Spatial Relationships - Hand Independence and Counterpoint (Part 2/5)

March 16/19 edit:  Major 1500-word update to the article below, exploring the connection between harmonic and spatial relationships at the piano.  Also includes 15 new images of how some of these relationships may be visualized and felt at the piano.  

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In the previous article, I explored active and passive relationships as a starting point for understanding how improvising pianists split attention between their hands. Pianists can use larger clusters of notes in BOTH hands to create the illusion of two separate and active voices. With both hands using higher levels of abstraction, a more holistic relationship emerges that includes the right hand, the left hand, and both hands together.

Discussing this holistic relationship in these terms may seem unfamiliar, but in practice, even amateur jazz pianists will have experience with this. This is demonstrated easily with two-handed voicings:

These voicings, made famous from Miles Davis’s So What, are stock vocabulary for jazz pianists. The arrangement between the hands is so ingrained that their structure could be used as abstracts, and extrapolated like this:

A pianist’s method of extrapolation is largely influenced by a holistic relationship between the hands. In this case, the two notes in the left hand and three notes in the right hand (2-3) form one unit that’s characterized by the distribution of notes between the hands, the fingers used to play them, the spatial distance between the hands, and the spatial distance from the body. To demonstrate further, if we change the spatial arrangement in the voicings from 2-3 to 3-2, we would get this: 

This sounds identical, but creates a vastly different physical relationship between the hands.  Depending on the skill of the pianist, this new physical arrangement would result in a different method of extrapolation and different improvisatory decisions. If we keep the same musical arrangement as above, you can clearly see (and feel) the different rhythmic interplay between the hands:

It might not sound like they’re codependent, but the hands are physically working together spatially, rhythmically, directionally and functionally while improvising. These relationships are at the heart of a pianist’s improvisatory choices and influence how they extrapolate from larger clusters of notes and higher levels of abstraction. Improving hand independence and counterpoint is a matter of practicing exercises that target these relationships. They all overlap in practice to some degree, but I think it’s important to try and isolate them, and discuss them in detail. 

Spatial Relationships

“Music is the space between the notes.”

-Claude Debussy

Debussy’s quote contemplates the relationship between sound and silence. In keeping with the theme of these articles though, for musicians and improvisors, there is no such thing as a “note” unless paired with some physical gesture. The “space between notes” then, literally means the space and relationship between instrument and body. 

For pianists, I use “spatial relationships” to characterize the spatial distance of the hands from the body, the spatial distance between the hands, the distribution of notes between the hands, and the fingers used to play them. An even more holistic characterization would include the positioning of the body in relation to the piano (sitting position, posture, wrist/finger technique etc.) and the breath. However, these are probably best left to a specialist in a subject like Alexander Technique, so I’ll leave that for future exploration.

Practicing for improvisatory contexts is normally focused on exploring harmonic, melodic and rhythmic material. Because of this disconnect from physical gestures, pianists often take the physical dimension for granted and unknowingly develop spatial “comfort zones” that restrict their playing. For example, lets divide the piano into three regions in relation to the body - left of centre (low), right of centre (high) and centre (mid). The right and left hands can be positioned in any of these regions. In total, there are six hand positions:

(Obviously, there is ambiguity in the separation of these regions and are only meant to be seen as rough, broad structures)

The Bill Evans transcription from the previous article has both hands in the mid region:

For pianists who play in jazz ensembles, this is a typical arrangement that’s reinforced with practical use. In a jazz ensemble, pianists typically don’t play bass notes, so the low region isn’t used. The right hand will often make use of the high region, but if the left hand wandered up to the high region, the ensemble would lose mid-range, harmonic support. So, in jazz ensembles, the left hand typically doesn’t play in the high region.

Inexperienced pianists will struggle when required to play outside of their “comfort zone” and adopt unfamiliar spatial arrangements. This is because when practicing harmonic, melodic and rhythmic concepts, pianists are also practicing physical gestures and spatial relationships, albeit unintentionally. For example, after learning the Bill Evans transcription, what if you played it like this:

Transposing this passage to different regions on the piano would feel somewhat familiar, but may also warrant extra practice to accommodate the hand’s new spatial relationship with the body. In improvisatory contexts, a pianist who is unfamiliar with the different regions on the piano will have an instinct to avoid these regions in the first place.  While improvising and facing different improvisatory choices from moment to moment, the hands will generally take the path of least resistance, which, very broadly speaking, includes staying within spatial “comfort zones.”

