Hand/Mind Coodination Exercises:
There are three exercises described below. They all involve tapping rhythms which involve both hands. Scroll down or tap the link to open each one in sequence.
Chorus Verse Exercise and Comping exercise
Most of the exercises on this site are much easier to share as videos than as text and graphics, so I will gradually make those videos and post them. Describing music and musical exercises in words can be really laborious to write and even more laborious to read. So the written texts will describe the exercise, but the more important purpose will be to make clear the pedagogical benefits of working with it as well as suggestions (for both teachers and students) for its presentation and practice. With very few exceptions, all the great teachers have stressed the importance of awareness rather than mechanical repetition. This includes awareness of the structure and characteristic strengths of the fingers and the body in general, the structure and emotional requirements of the music, and the organization of the instrument itself. It’s important to have a clear understanding of what you’re practicing and the reasons you’re working on the materials at hand. What is the rationale for this practice; what are the expected and anticipated outcomes; how the practice of this material may play a part in the process of becoming an accomplished musician.
REDUCTION PATTERN
REDUCTION PATTERN FOR TWO HANDS
Reduction Pattern: a meter-modulation exercise based on the sequence: ||876543||
The exercise uses a simple rhythmic form:
Four repetitions of 8 beats + four repetitions of 7 beats + four reps of 6 + four x 5 and + eight times 3. Using only numbers the form could be written like this:
||: 4x8 / 4x7 / 4x6 / 4x5 / 4x4 / 8x3 :||
These exercises are based on a simple process:
A phrase of 8 beats is played four times. The final beat is eliminated, leaving a 7-beat pattern. After four repetitions the final beat is eliminated, leaving a 6-beat pattern. When you get to only three beats, you repeat that pattern 8 times and then begin again with the 8-beat pattern.
The exercise is as much about movement as rhythm. Sitting down for the exercise, the LH plays twice on the top of the left thigh and twice on the side of the thigh (or the floor to the left of the left leg). Any two locations will do, as long as there is movement involved, preferably a large movement such as torso bends. It could be thigh and floor or two drums, or it could be realized as two notes or two chords on a keyboard. A second repetition of these four articulations gives the complete 8‐beat pattern. As the pattern reduces in length, the RH continues to have only two articulations: the off-beats (the “ands”) of counts one and two.
In the notation below, the top of the left thigh is shown as the higher ‘a’ in the bass clef, and the side of the leg is represented by the lower ‘a.’ The RH plays on the top of the thigh (or on any other surface).
Reduction Pattern: 876543—Condensed score
Reduction Pattern: 8-7-6-5-4-3—simple piano realization
Audio track of piano realization
Here are a few notes on the pedagogical ideas behind this exercise as well as some tips for practicing.
For me, good exercises have some qualities in common. They ideally challenge all of our intelligences. They should not be too complicated intellectually or physically—that is, not out of reach—but they do require work and often involve a search for a new approach. This exercise demands several layers of counting, and the suggested physical movement (described below) actually offers some help in meeting that challenge. Besides the obvious skills that are required (coordination of the arms and the ability to direct energy into un‐stressed places in a metric pattern), it also requires us to hold several layers of rhythmic flow in the attention, to see ahead, and to remain relaxed within an intense flow.
I will try to share some aspects of how I engage with this kind of exercise so that I can stay in touch with all the ongoing levels of ‘counting’. This is all difficult to put into words and can sound mildly inane, but I’m certain that many of you do something similar.
I trust my body to count up to two. Even if we don’t verbally number things and experiences, we instinctively rely on counting to two: “this one” and “that one.” We walk with this leg and then pair it the other leg. There is some sense in the body that a “two” is somehow complete, at least in its inherent suggestion of symmetry. And in the counting of events, we know that the initiating moment is complemented with a gesture of closure: paired experiences.
