Tuesday, January 31, 2006

Fun with Hemiolas, Part 1

Two analyses of interesting and special hemiolas are coming up soon. To prepare for them, here's a general discussion of what hemiolas sound like, along with a listening experiment to try.

Grove Music Online defines the modern (post-1600) hemiola as "the articulation of two units of triple metre as if they were notated as three units of duple metre." This statement delicately steps around the question of how we hear hemiolas. If two bars of 3/4 (e.g.) are "articulated as if" they were three bars of 2/4, then do we hear them temporarily switch to 2/4? Or does "articulation" mean only that there is a rhythm suggesting 2/4 (such as three half notes), and that we notice that it could have been in 2/4--but isn't?

Neither of these possibilities seems right. When I hear a hemiola, my 2/4 "sensors" are activated; I am experiencing duple meter, not just entertaining the possibility of it. But the duple meter doesn't replace the notated triple meter; my 3/4 sensors remain active as well. The result isn't just two meters (2/4 and 3/4) superimposed, going on both at once. It is a hierarchical relationship. Here are a couple of metaphors for this relationship:

- 2/4 is the "surface" meter, and 3/4 is the "underlying" meter. (Or 2/4 is the figure, and 3/4 is the ground.)

- 2/4 is a fictional meter, a "story within the story" told by the 3/4 meter. We experience it, but we know it's not real.

The most hemiola-heavy music I know is a Broadway tune. But it's not "America" from West Side Story! It's "A Weekend in the Country," from Stephen Sondheim's A Little Night Music. Here are the opening bars of the A section:


The first three measures articulate 3/4, which is actually duple meter on the eighth-note level because it groups the eighth notes in twos. (On this level 6/8 is triple meter, grouping the eighth notes in threes.)

Here's the experiment to try:

First, sing or play the tune as if the first three bars were actually in 3/4, without any quality of 6/8 in them. It helps to tap the quarter note (duple) beat as you sing:


Without the presence on some level of 6/8 meter, "-end" and "-try" fall unequivocally on the beat. This sounds clumsy and punchy. If the song's hemiola were meant to sound like this, then the song would be pretty bad! In practice, we can't actually hear the song this way, because its accompaniment is in a straight 6/8. (Unless we hear the song as polymetric, with pure 3/4 in the melody vs. pure 6/8 in the accompaniment. This seems wrong to me, for exactly the reason shown above: the melody is bad in pure 3/4.)

What about hearing the first three bars as only suggesting 3/4, without actually being in 3/4 in any sense? Try singing the tune this way. The only syllables on the beat will be "week-" and "coun-". Add a little rubato to delay "-end" and "-try", which are now unequivocally off the beat:


This also seems wrong. It lopes along slowly, uncertainly, without any forward drive.

"A Weekend in the Country" sounds best when the first three measures include both 3/4 and 6/8, with 3/4 the hemiola meter and 6/8 the "underlying" meter. "-end", "in", and "-try" then get a special lift because they are both on the beat (in 3/4) and off the beat (in 6/8). Being on the beat makes them active and strong; being off the beat keeps them light on their feet.

More precisely: As rhythmic events, "-end", "in", and "-try" are on the beat of the 3/4 hemiola meter. But as metric events in the hemiola meter (second beats in 3/4), "-end", "in", and "-try" are off the beat of the underlying 6/8 meter.
Instead of the usual two-level relationship between rhythm and meter:

- Rhythmic events are defined as
- Metric events (downbeat, onbeat, offbeat, etc.)

a hemiola creates a three-level structure:

- Rhythmic events are defined as
- Hemiola metric events (downbeat, onbeat, offbeat, etc.) are defined as
- Underlying metric events (downbeat, onbeat, offbeat, etc.)

Are rhythmic events in a hemiola also defined as underlying metric events, skipping over the hemiola-meter level? We'll find out in an upcoming analysis.

To close, a few notes on "America":

Unlike the hemiolas in "A Weekend in the Country," the hemiolas in "America" are supposed to be punchy and percussive. They occur in the melody and the accompaniment together. Should we hear them as genuinely changing the meter? I say no. If you try changing the whole song to 3/4, making the hemiola meter into the regular meter, the formerly-hemiola measures sound wooden and dull. In the real version, something else is operating to make the hemiola measures lively--that something being the underlying 6/8 meter.

The meter of "America" is notated as "6/8 (3/4)." This is a nice way of showing that 3/4 is present in some sense, but that 6/8 is privileged as the real, underlying meter. ("Real" and "underlying" are metaphors, of course.) If the song were instead in "3/4 (6/8)," it would sound rather different: the hemiola would apply not to "(A)-mer-ic-a," but to "I like to be in..." This would put the hemiola's extra energy in the wrong place.

