Thursday, February 16, 2006

You want Beatles analyses? This guy's got Beatles analyses...

A musicologist named Alan W. Pollack created analyses of every song the Beatles ever wrote. It took him eleven years. Apparently these analyses are well known in online Beatles circles. You can find them all here, with commentary by Ger Tillekens.

Pollack combines a whole lot of technical detail with compelling descriptions of how he hears the songs. Here's a quick example from "Being for the Benefit of Mr. Kite":

You might say that different parts of this song are respectively in the keys of d, c, and e minor, but I think it's a cop out to describe the song as simply spanning three different keys and leave it like that...

...I believe the home key of this song is e minor, and that the opening in d minor, and the starting of the verses in c minor is a clever ruse perpetrated intentionally to throw you off balance. It's sort of the harmonic equivalent of one of those multi-planed Escher engravings where your sense of the direction pointed to by gravity's rainbow depends on where on the page you focus your gaze.

Now that's the kind of analysis that makes me want to go hear the song!

Thanks to Roger Bourland's Red Black Window for pointing out this resource.

Wednesday, February 15, 2006

Fun with Hemiolas, Part 2

"My Favorite Things"
The Sound of Music (1959)
Lyrics: Oscar Hammerstein II
Music: Richard Rodgers
3/4 time

As I described in my last post, a hemiola creates a temporary duple meter that occupies the foreground of our hearing, while the triple meter continues in the background. Grove Music Online's definition--"the articulation of two units of triple metre as if they were notated as three units of duple metre"--doesn't describe what it's like to hear the hemiola, but it does describe the conditions under which a hemiola occurs.

Here's the beginning of the last section of "My Favorite Things":


All the words in the first two lines, except for the "the"s, come at two-beat intervals:

When the dog bites,
When the bee stings...

These two-beat intervals create a 2/4 (duple) hemiola meter, with the words falling on the hemiola's downbeats.

But where are the "two units of triple metre" that get articulated as three units of duple? The notated meter begins each two-bar group with a quarter-note rest. These rests don't begin the hemiola's "three units of duple metre." in fact, they don't begin any units of the hemiola's duple meter! I hear the hemiola meter as follows, with each three-bar unit under a bracket:


The previous section had ended on a dramatic C over a V9 (B) chord. The first melodic B on "When" resolves this C, encouraging me to hear "When" as a hyperdownbeat in the hemiola meter.

(It's also possible to hear three-bar units begin on "dog" and "bee", instead of on "When". But to me, this hearing is less compelling.)

The above image doesn't show how the notated 3/4 meter continues in the background. It's the relationship between that background meter and the hemiola meter that creates the special experience associated with hemiolas.
When the hemiola meter and the underlying meter line up normally, their disjunction occurs on a middle metric level:


Both the hemiola meter and the underlying meter agree that "week-" is metrically very strong, a downbeat. Both also agree that "the" is metrically weak, an offbeat. The points of dispute are "-end", "in", and "-try": they're strong beats in the hemiola, but weak beats in the underlying meter. They are the carriers of the hemiola's special feeling, because they are treated differently by the hemiola meter and the underlying meter.


In "My Favorite Things," the story is different:

- The "When"s are very strong hyperdownbeats in the hemiola 2/4, but weak beats in the underlying 3/4.

- "Dog" and "bee" are points of agreement between the hemiola 2/4 and the underlying 3/4, because in both meters they are on a middle metric level: downbeats, but not hyperdownbeats.

- "Bites" and "stings" have striking accent marks, but are actually the most typical in their relationship between the two meters: they're downbeats (medium strength) in the hemiola meter, but upbeats in the underlying meter.

There's an unusual sort of balance between "When" and "dog", and between "When" and "bee". In the hemiola meter, the "When"s are stronger; in the underlying meter, "dog" and "bee" are stronger. Overall, the words seem equally strong to me, as if the hemiola 2/4 and the underlying 3/4 have combined to give each word an average metric strength that evens out.

