Directional Relationships at the Piano

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At the end of the (previous article) on spatial relationships, I made four observations that I believe are relevant for practicing hand independence and counterpoint.

Harmonic relations between notes can be physically expressed in different ways
Physical relations between notes can be harmonically expressed in different ways
Spatial relationships include the physical distance between two notes, but also between clusters of notes.
Harmonic and spatial awareness across the keyboard is experienced as a kind of “phantom hand.”

These four observations were from exploring the significance of spatial relationships at the piano. In this article, I’m going to explore moving through space and directional relationships.

Admittedly, thinking about directional relationships and their relevance to hand independence at the piano adds an overwhelming amount of complexity. They’re also deeply connected to active/passive, spatial, and rhythmic relationships, making it difficult to write about them in a logical, linear way.

So, the rest of the article is a collection semi-related thoughts and reflections that attempt to highlight directional relationships and their connections to physical gestures and piano improvisation.

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Three Types of Directional Relationships (100 words)
Directional Relationships Over Large Distances (250 words)
Directional Relationships Over Smaller Distances (200 words)
Spatial Relationships in Time (700 words)
Chunking Large Directional and Spatial Relationships (800 words)
Chunking Small Directional and Spatial Relationships (1000 words)
Directional/Spatial Relationships and Improvisational Foresight (1000 words)
Directional Relationships and Meter (1200 words)
Directional Relationships in Two Hands (2600 words)

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Three Types of Directional Relationships

There are three kinds of directional relationships, or “types of motion:” similar, contrary and oblique.

For pianists, it’s helpful to divide these relationships into two categories: Moving across large distances and small distances. Recalling my article on spatial relationships, I divided the piano into three regions in relation to the body – left of centre (low), right of centre (high) and centre (mid).

A physical gesture that moves across these regions could be considered a large distance. Small distances include motion within these regions. As with the regions themselves, there is ambiguity in the separation between large and small distances. I don’t intend to offer a definitive distinction, only to use them as broad structures to help give insight into these relationships.

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Directional Relationships Over Large Distances

With three types of motion and three regions of the piano, we have thirty different directional relationships over large distances (not including hand-crossovers!). Please feel free to double-check my count:

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Contrary – 2 types
Similar – 12 types
Oblique – 16 types

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Instead of illustrating every one, for now, I’ll only illustrate the ones I can find examples of in jazz music. As I update this article, maybe I’ll eventually have examples of all thirty!

It’s notable that the history of jazz piano is rooted in ragtime and stride, which are characterized by the left hand moving between low and mid regions (mostly oblique motion). It would be interesting to see what kind of correlations exist between the evolution of jazz piano and more diverse directional and spatial relationships.

For example, there are clear stylistic differences between say, Erroll Garner and Brad Mehldau. Differences in style could be thought of as differences in spatial and directional relationships (among others). Garner was more likely to use dramatic physical gestures, covering larger distances across the piano. Mehldau is often more contained within particular regions.

But stylistic differences don’t necessarily reflect a pianist’s awareness. Just because Mehldau plays within a particular region, doesn’t mean he isn’t spatially aware of the other regions. In this case, similarities between Garner and Mehldau could be found at higher levels of abstraction. It’s their method extrapolation that are different, not their awareness. Certainly, there would be differences in their awareness too, but both pianists are considered to be drawing from the same jazz tradition, so this is where those connections, in any, could be observed.

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Directional Relationships Over Smaller Distances

Observing directional relationships over smaller distances is more nuanced and complex. At the highest level of magnification, we could analyze every moment note-by-note and see the three types of directional relationships. This analysis is useful, and ultimately, maybe these are the building blocks that connect with physical gestures.

But we also know that notes and physical gestures are chunked into higher levels of abstraction. So, an analysis of directional relationships over smaller distances could also include lower levels of magnification and general movement though time. Smaller distances can include motion confined to a particular hand position and cluster of notes. It can also include motion between hand positions and clusters of notes, which involve finger crossovers and the moving of anchor points. Over time, smaller distances can add up to cover larger distances.

