“Fifty-fours”

Jan 24

The spatial aspect of rhythmic perception

Rationale for the 54s exercise.

First, I'd like to share a few things about rhythm in general:

THOUGHTS ON TEACHING RHYTHM

Acquiring advanced skills in the area of musical rhythm can be elusive. Musicians often find this to be true of the whole spectrum of rhythmic skills: solo and ensemble performance, listening, memory, transcription, and notation. This is due in part to the fact that there are no fixed, objective definitions regarding the various phenomena and terminology associated with rhythmic flow; almost all rhythmic terminology and perception is relative, with each term being defined by others in a closed loop of other terms. So, like all the most common aspects of determining time and duration, we need an external reference against which we can determine time flow: a metronome, a clock, the apparent movement of the sun, etc. Otherwise, as with objects in space, time simply ‘floats’, much like celestial objects have no ‘fixed’ location—no fixed coordinates.

The perception of musical continuity is dependent on the presence of discontinuity

The natural world presents many varied impressions of time-flow. The sensation of passing time is typically engendered only when there are perceivable changes, either externally, in the environment, or internally, within one’s body or psyche. The flow of time of a lazy summer day may proceed like one continuous, uninterrupted sensation, and only with the presence of some kind of interruption is the sensation of passing time produced. Such interruptions (lunch, tea, email, a mosquito, a phone call, …) in an otherwise uniform flow of the hours can result in a segmentation of the day. And our comparisons of these segmentations help to establish the sensation of passing time.

Such divisions may have a kind of ‘rhythm’ to them, but, for the most part, only when those segments are marked by a more or less periodic recurrence—that is, a perceivable, repeating interval of passing time—is there typically created the sensation of rhythm. And, just as significant, is the duration or speed of these intervals. There is a somewhat limited of bandwidth of frequency (or speed) within which intervals of time will be sensed as rhythm. Intervals that are too long or too short cannot produce the bodily sensation of rhythm.

While we normally sense time in relation to some external ‘grid’, such as the movement of a time-piece, music normally includes its own grid as part of the texture. There are relatively short grids, such as produced by the plucking of a walking bass line or by the left-hand ostinato patterns heard in the piano work of Keith Jarrett; a longer time-grid might be created by the repeating sequence of harmonic changes as in a blues; a still longer grid can be heard in a classical variations form. So some element(s) in the musical texture can become the reference for the perception of flow of the music as a whole. Music which has neither an internal or external reference tends to present a sensation of ‘floating’. This ‘float’ be a very attractive element (as, for example, heard in Debussy’s Afternoon of a Faun); so music does not require the presence of a beat to be appreciated as good music.

A surprising realization may arise from exposure to different world music traditions, and it becomes evident that there are many ways by which continuity requires its opposite: discontinity. And, actually, one cannot exist separately from the other.

to which musical continuity is very much linked—and is perhaps even dependent on—musical discontinuities.

At the level of individual sounds, phrases, or larger units, the character of the discontinuities influences the quality of musical continuity. Mozart’s music is often characterized by the manner in which he connects many shorter phrases and cadences into a larger continuity; Palestrina’s music does not often project a rhythmic vitality partly because the closure of his motifs, phrases, and cadences is often disguised by overlapping material in another voice. His music, then, seems to flow on with a continuity absent in Mozart. Of course, both master composers have written music revealing the strongest sense of continuity, even if the character of their “ongoingness” derives from different materials.

The flow of time may be marked by the repeating pulsations of the heart, the recurrent waves of the ocean, the succession of seasons, or the cyclical movements of the moon, and these recurring time intervals could be characterized as “rhythms.” But rhythmic patterns are most perceptible as musical units when they recur with perceptible and predictable regularity (periodicity) and when when their recurrence is neither too slow or too fast. The body and psyche have upper and lower limits for being able to sense the presence of rhythmic flow.

Rhythmic Pattern vs. Musical Rhythm: The Influence of Shape

There is more than a semantic difference, though, between a rhythmic pattern and a musical rhythm. In my own teaching, I began to see the need to make such a distinction clear, because the standard vocabulary with which we refer to rhythmic elements is not very helpful in the education of young students. This was made very evident to me when, as a new teacher of undergraduate musicianship courses, began to identify some of the most common difficulties experienced by students when they attempted to imitate (echo-clap) or notate a rhythm that was given by means of clapping. Many students could not follow and recall the simplest patterns, such as mixing single-pulse clapping (continuous clapping with no rests) together with two-pulse units (clap-plus-rest, for example, (x-x-x-x-x-xx-x-xx-)

I soon enough realized that, since the actual sound of each individual clap is the same duration (“long” claps don’t actually have a longer, more sustained sound but only a longer gap between subsequent claps) and, because clapped rhythms are not typically performed with much (if any) dynamic or timbral contrast, clapping does not convey very much about rhythmic shape. This led me to think more about the difference between a musical rhythm and a rhythmic “pattern,” that is, a simple succession of long and short durations. It is worth thinking about this issue if you are a music teacher, because …

… in addition to the tempo and length of musical patterns, their accurate perception and effect is very much dependent on the extent to which the pattern conveys a sense of shape. Shape is tricky to define, but it might be considered as one of the most rudimentary manifestations of form or structure. At the most basic level, and for the mentioned objective of transmitting a rhythmic pattern to group of musicians, the creation of shape first of all requires that the beginning and ending of each rhythmic unit need to be clearly distinguished. I use the word unit, since the perception of shape involves similar elements whether it be a rhythmic phrase, gesture, or a rhythmic motive.

And at another level, sensing musical units is very much influenced by the specific elements in the musical line which actually guide our attention. Those elements are what can create the sensation of crusis (the actual moment of either beginning or renewal), anacrusis (moving the attention toward each next point of renewal), and metacrusis (the motion following a crusic moment.)

This is quite important because the perception of musical patterns is strongly influenced by whether and how they transmit a sense of their shape or structure. It is interesting to ask: on what basis is the sense of wholeness or completedness of a pattern established, and how is that conveyed to the listeners? I think that most musicians would agree that musical shape is what communicates a sense of direction by means of contrasts in dynamics, articulation, tone colour, and much else, including, of course, melodic and harmonic elements. Perception of the beginnings and endings of musical units (such as phrases and motifs) is very much dependent on those elements in a musical line which direct our attention toward each point of initiation and renewal (crusis), the way the music moves our attention toward each next point of renewal (anacrusis), and metacrusis, (the musical movement following after each crusis).

Rhythms arise in a relative context

Analogous to melody and harmony, musical rhythms necessarily arise in a relative context, that is, as succession of articulated moments heard against something with a more regular character. It’s possible to create rhythmic textures on the basis of nothing more than a steadily recurring pulse, one which can then be creatively used as a ‘foil’ or ‘ground,’ and against which a second line can create playful agreements and divergences by means many kinds of variation: diminished and augmented values, accents and silences, and so on. While most rhythmic sensations typically arise from the interaction of two of more simultaneously heard musical layers, a composer or improviser can also produce the impression of two interacting layers even within a single musical line (as is common, for example, in the solo instrumental suites of J.S. Bach).

So the impression of rhythm usually involves the integration of two or more lines of musical continuity. Similarly in the realm of pitch, a single tone cannot convey a sense of scale or key centre, nor can a single tone create the phenomenon of interval or triad. For example, a single tone will not be heard as ‘doh’ or any other function except in relation to surrounding tones. A pitch accrues its larger musical meaning, its ‘identity,’ only in relation to a ‘family’ of related tones. These neighbouring tones establish an auditory environment which can ‘locate’ the meaning of the tone and thus imbue it with musical meaning. (Perhaps, by analogy, the ‘geometry’ of a single note is like a one-dimensional point; a musical interval may be likened to a line, which has direction but no area—no ‘body’; three tones can form like a triad.

Likewise, a steadily recurring sensation of an unchanging sound, while it can establish a “one-dimensional” continuity—that is, a simple sensation of ‘ongoing-ness’—in the absence of a second element of flow, the sensation of musical rhythm would not arise. That second layer can be created by a source separate from the ongoing pulsations, or it can arise internally (within the first flow), by means of differentiated elements within that flow (e.g., changes in timbre, texture, dynamics, articulation, pitch, etc.)

