Systemizations

For the Dalcrozian, systemizations have frequently occurred throughout our course, although for many of us they might have been found under other names: series, sequences, patterns, or sometimes, simply, phrases. One of the first systemizations I experienced in my Dalcroze training happened in a class on augmentation and diminution back in 2003. After working through several exercises involving augmentation and diminution of various patterns, our teacher Lisa Parker, improvised music for an anapest (short-short-long) pattern presented as the following phrase:

We discovered the phrase first by listening to Lisa’s improvisation, and we demonstrated it through gesture and movement in many ways: alone, with a partner, with body percussion, improvised choreographies, and vocal improvisation. We conducted arm beats as we moved, sometimes conducting at various durations: first with q arm beats and then with e and h arm beats. Using arm beats was a challenging dissociation from the patterns I was stepping, but it also helped me to organize and understand the rhythmic structures in a musically satisfying way. I remember it being so helpful to have the augmentation and diminution presented in one phrase so I could practice how the patterns felt in relationships to one another. I gained new insights into the unique feel and character of each rhythm.

I also recall how this type of activity challenged my memory, as we did not write it down until after we had performed a multitude of repetitions and with a wide variety of musical affects and styles. After experiencing many reaction-type activities in the first part of class, I welcomed the idea of a phrase because it allowed me to prepare for each iteration of the rhythm in musical time. That type of preparation enabled me to think ahead and plan for shifts in energy and nuance. What joy we all felt when we finally were able to coordinate our minds and bodies through Lisa’s beautiful music!

Until the Dalcroze Society of America formed the Professional Development Committee in 2012, it was not common for many of our United States diplômés and teacher trainers to use the term “systemization.” Personally, even though I had been doing activities like the one described above throughout my Dalcroze training in the US, I did not learn of this term until 2008, when I studied at the Institut Jaques-Dalcroze (IJD) in Geneva, Switzerland. One of the revered solfège professors at the IJD, who was also the former dean of the professional students, Madeleine Duret, wrote that to systematize means establishing logical sequences in rhythm, meter, melody, or harmony. At the Dalcroze School of Music and Movement, where I am the program director, we use the following definition, found in Embodying Music, volume 4:

A systemization (also sometimes written as systematization or systemisation) is a logical, ordered pattern of a given musical or movement concept within the context of a phrase, where the idea is manipulated to demonstrate specific dimensions of its identity. Systemizations often demonstrate the subject in several of its variations, capacities, or transformations. Typically, systemizations manipulate a given subject throughout the course of a measure, phrase, or other larger form. Systemizations can be represented at an instrument, with the voice, the body, or other materials. (Dittus 2020, 113)

Though the term might be a more recent development, its use and practice by Dalcrozians is quite storied. As a Dalcroze teaching strategy and/or technique used by Dalcroze practitioners, systemizations are quite flexible and can be used in all branches of Dalcroze study: eurhythmics/rhythmics, solfège, improvisation, plastique animée, and pedagogy. There are many global benefits to this type of activity in the Dalcroze hall because systemizations challenge us in several key areas:

1. Memory
2. Preparation
3. Control and coordination
4. Phrase and structure

Systemizations exist in all kinds of repertoire in the standard repertoire from the Common Practice Period (1650–1900), but also in music of the twentieth century and today. Although these examples may not be as strict in design as what we might do in a class, they still offer inspiration in envisioning new structures.

Regardless of whether an example is “strict” or not, systemizations offer Dalcrozians succinct ways to practice any number of important skills such as shifting weight, coordination, and balance. Because there is so much variety in how systemizations can be structured, the specific objectives of each systemization are unique.

Systemizations allow for Dalcrozians to fit a great deal of musical material into a relatively small package, which can aid in efficiency in our teaching while still maintaining a high level of artistic integrity. Systemizations have other practical uses in Dalcroze pedagogy because they allow for diverse elements to be placed in dialogue with one another, allowing the mover to experience the rich interconnectedness inherent in phrasing, form, and structure. While I will focus my discussion on musical subjects, please keep in mind that systemizations can be used in dance, theater, therapy, etc. In the next section, we will examine several examples of different types of systemizations.

Rhythmic Systemizations

Systemizations with Rests

Example 1a is a classic example of a systemization using changing rests throughout a measure of 4-time. The systemization could be described as follows: The first measure places the rest on beat 1, the second measure places the rest on beat 2, the third measure places the rest on beat 3, and the fourth measure places the rest on beat 4. Try stepping/clapping/improvising on this phrase.

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Systemizations with Quarter Rests

Example 1a: 1 → 2 → 3 → 4

Example 1b: 4 → 3 → 2 → 1

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Example 1c: 4 → 3 → 2 → 1

Example 1d: 1 → 2 → 3 → 4

What do you notice? How does each pattern feel in relationship to one another?