I’m unsure the extent we should consider all of these levels of magnification when observing, analysing and practicing directional relationships. This may become clearer as I continue writing and practicing. In the meantime, here are a few interesting examples of two-part counterpoint in jazz music that generally move over smaller distances.

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Spatial Relationships in Time

In the previous article, I introduced the idea of spatial awareness and the “phantom hand.” At any given moment, just because a pianist isn’t actively playing the root of a chord or other harmonic relations, doesn’t mean they aren’t spatially and visually mindful of where they are. Similarly, just because a pianist isn’t actively playing the downbeat, doesn’t mean they aren’t mindful of when it is. The nature of this awareness encompasses many other aspects of playing the piano and also crosses into the realms of human physiology and cognition which are way beyond my specialty. So, I’m not able to easily quantify it. But I believe I can isolate certain features of this awareness, and observe the way it shapes our playing and improvising.

For example, in ragtime and stride music, a common pattern for the left hand could look like this.

When playing the roots, awareness includes the gestures and hand positions needed to play the chord on the next beat.

Likewise, when playing the chords, awareness includes the gestures and hand positions needed to play the roots on the next beat.

As the hand plays and moves back and forth, there’s a relationship between the hand and the phantom hand that’s important to acknowledge. At some point, awareness becomes action; the future becomes the present. If you’ve ever played a piece by memory, you know there’s a specific point in time you need to focus your attention. There’s a delicate balance between focusing on what your hands are playing, and what your hands are going to play.

If you focus too much on what your hands are presently playing, it’s easy to lose sight of the music ahead. So, we use awareness, the phantom hand, and foresight to focus one measure (or one second) ahead to anticipate the music unfolding. As the music flows, there’s an event horizon so to speak, a point of no return, when the future becomes the present and the physical gesture is all that’s left between thinking about playing and actually playing. The hands take over with a kind of auto-pilot, maybe drawing from larger clusters of notes and higher levels of abstraction. Either way, we trust them to extrapolate from these clusters and perform as we keep our focus on the music ahead. The hand’s auto-pilot has a short memory though. Focus too far into the future and they’ll forget what comes next.

Again, these are only my observations. I don’t know any science on memory, cognition, and focus, or how it applies to playing the piano. But I DO believe that this point of focus is moveable. Or at least, it’s a skill that needs attention. Try it! Here’s a simple stride pattern:

Below is a list of questions to help guide your observations. Whether you’re a beginner or advanced pianist, these questions are relevant for improving your focus and isolating its behaviour while you’re playing:

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To what degree are you anticipating the next root and the next chord?
To what degree are you anticipating the change in harmony in measure 3?
If you’re reading the music, how far ahead are you reading?
How often do you look down at your hands? Do you always look down at the same times?
Is there a correlation between the music and when you look down at your hands?
Is there a difference in focus between reading the music and playing it by memory?
To what degree are your hands on auto-pilot?
How does your focus change if you play this pattern at different tempos?
If there were four bars of Ab, and four bars of Eb7, how would that change your focus?

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How is this relevant to directional relationships? For one, directional relationships are like spatial relationships in time. With this added dimension, concepts like anticipation, foresight, memory, and awareness become relevant. These are trained skills. In a way, when practicing directional relationships, these are the skills we’re actually trying to improve.

Further, focus, anticipation, and awareness in one-handed stride patterns are complex in and of itself. From my (article) on active & passive relationships, I’ve also mentioned that focus is a limited resource. So, when you add directional relationships between TWO hands, it’s more important than ever that we train ourselves to focus our awareness efficiently.

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Chunking Directional and Spatial Relationships (Larger Distances)

A reoccurring idea in these articles is the chunking of notes and physical gestures into higher levels of abstraction. This simplification allows pianists to access a kind of auto-pilot so there is more freedom in where they focus attention. For example, pianists don’t think about every individual note when playing a major scale. They simplify and chunk those seven notes into a couple of hand clusters.