So I can begin to sense the two left hand gestures on the top of the thigh as ‘this one’ (initiating or starting) and the ‘second one’ (finishing or ending). I don’t have to think about it and I certainly don’t verbally count it. There is a distinct feeling-sensation is generated by this first, initiating event such as the impression counts itself, so to speak. Similarly for the second event. It is so often perceived as a compliment to the first—as intimately paired as the toc is with the tic. The feeling‐sensations induced by those actions are something like the pairing of initiation and closure. And then, following the pair of articulations on the leg, the left hand continues with a pair of articulations on the floor. When I try to extent the pattern with more articulations, the first two strikes on the leg may begin to be sensed as a single larger, compound gesture. “One!” And the second pair of articulations on the floor can then feel like “Two.” So each pair begins to feel like a single thing: the first pair on the thigh and the second pair on the floor. Reification can lead to grouping which can lead to the simplification of any form of “keeping track” of things (such as counting them).
So I am still only counting up to two. It is a pair of twos—two twos. This is not just an idea; it is how most musicians sense the flow of measured time even if they do not describe it as I have done. Musicians (and other artists) almost always try to reduce the number of structural elements by grouping them. And it is more or less what everyone seems to do, even if involuntarily. We tend not to hear a clock as if it were sounding, “tic tic tic …” but we hear it as “tic” followed by “toc.” If we listen attentively we can often find ourselves superimposing two different sounds, so that the “toc” really seems to differ from “tic.
After studying with teachers from various traditions, I am persuaded that most cultures share a similar sense of rhythm, that is, we hear either single unpaired events or a pair of occurrences. So the body senses groups of ones and twos. Groups of three seem to be sensed as a pair plus an unpaired articulation [2+1] (or, less commonly, as [1+2]). Fours tend to be a pair of pairs, and so we typically count and sense fours as either [1 & 2 &] or simply as [1 2], while internally sensing an unarticulated event in between the counts.
So this particular reduction exercise involves three levels of counting: 1) the counts in each phrase (from 8 to 3), 2) the number of repetitions of each phrase (4 reps for each phrase and then 8 reps for the phrases of 3), and 3) counting 2 LH articulations on the leg and 2 on the floor.
Even in this rather simple exercise there is more to keep track of than the mind can do on its own, and so the player may learn to trust and rely on the intelligence of the body. In this way the musical form of striking the leg and floor (two here, two there …) can actually help me count up to 8 or 7 or 5 or to whatever number. Especially with the inclusion of the torso bends, the counting has a physical form. This aspect of ‘body-counting’ is most obvious in the gestures of an orchestral conductor but it seems that almost all musicians have some form of either visible or internal movement that enables non-verbal, non-intellectual counting. If you watch performing musicians, you can usually discern torso bends, foot rotation, and any number of variations on bodily movement that helps them count beats or repetitions. At one’s instrument, the harmonic changes can be relied upon to keep track of the count.
On the attached notation of the exercise, there are three different pitches shown for the right hand for the eight repetitions of three. This is an added layer of musicianship and it most always seemed of interest to all the students. The three right-hand pitches (e, a, e’) signify three different locations or sounds. We played them on three places along the thigh, but they could be played on drums, or on the piano as pitches or chords. The location then did the counting. For example, the movement of the RH in the eight repetitions of the threes could be used to tell you when eight reps have transpired: [center, right, center, left center, right, center, left] In fact, the entire exercise can be worked at the piano, where you can use pitch to cue yourself. Lastly we were asked to end the exercise on the very last 8th-note rather than on the more organic location of the downbeat. Intentionally ending on an a typical beat or pulse helps to sustain the attention right until the end of the exercise.
CHORUS/VERSE EXERCISE
As with most of the uploaded materials, the actual ‘exercise’ is only a focal point for musical work. The way it is presented, the sequence of the accumulating exercises and discussions—all that is really the “exercise.” The Chorus/Verse material is related to the Reduction Exercise but goes much further in terms of form.
PALM TURNING:
The Cross-Rhythm of Two-Against-Three
This is simply a realization of the cross-rhythm < two-against-three > in a very slow tempo. Depending on which hand begins, it can be considered an exercise in <three-against-two>.
However there is also an unusually demanding aspect of simply body movement.
