How do you teach measure groupings (hypermeter) to your intermediate-level students?

 

I was introduced to measure groupings when I was a college junior–not by a teacher but a classmate. We were rehearsing the scherzo of the Beethoven Cello and Piano Sonata No. 3, Op. 69 (see Excerpt 1).

We did our first run-through at a moderate tempo just to see how it would fit together. Then as we were going to speed up individual sections, my partner advised, “My teacher told me it sounds better if we ignore every other bar line.” I wasn’t exactly sure about what he meant, but I knew that he was studying with the principal cellist of the St. Louis Symphony Orchestra, so I was all ears. He demonstrated part of the ‘A’ section, continuously alternating between “strong” and “weak” measures. It made perfect musical sense! It was vibrant, flowed more easily, and sounded more three-dimensional. It frolicked like a piece of jazz, with the syncopations kicking the music incessantly forward even more than before. In subsequent practice and rehearsals I pretended it was in 6/8 so it would be easier to keep it self-sustaining (technically, 6/4 would have been more accurate).

Musically speaking, our scherzo blasted off after this and we never looked back to feeling individual measures, but we still needed to be mindful of the accuracy of the syncopations. We even discovered that certain parts worked better in four-measure groups rather than two. This was my first conscious experience with measure groupings and it was an exciting one, particularly since the discoveries were generated and shared with a colleague. I didn’t learn the term for it (hypermeter) until years later when I was doing my doctoral studies, but I kept an eye and ear open for it from that initial point onward. I subsequently came to realize that any repertoire to be played “in one” (most scherzi, not just this one) and many fast pieces in cut time or triple meter (for example, many Scarlatti sonatas) were good candidates for measure groupings.

An early-advanced piece by Beethoven that uses hypermeter is the first movement of his Piano Sonata in G Major, Op. 79. Note the omitted barlines and the altered time signature (the original is in 3/4) (see Excerpt 2).

This is a clear example of music that starts on a hypermeasure upbeat –the first real downbeat does not occur until the notated second measure, therefore the entire first measure functions as an upmeasure . Notice how the harmonic and melodic rhythm confirm this feeling of a larger 6/4 meter in the ensuing music. This pattern continues during the entire movement except for an occasional “hypermeter change” to 3/4 at the end of the exposition, and at times in the development section. Played in this way, this music has an infectious swing and sway that reinforces its sparkle and wit; played strictly in 3/4 as notated, it doesn’t quite leave the ground.

Another fascinating example of hypermeter from Beethoven is found in the first movement of his Piano Sonata in C Minor, Op. 10 , No. 1. Before teaching this piece to an undergraduate some years ago, I explored its hypermeter in my studio practice. It was clearly in 6/4 but not consistently so. At first, because of the opening loud and long two-handed chord, I assumed that it started on a hypermeasure downbeat. Then I experimented and was surprised to discover that if I instead treated the first notated measure as an upmeasure (as in Op. 79 above), the propulsion and phrasing of the entire main theme group was even more compelling. (See Excerpt 3. Note the omitted barlines and altered time signature.)

This approach also created a different feel for the extended thematic material (starting at m. 22), which now did put the forte chord on a hypermeasure downbeat. This is not the only way to interpret this movement, but to me it sounds as artistically valid as any others I have heard.

Although measure groupings start to show up more prevalently in intermediate and advanced-level literature, there are examples in elementary music where the concept is applicable. For instance, “The Horseman’s Night Ride” by Nancy and Randall Faber, in the Performance Book, Level 2a of Piano Adventures (see Excerpt 4).

When this is played up to speed with an awareness of the eight-measure phrases, it emerges as having a hypermeter of 6/4. It actually could have been notated as a 6/8 composition, but then it would not have fit into the concept structure of the method series at this level. There are many other pieces like this in the early level books of modern piano methods.

Our two authors this issue, Matthew Hagle and Michael Benson, share numerous insights as they elaborate on hypermeter and discuss its teaching implications in other repertoire. After reading their articles for the first time, I was reminded of two important facts: 1. The fewer downbeats there are, the more likely that the music will flow and soar. 2. When teachers are on the lookout for hypermeter in any piece they teach, then rhythm, phrasing, and tempo become interdependent. This happily clarifies and simplifies the music for the teacher and student, and thus ultimately for the listener.