The more repetitive and familiar a particular pattern, the easier it is to memorize, simplify and chunk the physical gestures required to play it. This process of chunking notes and physical gestures can include moving through space and directional relationships. For example, here’s a simple one-handed stride pattern:

When first learning an unfamiliar hand motion, practice is spent visualizing, anticipating and being aware of the gestures and hand positions needed to play the notes on the next beat. If you can play this, you’ve learned how to balance your focus between thinking about playing and actually playing. Hopefully at some point you can encode and chunk these spatial relationships and hand movements into one stride pattern in Ab. So, while playing, attention can be focused elsewhere. Here’s a subtle variation:

This pattern is slightly less repetitive. To play this pattern, we’ll need to expand our spatial awareness and foresight to include the fifth in the bass. Including the Eb in the bass involves travelling a larger distance, but the back-and-forth, left-to-right hand movements are still predictable and familiar. Overall, though this addition adds a bit more complexity, it’s still possible to chunk this pattern into smaller parts, and be freer with focus.

We can apply this same process of practicing, visualizing, anticipating, and being aware of future gestures to any spatial/harmonic arrangement. Instead of Ab, suppose we isolated a pattern in E7:

With enough practice and familiarity, this pattern, with its repetitive and predictable hand movements, can also be chunked into one stride pattern in E7. I chose E7 to emphasize that this process applies to all spatial and harmonic arrangements, not just the ones you’d expect (like Eb7). The next logical step is to combine these two patterns:

In my experience through observation, even though the two patterns in Ab and E7 are individually familiar, a change in harmony requires extra focus to anticipate the new spatial arrangement. This makes sense: a change in harmony creates a more complex and less repetitive pattern. Isolating and chunking the gestures needed to play the Ab and E7 patterns on their own is helpful, but combining them creates a brand-new sequence. Practice now needs to include isolating and anticipating the spatial change between Ab and E7.

So, practicing this stride pattern has four steps:

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Isolate a set of spatial/harmonic relationships (Ab)
Isolate another set of spatial/harmonic relationships (E7)
Isolate the spatial changes from Ab to E7
Isolate the spatial changes from E7 to Ab

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With this process of gradually adding complexity, including more chords and harmonic variance would similarly involve isolating the spatial arrangement for a new chord, and then isolating how the space changes between this new chord and other chords. Practicing is a matter of visualizing, anticipating, chunking and being aware of these changes. Try it!

Another pathway to gradually increasing complexity is adding different directional changes. For example:

Adding directional variance adds complexity in two ways: The first is that the motions themselves are more complex. This pattern moves in four steps (Up-Up-Down-Up), where the original is in two steps (Up-Down).

The second is in its new relationship to meter. This requires a dedicated section, and eventually an entire article to explore thoroughly. But in brief, moving the hand ‘right’ to approach the downbeat is different than moving the hand ‘left.’ This may seem like a dull observation now; it may be easier to appreciate at faster tempos. You could also try playing this pattern, which is directionally identical, but rhythmically and metrically different:

These kinds of rhythmic and metric relationships will be explored later. In the meantime, we can focus on the directions themselves. Pianists can isolate different sequences of ‘up-down’ to practice visualizing, anticipating, and chunking them. Practicing this pattern (Up-Up-Down-Up), can also be applied to different harmonic/spatial arrangements and the four steps above.

In a way, with this process of gradually increasing directional/spatial complexity, and chunking patterns into smaller parts, we’re slowly assembling a vocabulary for improvisation. With practice, the left hand will more easily pull from sets of learned physical gestures that have been encoded and chunked in a way that allows attention to be focused more freely. In jazz piano music, these dramatic jumps across large distances are less common in the right hand. But the same process of isolating directional and spatial changes would be used to learn those patterns too.