like You” so powerful is a combination of more salient things: solid songwriting, tried-and-true chord progressions (here, I-iii-vi-IV and I-V-vi-IV), the contrast between the vocal ranges of the verses and the chorus, etc.  And of course, it always helps to have a very, very talented performer behind the microphone.

Becky Sullivan


1 All Things Considered only has two hours of airtime a day to devote to all of the news, and though they do an admirable job of considering all things, it’s asking a lot to spare more than a few minutes for extended music theory pedantry about the exact definition of a very specific musical term (no offense to self). So instead, Rob Kapilow provides a correct example from the classical literature, then the discussion moves on to other moments in “Someone Like You” (though, unfortunately, they are also incorrectly labeled appoggiaturas). 

2 This definition is the current standard for music theory classes and comes from my experience/textbooks in music theory classes in both high school and college. There is one major alternative view that calls an appoggiatura any accented non-chord tone that resolves by a step. This old-fashioned definition is not taught or widely used because it erases the (useful) distinctions between several different kinds of non-chord tones.

3 The other song this listener indicates, the Beatles’ “Try to See It My Way,” is unfortunately not an example of appoggiatura. The non-chord tones in question this time are accented neighboring tones again.

4 Man, that song is really nice. I’ll even admit to tearing up a bit in the new Muppets movie when Animal broke out with the drums.

5 Most of my failed appoggiaturas were similar to those misidentified by NPR – accented passing or neighbor tones (which fail because their approach is by step, not leap), or they were chord tones that sounded like non-chord tones on first listen.  Other times, the non-chord tone was unaccented (it fell on an offbeat), or it appeared at the start of a phrase (meaning it had no approach at all). 

Songs cited:
  • Adele Adkins and Dan Wilson, “Someone like You,” performed by Adele on 21, © 2011 by XL Records, XLCD 520. 
  • Paul Williams and Kenneth Ascher, “Rainbow Connection,” performed by Kermit the Frog on the Rainbow Connection / I Hope That Somethin’ Better Comes Along 7″, © 1979 by Atlantic Records, STA 37283. 
  • Grizzly Bear, “Two Weeks,” Veckatimest, © 2009 by Warp Records, WARPCD182.

Ostinatos: repetition isn’t just to annoy you

Y ou know that feeling where you just can’t get a tune out of your head?  It might drive you nuts – especially if it’s the Black Eyed Peas’ “I Gotta Feeling” stuck there yet again (it happens to all of us).  Annoying to us, yes, but songwriters and composers collectively say “mission accomplished” when that happens.  They even have tools to help make it happen.

One especially effective earworm device started showing up a lot in the Baroque Era.1  It’s called the ostinato, which is basically a ten-dollar music theory word for a short musical idea that gets repeated over and over (and over) again while other things change around it.2  (If that sounds kind of annoying, note that “ostinato” comes from the same Latin root as “obstinate.”)  Here’s a charming example from St. Paul’s Suite by turn-of-the-twentieth-century composer Gustav Holst.  Listen for the violins – specifically, to how they never change.

The violins play an up-and-down pattern over and over and over again.  The rest of the music swirls around it, using the violin ostinato as a sort of backbone to the entire movement.3  The repeated idea is a point of stability, lending a consistent element to a section of music. This consistency helps make sectional changes more apparent as well – if the composer either drops the ostinato as the music changes, or returns to the ostinato when music of an earlier section returns, that recognizable little musical lick helps make these changes very apparent.

Ostinatos can do more than clarify form and add structure to a work.  The relentlessness of an ostinato can be used with great effect to create a tense, nervous mood.  Take the title theme to the classic Alfred Hitchcock film Vertigo.  Composer Bernard Herrmann keeps that unnerving arpeggio going through the violin part, creating a feeling of tension and nervousness.