This seems to do justice to the way "When", "dog", and "bee" are stressed linguistically in the lyrics. For comparison, if the hemiola is normalized (putting the "When"s on the hyperdownbeat in both meters), then the "When"s are stressed too much:


And if the hemiola is removed (a remarkably easy operation), then "dog" and "bee" are stressed too much:


In the real version, the balance of stress is ideal:


But even if the "When"s and "dog"/"bee" sound equal in strength, their strengths are not the same. "Dog" and "bee" have a solidity and weight to them, because they are downbeats in both the hemiola meter and the underlying meter. (This weight goes well with "dog" and "bee" simply being held longer.) The "When"s are less solid; they have the hemiola magic, the floating quality, that comes from being upbeats in the underlying meter. But the "When"s are also exceptionally dynamic and active, because they are hyperdownbeats in the hemiola. This dynamic quality fits the sound of the syllable when, which begins with a wind-up--the wh phoneme opening out forcefully into the vowel.


What happens to the hemiola at "When I'm feeling sad"? "When I'm feeling" keeps it going, with exactly the same metric pattern as the previous two lines. But when we reach "sad", the hemiola is definitely over: "sad" falls on the hyperdownbeat of the 3/4 meter, breaking the pattern of quarter-note rests that had helped the hemiola maintain itself.

In fact, once we reach "sad", the entire line "When I'm feeling sad" loses its hemiola retrospectively! "When" becomes an unequivocal upbeat; "feel-" remains a downbeat, but becomes an ordinary downbeat instead of a hemiola-meter-and-underlying-meter downbeat.

This retrospective erasure of a hemiola is quite an astonishing trick. We don't interpret any particular moment, either in real time or retrospectively, as the moment at which the hemiola meter has ended. The hemiola meter seems suddenly to have melted away gradually!

From a linguistic point of view, the hemiola erasure works because "sad" receives the strongest stress in the sentence. We're not disturbed that "When" retrospectively becomes metrically weaker than "feel-", because both of those syllables are now metrically weak compared to "sad."

Here are the complete lyrics of the last section of "My Favorite Things":

When the dog bites,
When the bee stings,
When I'm feeling sad,
I simply remember my favorite things
And then I don't feel so bad.


Among the first three lines, "When I'm feeling sad" not only has the clearest stress profile (it moves toward "sad"), but also carries the most compelling meaning. Dogs biting and bees stinging are strong, visceral images, but we don't really believe that they are constantly happening to Maria von Trapp. We can really believe that Maria often feels sad, and that she revives herself by thinking of her favorite things.

In the context of the whole song, "When I'm feeling sad" is a turning point: the song changes from an enumeration of visually oriented examples (mostly of favorite things, and then of bad events) to an outright description of personal emotions. (This is a common move in Broadway and Tin Pan Alley songs. In an earlier post, I described how "Let it Snow! Let it Snow! Let it Snow!" moved from being about a cozy physical environment to being about love.)

This change is paralleled by a change in the form of the song's statements. In the first three sections, Maria lists appealing images, sounds, and experiences, and adds, "These are a few of my favorite things." She is making a dispositional claim about herself, that she favors these things; she doesn't recount instances of actually experiencing them, or plans to experience them in the future. In the final section, Maria changes to actually describing a course of events: she feels sad, then she thinks of her favorite things, then she's better.

This more active, narrative mode is in turn reflected by changes in the rhythm of the vocal line. In the first three sections (48 measures total), every phrase begins on the hyperdownbeat, every phrase fills four measures, and every single syllable (except those that end phrases) lasts a quarter note! These features portray Maria's hypnotic state of recollection as she recalls her favorite things; they even begin to put us in such a state as we listen. (Yet Maria is still audibly awake, aware, and speaking to her audience rather than to herself.) In the last section, there appear upbeats, varying phrase lengths, and varying syllable lengths. These more normal features bring the song out of its recollective mode and put it into active narrative time.

This leads to one way in which the hemiola, and the remarkable transition out of it, pay off. The hemiola begins each phrase on the hyperdownbeat ("When"), just as the preceding dreamy sections did. When the hemiola melts away at "sad", the preceding "When I'm" is retrospectively revealed to have been metrically weak. Suddenly, we realize that in the prevailing meter (not just in the underlying meter behind a hemiola), we've been hearing a phrase that began on an upbeat. This aspect of the transition to active narrative time has been completed elegantly, by retrospective revelation rather than by a potentially clunky shift in real time.

I'm not going to get into the incredibly rich area of pitch, harmony, and linear motion in "My Favorite Things." If you have any thoughts about these areas, or about the metric matters I've discussed, please do leave them in a comment!

Coming soon, the final installment in the hemiola miniseries...