Freedom from the ‘tyranny of the bar line’

by Matthew Hagle

Hypermeter is a topic with a formidable name, and it has been a recent source of much interesting theoretical abstraction. However, it is also an intuitively musical idea that can lead to more naturalness and flexibility in playing. The term refers to grouping measures into patterns that work in the same way that beats do in individual measures. To explain more fully, let’s consider how beats usually work in a measure.

People often think of rhythm in terms of beat levels and stresses. On the level of the beat, a 3/4 measure usually has one primary stress on the downbeat followed by two unstressed beats. If we think of the first subdivision (eighth notes), there will be two eighth notes per beat, with the first one stressed and the second one not. We will have descended one rhythmic level, from beats to subdivisions, and you could do the same thing again in order to think about sixteenth notes and their stresses, and so on, continuing indefinitely.

When thinking about hypermeter, instead of going down below the level of the beat to subdivide it, you go above it to think about the way measures fit into metrical groupings, with their own stresses. So a four-measure phrase in 3/4 could be thought of as a giant 12/4 measure (called a hypermeasure ), or perhaps two 6/4 measures. The entire phrase would function as one big measure, with the written measures functioning as beats.

What are the advantages of thinking this way? The most immediate one is that it frees you from the “tyranny of the bar line.” The fact is that time signatures and bar lines are conveniences imposed upon the music for readability, yet the composer’s primary level of interest is often not on the beat or measure, but on the phrase. As teachers, we often emphasize beats and bars when trying to teach students to keep a steady pulse. The resulting playing might have exactness but could lack flow or naturalness. Thinking about measure groupings puts the emphasis back on the phrase, and this approach can allow the student to feel, hear, and think about the phrase’s natural stresses, leading to a more musical performance.

Examples of hypermeter

I have rewritten a few musical examples to produce hypermeasures. Example 5 (which was first noticed by the distinguished theorist Edward Cone in his book Musical Form and Musical Performance ) 1 is from the beginning of Chopin’s Prelude Op. 28, No. 7 in A Major. One danger in performing this piece is that an unnoticed accent on the half note that begins each even-numbered measure will make the phrasing bog down; one hears this surprisingly often in student performances:

Audio Clip 1 mp3, 500kb.

When the meter is rewritten as 6/4, the even-numbered measures gain a lightness that substantially aids the flow of the piece. These 6/4 hypermeasures also create a clear four-bar phrase, clarifying an important element in the piece:

Audio Clip 2 mp3, 400kb.

The next example is not an intermediate-level piece, nor even strictly an example of hypermeter, but it is such an intriguing application of creative rhythm rewriting that I want to include it. It comes originally from the fertile musical brain of the great pianist Artur Schnabel (and I’ve heard other examples of this type of rhythmic rewriting in the teaching of Schnabel’s students such as Claude Frank, Leon Fleisher, and Maria Curcio Diamand). This example, from Brahms’s Rhapsody Op. 119, seems to be a five-bar phrase in 2/4 time.

Audio Clip 3 mp3, 230kb.

In its rewritten version you can see that by rewriting the last two bars in 3/4 time, Schnabel has changed it to a regular four-bar phrase, making clear an underlying ambiguity in our way of hearing it:

Audio Clip 4 mp3, 230kb.

In my perception of it, the phrase flips back and forth like one of those perspective-shifting pictures where the vase changes into the two faces.

My last example is a very familiar one: Mozart’s “easy” Sonata in C major, K.545. To my mind, Mozart’s music is a prime candidate for finding hypermeasures because his surface rhythms can be very balanced and regular at times. I’ve heard performances of this piece that accented the first beats mercilessly, creating boredom where there need be none.

Audio Clip 5 mp3, 370kb.

In rewriting this piece, the first four bars create one measure, with the “accent” on the third hyperbeat (due to the melodic emphasis and change of harmony); the next four bars create exactly the same pattern (due to harmonic tension).

Audio Clip 6 mp3, 370kb.

Certainly there are other ways to read these measures, but the point is that creating these large-scale groupings forces us to think about phrases and their relationships. Thinking, feeling, and hearing these relationships will help create a sense of long line and maturity in the playing. (Ed. note: Think of how many student performances of Für Elise would benefit from this same approach!)