We could also invert the first phrase so that in the first measure, the rest lives on beat 4; in the second measure, the rest lives on beat 3; in the third measure, the rest lives on beat 2, and in the last measure, the rest lives on beat 1.

When we compare/contrast the systemizations in examples 1a and 1b, they feel quite different from one another. In example 1a, the rhythms can feel anacrusic. In each measure, the anacrusic phrasés are shrinking in length while the metacrusic pulses are increasing. (Phrasé is a French term referring to musical gesture and phrasing.) See example 1c, which adds annotations to example 1a.

Example 1b, which contains the same rhythms but is structured differently, does not have the same measure shape. Instead, the notes before each rest get an emphasis and can feel rather syncopated, as indicated by the asterisks shown in example 1d.

Of course, it all depends on how the improviser realizes each series. What harmonies are used, where the harmonies are placed, the shape of the melody, and the articulations used all impact how we hear and understand the material. But all this rich musical material comes from the humble systemization.

Systemizations with Sixteenth Notes

Example 2 is the same idea using sixteenth notes; how does it compare to the phrases using rests?

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Systemizations with Four Sixteenth Notes

Example 2a: 1 → 2 → 3 → 4

Example 2b: 4 → 3 → 2 → 1

Each of us might feel these two phrases in our own ways, which is one of the great things about how Dalcroze education operates. However, one of the things that I look for when I teach this pattern is how people negotiate weight along with time, space, and energy. The movement of the four sixteenth notes is demanding, and it encourages the mover to lean into the short notes with their entire body while lifting the body up and slightly back as they near the end of each group (especially when the systemization ends with four sixteenths; it’s a really challenging inhibition and coordination event!). When I do the same structure with rests, I might look for entirely different things. For example:

Do the movers arrest their motion during the rests or do they fill the rests with silent gesture? (Both are valid to me, but it’s an artistic choice.)

Can the movers maintain their balance during the rests or do the rests create instability?

Are the rests incorporated musically and with flow, or do the rests make the rest of the phrase feel wooden and disjointed?

Rhythmic Systemizations in Opposition and Dissociation

The next systemizations use patterns in opposition and dissociation, which can be readily performed in the body with feet versus hands, voice versus hands, or left hand versus right hand. They could also easily be performed between two people: one performs the lower voice and the other performs the upper voice.

Beats vs. Divisions

This systemization uses patterns of beats and divisions. In the first set of example 3, the phrases have a structure of four dotted-quarter-note beats in the lower voice and four groups of three divisions in the upper voice, and then the roles reverse. The second set of phrases is similar but shorter, each group lasting two beats instead of four. The final set of phrases change every beat.

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Systemizations with Beats vs. Divisions

In groups of 4, 2, and 1

In George Frideric Handel’s Gigue in D Minor, we see elements of this systemization. Although the time signature is different, the meter is the same (compound quadruple), and the feeling is quite similar.

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Keyboard Suite in D Minor, HWV 437

IV. Gigue

George Frideric Handel

Beats vs. Patterns

You can imagine a similar structure of beats versus patterns. For example, perhaps instead of beats versus divisions in compound meter, the systemization could use beats versus a rhythmic pattern.

For instance, example 5 shows beats versus amphibrach (short-long-short) patterns.

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Systemizations with Beats vs. Patterns

Amphibrach patterns in groups of 4, 2, and 1

Syncopation Systemizations

Example 6 shows a great example of off-beat syncopation in a similar structure to the previous example, but slightly different: 8 + 8, 4 + 4, and 2 + 2 + 2 + 2.

What other phrase structures might you imagine?

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Syncopation Systemization

In groups of 8, 4, and 2

Metric Systemizations

Systemizations with Changing Meter

I really enjoy working on systemizations of changing meters of all different kinds. Example 7 is one of my favorites.

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Systemizations with Changing Meter

4-time, 3-time, 2-time

3 + 2 + 2 or 2 + 2 + 3

This is a great way to compare the feeling of each type of simple meter: duple, triple, and quadruple. The structure is two measures of 4-time, followed by two measures of 3-time, followed by four measures of 2-time. On first glance, it appears very asymmetrical, and, in fact, it is. However, because of the systematic nature of the changing metric structure, it can work very well and feel rather balanced.

Another systemization that I enjoy doing with elementary school children and teenagers alike is to compare measures of 2 and 3 in various patterns.

I might ask the students in groups of two to “bounce-catch” a ball to each other in measures of 2-time and then “roll the ball” to each other in measures of 3-time. After exploring the game with verbal reactions, then I can introduce a series of meters for the students to experience. It’s always great fun!

Incidentally, this 3 + 2 + 2 version is the basis for the 3^rd movement of Brahms’s Piano Trio No. 3 in C Minor, op. 101, shown in example 8.