Next time, we'll examine a hemiola that might not even agree with the underlying meter about where the downbeats are! Until then...

Friday, January 27, 2006

Mozart: Piano Concerto in Eb, K. 482, last movement

Piano Concerto in Eb, K. 482, Last movement: Allegro
Wolfgang Amadeus Mozart
Eb Major, 6/8 time
First 8 bars


I did not plan for the first few Unconquered Sound analyses to have a common theme. Yet they do: music that has obvious charm, but that also has a less obvious psychological intensity that builds up after the first few measures.

The beginning of this theme has a remarkable floating quality. Various notes in mm. 1-2 (and, analogously, in mm. 3-4) are accentuated: the Eb on the downbeat of m. 1 as a starting place and a metric strong point; the Eb on the downbeat of m. 2, as the target of the preceding Eb's; and the final G in m. 2, which is the highest note so far and is notable simply for being different from Eb. No one of these accentuated notes seems to dominate the others, so that the whole theme seems to hover in a state of continuous, moderate accentuation. Even the last three repeated Eb's in m. 1 maintain this state, simply by being Eb's. If they weren't all Eb's, then individual notes would jut out:


mm. 3-4 repeat mm. 1-2 a step higher, on F and Ab. Because the analogy between mm. 1-2 and mm. 3-4 is so clear, it is easy to hear rising stepwise motions across the four measures, from Eb up to F and from G up to Ab. These rising motions don't seem especially dramatic or intense; they have the feeling of a natural, unforced expansion.

The next step in this natural expansion would be to reach G and Bb in mm. 5-6. This in fact does happen. Yet Bb comes early, on the downbeat of m. 6 instead of on the fourth beat. We can tell slightly ahead of time that this will happen, because the 32nd-note turn appears on the last beat of m. 5.

For me, the downbeat of m. 6 is the moment at which the whole theme really comes to life. Here are some relatively simple reasons why the Bb is energized:

- The pattern established in mm. 1-2 and mm. 3-4 has been broken by Bb coming early. This is a small surprise, creating a little burst of emotional energy.

- By reaching its highest note (Bb) earlier than expected, the theme suddenly pulls upward more strongly. (It doesn't seem to want to pull upward beyond Bb, though.)

- The Bb is the first note so far to be fully, unequivocally accentuated. It's on the downbeat of m. 6, and there isn't any note on the fourth beat to counterbalance it. Because it is also the highest note, it's quite a forceful stroke. (At the same time, it's quite delicate on the piano at a modest dynamic!) The theme still floats, but now a note stands out from the floating background.

Yet these reasons don't seem to me to tell the whole story. They show why the m. 6 Bb is energized, but not why the whole theme comes to life. When m. 6 arrives, I hear all of mm. 1-6 take on a stronger character, become more three-dimensional.

Here is a reason why this might be so:

The most obvious motion leading the whole theme up to Bb is the stepwise motion G-Ab-Bb. But by falling on the downbeat of m. 6, Bb becomes analogous to two other earlier events: the Eb on the downbeat of m. 2, and the F on the downbeat of m. 4. It's possible to hear Bb as the climax of the motion Eb-F-Bb, a more buoyant and expansive motion than Eb-F-G or G-Ab-Bb.

Eb-F-Bb might seem arbitrary, the result of "picking out notes" rather than a real musical experience. It doesn't have the advantage of being stepwise like Eb-F-G or G-Ab-Bb; stepwise motions are easy to appreciate because their pattern is so simple and direct.

But there is reason to connect F and Bb, beyond their falling on analogous downbeats. The m. 4 F is harmonized by V; the m. 6 Bb is harmonized by I. Both F and Bb are the fifth degrees of their harmonies. This is the first time in the theme that two notes have expressed the same degree of different harmonies. (I'm putting aside the little low-Bb upbeats to m. 1, 3 and 5.)

This relationship between F and Bb may not seem like much to go on. (And it doesn't have anything at all to do with Eb.) But the rest of the theme (mm. 6-8) reiterates the relationship clearly and boldly. We come back down from Bb to F to Eb, reversing the Eb-F-Bb motion. And Bb and F each have triads arpeggiated below them: Bb-G-Eb (I) in m. 6 is followed by F-D-Bb (V) in m. 7, hammering home the fact that Bb and F are each the fifth degree of their respective harmonies.