Teaching rhythm

For most of the five decades during which I taught university courses in focused on musicianship and improvisation, I most often chose to begin rudimentary rhythmic studies with a focus on pulse, rather than on the more common points of departure, such as beat and meter. While the latter terms are somewhat easier to define and teach, and they are visually represented by traditional graphic representation which is relatively simple and direct, and while those rhythmic elements are also best able to highlight the larger dimensions of rhythmic structure, over-emphasis and preferential treatment of those elements may inadvertently discourage students from properly appreciating the primal element of flow and continuity: pulse

I have noticed that typical rhythmic instruction, both live and published, often begins by glossing over or deemphasizing the shortest, most ‘particulate’ aspect of time flow, in favour of learning about beats and meters. I imagine that there is an assumption that, because these smallest units of duration are almost always addressed as fractions of a larger whole, then the larger units must be understood first. While that makes sense it risks depriving the student of contact with the rhythmic granularity of music. It might be like being given an hourglass timer which, instead of containing fine grains of salt or sand, was filled with pebbles or marbles. How could you reliably keep track of the passing time? Or imagine trying to cook a three-minute egg using a sundial as a timer.

And the concept of granularity has many more applications than only in its exclusive relationship to musical time. For example when we have offended someone, it may not be so much because of what we said but for what was revealed by the small fluctuations of pitch and timing in our vocal delivery, in other words, how we said it.

But, in any case, there are other issues as well.

There are some issues that arise from intellectually prioritizing the larger units of time.

The quarter-note is often described as occupying one fourth or one quarter of the length of a 4-beat measure, just as a 25 cent piece is a ‘quarter’ of a dollar; the sixteenth-note is a quarter of a quarter-note; an eighth-note within a tripletted division of a quarter note would get 1/3, and a dotted eighth-note within a triplet division of a quarter-note would get 3/6 value of the triplet; and a double-dotted half-note is counted as one and seven-eighths of a half note. Those students who were in any degree alienated, confused (and possibly terrorized) by secondary school instruction with fractions would soon begin to self-identify by their groans. Otherwise such students tend to go into a kind of intellectual hibernation, hoping to re-emerge when the coast is clear; when the counting and calculating is over. If you try to demonstrate half of a beat with clapping, the issue becomes more obvious. How do you show half a beat? It cannot be done by stopping your hands before they meet. We cannot clap half a beat until those halves have been defined and sensed as whole units.

[Sidebar: I have experimented with a few different aspects of this question. I might ask someone in the class to clap four beats. They will almost always clap four times and, if questioned about it, they will confirm by counting simultaneously with each of the four claps: “One, two, three, four.” Have four beats actually elapsed? Or only three?

Then they can be invited to clap only one beat. When they only clap once, I ask if the whole beat is only in the clap itself. We know where the beginning of beat 1 is; where is the end? Well, obviously, it’s when you say “two.”

Inconsistencies have come up when numbering things. When referring to someone’s age, we number it only when that period has been completed. We say that the baby is ‘one’ only at the end of that first year, not the moment it is born. But when speaking about music, the beat is traditionally numbered when it begins. Therefore, when we’re counting, “1, 2, 3, 4”, only three beats have elapsed at the moment we say “four.” Four beats will have elapsed if we counted to “five” (or if we return to the count of “one”). Perhaps you can see the depth of confusion that can ensue when trying to put numbers on passing time. But then, here’s a tricky question: On which beat is the exact mid-point of a five-beat measure?]

=MORE ON TEACHING RHYTHM

There are a number of real advantages to beginning rhythmic instruction with the shortest units and then, later, working with the duration of larger units as accretions of the smallest ones. Obviously, if these small durations are not introduced as fractions of a larger unit, they can be displayed with simple graphics showing that there is a sound on a pulse or there is not. There is then no need to display them as note-heads with beams or double-beams. Actually there is no need at all to show these ‘pulses’ as note-heads, and there are advantages to show them simply as exes or even as a succession of vertical slash-marks.

(There will be many graphic materials to illustrate these points but, for now, here is the rhythm of the opening of Eine Kleine Nachtmusik in what I usually call “pulse notation.”

[X - - x x - - x x x x x x - - -] and so on. And adding a separator of some kind can help to show the larger groupings of beat units or measures:

[X - - x |x - - x |x x x x |x - - - ] Students can learn to use such notation for real-time rhythmic transcription (‘dictation’) by using quick slash marks instead of exes and hyphens. I will elaborate on this later on this page.

Below I have used spaces to show the larger groupings:

{ / • • / / • • / / / / / / • • • } And the same phrase of Mozart can be shown with any two graphic symbols, with one symbol representing an articulated pulse and the other showing an unarticulated pulse. For example:

[ A B B A | A B B A | A A A A | A B B B ]

Using alternative symbols in this way can be fun for younger students but the point is nevertheless made evident that one way of sensing and notating a rhythm is to distinguish moments where some pulses are marked with a sound.

| ∞ § § ∞ | ∞ § § ∞ | ∞ ∞ ∞ ∞ | ∞ § § § |

From a pedagogical point of view, the unarticulated pulses can be regarded either as silences (rests) or as the sustaining of a previously articulated pulse. For the first few classes, I don’t make this distinction; it’s simply a pulse with no new event. This allows many students to relax about transcription work because a pulse either IS or ISN’T needing to show an articulation. It can be useful at this point for a teacher to explain that the actual duration of a note is one of its characteristics which are often left somewhat ambiguous by many composers. Notes are often held for longer or shorter than indicated in the score, because duration depends on the resonance of the instrument, what is taking place in in the rest of the texture, the reverberation time in the concert hall, etc. A line of quarter-notes in the basso continuo part of baroque music is often given an articulative pattern in order to provide a specific quality of momentum. So, for example, the quarter-notes in the line below are often played in two-note groupings XXXXXXX, providing some ‘air’ as well as rhythmic liveliness.

It would be good for you to view a few of the relevant exercises in order to have a clear idea what I mean to convey. The point is that these exercises help to insure that the student is grounded in the physical sensation of passing time and not merely numbering it.

∞∞∞Douglas’ exercise of changing counts

“Changing the Phrase Length” (verbal description below, but a video is needed.)

The teacher holds up a card or a number of fingers to show the number to be counted by the group. There is no break in counting (which should be fairly fast) but the teacher will show a different number while the counting is proceeding; the class must switch to the new number beginning the next time they say “one.” Each number gets the same duration so a phrase of ‘3’ will take less time than a phrase of ‘4’. [The teacher has to have good timing, showing the new number before the next count of “one”. 123412341234|123123123123|1234512345123451234512345|12121212

When we learn about rhythm beginning from the smallest units—which can then be grouped in order to form larger units—we do not need to understand musical durations as fractions of a larger whole. The duration of each musical pulse can be sensed as a whole, undivided physical sensation. This is, perhaps, a bit analogous to the way the Greeks thought about “atoms,” that is, the units of matter which they considered to be indivisible. These smallest ‘indivisible’ moments in music are what we can call pulses. If you are correctly tapping the pulse along with some ongoing music, then no new articulation should occur between successive pulses. They are already the finest units in the flow. (But note that, in other languages, pulse has a different meaning; for example, in Spanish, it translates as “beat.”)

======================================================= Feb 13 11:17 pm

I named this exercise, “Fifty-fours,” simply because it comprises 54 pulses. The intention for its formulation was partly the a result of observing how easily music students—even at the university level—can be stymied by some rather rudimentary rhythmic issues, such as metric modulation, double-dotted notes, tuplets, and simple cross-rhythms; it was also very much intended to address issues with remembering rhythms. Highlighting the aspect of visualizing rhythms has been an important goal with much of my material. Seeing rhythms as having shape is something I very much appreciated learning about in my studies of Carnatic rhythm, where there are a number of definite categories of rhythmic shape (yati), which names all derive from ordinary objects and processes: river delta (progressively expanding), cow’s tail (thinning), hourglass (narrowing and widening), etc.