For those who just want to get the exercise done without any theoretical understanding, here is the short explanation of what to do. To be sure you’re getting a reliable result, you are best advised to actually do these steps in the given order.
§ § §
Step 1:
Set up phrases of threes in the LH by tapping on the thigh and naming each of the three beats: 1- 2 - 3.
Step 2: Diminish the flow
Diminish the flow of the counting so that you are counting two subdivisions per beat. So, over the same three taps, at the same speed, you count: 1 & 2 & 3 &.
Remember that the word diminish means that you are diminishing (making smaller or shortening) the duration. In this case, you are shortening the duration of the counts so you can fit in the “and” without speeding up the number counts. The effect of that is that you are speaking twice as fast. [Without any other qualifiers, diminution is assumed to be a halving of the values, or a doubling of the speed of the pulse flow. You can find many examples of diminution by threes, fours, etc.]
Step 3: Change the names
Change the names of the subdivisions from 1 & 2 & 3 & to 1 2 3 1 2 3
Remember that 'subdivision' is another name for the pulses flowing 'inside' each beat. But by changing the names, you have now diminished the flow of the threes in the LH, so that you are now counting two groups of three against the three LH beats. And that means that the sensation has changed from three groups of two pulses to two groups of three pulses. In step 5, you now mark this with the RH.
Step 4: Mark the beginning of each group of the new threes in the RH.
That means you tap the right thigh when you say “one.” You are now tapping two-against-three: the RH is tapping two groups of three pulses against the LH, which is marking three groups of two pulses. You are now ready to go into “cross-phrasing” or a cross-rhythm at a higher “level.”
Step 5: Create phrases of two beats
Without changing anything else, you can now create two-beat phrases in the LH by turning the palm upward on every even numbered beat, that is, [Down / Up]
Step 6: Create phrases of three beats
Maintaining everything you’re doing, you can now create three-beat phrases (that is, phrases of three beats) in the RH by turning the palm upward on every third beat, that is, [Down / Down / Up]
§ § §
The more detailed explanation:
Some people can become confused by too much explanation, so the following detail is for those who like to be really clear about each step they take in their learning and practicing.
First: The arithmetic theory of the exercise:
The cross-rhythm above rationalized on the basis of rhythmic diminution. If you have a steady count of three and then count at double that speed, and if you then name those faster beats also as one-two-three-one-two-three
The LH was given to mark a steady beat and you were invited to name the beats as “one – two – three.” When that felt established, I suggested that everyone sense a diminished pulse flow inside each of these three beats, naming them “one-and-two-and-three-and.” You are now speaking six words in the space of three beats. It’s important not to fixate on the names of the beats but on the fact that there are six impulses within the three beats. The names of the beats and sub-beats are, to some extent, irrelevant. Instead of naming them “one-and-two-and …” you could just as well have named them: “one one one…” or “two two two two” or even “and and and and.”
This was to see that the names of the subdivisions could be changed without disturbing the sensation of the beat. We then renamed them as,
“one-two-three-one-two-three” and then, with some accentuation, as ONE-two-three-TWO-two-three.” The formation of two quicker threes against the single slow three of the LH was realized by the RH which tapped on the first of each of the two groups of three.
Voice:
||1 2 3 || (counting aloud)
||1 - 2 - 3 - || (counting aloud and sensing a double-speed flow of pulses)
||1 & 2 & 3 &|| (counting the same three beats but also naming the diminished flow with “and”)
||1 2 3 1 2 3 || (renaming the six pulses as two groups of three)
||1 2 3 2 2 3 || (This shows the two groups of three in numbers: One-2-3 and Two-2-3)
RH:
1 - - 2 - - (right hand marks beginning of each group of 3)
I explained that, when we speak of the cross-rhythm “two against three,” it is actually just a short-hand way of saying that two groups of three-pulses-each [xxx and xxx] were being regrouped over those same six pulses into three groups of two-pulses-each [xx and xx and xx].
You can see the grouping in many different ways but it adds up to the same thing.