So we are left with two hearings of the theme. In one hearing, we move upward by step in mm. 1-6: Eb-F-G and G-Ab-Bb. In the other hearing, we realize that we have moved upward from Eb to F to Bb in mm. 1-6, and we come back down the same way (Bb-F-Eb) in mm. 6-8. These two hearings coexist in the same way that the two hearings of "Let it Snow!"'s first eight bars coexist (see 1/11/06): in analysis they get separated, but in normal listening they fuse.

It's the fusion of these two hearings that gives the theme the character that I described as stronger and more three-dimensional. The coexistence of two patterns itself has a character of richness, above and beyond the patterns' individual qualities. If you cook, you may have had similar experiences: putting multiple kinds of hot pepper in a dish, for instance, can create a deeper, more subtle spiciness than any one kind has by itself.

Here's a nice trick to help you hear Eb-F-Bb in mm. 1-6. These are the first bars of La Marseillaise, in Eb:


Listen to them first, and then to the K. 482 theme. This analogy will make your sense of Eb-F-Bb in K. 482 stronger than normal, but it works at all because Eb-F-Bb is already there.

In retrospect, it was only half true to pick out the downbeat of m. 6 as the moment when the whole theme takes on a stronger character. The Bb-F-Eb descent in mm. 6-8, with triads arpeggiated below Bb and F, had not yet occurred at the downbeat of m. 6--so it had not yet reinforced the parallel Eb-F-Bb ascent in mm. 1-6.

Once again, I hope you've enjoyed the analysis! My favorite recording of K. 482 is with Annie Fischer on piano and Wolfgang Sawallisch conducting, reissued on Seraphim (#5 68529 2, a 2-disc set that also includes K. 466, 467, and 488).

Monday, January 16, 2006

"Do-Re-Mi"
The Sound of Music (1959)
Lyrics: Oscar Hammerstein II
Music: Richard Rodgers
C Major, 4/4 time
16 bars

Do, a deer, a female deer
Re, a drop of golden sun
Mi, my name, I call myself
Fa, a long long way to run
So, a needle pulling thread
La, a note to follow So
Ti, a drink with jam and bread
And that brings us back to Do!


What could be more cheerful or simple than "Do-Re-Mi"? More basic than a rising scale? You guessed it--I'm going to argue that this song is sophisticated and precise in what it expresses. The rising scale is indeed the basis of the song, but a lot goes on under its cover.

Let's look at the first line. What we find is going to apply, more or less, to the first four lines:

Do, a deer, a | fe - male deer
C D E C E C E
I (tonic harmony throughout)

Starting with the first "deer," the accented syllables in the line are sung on E, and the unaccented syllables are sung on C. The relationship between E and C seems something like the relationship between figure and ground in a picture: E is the figure, the primary target of attention; C is the ground, underlying and coloring our perceptions.

But at the beginning of the line, the strongly accented "Do" falls on C rather than E. (The theme of the song requires that "Do" fall on the tonic note, as that's the note that receives the syllable "Do" in solfege!) "Do" is attention-getting linguistically because it stands alone, not part of any larger word or phrase; it's attention-getting musically because it falls on the hyperdownbeat of the two bars of music. ("Hypermeter" is large-scale meter, in which each measure's downbeat is like a single beat.) Arguably, "Do" is more emphasized than any of the syllables that are on E.

So in this line, the pitch C makes a transition from being the focus of great attention to being in the background. On the first three syllables, we rise from C through D to E; then we stay on E, with C an added presence.

This illustrates the meaning of the lyric quite strongly. We make the transition from the solfege syllable "Do", sung on C, to the mnemonic definition for it, sung on E. Yet C remains present while we hear the definition, telling us that we are still hearing about "Do". This creates an analogy, which we can pick up subconsciously:

The difference between a term and its definition
is to
the fact that it's still all about the term

as

Melodic motion from C to E
is to
the continued presence of C

There's one more thing to hear in this line, that actually contradicts some of what's written above. We can hear the C-to-E motions on "a fe-" and "-male deer" as miniature, compressed repetitions of the opening C-D-E motion. Heard this way, the C's aren't in the background; they are taking us, momentarily, back to the start so that we can keep engaging in the line's main melodic motion of getting from C to E.

Now here's the fifth line, which is identical to the sixth and seventh lines except for rising transpositions:

So, a nee - dle pull - ing | thread
G C D E F G A
V of IV (applied dominant) --> IV

The A that sets "thread" is, like the mnemonic defintion's E in the first line, the third degree of the harmony at the time it is heard. We move from "So", on G, to "thread," on A. But this motion is much different than the motion from C up to E in the first line! There, C remained present throughout the line, the ground to E's figure. Here, G is swept away by the harmonic change from V-of-IV to IV when we reach A. This harmonic change (an applied dominant resolving) carries a lot of momentum.

