Friday, March 03, 2006

Fun with Hemiolas, Part 3

Piano Sonata in Bb, D. 960, Third movement: Scherzo
Franz Schubert
Bb Major, 3/4 time
Trio (in Bb minor)

I'm not happy with the way this post came out. Although it describes an engaging example, it doesn't follow through in a convincing way to a clear point. Please help me by posting your own thoughts on the D. 960 Trio in the "Comments" section.

If there were a "Guide to Creating Hemiolas," it would be very short:

1. Put prominent musical events where you want the downbeats of your hemiola meter to fall.

2. Don't put prominent musical events on the downbeats of the underlying meter, except where they're also downbeats of your hemiola meter.

The logic behind Rule #2 is obvious: if the notated meter is going to retreat to the perceptual background, then presumably it can't be privileged over the hemiola meter by things we actually hear.

The Trio of Schubert's Piano Sonata in Bb, D. 960, flagrantly violates Rule #2. Left-hand quarter notes, marked fzp, fall on underlying 3/4 downbeats which aren't also 2/4 hemiola downbeats. But it's possible to not hear these fzp's as ruining the hemiola. The left hand also includes staccato, non-fzp quarter notes, which fall on weak beats (in both 3/4 and the hemiola 2/4); these notes give the impression of having been delayed a beat, so that they're out of sync with the chords in the right hand. By analogy, the fzp notes also come to sound like delayed, weak-beat events in the hemiola meter.

If we take out the non-fzp quarter notes, then the fzp notes stop sounding like hemiola-meter syncopations and start sounding more like explicit 3/4 downbeats in the foreground:

Even in the real D. 960 Trio, it's possible for the fzp's to become explicit 3/4 foreground downbeats that break the hemiola. This happens when the Trio is played in a loping, swinging way. As explicit, foreground downbeats, the fzp's become heavy, like reference books dropped on the floor; they remain tolerable at all only because they're syncopations on the level of hypermeter (i.e., they fall on "weak downbeats").

I think the Trio sounds much better when it rushes along, hushed and subterranean, in a kind of angry stage whisper. This requires the right hand's rhythm to be played with snap and verve, bringing the hemiola meter to life: BMMM BMMM bup-bup-BMMM BMMM bup-bup-BMMM BMMM... The fzp's then become cross-accents against the right-hand rhythm, in an almost Jamaican way. (This is a bit of fictional characterization--I unfortunately know almost nothing about Jamaican music.) A fast tempo is crucial to making this happen.

But even if the fzp's sound like syncopations and don't push the 3/4 meter to the foreground, the fzp's and the underlying 3/4 meter might still have something to do with each other. We hear the fzp's; we experience the underlying 3/4 meter in some sense; the fzp's are simultaneous with 3/4 downbeats. Can we describe some experience that includes both?

Back in "Fun with Hemiolas, Part 1," I offered this phenomenology of hemiolas in general:

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.)

In the D. 960 Trio, the fzp quarter notes are accentuated in their capacity as rhythmic events. Their identity as syncopations comes from the top two levels of the three-level structure: they are accentuated rhythmic events defined as hemiola-meter weak beats.

Within this model, the experience that I have of the fzp's vis-a-vis 3/4 is actually simple to describe: in addition to serving as hemiola-meter weak beats, the fzp's "skip over a level" and get defined as underlying 3/4 downbeats. That is, the accentuated, intrusive fzp's pass their accentuation on to the downbeats of the 3/4 meter, a meter that nonetheless stays in the background of my awareness.

This last statement contains a big dose of self-contradiction: things that are accentuated generally don't remain "background" or "underlying." But this contradiction describes exactly how the fzp's sound to me. The best metaphor I can think of is some neurotic impulse which gives me a jolt but which my conscious mind rejects. Each fzp's status as a hemiola-meter syncopation (cemented by its analogy to the preceding left-hand quarter note) serves as a cover, a rationalization, for this jolt.

This metaphor takes the 3/4 meter from the innocuous pictorial "background" to the more menacing "neurotic unconscious." The creepy sound of the D. 960 Trio did a lot to inspire this rhetorical move. In any event, the metaphor illuminates one aspect of experience which could play a role in lots of musical analyses: Being accentuated or salient is not necessarily the same thing as being up-front and conscious.


Anonymous elf said...

The Shubert is an accompanimental syncopation which has not the slightest intention of defying the triple meter. Certainly Schubert used hemiolas, as did Bach and Brahms. They were signature cadential rhythmic distortions for both Bach and Brahms and abound throughout their works. But your example is not one of hemiola.