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Piano Trio No. 3 in C Minor, Op. 101

Mvt. 3

Johannes Brahms

12 Eighths Systemization

Here is another example invented by Jaques-Dalcroze himself: the 12 eighths. In the classic systemization of the 12 eighths, there is one measure of each meter: {2/h.} + {3/h} + {4/q.} + {6/q}. However, throughout the activity, the eighth note value remains constant so that the feeling of each meter can be more easily felt. In these cases, the round and swingy nature of compound meters is felt in stark contrast with the somewhat vertical and angular simple meters.

It also shows how divisions can be felt differently from subdivisions. For example, in measures of  {2/h.}, the beat durations are {h.}, the divisions are {q q q}, and the subdivisions are {eeeeee}. Similarly, in measures of  {3/h}, the beat durations are {h}, the divisions are {q q}, and the subdivisions are {eeee}. In the last two meters, the role of the eighth note changes from subdivision to division. So, in measures of  {4/q.}, the beat is the {q.} and the division is {eee}. Similarly, in measures of {6/q}, the beat is the {q} and the division is {ee}.

In the version shown in example 9, the durations of each beat are in the lower voice while the subdivisions/divisions are in the upper voice. There are many versions of this systemization; this is a simpler one.

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12 Eighths Systemization

For more examples of how Jaques-Dalcroze used this systemization in various contexts, the book Cours de Vendredi 1931–1932 is a valuable resource. It was collected by Mari-José Ekström-Julliard in 1999 and published by the Institut Jaques-Dalcroze in Geneva.

Melodic Systemizations

Example 10 is a solfège systemization using the pentatonic scale (the numbers represent scale degrees). Try singing and conducting this systemization for yourself.

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Pentatonic Anacrusic Systemization

In compound meter

Here, we see additive eighth notes to each anacrusic gesture in compound duple meter. Further, as the systemization unfolds, we discover that the scale outlined is pentatonic, which presents some interesting challenges to the singer to stay in tune and negotiate the various leaps within the scale and between the starting and ending points of each phrasé.

Similar compound meter systemizations can be found on page 34 in Jaques-Dalcroze’s Rhythmic Movement, volume 1, although these are purely rhythmic, notated without melodies.

A more common version of this systemization exists in simple quadruple meter, shown in example 11. Aside from the melodic and rhythmic elements presented, it also offers another type of structure: a harmonic systemization. Here, each harmony in the left hand arpeggiates a diatonic 7^th chord that beautifully supports every scale degree in the melody. I would not say that this presents functional diatonic harmony of the Common Practice Period, but it does offer diatonic planing in sequence!

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Major Scale Anacrusic Systemization

Example 12 shows a great example by Beethoven from the finale of his Symphony No. 1 in C Major, op. 21, which is a superb variation of the systemization from example 11!

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Symphony No. 1 in C Major, Op. 21

Mvt. 4

Ludwig van Beethoven

Harmonic Systemizations (sequences)

Finally, other applications of systemizations include harmonic systemizations or sequences. We can find examples in literature of descending 5ths, ascending 5ths, and descending 3rds. When improvising for classes, the 5–6 technique can be a useful framework.

This Minuetto by Scarlatti from his Sonata in C Minor, K. 73, shows a beautiful example of a sequence of descending 5ths.

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Keyboard Sonata in C Minor, K. 73

Minuetto

Domenico Scarlatti

In Beethoven’s Sonata No. 21 “Waldstein,” op. 53 mvt. 3, we can see an exciting example of ascending 5ths!

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Piano Sonata No. 21, Op. 53 (“Waldstein”)

Mvt. 3

Ludwig van Beethoven

Aside from a wealth of popular music, sequences of descending 3rds are common in classical literature too. The end of the first movement of Brahms’s Cello Sonata No. 2 in F Major, op. 99 (shown in example 15) showcases a great descending 3rds progression!

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Cello Sonata No. 2 in F Major, Op. 99

Mvt. 1

Johannes Brahms

When improvising on the piano for systemizations, chord progressions like the 5–6 technique shown in example 16 are invaluable. These progressions lend themselves to repeating rhythmic motives for long periods of time as students practice a systemization. Using these progressions also allow teachers to focus attention on the students. Plus, they are harmonic systemizations themselves!

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Harmonic Systemizations (Sequences)

Ascending 5–6 Technique

Descending 5–6 Technique

In the ascending 5–6 technique, note the intervallic motion from a 5th to a 6th between the bass and soprano. In the descending 5–6 technique, note the parallel 10ths in the outer voices and the intervallic motion from a 5th to a 6th between the bass and the alto.

Closing Thoughts

While this article has offered several ways of approaching and understanding the use of systemizations in the Dalcroze hall, it is by no means the final word on how they can be used. Dalcroze education is a constantly evolving philosophy, and practitioners are encouraged to create their own applications of systemizations. There are limitless options afforded to the Dalcrozian who is curious and interested in exploring new ways of knowing, and the systemization is no exception. This limitless opportunity to create continues to encourage me even after over twenty years in this method. I hope to see some of your favorite systemizations on the DSA blog or perhaps in a future issue of Dalcroze Connections!