It no longer seems certain that the term "So" is the line's most accentuated syllable. Within the mnemonic definition ("a needle pulling thread"), "thread" is massively accentuated: it's central harmonically and metrically, plus it's the target of a sweeping C-D-E-F-G-A scalar motion. This motion sounds like a miniature version of the whole song so far, raising the possibility that the final A in some sense jumps the gun and arrives too early, before "La" shows up.

All this changes the relationship of the solfege term and its definition. Now the definition drags along the term, in the way that a large, exuberant dog drags its owner along on a leash. And the definition urges toward its final word, the word that completes it. The song has become a game: the sheer joy of thinking of definitons for solfege syllables has taken over from the need to carefully express how the syllables relate to their definitions. Maria von Trapp, the protagonist who introduces the song, has dropped her pedagogical impulse and is reaffirming The Sound of Music's central premise: just by being bold and loving life, we can develop into the best people we can be.

This overstates the case. "Do-Re-Mi" is a joyful song from the beginning, and the pedagogical quality remains to some degree throughout. But there is a major change in the song's tone starting in the fifth line. In the sixth line,

La, a note to fol- low | So,
A D E F# G A B

"So" is sung on a B, rather than on its correct G. This doesn't disrupt the song's theme, as "So" isn't being defined in this line, but it shows how much joyful looseness has been injected.
("So"'s appearance here is also due to the impossibility of creating any mnemonic definition for "La," let alone one that rhymes appropriately!)

Like "Let it Snow! Let it Snow! Let it Snow!", "Do-Re-Mi" undergoes an emotional transformation. In "Let it Snow!", the transformation (from physical coziness to love) was mostly the work of the lyrics; here, the music does more of the work.

Wednesday, January 11, 2006

"Let it Snow! Let it Snow! Let it Snow!"

"Let It Snow! Let It Snow! Let It Snow!" (1945)
Lyrics: Sammy Cahn
Music: Julie Styne
F Major, 2/2 time
32 bars + upbeat (my "m. 1" starts with the word "weather")

"Let It Snow! Let it Snow! Let it Snow!" is typically heard as part of Christmas-music collections. This context tends to blanket the song with an aura of warm, fuzzy nostalgia. But it's actually quite powerfully romantic and psychologically sharp. I think it's a marvelously crafted song.

The song is in an AABA form: four eight-measure-long sections, of which only the third is different from the others (hence the "B"). Here are the lyrics:

Oh, the weather outside is frightful
But the fire is so delightful
And since we've no place to go
Let it snow! Let it snow! Let it snow!

It doesn't show signs of stopping
And I've brought some corn for popping
The lights are turned way down low
Let it snow! Let it snow! Let it snow!

When we finally kiss goodnight
How I'll hate going out in the storm!
But if you'll really hold me tight
All the way home I'll be warm.

The fire is slowly dying
And, my dear, we're still goodbying
But as long as you love me so
Let it snow! Let it snow! Let it snow!


(NB: It's "brought some corn," not the often-misstated "bought some corn"!)

The theme of this song, and the significance of the hook ("Let it snow! Let it snow! Let it snow!"), change over the course of the song. At first, the song seems to be about the pleasure of being in a cozy, warm, indoor place while it's snowing. But hints slowly build to suggest a more romantic theme. In the second "A" section, "The lights are turned way down low" is a delicate first hint. The "B" section takes things much further: now there's a kiss goodnight and holding tight. "All the way home I'll be warm" actually undercuts what had been the song's apparent theme--it seems that the singer doesn't have to be in the cozy, warm, indoor place to be happy. Finally, the last "A" section ends with the full statement of the song's revealed significance: "As long as you love me so/Let it snow! Let it snow! Let it snow!"

Overall, the song is devoted to representing a constant, pleasurable situation, although the situation changes from being cozy indoors to being loved. The music supports this with a certain calm, mellow stability. Yet at the same time each "A" section builds up great momentum toward its last line, which after all does feature a lyric with three consecutive exclamations. How can a song be so mellow and so energetic at the same time?