Beyond analysis–musical activities

The explanation I’ve just given might be interesting to a teacher, an intermediatelevel adult student, or an intellectually mature teenager. However, I would not suggest analysis as the only or best way to teach this. Just as meter becomes something we internalize on an aural and kinetic level, so can higher-level rhythms. It’s not necessarily an intellectual activity, and we don’t necessarily have to teach it as such. Here are a few activities for creating understanding and awareness:

Conduct the phrase
Take a few minutes to teach students the basic beat patterns of conducting. If they play other instruments or sing in a chorus, these patterns may already be familiar to them. Apply the beat patterns at different rhythmic levels: for example, the Chopin example could be conducted in three different ways. First, in 3/4, with three beats per measure, as it is written on the page. Sec ondly, in rewritten 6/4 time, with two beats per measure. Thirdly, hypermetrically in subdivided 4/4 time, with each group of two 3/4 measures equal to one beat. Point out how downbeats carry physical weight when you conduct them; therefore moving the downbeat changes the feeling of the phrase.

Change the tempo
Play the musical example at very different tempos for the student. Often a faster tempo creates longer phrases , while a slower tempo forces the listener to pay attention to beats or possibly subdivisions. You can also have the student do the conducting at different tempos, to show how different beat patterns are physically forced upon the musician by tempo.

Rewrite
Take the musical example (or perhaps a simpler rhythm first, to start with) and rewrite the rhythm with the student in a different meter. This could start with a simple “multiple” of the rhythm (changing 2/4 to 2/2), going on to a more unusual change (3 bars of 4/4 become 4 bars of 3/4), and proceeding to a hypermetrical perspective (rewriting measures as beats). Play the examples for the students and explain what differences the changes make, if any. Creative or compositionally-minded students will especially enjoy this.

Breathe
Have students regulate their breathing according to the progress of the phrase. A good way to start is to have them inhale or exhale alternately on every beat, half-measure, or measure according to the tempo. Explain to them how singers and wind players have to coordinate their breathing with the phrases, and look at the phrases to see how that would affect tempo and emphasis. This article is intended to offer an entry point into a fascinating and musically rich topic. Hopefully, the ideas presented here will lead to fruitful teaching and musical experience. Creative and thoughtful teaching of rhythm can enhance musical performances, and phrase and measure grouping can be a potent tool in any teacher’s toolbox.

Endnote

1 Cone, E.T. (1968). Musical Form and Musical Performance . New York: W.W. Norton, p. 79.

Listening on a larger scale

by Michael Benson

Introducing any new musical concept should be done in a way that is motivating for the student and well-sequenced into the student’s musical curriculum by the teacher. During initial experiences with a musical concept, the teacher should allow opportunities for the student to experience the musical concept through listening to a model performance, for instance, before sharing a formal explanation or definition of the musical concept. To that end, when I introduce measure groupings or hypermeasures to my students, we listen for collections of measures that seem to belong together before attaching a name to the musical concept.

In his 1968 book, Musical Form and Musical Performance , Edward T. Cone introduced the term “hypermeasures” and defined them as large-scale measures that exhibit similarity of motivic, harmonic, and rhythmic construction. 1

Beethoven’s Bagatelle, Op. 33, No. 3 – The analysis

Based on Cone’s definition and on what I hear, Ludwig van Beethoven’s Bagatelle in F Major, Op. 33, No. 3 contains hypermeasures throughout. The opening eight notated measures consist of four in F major followed by four in D major. These constitute two hypermeasures. (See Excerpt 8 on pages 32-33.)

The similarities in structure that create the hypermeasures are: • An upward motivic leap: a 4th in m. 1, a 5th in m. 5. • The following downward motivic leap: a 3rd in m. 2, a 4th in m. 6. • Mm. 3-4 are similar to mm. 7-8, rhythmically and motivically. • The melody resolves to the tonic in each: F Major in m. 4, D Major in m. 8.