Of course, different regions on the piano are also characterized by different functions and textures – playing “bass notes” for example. Unfamiliarity with different functional relationships will also contribute to pianists keeping to spatial comfort zones, but I’ll discuss this in another article.

As mentioned, the hand’s position in relation to the body isn’t the only factor contributing to spatial relationships. Suppose you were to play the Bill Evans like this:

Not only is the left hand in an unfamiliar position in relation to the body, but it’s in an unfamiliar position in relation to the right hand. Depending on the skill of the pianist, this new arrangement may require extra practice. This is because of certain rhythmic and spatial codependencies between the hands. Spatial codependencies can also be demonstrated by keeping the left hand at its original position, but transposing the right hand up one semitone:

This transposition literally creates new “space between notes” and a different relationship between the hands, making it unfamiliar and difficult to play without practice. Recognizing this relationship is very important for practicing hand independence, practicing counterpoint and creating exercises. Not only is the spatial distance between the hands relevant for understanding their codependences, but it’s also deeply connected with a pianist’s feeling of harmonic consonance, dissonance and resolution.

For example, the octave is heard as the most consonant and stable relationship between two notes.  At the piano, the physical distance between two notes an octave apart is approximately 17cm.  Pianists have a precise awareness of this distance – this feeling of consonance.  If you ask a pianist away from the piano to show with one hand the distance of an octave, their thumb and 5th fingers will be close to 17cm apart.  This relationship is experienced visually, as well as spatially.  

At the piano, an octave is unique because it’s the only interval where both notes are always the same colour (black or white).  As the hand moves in parallel octaves, ascending or descending, the visual and spatial relationship is also transposed in a predictable way, following a parallel sequence of black and white notes. 

Experienced pianists develop physical awareness of all intervals. This includes the physical and visual distances between intervals, and how they have different variations of black and white notes.  A perfect 5th from C-G is two white notes.  But a perfect 5th from B-F# is a white note and a black note. Moving an interval in parallel ascending or descending creates a kind of dance and juggling of white and black notes.

Gravity is often used as an analogy to describe a hierarchy of harmonic motion, consonance and dissonance.  If this analogy is valid, then I would propose that these kinds of spatial relationships at the piano are part of that same hierarchal system.  As the hands move around the piano they are participating in a harmonic, gravity field of sorts, which includes the spatial distance between notes and this juggling of white and black notes.

To further complicate this relationship, an interval at the piano can often be physically expressed in different ways with different fingers. For example, in the right hand, a major 3rd from C to E can be comfortably played 1-3, 2-4 and 3-5.  In relation to a tonic, harmonic gravity doesn’t change between these three variations, but the physical expression of that gravity changes. 

Though more complex, these concepts are similarly relevant when playing two notes with two hands:

The physical expression of consonance, dissonance and harmonic gravity is now is now shared between the hands.  As the notes moves in parallel, both hands are dancing and juggling with a certain sequence of white and black notes.  In the figure above, the hands are using the 3rd fingers to play C.  With five fingers on each hand, there are 25 different ways to physically express an octave, and each arrangement creates a different spatial relationship between the hands.  These differences are easily shown with these two examples:

The distance between the two notes (17cm) is always the same, but you can clearly see that the space in between the hands is different.

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Spatial relationships and harmonic relationships are connected. For pianists, consonance, dissonance and harmonic gravity isn’t just heard, it’s visualized and felt through the hands. Though it would be interesting to try and formalize these connections, that’s not my goal here.  My goal is to acknowledge them and create better exercises to become a better pianist.  From this, I’ve made four observations that will inform how I create and practice counterpoint exercises. 

I’ve already mentioned the first: harmonic relations between notes can be physically expressed in many different ways.  The number of fingering and spatial possibilities between the hands is enormous, but some physical expressions are more optimal than others (you can also play C-E with 1-5, or with two knuckles).  All of these different fingering and physical variations then, are all part of the same hierarchal, harmonic, gravitational system at the piano.  More optimal fingerings and hand positions have more ‘mass’ than less optimal fingerings of the same notes.  Through practice, an improvising pianist’s goal is to become more familiar with these different physical expressions and hierarchies.  Exercises can be created to encourage different, optimal fingerings of the same notes to improve range of motion.  This way, improvising will still be physically efficient, and not restricted to spatial “comfort zones.”