As with most of my exercises it was also formulated to address the confusion and intimidation resulting from the association with bad experiences in math class and a general weakness in ‘keeping time’ or performing simple rhythms. If you’ve never heard of the terms listed above, they will be all be explained and demonstrated in the following material.

Pulse has no fixed musical definition, but I used it to signify the shortest (or fastest) unit of musical flow in a piece or in a shorter section music. Beginning rhythm instruction with a focus on pulse, rather than beat or meter, makes it possible to refer to whole units of time, thereby avoiding the problems that arise from speaking about musical durations as fractions of a larger whole. It cannot escape the notice of an observant teacher that fractions tend to scare, confuse, and alienate many students, particularly those who had trouble in school with fractions, decimals, ratios, with and understanding the relationships between parts and wholes.

Too many students become confused early on, even by the simple notion of a quarter-note. Since most of our first pieces are in 4/4 meter, teachers typically explain that it gets one beat because it is a quarter of the whole measure, just like there are four quarters in a dollar. Very soon they will come to another simple piece in 3/4 time and now the quarter-note no longer computes logically as a quarter of a measure. Teachers that I have observed often do not have a simple and ready explanation for this discrepancy, and these students often enter a university musicianship class with a decided unease concerning the use of a vocabulary that typically relies on numbers and numerals instead of bodily sensations.

Once these students are relaunched into a rhythmic study and practice which uses only whole numbers they begin to relax, understand more, and enjoy their rhythmic development. Moreover, students seem to benefit greatly from the ability to hear, sense, notate, and work with the finer granularity of time-flow.

Consider the impossible task of cooking a 4-minute egg using a sundial that cannot display minutes; imagine the difficulty using an hourglass timer in which finely grained salt crystals were replaced with beach pebbles. The flow of time could not be well measured, if at all. How could anyone dance to music which only played downbeats; how could an orchestra be coordinated if the conductor gave only downbeats? Picking up a small coin while wearing ski gloves is another among many examples where it is necessary to reach out with something sufficiently fine to correspond and make contact with the intended object. Finer gradations in our time-sense are not always necessary but, for the most part, they are particularly critical for sensitive and accurate interpretation as well as for deeper appreciation of many kinds of music. For more on this, you can check out some other pages on this site such as: Guiro Elaboration.

Delaying the introduction of standard rhythmic notation:

I also postpone the introduction of standard rhythm notation until many fundamental rhythmic issues are internalized. This is because I have seen that rhythmic impressions need to be literally incorporated as bodily sensations before getting the intellect involved, that is, before we starting thinking about them. Rhythmic knowledge—ideas and notions about rhythm—remain unusable until they are alive in the physical body. However, since this is a website, the kind of live transmission of musical sensibilities that is most effective (and fun) has to be approached with various workarounds using text graphics and video. This is an unfortunate compromise but there will still be copious material for help with learning about rhythm.

Pedagogical commentary (2):

Much of the work I present to students is in the form of multi-purpose, multi-layered exercises, often intended for elaboration over several weeks. Exercises are most often presented without notation, because I have found this to stimulate the students’ attention and curiosity and their own powers of visualization. Only after the material is internalized, is the notation distributed, and then mainly to serve as a reminder of their work. Most exercises are considered not as finished forms but as templates, intended to prompt students to formulate their own exercises by changing the material to what they need.

So, while the exercises comprising the “Fifty-fours” are all useful and very varied, the exercise itself is nothing special. It’s more like the hub of wheel that has lots of spokes, and it is presented here as a launching site for going deeper into rhythmic skills, rhythmic theory, notation, the division of attention, memory, improvisation, and more. It is intended not only as a set of materials for you to work with, but also to show you ways to formulate your own exercises. You can try to work with these exercises as you read along; the sequence of images and exercises are varied and graduated in difficulty.

The way an exercise is introduced—the way it is set up for oneself or one’s students—must be considered as integral to the exercise. There’s an ecological sense to this notion: that the style and mode of presentation is not something separate from the exercise material that you are sharing. [Just as an animal or plant needs to live in an environment which has the right conditions for development, each exercise also depends for its successful transmission on the best conditions.] And that presentation may include additional resources shared through handouts, a school library, or internet links. And further, those additions can also include the introduction of lively and insightful anecdotes, appealing images, live demonstrations, and even recordings of great artists which reveal usages of the materials so thoroughly disguised as to entirely escape our notice. And, with all this, your students should be able to glean the fact that the very same material can be given many alternate presentations, making it feel entirely different and serve different aims.

So here’s one teaching sequence for this material. It is obviously artificial and very simplified.

==============================================================

One Scenario for Presentation: an imagined classroom sequence

Occasionally a new teacher may find a simulated lesson to be very helpful. Writing it out in this manner may seem like a dumbing down of the material and the process, so you have to imagine that it can be used with young children as well as professional musicians needing support for their rhythmic sensibilities. A video will soon replace this but, since a video cannot show options for continuity as neatly as text, I offer this text-based version of the lesson on “fifty-fours.”

============ FEB 14 1:35 pm

Teacher: Let’s do some call and response rhythm work. Nothing will be written down, so it will be entirely orally transmitted. I’ll clap a pattern and you try to repeat it with me when you can. I’ll repeat it three times so you can be sure where it begins and ends. But try to join in only after you’re pretty sure you’ve got it.

IMPORTANT TO KEEP IN MIND! — A clapped sounds have a very short duration and, except for some small deviations in the sound, each clap tends to sound more or less identical to all the other clapped sounds. So when playing rhythms for teaching purposes, it’s important to remember that the durations of clapped rhythms convey their duration only through the silent gap between repetitions and not through their actual sound. In other words, a whole-note clap will sound identical to an eighth-note clap. And since there’s no possibility to perceive duration in the clapped sounds, duration must be inferred from the length of the silences between successive claps. So using clapped sounds for transmission of rhythmic information (especially for testing the acuity of students’ rhythmic perception) is very misleading and inefficient. Clapped sounds also cannot transmit much in the way of phrasing or cadence, making it a bad choice, despite the fact that hands are so tempting to use.

Therefore it’s best to use sound sources which can clearly convey the durations needed by the teacher. A piano is a reasonable source for this, since it has a clear attack and quite audible sustain and decay.

[LINK to: Sound file will play a 12-pulse pattern: four groups of two pulses followed by four single pulses]

In number notation it could be written as:

|| 2 2 2 2 1 1 1 1 | 2 2 2 2 1 1 1 1 | 2 2 2 2 1 1 1 1 || or, in “pulse notation”

|| x - x - x - x - x x x x | x - x - x - x - x x x x | x - x - x - x - x x x x ||

The students join in as they are able to discern the pattern. I stop to listen and observe to make sure that they all have it. If too many are having trouble, I do not move on to another pattern but help them as needed. “What do you hear? Can you hear that there are some longer claps (longer spacing) followed by shorter ones?” Some students find clapping difficult to follow because each articulated pulse actually sounds the same. In that case I might sing or play a simple melody on that rhythm, e.g.,

||:C - G - F - G - D F E D :||, and I would include articulation to make the phrase as clear as posible. Alternatively I might use rhythmic syllables such as solkattu from Carnatic pedagogy):

||: Tom - Tom - Tom - Tom - ta ka di mi :||

When they can all hear that pattern and when everyone is able to accurately echo clap the rhythm, I continue with another pattern in some obvious way—for example, by extending the string of ones …

[Sound file]: 2 2 2 2 1 1 1 1 1 | 2 2 2 2 1 1 1 1 1 | 2 2 2 2 1 1 1 1 1 |

[The class joins in when able] {then the teacher moves on to the next pattern}

At this point, some people may be having some trouble. You can scan the room to see if those people are (even inadvertently) keeping a beat (tapping their foot, inwardly nodding, etc.). Those people will not likely be tapping their foot at the pulse speed; more likely they will be tapping to mark groups of two or four pulses. They will experience an unanticipated difficulty, since this 13-pulse pattern will not align with any traditional beat/meter structure; the resulting mismatch and rhythmic dissonance will probably make it too difficult to maintain the pattern.

