We first met the idea of hypermeter briefly in the Other Rhythmic Essentials chapter. As discussed there, the strong–weak style of patterns we have seen within measures do not necessarily only operate within the measure and stop at the measure-length pulse. Especially when we have short measures and fast music (like a presto in [latex]\mathbf{^3_4}[/latex]), there can be a strong sense of such metrical relations at “higher” multi-measure levels. In Western tonal music, just as the most common division/grouping within measures is by twos (and thus fours, eights etc), so it is also with hypermeter. That said, grouping by threes is also eminently possible, as are fives and sevens. When you look more closely, you notice that interesting composers frequently rove between these options fluidly in a way that would be extremely unusual at the counting (tactus or beat) level.

Hypermeter in 3s: “ritmo de tre battute”

One of the most famous, explicit notations of hypermeter is the “ritmo de tre battute” section of Ludwig van Beethoven’s Symphony No. 9. This marking literally means “rhythm of three bars/measures”, so here we have Beethoven explicitly stating that he intends for the measures to group in threes. In doing so, the instruction also makes explicit the assumption that the grouping had been in twos and fours up to that point. Example 1 reproduces the four-measure grouping seen in the Other Rhythmic Essentials chapter:

Example 1. 4-measure hypermeter at the start of Beethoven 9/iv from the Other Rhythmic Essentials chapter.

Now Example 2 shows the later “ritmo de tre battute” section (from m. 152) with comparable “hypermeter counts” as well as (editorial) double barlines to show each group of 3.

Example 2. 3-measure hypermeter from measure 152: “ritmo de tre battute.”

Note that we’re talking about the periodicity of the grouping here: that is, grouping in threes or fourss. There’s plenty more to say about the phase: that is, which measure in the cycle should be counted as “1.” There’s a lot to argue for the phase shown in this movement, although the dominant-to-tonic movement in the first to second measure of the figure sure might make you wonder about starting the phase a measure later.

Finally, for the sake of comparison, Example 3 sets out that same “ritmo de tre battute” section re-notated explicitly in [latex]\mathbf{^9_4}[/latex] to place both 3-grouping metrical levels within the notated meter.

Example 3. The 3-measure hypermeter from Example 2, re-notated in [latex]\mathit{^9_4}[/latex].

Hypermeter in (Performance) Practice

Western classical notation uses measures and bar lines partly for coordination among musicians, but also to imply the meter of the music. The first beat of the measure—the downbeat—is taken to be the strongest beat of the measure.^[1] Notating the same music in different time signatures makes a big difference: if you shift the music to put the downbeat at a different point in the cycle, you can expect the performance to sound different.

The same principle goes for hypermeter. In the Beethoven example above, where the hypermetrical grouping is in fours, musicians will tend to perform it with a kind of [latex]\mathbf{^{12}_{\:4}}[/latex] pattern in mind; where the “ritmo de tre battute” shifts us to thinking in terms of a three-measure hypermeter, then we get something like the [latex]\mathbf{^9_4}[/latex] shown in Example 3.

That all said, do not expect the conductor to start beating in triple meter! Why not? Well, if the music is notated in [latex]\mathbf{^3_4}[/latex], and the conductor is clearly beating in a triple meter pattern, then it would be entirely understandable for some musicians to think that the conducting relates to the [latex]\mathbf{^3_4}[/latex] time signature. Professional orchestral musicians know Beethoven’s Ninth well enough to avoid this pitfall, but that cannot be assumed for less-known works, and why risk it anyway? Conductors know how to indicate hypermetrical structure without changing the beating pattern, just as they know how to indicate phrasing and other matters.

Additional Levels of 3s at the Fast End?

Like a compound triple time signature ([latex]\mathbf{^9_4}, \mathbf{^9_8}[/latex], etc.), “ritmo de tre battute” explicitly sets out two levels of three-grouping. Arguably, it’s the two adjacent levels of three-groupings that’s notable here—the fact that Beethoven notates it with one of those levels in the hypermeter is less significant.

So, can we have more than two levels of three-grouping? Well, [latex]\mathbf{^{27}_{\:x}}[/latex] time signatures are not seen (at least in this style), and neither is anything like “ritmo de 9 battute”, but Beethoven does occasionally use three sets of three levels in his late style, i.e., adding another layer of triple at the “short” or “fast” end of the spectrum. This is always notated with triplets: another way to get three-grouping into the metrical structure without having to include it in the time signature. Examples include:

• In movement 4 of the String Quartet No. 14 (Op. 131), there is an “Adagio ma non troppo e semplice” section in [latex]\mathbf{^9_4}[/latex] time (from m. 186), so we already have two levels of threes right away (3×3 quarters). Later, it briefly uses eighth note triplets long enough to perhaps be called a metrical level (mm. 223–225, or 5–7 measures before the final Allegretto reprise).
• The second movement of Beethoven’s last piano sonata (No. 32, Op. 111) is an “Arietta” in compound time signatures: [latex]\mathbf{^{\:9}_{16}}[/latex] at first but also [latex]\mathbf{^{\:6}_{16}}[/latex], and [latex]\mathbf{^{12}_{16}}[/latex] for some sections. Additionally, some of those sections use triplet sixteenth notes to give another three-level. When this happens in [latex]\mathbf{^{\:9}_{16}}[/latex], we have three levels of three-grouping that could have been written as [latex]\mathbf{^{27}_{32}}[/latex] (Example 4).That said, the hypermeter is regular, so 3×3×3 seems to be the limit for now. And the triplets in [latex]\mathbf{^{\:6}_{16}}[/latex] and [latex]\mathbf{^{12}_{16}}[/latex] add another three-grouping, but with two-grouping in the metrical levels.

Example 4. Three sets of three-groupings (effectively 27!) in Beethoven’s Op. 111.

Sensible Limits and the Psychology of Meter

Where do we stop looking for metrical levels above and below? Some accounts of hypermeter have extended the idea to entire movements, describing them, for example, in terms of a huge upbeat–downbeat pattern (see the end of Cooper and Meyer 1963). The psychology literature suggests a more modest scope, with meter giving way to form not necessarily at the limit of the notated measure, but also not far beyond. The idea is that we struggle to perceive metrical cycles and patterns when the pulse is too short (about ⅒ of a second) or too long (a few seconds, depending on the internal content). So in practice, it makes sense to consider hypermeter when the measure is very short (like the [latex]\mathbf{^3_4}[/latex] presto discussed above) but not for too many more levels beyond.

Not Limited, and Perhaps Not So Sensible Either

Composers, theorists, and especially composer-theorists reading this may be wondering about the extreme cases. Notwithstanding the psychological limits to meter as distinct from form, what’s the structural limit, the ne plus ultra? In other words, how many levels of three-grouping can we stack on top of one another? Mark Gotham’s “Sierpiński’s Triangle” (Example 5) is a piece composed to group in threes at every structural level from, the individual notes right up to the highest formal units. The title “Sierpiński’s Triangle” refers to a triangle-fractal pattern that shares something of the same structure. The musical piece is the first movement of a set titled Tesselations. 

Example 5. Three-groupings all the way down (in meter and in form) as a compositional plan in “Sierpiński’s Triangle” by Mark Gotham (download score).

1. Coming soon!