Rhythmically, I consider each measure as one beat in a larger 4/4 measure. Those larger “measures” have strong beats (i.e., mm. 1 and 3) in the same way there are strong beats within a single 4/4 measure (beats 1 and 3). Therefore, mm. 2 and 4 are weak just as beats 2 and 4 in a normal 4/4 measure. Notice also that in this excerpt each hypermeasure begins with a new harmony on a tonic, followed by a dominant seventh chord on hyperbeat 3, which then resolves. Beethoven acknowledged this harmonic shift by including a piano dynamic level for mm. 1-4 and pianissimo for mm. 5-8. A similar pattern occurs in mm. 9-16: piano for mm. 9-12 and forte for mm. 13-16. In other words, the dynamic markings help delineate the hypermeasures in the Bagatelle .

Overall, this binary form piece is notated in 6/8. But because the feeling of the initial eight measures (two hypermeasures) is repeated throughout with small variations, the hypermeasures also continue. The A section (mm. 1-16, with a repeat) has one hypermeasure every four notated measures. In the contrasting B section (mm. 17-32) there are three hypermeasures. 2 The A' reprise (mm. 33-62, with repeats written out explicitly) follows with variations of the opening material. At mm. 63-74 the B section material returns with a final cadence in F major following another hypermeasure extension.

Incidentally, the last two measures represent the highest (f3) and lowest notes (FF) available to Beethoven on his five-octave fortepiano – most likely an instrument built by Anton Walter. This might explain the fortissimo dynamic marking and the first pedal marking Beethoven included in this piece (however, the pedal mark is not in all editions).

The pedagogy

How do we teach this information to intermediate level students (or any student for that matter)? Why does it matter with regards to performance? I believe that if a student studies Beethoven’s expressive markings (especially the contrasting dynamics) and listens carefully, the hypermeasures will be observed and most importantly, heard. This allows the student to directly experience the hypermeasures. If musicians at any level perceive groups of measures as a unit, they are then listening on a larger-scale and thus are more likely to share an expressive performance. Timing, in music or life, is everything, and this is true in perceiving hypermeter as well.

Why not just teach the student to read and listen for the notated expressive markings? That would work for performing the score accurately, but it would not allow the student the deeper musical understanding afforded by the harmonic, motivic, and rhythmic elements. This understanding allows the developing musician to communicate both the phrasing and the hypermeter. (Phrases are units of musical form while hypermeasures are metric units. 3 Therefore, hypermeasures refer to the organization of time while phrases refer to both time and pitch, and by extension, slurs, articulation, dynamics, pedaling, etc.)

Once students have experienced hypermeter in this piece I can then introduce the term, and my next goal is to help them internalize the concept. This is achieved by comparing and contrasting the experience with similar pieces. Then to reinforce it, I have the student apply it to repertoire previously learned, and/or to new music as well. As long as the teacher is available to answer questions and practice the application of the new concept with the student, the final step of student ownership will follow as the student applies hypermeter to other appropriate repertoire. 4

Experiencing hypermeter helps intermediate students learn that not all measures are created equal. This may translate into relaxing technically or breathing more during “weak” measures while imbuing more energy into the “strong” measures. Hearing a metric ebb and flow over larger portions of music can inspire the student to shape longer musical lines with a forward movement and naturalness that might otherwise be difficult to achieve. It can also help the intermediate level student hear music less vertically. I believe any music teacher would welcome these longer lines and most importantly, students who have now taken ownership of their own listening and learning.

Endnotes

1 Cone, E.T. (1968). Musical Form and Musical Performance . New York: W.W. Norton, p. 79.

2 From beat two of m. 16 through beat one of m. 20 and again from beat two of m. 20 through beat one of m. 24 there are two hypermeasures. From beat two of m. 24 through the end of m. 31 there is an extended hypermeasure. This extension of similar musical material, mm. 24-31, prolongs and intensifies the musical phrase and delays the beginning of the return of the A' section at m. 32.

3 Stein, D., Ed. (2005). Engaging Music . Oxford: Oxford University Press, p. 19.

4 For further discussion on teaching a new concept, please referenceMarienne Uszler’s chapter 16 in The Well- Tempered Keyboard Teacher ( New York: Schirmer Books, 2000), p. 246.

In the next issue: When is it appropriate to leave rhythms UNperfected for a given student? Have I misassigned a piece in that case?

 

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