Then, after retreating to the original pattern again [2 2 2 2 1 1 1 1 ], I invite them to echo clap a pattern with a prefix of only three groups of 2:

[Sound file]: 2 2 2 1 1 1 1 || 2 2 2 1 1 1 1 || 2 2 2 1 1 1 1 || [Class joins in when able] {then the teacher moves on to the next pattern}

… then only two groups of 2

[Sound file]: 2 2 1 1 1 1 || 2 2 1 1 1 1 || 2 2 1 1 1 1 || [Class joins in when able]

Again, at this point, those keeping a beat will find confusion, since the pattern will not likely align with it.

The following pattern (of seven pulses) certainly discourages dependance on any regular beat. Sometimes a class can be persuaded to sense the pattern in two ‘unequal’ beats (ref. Dalcroze) by tapping or stepping on the first ‘2’ as wwell as the first ‘1’. So the first beat comprises four total pulses, and is followed by three additional pulses.

[Sound file]: 2 2 1 1 1 || 2 2 1 1 1 || 2 2 1 1 1 || [Class joins in when able] {then moving on to the next pattern}

[Sound file]: || 2 2 1 1 || 2 2 1 1 || 2 2 1 1 || [Class joins in when able] {then moving on to the next pattern}

[Sound file]: 2 2 1 || 2 2 1 || 2 2 1 || [Class joins in when able] {then moving on to the next pattern}

[**From here one could opt to hyperlink to the the exercises in Khanda diminution and Khand augmentation. These files are not yet ready to be uploaded.]

Teacher: (Leaving time for exchanges in between the following prompts to the class …) So how would you describe the basic content of these rhythmic patterns? What do they have in common? What did you actually hear? How were you able to play these rhythms after hearing them only three times? And some of you learned them after only two repetitions! They’re all just clapping sounds. All the sounds are the same and all very short. So how did you even know where the pattern started? (A discussion typically ensues with generous contributions from the students. A synopsis follows…)

Some typical student responses: (written in point form)

a/ I saw that you nodded your head (and you leaned in and moved your shoulders …) when each new repetition began. Your gestures ‘gave it away.’
b/ The shorter claps were played with a crescendo and you played louder on the first clap of each repetition. Also, your eyes and face were more animated at the beginning of each pattern.
c/ The longer claps were always always bunched together, and they always started the pattern. The shorter ones also came in a group and they always led up to the longer ones. They sounded like “pick-ups” or “upbeats” leading to the next downbeat.

Teacher: (written in point form)

a/ That’s right. That nodding is natural … organic, and it is often unintentional and unconscious. You may not even see it in others (or even in yourself) unless you’re looking closely for it. The body involuntarily moves in sync with the musical stresses of accents, downbeats, beginnings of phrases and motives, and so on. This is a wonderful area to research further. From Wikipedia, for example: “Entrainment occurs when your bodily movements synchronize- two distinct acts occur at the same time- with the music. The regions identified were the basal ganglia, the supplementary motor area, and the auditory cortex. To sum up, when you hear a beat, your motor, and auditory brain areas are getting connected.”

b/ That small crescendo is very natural. When the final notes of a pattern continue into another phrase, they are often charged with the energy of anticipation. That’s called the anacrusis of a phrase, and it often expressed by the player and felt by the listener. We like to ‘lean into’ or prepare for the beginning of a new phrase, just as we like to anticipate a new beginning to things. And yes, you can often see it in the musician’s face and whole body.

c/ This is a sign that you became aware of the structure of the motive. Some long plus some short claps created a distinction in the shape of the rhythm and, by the third iteration, you could confirm that the long claps (the longer spaces preceding the subsequent short ones) marked the beginning of the pattern …

Teacher: So did everyone hear longer and shorter claps? Good … because if I sing, each note could be held for a different length. But the clapping sounds themselves are all the same length. It’s the intervals of time between claps that differentiates them; the ‘longer’ claps simply had more space—more silence—following each clap. This can be tricky for many people, and that’s why clapping is not the best way to introduce teaching about rhythm. But since we are using clapping for now, I ask: Were the ‘longer’ ones all the same? Were the shorter ones all the same? If this was so, then this pattern was composed using only two different rhythmic values: the shorter one (ones) and the longer one (twos). Let’s try some other patterns with different forms. By that, I mean patterns with different combinations of twos and ones.

2 2 2 2 1 1 1 1 1

2 2 1 1 1 1 2 1 1 1 1

2 1 1 1 1 2 1 1 1

2 1 1 2 2 1

2 1 2 1 2 2 1 1

1 1 1 2 1 2 2 1 1

Teacher: These patterns were given this way for three reasons: 1/ to realize that a sense-able pattern can be created with only two values, 2/ to hear the pattern without the help (or the hindrance) of hearing them in the context of a meter. In fact, my idea is to temporarily thwart the tendency we all have to feel a beat (or even a meter) behind each pattern. 3/ to make audible the formal structure (the internal groupings) of a pattern, because once we put it in a metric context, we do not usually hear the internal shape of the pattern.

* Once everyone is agreed that there are only two durations in this pattern (the longer and the shorter ones) and that the longer one is twice the duration of the shorter, I want to extend the usefulness of this experience by saying that almost all the rhythms found in the music of the world can be heard as combinations of longs and shorts (twos and ones). It is a bit too reductionist to really perceive them as such, and it would kill much of the enjoyment of the flow of the rhythm to listen in that way. But if you wanted to transcribe or remember the rhythms in the music you’re listening to, you need some tools to parse and make sense of them. In the end it is not such a coarse reductionist approach. After all, the essential difference between oxygen and arsenic is the number of protons in their nucleus. Numbers seem like an abstract quality, but they are in some ways the basis for the differences in the elements of our world.

Teacher: So there are only two lengths of claps? The long one and the short one. How many short ones would fit into the same time as the longer one? Let’s have half the class clap the long ones and the other half the short ones. … So it seems that one long one takes twice the time as two short ones. Is that right?

When the group has become good at it, Invite individuals to try

The 54s work will be fully elaborated later in this page but just so you know what’s coming, here’s the 54s pattern written out and accompanied with an audio recording. The notation is a kind of pulse-notation: every syllable and hyphen receives the same value. So the first two lines below each take four pulses; lines 3 and 4 each occupy 5 pulses. It is presented below first in syllables and then in numbers.

Tom - Tom -

Tom - ta Tom -

Tom - Tom - ta Tom - Tom -

Tom - ta Tom -

Tom - Tom -

Reciting the 54s pattern with syllables: plain no beat

Reciting the 54s pattern twice with syllables: with audible beat

The numbers below represent the pulse count in each word (or vocable or rhythmic syllable). The hyphens represent a pause of the same duration as each syllable. The pause could be thought of as a “rest” (silence) or as the extension of the previous syllable. For the purpose of this exercise, it doesn’t matter.

2 2

2 1 2

2 2 1 2 2

2 1 2

2 2

The pattern above has a total of 54 pulses, hence the name of the exercise. This pattern could have been shown as a linear display, like standard music notation, but it is not helpful at all, because it does not show the pattern’s organization. This post stresses the aspect of spatialization in order to demonstrate some of its pedagogical advantages. Visualization strengthens memory, and having a clear sense of shape makes it far easier to maintain in visual memory. Having the pattern internalized allows you improvise with the materials. So, as stated above, while this pattern is the featured material of this blog, it is presented here mainly as a way to gather various related concepts and skills. We’ll get to it soon enough.

So to begin, listen to this short and very simple rhythmic pattern and try to repeat it. It is spoken three times.

As you can probably hear, there are only two vocables (or syllables)—Tom and Ta—and you might be able to judge that the Tom is twice the duration of the Ta. If you clap along at the tempo of the ‘ta’ syllables while reciting the pattern, you can sense that the ‘tom’ takes two claps while the ‘ta’ takes only one. Listen again to confirm that you hear this.

Here are a couple of different methods for notating that rhythm. It’s good to have options so you can use the method that best suits your needs as well as the character of the material. The first method uses a hyphen to show that there is another rhythmic pulse after each Tom; there’s nothing after the ‘ta,’ since it occupies only one pulse. In another location on the website, there’s some instruction in “pulse notation” which will help you notate more complex rhythms, even if you do not know how to notate them in the traditional way.