[123456] as 2 groups of 3 = [X y z X y z] or [x - - x - - ]
[123456] as 3 groups of 2 = [Y z Y z Y z] or [y - y - y - ]
Once again: the graphic above shows, by the alignment of the two lines, that the same six pulses are regrouped: first as 2 groups of 3 and then as 3 groups of 2. When these two groupings are played simultaneously, while only articulating (sounding) the first one of each grouping, then one hears 2 crossing the 3. I said that, for small numbers (certainly below six), performers could most accurately understand and practice cross rhythms as two different groupings of a fixed number of pulses (like a common denominator) performed one against another. For large numbers such as typically seen in Chopin (e.g., 15:4) one should take this to be an interpretational instruction – an invitation to improvise the relationship between the lines, that is, an invitation to tastefully distribute the fifteen RH notes over the time of the four LH notes. Such use of high numbers or difficult ratios would rarely be considered as a demand to perform a true cross rhythm.
We then worked the exercise toward thinking about and sensing “cross phrasing:” playing higher level cross rhythms “over” the 2:3 cross rhythms. First we found a way to show and support the cross rhythms with hand gestures (turning the palm down or up). So the LH showed its three beats as Down/Down/Up while the RH showed its two-beats as Down/Up. Then, using this material, we used gestural patterns which did not work out evenly with the cross rhythms, thus producing higher level patterns which overlapped (or “crossed”) the initial 2:3 cross rhythm.
The realization of the second stage of the exercise (“cross-phrasing”). This is where there is a “crossing” of the cross-rhythms. This is achievable by creating any kind of distinction (sound, sensation, gesture, …) in the normal phrasing of each hand’s pattern. So it can be effected by using accents, different pitches or chords, instrumentation, etc.
The first realization (below) with movement of the hands shows the gestures in parity (in agreement) with the cross rhythm. D = palm down; U = palm up. Note that the LH is shown above the RH, and note that it takes a single iteration of the LH shape to arrive together with one iteration of the RH pattern. This is because the LH is playing a phrase in three and also shows the same number (three) of gestures: Down Down Up. The RH is in two and shows the phrase also in two gestures: Down Up.
LH D – D – U – D – D – U –
RH D - - U - - D - - U - -
Below is the same as above but showing bar lines to indicate the completion of the larger group of three for the LH. Note that the pattern with movement of the palm still expresses only the cross rhythm 2:3.
LH D – D – U – |D – D – U – |
RH D - - U - - |D - - U - - |
Written below is the pattern as it expresses, through the use of “substitution,” (in this case a substitution of gesture) a higher level of cross rhythm (or what I’m calling cross phrasing).
The LH shows the 3 articulations of the 2:3, but by its expression of “Down-Up-Down-Up” it is now shaping a phrase in twos.
The RH is the “2” of the 2:3 but its phrases are now shaped in threes since is plays “Down-Down-Up” etc. In other words, it takes four iterations of the full RH movement to arrive together with nine iterations of the complete LH movement. Thus, while the cross rhythm of the articulative pattern is 2:3 (the fundamental relationship of the beat of the Left to the Right hand) there is a higher crossing pattern of 6:9 (i.e., the Right against the Left). It is that latter cross rhythm that I’m giving a separate name of cross phrasing. It is just another level of cross rhythm but, since we hear it more as form and not as the fundamental physical rhythm, I think it’s worth giving it another name to signify another kind of experience.
LH ||:D – U – D – |U – D – U – | D – U – D – |
RH ||:D - - D - - |U - - D - - | D - - U - - |
LH | U – D – U – |D – U – D – |U – D – U – :||D etc.
RH | D - - D - - |U - - D - - |D - - U - - :||D etc.
This idea of achieving ‘higher’ level shape by means of substitution is one of several strategies for entering more complex musical territory without a significant increase in “maintenance” energy, i.e., with only a marginally greater demand on attention. (Translation; You can do more interesting things without necessarily adding difficulties.) In class, we did not try to realize any of this using other substitution values (texture, harmony, melody, timbre, etc.), but that is the next step each person should take.