My second observation is the flipside of the above: physical relations between notes can be harmonically expressed in different ways.  Here’s an example:

When the chord changes to Bb, the cluster of notes in the right hand stays the same.  But because the harmony changes, the weights of each of the notes are now felt differently. In the first measure, the thumb is the physical anchor point for the right hand.  It’s also playing the tonic.  Physical stability is connected with harmonic consonance and stability.  In the second measure, the thumb is still a physical anchor point, but is no longer playing a harmonic stable note.  Overall, harmonic stability shifts from the fingers 1-3-5 in the first measure to 2-4 in the second measure. 

This is one way of visualizing how harmonic gravity shifts and how it’s connected to a pianist’s hand.  It’s convenient when physical anchor points are connected with harmonic stability, but considering this, exercises may be needed to help the hand become more adaptable. 

My third observation concerns a pianist’s method of extrapolating from larger clusters of notes and higher levels of abstraction.  Spatial relationships include the physical distance between two notes, but also between clusters of notes.  Even though we’re discussing two-part counterpoint, pianists can use the same clusters, and extrapolate from them in different ways.  For example, a more complete analysis of the first measure of the Bill Evans transcription could look like this:

Each note is harmonically, intervallically and spatially related to the other notes. You’ll notice that even though the harmony in this measure is Cm7, the hands don’t actually play a C.  But the hand clusters are formed with some kind of awareness of the tonic.

For inexperienced pianists, it’s possible there actually isn’t any awareness of the tonic, or at least, it’s something that needs improvement.  Students can be given stock voicings without being taught their connections to broader harmonic and spatial structures.  In this case, the “root” of the chords above is Bb.  Obviously, this represents a gap in harmonic and spatial awareness that needs to be filled.  Even though he’s not playing a C, Bill Evans is certainly aware of where it is.  So, what is “awareness of the tonic” and how is this awareness experienced?

This brings me to my fourth observation: Harmonic and spatial awareness is formed horizontally across the keyboard.  Even though they aren’t always played, pianists can still be visually and physically aware of harmonic and spatial relationships.  I think this awareness is experienced as a kind of “phantom hand.”  Considering this, the voicings above could be visualized like this:

The phantom hand represents an awareness of harmonic and spatial possibilities, so it isn’t restricted to an awareness of roots.  For example, playing a root in the left hand for C major, will reveal a tonal awareness across the keyboard:

Different pianists will be aware of different things.  Jazz pianists may be more aware of the B minor pentatonic scale over a C root:

Depending on their experience, a pianist’s awareness may also extend to a harmonic hierarchy in relation to C:

As discussed above, harmonic relationships are connected to spatial relationships.  So, as tonal awareness is revealed across the keyboard, so are possible hand positions, anchor points and note clusters.  This is why I refer to a phantom ‘hand’ and not just ‘tonal awareness.’  When I visualize the B minor pentatonic scale across the keyboard, I imagine all the note clusters that are formed when my thumb is on B, D, E and A, but not F#.  Having my thumb on F# limits my range of motion, so it will be generally excluded from possible hand positions.

In another article, I’ll explore how functional relationships are intertwined with these harmonic and spatial relationships.  In brief, because the left hand is positioned closer to the lower region of the piano, it’s usually playing roots and wider intervals to support harmonic relations.  For this reason, I think a pianist’s awareness of harmonic and spatial relationships is usually built from left-to-right.

Awareness is more likely to look/feel like this:

And not this:

Functional relationships, and this left-to-right awareness influence the way pianists interact with spatial relationships and play counterpoint, which is why I mention it briefly here.  When playing two notes an octave apart, the hands seem to be equal partners in the expression and feeling of that interval.  Without much context, that may be the case.  Considering functional and active/passive relationships though, one hand is often subservient to the other.  Depending on its melodic, harmonic, background, foreground function, the left hand could be informing the spatial positioning of the right hand and vise versa.  

In the next article, I’m going to discuss moving through space, directional relationships and how they’re relevant to improvising and playing counterpoint.