It could also be written with the ‘Tom’ notated as one whole rhythmic unit (without the hyphen), while the ‘ta’ syllables are underlined. The underline, like a beam or flag in standard mensural notation, is another way to show that they are to be spoken at twice the speed. There are two ‘ta’ syllables for every one ‘tom.’ Here is that way of visualizing the durations.

|| Tom Tom Tom Tom ta ta ta ta | Tom Tom Tom Tom ta ta ta ta | Tom Tom Tom Tom ta ta ta ta || Tom

I show this because the use of vocal syllables has proven to be among the strongest and most efficient (and fun) ways to develop your rhythmic skills. I learned this myself through my studies of South Indian (Carnatic) music, and the rhythmic sensibilities of my students have been greatly accelerated with their use.

Now try reciting pattern #3. You will hear it spoken three times.

You can try notating it in syllables or standard notation. Here’s one correct transcription. Remember that the hyphen takes the same duration as the syllable.

Tom - Tom - Tom - ta Tom - Tom - ta Tom - - -

plus two other correct transcriptions of the pattern in mensural notation

To convey a pattern to someone else, it is necessary to hear it at least twice because:

a/ it helps reinforce the transmission to the listener but, more importantly,

b/ it is the only way to really ascertain the end of the pattern.

Students very often do not really acknowledge the silent extension of a pattern and they frequently will fail to include unarticulated pulses in their transcription work. Those extra hyphens might represent silent pulses or they might represent the sustaining of the final sound of a pattern. To know how much space exists after the final sound, you have to hear the beginning of the next iteration. In order to do this effectively, you have to sense the speed of the pulse-flow, that is, the flow of the fastest notes or events. In this pattern above, the ‘ta’ is the shortest (“fastest”) unit, and so that is what serves as the reference. So the ‘ta’ is the speed of the pulse. Just as the grains in an hourglass timer (image below) must be small enough to create an even sense flow, the pulse in music is the ‘granularity’ of the rhythm.

My first mridangam teacher, Tanjore Ranganathan, told me of one of his students whose reason for coming to study Carnatic rhythm was that he wanted to be able to sense so many moments in a musical flow that he could drive a truck between two consecutive beats. Fanciful, but it’s an evocative image.

If you tap at the pulse speed you can sense three additional pulses after the final Tom of each iteration. Here is pattern #3 again with a quiet tapping at the rate of the pulse. Listen and try tapping while reciting the pattern.

Just to be clear, the end of the third iteration comes right after the final ‘ta.’

Tom - Tom - Tom - ta Tom - Tom - ta Tom - - -

Tom - Tom - Tom - ta Tom - Tom - ta [Tom]-

We’ll learn about Pulse Notation a bit later but it’s pretty simple to learn. The advantage of the technique is that you do not stop playing the rhythm until you’ve finished the whole thing. That way you don’t forget it. And more importantly, the notation is actually just a performance which leaves a trace of the pattern on paper (or computer screen). You begin by making a simple one-stroke mark on each pulse. A simple dot will do, as long as it’s clearly visible. Then, when there’s a new sound (a new articulation) you can make a longer stroke. So you don’t yet bother with how long the sound lasts but only to show when there’s a new sound and when there is not.

So you start a row of dots, like • • • • • and substitute a line whenever you hear a newly articulated sound. So the pattern above would look as below.

| • | • | • | • | | • | • | • | • | | • | • | • | • |

I’ll go into more detail later and there will be a video demonstration.

Now try learning a pattern that does not conform to a convenient meter. So if you find yourself superimposing a beat, you may encounter some rhythmic dissonance and it may create more trouble than if you simply attend directly to the Toms and Tas.

You should hear three repetitions of Tom and three of Ta. This could be written with numbers as:

|| 2 2 2 1 1 1 2 2 2 1 1 1 2 2 2 1 1 1 || [Ends with a final “Tom”]

Some people like the simplicity that can be revealed through abstract representation and others are only reminded how much they struggled with math in their younger years. But for those who might find it helpful it could be visualized in math shorthand as shown below. All it says is that you play three groups of 2 followed by and three single syllables … and you do that three times.

[ (3 x 2) + (3 x 1) ] + [ (3 x 2) + (3 x 1) ] + [ (3 x 2) + (3 x 1) ] END

or even as: 3 x [3 x 2 + 3] END

Unfortunately, most rhythmic instruction uses clapping, which makes for additional difficulties because there is no hint as to the duration of an articulation. This is especially awkward for students in a ‘dictation’ test. At least with Tom and Ta, the syllable itself is the cue. Listen and try to work with this pattern. As with all the rhythms in this post, it is also comprised of only ‘ones’ and ‘twos’. It may be more difficult with clapping so it will be followed with a performance using vocables. After three repetitions, there is a final clap to mark the next ‘downbeat.’

Using numerical values for the durations, the patterns #6 and 6a are < 2 1 2 1 2 2 1 1 >

Notating it with syllables, it looks like < Tom - ta Tom - ta Tom - Tom - ta ta >

Materials for your practice:

There is some heavy-duty work with permutations on this website since permutation is among the oldest and most ubiquitous types of creative variation. One small assignment for my improv students was to make a list of all (70) permutations of four ones and four twos (11112222). This was intended for putting together a lot of material for sight-reading, performing and notating in different metric groupings such as 12/8 and 3/4. Have a look at this student’s work, or just look at the file below.

You can use these patterns for practice. Try performing them at sight, direct from the numerical notation. Then try to substitute Tom and Ta or any other pair of vocal syllables. Try playing the 2s with one hand and the 1s in the other. Try using two different drums or chords or any sound source. You can play in a very slow tempo and treat the 2s and 1s as metric units to be filled in with quicker material. There are many other variant methods of realization.

In another location on this website there will be reliable information about the proper way to notate these rhythms in different meters using different values.

Before going into the exercises related to the Fifty-fours, here is a link to one of many realizations of the pattern itself. It uses two hands for the twos (right/left) and only the RH for the ones. So for 1 1 2 2 you would say “one one one-two one-two and the hands would play

[Right, Right, Right-left, Right-left]. The linked score below shows the 54s using this realization.

Fifty-fours with two hands

After you do that, try the same pattern starting with the left hand, that is, try reversing the two parts. A number of other variant realizations will follow but while you’re here try it with forearm rotation. A single stroke would involve the gesture of supination—rotating toward the thumb—and a double stroke would be supination followed by pronation. There will be a video demo of this.

Rationale for the Fifty-fours exercise

Here are some of the expected benefits of working with this exercise

Perceiving rhythm from the smallest (fastest) to the largest (slowest) rhythmic units

This exercise assists with the perception of rhythmic granularity, i.e., of pulse flow: the ultimate (in the sense of the smallest) quantized, whole units of the flow of musical time. These might be analogous to the atoms of matter: its simplest level of organization. It is not possible to accurately perceive, perform and transcribe rhythm without being grounded in the pulse.

Sensing rhythmic flow even in the absence either beat or meter

This exercise intentionally thwarts one’s reliance on beat and meter as our main approach to measuring and organizing the rhythmic aspect of music. It can be painful to observe young music students needlessly struggling with the fractioning of time flow. Young students need not be perplexed by trying to understand an eighth-note as “half” a quarter-note beat. And students can be easily confounded by hearing their teacher say that a quarter-note is so called because it is a quarter of a 4/4 measure, even though the same term is used if the quarter-note appears in any other meter. Working initially from the level of pulse helps to bring rhythmic perception directly to the body, without unnecessary participation of thought. More on this later…

Visual/geometric organization of time

It is almost impossible to learn the 54s piece just from repeated hearings, that is, without a score. If such a long pattern is only perceived in a linear fashion (as in performance), its form is not palpable and leaves a weak trace in memory. The exercise is one of many on the site which shows the value of sensing and internalizing the “shape” of the rhythm.