An easy first observation about the mellowness of the "A" sections is that each line falls in pitch. Except for the neighbor motion between F and G in m. 3, there is no upward stepwise motion in any of these lines. (I'll pass on comparing the falling pitches to falling snow. I think the relaxed feeling of falling by step is more important.) Yet there's upward stepwise motion between these lines, building energy from C (m. 1) to D (m. 5) to E (the upbeat to m. 7). The high E packs every form of instability in the book: it's a non-chord tone, an appoggiatura to D; it's harmonized by a fully diminished 7th chord; it falls on an upbeat. From this E, the last line ("Let it snow! Let it snow! Let it snow!") cascades all the way down to a restful F (the tonic) by step.

At the same time, there are less obvious ways in which the "A" section creates tensions that are relieved in the last line. In spoken English, the most accented syllable of the last word in a phrase often receives an especially strong stress. There are many exceptions, but the first three lines of each "A" section fit the pattern: try reading them with feeling, and you'll accentuate "fright-", "(de-)light-", and "go." From "fright-" in m. 2 to "(de-)light-" in m. 4, the music moves from F (I) to E (V). This creates a lingering tension that requires an F (I) in the melody to resolve it. But the third line (mm. 5-6) completely ignores the E, and takes a different path away from the first line (mm. 1-2): it raises the first line's melody and harmony by a step, ending on G (ii).

The beauty of this is that though E and G have arrived via totally different paths, they both have moved away from F by a single step, and both are simultaneously resolved when F appears on "snow!" in m. 8. (Of course, G's ii harmony doesn't go straight back to F's I; mm. 7-8 enact a cadential progression.)

In fact, the relationship of mm. 7-8 to mm. 1-2 and mm. 5-6 bears closer examination. As noted above, the high E falls on an upbeat. It's the first upbeat note that is higher than the downbeat note it precedes; it's the first upbeat note that really demands attention. If we put it aside for a moment and look *only* at mm. 7-8, we see...a repeat of mm. 1-2, with only small melodic differences! (There is a harmonic difference: m. 1 starts on the tonic, while m. 7 initiates the final V7-I cadence.) Even though we've climbed up to a high E to begin the last line, from a different point of view we've come back down to the C-Bb-A-G-F scale from the third line's D-C-Bb-A-G scale. That "different point of view" is the one created by the first three lines, in which important musical events start on the downbeat.

Of course, we don't ignore the high E upbeat when we're listening to the song. But I think we do register that, apart from that upbeat, mm. 7-8 are a return to mm. 1-2. This return gives the whole "A" section a mellow, well-rounded coziness that coexists with the tension-and-release pivoting on the high E. If you want to hear some of that coziness go away, try giving "Let it snow! Let it snow! Let it snow!" these pitches:

C D | E D C Bb A G | F

(The |'s are barlines.) This puts the high E on the downbeat, and removes mm. 7-8's hidden quality of returning to mm. 1-2.

One last thought about linguistic stress: The one line in the whole song that doesn't put its strongest stress on its last accented syllable is, of course, the hook: "Let it snow! Let it snow! Let it snow!" The music does put attention on the third "snow," but a spoken version wouldn't necessarily do so. This seems important, though I don't really know why. Look at these recomposed lyrics:

Oh, the weather outside is frightful
But the fire is so delightful
And since we've no place to go
We'll relax and we'll just let it snow!


Somehow it seems wrong that we have to wait for the last syllable for the "punch line"--even though so many musical tensions wait until that moment to resolve. I'd love to hear anyone's thoughts about why this might be so.

I'm sorry not to have much to say about the "B" section. I can offer one straightforward observation: the last line ("All the way home I'll be warm") is suddenly higher in pitch than the previous lines; the last line is also the line that breaks the cozy theme and fully paves the way for the love/romance theme.

I hope you've enjoyed this analysis...and I hope you enjoy the song! I'm particularly fond of a recording on iTunes by one Gary Grant.

Until next time...

Sunday, January 08, 2006

Welcome to The Unconquered Sound

Welcome to The Unconquered Sound! This is my forum for posting brief to moderately long analyses of music I enjoy.

I recently completed a music theory Ph.D. at a major northeastern university. There I had mentors who saw music analysis as a way of deepening one's relationship with works of music, and of kindling enthusiasm for them.

Kindling enthusiasm is my goal in this blog. If you find yourself wanting to listen to or play the music I analyze, then I've succeeded.

I intend to write for readers with a moderate amount of Western musical training. If you're a professional musician, an undergraduate music major, or anyone else with a similar education, then every analysis here should be comprehensible to you. Some analyses might be even simpler than that; others might bring in more advanced theory, which I'll explain as I go.

Why "The Unconquered Sound"? Partly because I feel that the sound of a work of music always transcends any particular analysis. Partly because I like the sound of the name.

Please feel free to post thoughts, ideas, disagreements, agreements, enthusiasms, or anything else.