O kay, so classical (and film) composers use the ostinato.  But pop musicians are guilty of using these catchy, repetitive lines as well.  Here’s an example from Sufjan Stevens – the song is “The Tallest Man, The Broadest Shoulders” from his 2005 opus Illinois. Listen to the piano, which starts up eleven seconds in.5

That little piano lick is the ostinato.  It’s useful to Stevens as an anchoring tool.  Because the song goes back and forth between two distinct sections, its presence immediately alerts his listeners when the A section returns later.6

In addition to its usefulness as a structural tool, ostinatos are also really good at creating mood.  Sometimes the repeated idea is extremely influential in establishing the character of an entire piece.  One good example is the synth line in the intro and choruses to M83’s hit song “Midnight City,” off of the 2011 release Hurry Up, We’re Dreaming.  We’re introduced to the ostinato immediately – it’s that scratchy four-note lick that repeats again and again.  It drops out when the verse begins, but every time the chorus returns, the synth line comes right back in all its anthemic, repetitive glory.

The vaguely sad and regretful tone of “Midnight City” owes a lot to the ostinato and its flexibility as the chords change underneath it.  It also strongly emphasizes the chorus (and the sense of arrival that comes with reaching a chorus).

But that’s not its only role here.  “Midnight City” also uses the ostinato to play a trick on the listener about halfway through the song.  Listen again starting around two minutes in, just as a chorus is about to end.  At 2:08, the next verse begins… or so it should.  But at 2:13, the ostinato is back, but it sounds weird – this is confusing.  We’re in a verse?  But with the ostinato?  We haven’t seen that before.  At 2:18, vocalist Anthony Gonzalez reenters with the verse, sung over the underwater-sounding version of the ostinato that entered just a few seconds earlier.  It’s a neat trick.  The verse-ostinato association here anticipates the final chorus, when the ostinato will finally return to its original form and help carry the song to its resolute conclusion.

And here you thought repetition was boring.

Nick Curry


1 The Baroque Era is the period of classical music beginning around 1600 and ending around the death of Johann Sebastian Bach. The distinctions between musical epochs are always a little bit fuzzy, but you might recognize this period as the time when people still thought harpsichords were a good idea.  

2 Despite the fact that it sounds like something you might buy from Starbucks, I think I can safely promise that ordering a “caramel ostinato” might not work out for you.

3 Ostinatos don’t have to be a repeated tune – repeated rhythms are fair game too. And there aren’t many repeated rhythms more iconic than this one from another Holst piece, “Mars, the Bringer of War” of The Planets.  The rhythmic ostinato is found earlier in the piece as well, but it really comes into the foreground here. And for added “Mars” fun, here’s an amusing scene from Venture Bros., where “Mars” plays/is sung as the henchmen suit up.  

4 Okay, you might be thinking “you said an ostinato is a repeated idea, I thought an ostinato wasn’t supposed to change!  And this one definitely changes.”  Well, like just about everything else in music, definitions are always a little bit fuzzy. A little bit of variation is okay, since the ostinato is still recognizable and the feeling created by the ostinato remains. 

5 Regarding the video: I couldn’t pass up the video with this glorious photo.  I’m a Kansan; we’re trained from youth to love open spaces.

6 If you listen to the way the pieces of this song fit together, you’ll note that two sections are repeated, creating an ABAB form. You can hear how the meter and key change between the two sections – in the ‘A’ section, the music alternates between 5/8 and 6/8 meter and is in a minor key, while the ‘B’ section features 4/4 time and is in a minor key.

Songs cited:
  • Gustav Holst, Ostinato, St. Paul’s Suite, performed the St. Paul Chamber Orchestra, conducted by Christopher Hogwood.  © 2003 by Deutsche Grammophon. 
  • Bernard Hermann, “Theme,” performed by the City of Prague Philharmonic Orchestra on the original soundtrack to Vertigo, © 1958 by Mercury Records, MG 20834. 
  • Sufjan Stevens, “The Tallest Man, the Broadest Shoulders,” Illinois, © 2005 by Asthmathic Kitty Records, AKR014.
  • M83, “Midnight City,” Hurry Up, We’re Dreaming, © 2011 by Naïve Records, NV824311.