Rhythmic “DNA” (just a fanciful term)

Learning about beat and metre is essential for understanding rhythm, but many of the world’s rhythms do not accommodate neatly into our customary organization of musical time. The smallest units and groupings can function as building blocks in the music of many cultures. Most rhythms of the world can be understood and perceived as a combination of ones and twos, i.e., single and double pulses. Acquiring facility with the ‘54s’ (and the associated exercises) provides an entree into hearing many different musical styles from around the world.

Memory

Memory is much enhanced with the understanding of a simple shape. Once the piece is absorbed in its spatial aspect, it is difficult to forget it.

Improvisation practice

“Fifty-fours” provides excellent work for variations, especially by substitution, augmentation, diminution, permutation, etc., and there is a great deal that can be done in terms of harmonic and melodic values as well. It’s important to remember that this should be taken as a template for your own practice. To work only with this shape and these 54 pulses is not sufficient to become facile in the world of rhythm. It is a big study.

Analysis: Structure vs. Ornament

When we try to compose, improvise, memorize, or simply try to understand a piece of music, we instinctively attempt to separate the essential from the extraneous. In music, architecture, cooking, or most anything else, we organize our perceptions by distinguishing between the most essential elements from those which elaborate them. For some composers, like J.S. Bach, the distinction is not always so clear as with the writing of other composers. While many of his ornaments may be decorative (as in the music of Chopin), most others are more integral to the musical line. This exercise refers to the decorative or elaborative use of ornamentation, because it treats these improvised figures as extraneous to the structure.

===================

VIDEO DEMO OF 54s GOES HERE.

Don’t forget: What is an exercise? This material can be tested in performance without transgressing my principle not to based course grades on the students’ improvisation.

Most of my exercises are layered so that they can offer ideas and practice in a number of areas. This one also is an exercise for co-ordination of mind and body, improvisation and other creative work, reading and memory. The big problem with the medium of a website is the lack of personal contact and the limited time in which to unfold the ideas and the working process. An exercise such as the “Fifty-fours” would normally occupy about four weeks (eight classes).

Materials: This exercise is another pulse-based exercise that begins with groups of single and paired pulses (ones and twos) in order to build up more complex rhythmic patterns. One of the aims is that these pulses will be sensed and grounded in the body. They are like the “atoms” of the rhythmic flow: the smallest indivisible units of duration.

Notation: In addition to using standard mensural notation, a special form of “pulse notation” will also be used. Here’s how it will be notated in this website. “Pulse” on this website is defined as the shortest duration in a piece or in the passage being considered. A single articulation on only one pulse will usually be written as ‘x’. A note which is held for an additional pulse OR a silent pulse—a rest—will usually be notated as a hyphen ‘-’. When needed later on, a distinction in notation will be made between a rest and a sustained note. A group of two articulations, will usually be notated as ‘x x’. And so two pulses with no newly struck sound will be notated as [- -]. The Fifty-fours pattern will be notated with these two symbols as well as using numerals and other symbols.

The Spatialization of Rhythmic Form

Making visual correlates of things we need to remember; it is an old practice. It has been used for the purpose of assisting the memory and also to get a clear overview of the form of all kinds of things: a piece of music, all kinds of maps, the tree of evolution, recipes, the members of your extended family, the earth’s layers, the location of all the circuit breaker in your house, and many other things.

This is Related to the spatialization of rhythmic order (structure?) in Carnatic rhythmic theory. an essential aspect of inspiration for this exercise is the notion, of the .

To cut to the chase: the form of the fifty-fours can be written in numbers, representing the duration of the successive phrases: 2+2+5+5+9+9+5+5+2+2 (= 54).

The pulse groupings of the form can be written as: [2+2]+[2+2]+[2+1+2]+[2+1+2]+[2+2+1+2+2]+[2+2+1+2+2]+[2+1+2]+[2+1+2]+[2+2]+[2+2]

After having an opportunity to struggle to learn this pattern, it is presented in the very memorable form of a barrel. Each line either repeats, expands or contracts. The notion of pattern-shape is something I first learned in my studies of Carnatic music. The musician may make such shapes obvious and audible, but the main idea is that it provides a way for the musician to quickly calculate, remember, and keep track of the rhythmic phrases in play.

2 2

2 1 2

2 2 1 2 2

2 1 2

2 2

This file represents a more or less “full” lesson, the starting point for which is the rhythmic pattern I call “Fifty-fours.” By the term full, I mean that it typically includes several weeks of varied work with this pattern—drumming, piano, singing, clapping, stepping, improvising, composing, ensemble work, etc.—emphasizing both musicianship and creative practice. It represents many variations of presentation and practice and so it naturally occupies several weeks of classes and personal practice before it becomes internalized.

So below you’ll find the following: a rationale for creating the exercise, a complete description in text, graphics, standard music notation, and a fairly fleshed out method or strategy of presentation to a class. In text form, it is quite lengthy, and not everyone will have the patience to absorb it that way, but the intention is to use the text file as a kind of “backup” for the video which will show the exercise as presented to a small class. The video will be divided into ‘chapters’ which could represent individual classes. Any one class can only absorb just so much, so they are typically left with a good challenge but then the exercise is further elaborated in a following class or within our online tutorials. Each of these presentations stress different combinations of musical skills: sight-reading, improvisation, composition, and so on.

Brief Rationale

*Developing stronger perception of “pulse”: the granular level of rhythmic flow

*Strengthening visual and spatial perception and memory

*Understanding that the ultimate groupings of musical time-flow—ones and twos—(the essential DNA of rhythmic structure) enables one to listen intelligently to the music of many different styles and cultures, that is, without unintentionally imposing values and listening habits inculcated by our own education.

*Learning how to use intentional motives for improvised practice

Expanded Rationale

These are some of the expected benefits of working with this exercise and those also in this same general category of “pulse-oriented” rhythmic work.

Rhythmic Perception

* Perceiving rhythm from the smallest (fastest) to the largest (slowest) rhythmic units

This exercise assists with the perception of rhythmic granularity, i.e., of pulse: the ultimate quantized, whole unit of musical time-flow. These might be analogous to the atoms of matter: its very simplest level of organization. It is not possible to accurately perceive and perform rhythm without being internally grounded in the pulse.

Sensing rhythmic flow even in the absence either beat or meter

This exercise intentionally thwarts one’s reliance on beat and meter to drive and measure the rhythmic aspect of music. This goes intentionally against the traditional approach to first learning about beat and meter. This has the advantage of delaying the introduction of fractioning of time-flow. Young students need not be confused by seeing an eighth-note as “half” a quarter-note beat. Students easily are confounded by hearing that a quarter-note is so called because it is a quarter of a 4/4 measure, even though the same term is used if the quarter-note appears in any other meter. Working initially from the level of pulse helps to bring rhythmic perception directly to the body, without unnecessary participation of thought.

Visual/geometric organization of time

It is almost impossible to learn the piece without a score, that is, just from repeated hearings. If it is only perceived in a linear fashion (as in performance), its form is not palpable and leaves a weak trace in memory. The exercise is one of many on the site which shows the value of sensing the “shape” of the rhythm.

Rhythmic “DNA” (just a fanciful term)

Even before approach beat and metre and the essential measures of time-flow, small groupings (like molecules?) function as building blocks in the music of many cultures. Most rhythms of the world can be understood and perceived as a combination of ones and twos, i.e., single and double pulses. Understanding the ‘54s’ provides an entree into hearing many different musical styles from around the world.

Memory

Memory is much enhanced with the understanding of a simple shape. Once the piece is absorbed in its spatial aspect, it is difficult to forget it.

Improvisation practice

Analysis: Structure vs. Ornament

When trying to compose, improvise, memorize or simply understand a piece of music, we instinctively try to separate the essential from extraneous. In music, architecture, cooking, or most anything else, we organize our perceptions by distinguishing between the most functional elements from those which elaborate those functions. For some composers, like J.S. Bach, the distinction was not always as clear as with the writing of other composers. Ornaments may most often be decorative, while others are more integral to the musical theme. This exercise refers to “ornamentation” as decorative or elaborative, because it treats these improvised figures as extraneous to the structure.