In addition there's no hemiola in either My Country 'Tis of Thee or America the Beautiful that anyone could possibly notice. Both tunes use a rhythmic pattern which is identical throughout the phrases of the tune. Da, da, da, da,duhda is all there is to My Country 'Tis of Thee, all four phrases. America the Beautiful isn't even in triple meter and ever pair of beats has a vigorous downbeat. If those tunes had anything like a hemiola in them they wouldn't ever have become what they are - popularly accessible melodies in a folk style.

Hemiola is a division of 6 beats into three groups of two at a cadence within the context of the division of those 6 beats into two groups of three. It's a syncopation intended to accelerate the rhythmic pulse towards the cadence, like the sensation of a rollercoaster approaching the bottom of a dip. However, it is not a distortion of the pulse throughout a piece, as in the Schubert.

In that case it is simply one of Schubert's devices to maintain rhythmic interest as a background to the violin solo which will come in a moment or two after your example.

4:12 PM  
Blogger Scott Spiegelberg said...

Hemiola is not so strictly defined as elf makes it. In most theory texts it is defined as the momentary obliteration of the global meter with a local new meter. This is done with regularly occuring syncopations that create a pattern that can be perceived as a new meter. There can be plenty of reasonable argument as to whether a particular example is a hemiola or not, based upon the perceptions of the listeners.

Interesting blog! I shall start reading regularly.

9:26 PM  
Blogger Marlon the Music Lover said...

elf, thanks for your thoughts. I've made my case about why I think the D. 960 Trio at least potentially involves hemiola, so I won't rehearse it here.

I would like to comment on a couple of other things you wrote:

(1) Hemiolas certainly are often used to accelerate toward cadences. (I like your roller-coaster simile.) But they do appear in other contexts as well. For example, Schumann's Symphony #3 ("Rhenish") begins with hemiolas. (That's actually an interesting case, because the underlying, notated meter isn't revealed until after the hemiolas!)

If you're interested in cadential hemiolas, there's an engaging article by Channan Willner about how they can overlap one another in Handel's music. I'm having trouble getting a working link right now, but it's in Music Theory Online (, vol. 2 no. 3.

(2) My analyses in Part 1 were of "A Weekend in the Country" and "America" (West Side Story), not "My Country 'Tis of Three" and "America the Beautiful." You've also mistaken the Schubert example here for something else--D. 960 is for piano solo.

Scott, I'm glad to hear you'll be reading more in the future! And thank you for your textbook reference to "momentary obliteration," which expresses beautifully what I argued against in Part 1. There I expanded on my belief that the global meter is not actually obliterated, but rather takes on a new and less obvious role.

1:24 PM  
Blogger Bearette24 said...

Marlon, you have found fellow hemiola fans!

5:00 PM  
Blogger Marlon the Music Lover said...

Well who doesn't like hemiolas? 8-)

7:17 PM  
Blogger Newfweiler said...

Does anyone know the etymology of "hemiola"? I always thought it should be

-- A medical condition ("Patient has a hemiola in the carotid artery")

-- A half-sized wind-up gramophone

--A bad-tasting breakfast cereal

--A sewing machine specialized for fancy hems

3:03 PM  
Blogger Martin said...

You're blog is GREAT. Do you have new stuff somewhere else?

12:05 AM  
Anonymous Lindsey N. said...

What about a "reverse hemiola", as in with the effect of not speeding up the tempo feel, but slowing it down?

An example of this can be found with "Think Of Me" from the "Phantom Of The Opera".

The underlying meter is simple quadruple(4/4) and/or simple duple (2/4). She sings the lyrics "spare a thought for" over three simple duple meter (2/4) measures, but it's as though she is in only one compound quadruple meter (12/8) measure.

This is not a meter change from simple to compound because The beat does not change to a dotted quarter note. The quarter note still gets the beat throughout, so the duration of the eighth note remains the same throughout as well. It's instead a change in the grouping of how the eighth notes are stressed.

This is how I would count it with the stresses:

ONE-and-two-AND | one-and-TWO-and | one-AND-two-and

Notice how it's counted as three simple duple measures but the stresses are in four groups of three? Would this not be a "reverse hemiola"?

I'm not sure how else I would analyze this, but maybe I'm wrong.

Do you have any examples of "reverse hemiola"? And would that even be the correct term to use?

11:31 PM  

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