When I was younger I always wondered why JSB’s scores had so many more notes than those of Handel. But on listening, I found that Handel’s music did not seem much simpler. There were just as many notes. One reason, I discovered, is that Bach wrote out many of the ornaments which Handel left in shorthand form because they were thematically integral to the music. Handel more frequently used symbolic notation, which invited the performer to execute them according to common practice. When Bach wanted something quite specific, he simply wrote it out. For him, much of what seems like ornamentation was thematically significant; that is they were part of the structure of the music.

Description of the Fifty-Fours Exercise and a Typical Manner of Presentation

While most exercises will have a rationale and a description of the contents of the exercise, several files will also have an extended description of the manner of presentation. HOW the exercise is presented is very often as critical as the actual material in it. (This is, in fact, analogous to the previous discussion of ornamentation. For some exercises the mode of presentation is integral to the exercise. For example, since one of the central reasons for conceiving of the 54s exercise is to try to ground the student in the sense of pulse, rather than beat or metre. So the exercise has to originate in pulse; it must somehow dissuade the students from trying to superimpose either a beat or meter on the material. This is simple but it can be tricky. And it might not be so easy to describe in words.

General Statement:

As with most direct “person-to-person” teaching, the method of transmission becomes an integral part of the exercise. Most of my own teaching has taken pace in classroom studios and was directed to about 16 people. These methods were also used for teaching in much larger settings: conference presentations, workshops, etc.

Actually in any group—even two people—one cannot assume that everyone will have a common understanding (even of the words used) or commensurate capacities. So the general protocol of presentation is to present all exercises in a “layered” manner: beginning at an entry level (without assuming any prior knowledge on the part of the participants) and rising to a professional level. The way to keep this from becoming boring for the more advanced musicians is to present not only the exercise material but also to present the manner of presentation. That is there is always an emphasis on pedagogy. This became a (justified) assumption: that most students will, at some point, try to pass along these skills—or even this exercise—to their own students, friends, ensemble partners, etc.

So the descriptions of the exercises will almost all have this feature, where the methods and styles of presentation are an important part of the presentation.

Work-shopping the Fifty-fours pattern

How to present and how to practice?

Here is a description and creative ideas for working with or presenting the Exercise: “Fifty- fours”

It is called fifty-fours only because there are 54 pulses in the whole pattern. What is important is not that there are 54 pulses. It is about the “shape” because I was illustrating the possibility of spatial memory and I related it to the notion of “yati” in classical Indian Music. But to understand what’s most important a little background needs to be included.

The presentation of this work often begins with some “Call and Response” rhythms. I give a short rhythm and the class has to clap it back, as accurately as possible. If the “response” is not crisp and clear, I assume that my pattern was too difficult and so I back off and make something simpler.

The first pattern might be something like: [1 1 1 1 2 2 2 2].

I often begin by clapping these rhythms, so the “rests” are irrelevant. The students focus solely on the articulation, that is, the moment that the sound is initiated.

I do not write them out nor are they ‘explained.’

Most students have no trouble with the pattern below, that is, they can learn it from repeated hearings.

In pulse notation, it might look this way:

|| x x x x – x – x – x - ||

The students don’t know what kind of note ‘x’ is, because it has not been defined. It could be a 16th-note, an 8th, or any value. But they must know that “x – “ is a duration twice as long.

So that pattern could be notated as four eighths followed by four quarter-notes. In standard notation it might look like the line below.

So to this point in the lesson, no distinction is made between the above pattern and the one below. Often teaching something new works best by minimizing the number of variables.

This rhythmic pattern can be recited verbally as:

“One, one, one, one, one-two, one-two, one-two, one-two.” Each syllable gets one pulse and so there are 12 pulses in total.

You could otherwise recite it more simply with eight syllables:

“one one one one two two two two,” but this will can confuse a few people because many musicians are not able to sense the “two” as a syllable of twice the duration as the “one.”

Some students who are put off or easily frightened or even alienated by numbers sometimes feel more engaged and can do better by naming them with two different syllables: “ta” (for a single pulse) and “tom” (one lasting for two pulses). So the pattern could be recited as eight syllables:

“ta ta ta ta tom tom tom tom”.

However, to make it even clearer, the “tom” should be followed with a hyphen to show that it is followed by an unspoken (unarticulated pulse):

||ta ta ta ta tom – tom – tom – tom – ||.

So at this point, you can begin to work with a variety of patterns, each comprising some ones and some twos.

For example:

2 2 2 2 1 1 1 1 or

2 2 2 1 1 1 1 1 1

ODD METERS:

It is advisable to “sneak in” some patterns totalling an odd number of pulses. It is important for the further development of the rhythmic sensibility, to thwart the students’ tendency to “fit in” rhythms to a known and easy metre. The reason to thwart this tendency is so that they are more attentive to each duration and to the form. Otherwise they rely on long- habituated listening patterns.

2 2 2 1 1 1

2 2 1 1 1

2 2 1 1 1 2 1 2

2 2 1 1 2 2 1 1 2 2 1 1 1

1 1 2 2 1 1 1 1 2

1 1 2 1 2 1 2 2

2 1 2 1 2 2 1 1

You can give them confidence in their ability to absorb and recall long patterns by creating patterns with extended form but which maintain a plainly logical basis.

|| 2 2 2 2 1 1 1 1 2 2 2 1 1 1 1 2 2 1 1 1 1 2 1 1 1 1 || [4x2 + 4, 3x2 + 4, 2x2 + 4, 1x2 + 4]f

ASSOCIATING DURATIONAL VALUES WITH: GESTURES, TONES, LETTERS, SHAPES, SIZES, COLORS, …

If the students have difficulty, you can associate one gesture with twos and another gestures with the ones. For example, using the LH for the twos and the RH for the ones will help many students internalize the form.

|| L – L – L – R R R L – L – L – R R R ||

Clapping palms together versus clapping the back of the hand against the other palm is also clear. Of course singing or playing the pattern with two chords or two tones is also a great help:

|| D - D – D – C C C || will help some students hear the rhythm [2 2 2 1 1 1 ]

|| 2 2 2 2 1 1 1 1 2 2 2 1 1 1 1 2 2 1 1 1 1 2 1 1 1 1 ||

The above rhythm may be more obvious sung or played with the tones below.

|| c – d – e – f – g g g g c – d – e – g g g g c – d – g g g g c – g g g g ||

And some people who are more comfortable with mathematical abstractions might get a better grasp with an algebraic representation such as

|| [4x2 + 4] + [3x2 + 4] + [2x2 + 4] + [1x2 + 2] ||

Other effective presentations commonly used in my classes have the larger and smaller values represented by different sizes of paper, all put down in a line. They can have the numbers written on them but relying only on size come closer to the perception of values of different duration. Color can also be an effective association, using a dark and a light color for different values.

Students love to gather around the grand piano and see coins laid out, using quarters for bigger values and dimes for smaller ones. Since music notation is already quite abstract, it can help to use many different objects for associative purposes. The twos can be written as the letter “O” or “W” and the ones can be written as “x” or “l” or any letter that appears ‘smaller’. So the same pattern written on the board could look like: ||O O O O x x x x O O O x

x x x O O x x x x O x x x x ||. When the students feel comfortable with this, it is instructive to reverse the associations, making the twos look like ‘x” and the ones like “0”. This is useful because there is nothing inherently shorter about a filled in quarter-note vs an empty oval used for a “longer” value.

And a nice creative departure can be approached using text—either an arbitrary one or one with personal meaning. For example the vowels below can be read as two pulses and the consonants as a single pulse (or vice versa):

A woman without her man is nothing. Hyperlink to lesson on Phrasing.

2 1 2 1 2 1 1 2 1 1 2 2 1 1 2 1 1 2 1 2 1 1 2 1 1 2 1 1.

A w o m a n w i t h o u t h e r m a n I s n o t h I n g.

NEXT STAGE: CREATIVE APPLICATION

Now that some of you are more relaxed about trying to remember a longer pattern, I suggest we try a much longer string of twos and ones. The reason for this is because as you become truly relaxed with a larger set of materials—a larger starting point—we can go to the next step of doing something interesting, something worthwhile with these insights and skills.

So in the next step, I might play the following pattern. I play it acknowledging their progression already shown in the preceding session(s), so they approach it with some confidence or, at least, with a positive attitude.

||2 2 2 2 2 1 2 2 1 2 2 2 1 2 2 2 2 1 2 2 2 1 2 2 1 2 2 2 2 2|| (Listen to the audio recording and perhaps look at this pattern put into standard notation using quarters and halves or perhaps eighths and quarters.)

By this time, the students usually thrust themselves into it but, most often, the majority of them cannot remember the whole pattern. Then I show it to them visually: with hand gestures. I show it as 10 rows of numbers, with each row going from left to right. So for the leader, the gestures go from right to left. (TAG: seeing from both my P.O.V. and the class’) The first row is shown up high, and each successive row is shown a little lower, so it presents like reading text. And to differentiate, I show the twos as an open palm facing them and the ones are shown as a hand in profile (so it looks thinner, almost like the number 1). Any two gestures can suffice. I conduct with my hands in this manner and most of them are able to get the pattern. I hold both hands high and lower them on each successively lower line. I start the line on their left side so they are “reading” it—the hands literally substituting for the numbers.

2 2

2 1 2

2 2 1 2 2

2 1 2

2 2

If they need more help we try a few things.

We recite the numbers, ignoring their actual durational values. We simply say:” two, two, two, two, two, one two, etc. I write it at the board so everyone can see it and recite it. After a few repetitions, the board is erased. Some students retain it; some come close but have gaps in their visual memory.

We stand around a grand piano and I put coins down to show the ten lines: 2 coins in each of the first two lines, 3 coins in lines 3 & 4 and 7 & 8. Five coins in the middle two lines (5 & 6) and finally two coins each in rows 9 and 10. With the coins placed this way, they can easily see the whole pattern as an expanding and contracting shape. It is now much easier to read and also to memorize. As they play it they realize that they begin reading their internalized image of the 10 lines.

We look again at the standard notation and we discuss what they see. We notice that everyone sees some version of the same thing:

*The first and last two lines have two quarters: two pairs of twos;

*Lines 3, 4, 7 & 8 have those two pairs with a little “spine” running along the centre’

*And the middle two rows are the same as 3, 4, 7, 8 but they have “bookends:” another quarter at the beginning and one at the end. It soon becomes difficult to forget and they can now be given a musical task to perform while keeping the pattern secure.

“Fifty fours” 2 2

2 2

2 1 2

2 2 1 2 2

2 1 2

2 2

Once the pattern has been internalized:

Here are the things we try in order to incrementally deposit the pattern in the body with increasing depth at each variation. The principle here is that variations are not created for esthetic reasons, but it helps isolate the central principle from the external elements that are merely the vehicles for transmission.

Engaging the legs and perhaps the whole body:

This is recognizable as a concern and a central element of the Eurhythmics branch of the teaching of Jacques Dalcroze. I personally did a couple of years of intentsive Dalcroze studies; what attracted me to that teaching was that my own teachers and my own experience showed me clearly that the intelligence and sensitivity of the body was a critical participant in one’s music education. The body is where all these ideas can become palpable experiences, and it is that ‘palpability’ that makes them useful for one’s engagement with music: performing, practicing, composing, etc.

Walking/Stepping : Corresponding/Contrasting

The production and sensation of rhythmic flow requires the presence and active participation of at least two “layers” of organized time-flow. One layer can be nothings more than a steady beat or meter; the other may be the actively creative patternings— either composed or improvised on the spot (or some combination). There is the third layer but it is awkward to describe it. Here’s one attempt. The third layer is based and dependent upon the experience, preferences, tendencies and habits of the one(s) perceiving the two layers. The perception of the listener is strongly affected by their precious experiences (prefeences, tendiencies and habits) and it will share a great deal with the experiences of others in the community and it will also have a certain uniqueness such that no one will ever really know what the ‘other’ actually experienced

Clapping in diff grids Sing with two tones

Sing/Play with each line beginning on Doh and asceding by step on ech new unit Syncopation

Then we try reciting or clapping the pattern while also keeping a steady beat. Sometimes this is known as placing a “rhythmic grid” over the pattern. The combination of any two rhythmic patterns, even if one of them is merely a steady beat, will always produce a third pattern—a third rhythmic element. Sometimes this is called a “resultant” pattern.

Performing the 54s pattern over a rhythmic grid will result in various naturally occurring misalignments (syncopated moments). That means that certain syllables will not conform to the beat structures we impose. This “rhythmic dissonance” is one of the attractive elements present in musical rhythm, just as harmonic dissonance is almost a ‘necessity’ for a melodic line.

For example if we step with our foot or clap hands every two pulses, |1, 2|1, 2|, etc., it will emerge this way:

||Do – |re – |Do – |re – |Do – |re mi |– Do |– re |mi – |Do - |re – |mi fa |– sol |- Do |- re |– mi | fa – |sol - |Do – |re mi |– Do |– re |mi - |Do – |re – |Do – |re – ||

If we align the text in three rows of nine beat each, it looks like this:

||Do – |re – |Do – |re – |Do – |re mi|– Do |– re |mi – |

| Do - |re – |mi fa|– sol|- Do |- re |– mi |fa – |sol - |

| Do – |re mi |– Do |– re |mi - |Do – |re – |Do – |re – ||

If the beat is taken every four pulses, it will emerge this way:

||Do – re – |Do – re – |Do – re mi |– Do – re |mi – Do - |re – mi fa |– sol - Do |- re – mi |

|– re mi - |Do – re – |Do – re – ||

||Do – re – |Do – re – |Do – re mi|– Do – re ||mi – Do - |re – mi fa |

|– re mi - |Do – re – |Do – re – ||

Notice that the pattern must be repeated for the beginning to again align with the beat. That’s because 54 is not divisible by 4. So at the (*) the pattern begins in the ‘middle’ of the beat.

And students are also asked to produce a beat comprising three pulses. While there is a great deal of Western music in “threes” (three beats to a measure; three subdivisions to a beat) it is not so common to find a pattern persisting in what feels like misalignment for this long. This is a graphic representation of that grouping in threes.

||Do – re |– Do – |re – Do |– re mi |– Do – |re mi – |Do - re |– mi fa |– sol - |Do - re |– mi fa |

|– sol - |Do – re |mi – Do |– re mi |- Do – |re – Do| – re – ||

Notice that even after a single iteration of the pattern the groupings in threes comes out smoothly on the beat. That’s because 54 is divisible by threes, producing 18 beats with three pulses each.

Do – re –

Do – re – Do – re mi – Do – re mi –

Do - re – mi fa – sol - Do - re – mi fa – sol - Do – re mi –

Do – re mi Do – re –

Do – re –

Fifty-fours (warning)

[warning] you are all welcome to use the ex for yourself or others. Don’t make the mistake of taking the form of the exercise as a unique example of the issue. A teacher once did that to his grade-school class and for an entire year he worked on “The Sokol Pattern.” It was actually this 54 pulse pattern but he never went past it and, of course, neither did the students in his class!

Fifty-fours [further suggestions]

Among the most important uses of most of these exercises is for self-diagnosis of your difficulties. Where, exactly, do difficulties arise and what is the actual cause? After all, an exercise is meant as a vehicle for working on what is difficult for you. (Is the difficulty in remembering the material? Coordinating the limbs? Discomfort with “rhythmic dissonance” such as persistent syncopation? The inability of the body to count to ‘x’ without a corresponding mental or verbal count? What are the actual difficulties?

Limiting your work to the easy parts is satisfying for your self-image (and that is also important for developing confidence), but if it precludes spending time on what is frustrating, what you don’t understand, what causes hesitations, uncertainty and what underminds your confidence, then your work needs to expand to include those awkward and painful issues. Overcoming those inabilities, even small ones, enhances one’s real confidence and, with greater confidence, one’s actual capability also expands.

CoordinationImprovisationReadingMemorySubstitution

Casey Sokol

“Fifty-fours”

The spatial aspect of rhythmic perception

Rationale for the 54s exercise.

Panorama of the Goldberg Variations plus Invaria

“Guiro Elaborations” Working with the granularity of rhythm: a pattern comprising only groups of one and two pulses