An Instrument is an Egg

The piano diagrams are attempts to render visual the conceptual frameworks that mediate our engagement with instruments via a given repertoire. When we approach a piano, the cardinal ordering of keys, hammers, and strings is not the instrument we have access to. All interactions with instrumental mechanism take place via some conceptual ‘screen’ that binds points along the surface into a neighborhood, which is ingrained into the musculature in training. As such the act of composing can be understood as the construction of one of these neighborhoods – a particular constellation of privileged points of attraction that interface the performer with the instrument, that grants us access to instruments by opening spaces of possibility out of what before was only potential.

Imagine that first time you sat at the piano, completely ignorant of any technique. The surface of the keyboard extends along this horizontal plane, and aside from the black key/white key dichotomy, any key is just as likely as the next to be played. There are no learned exercises to regurgitate, no scales, melodies or chords to grab onto. This is keyboard surface as more or less ontologically symmetrical. The piano we perceive as beginners may be closer to what Manuel De Landa terms a flat ontology, consisting of unique, singular individuals, differing in spatial distribution but not ontological status. In that first lesson the teacher establishes basic postures and regions of bodily interaction conducive to proper technique, and isolates a particular position to be explored more in depth. We have already raised the status of certain spaces, initialized the construction of a conceptual screen or neighborhood, and broken the ontological symmetry of the beginners mind. Pedagogical practices enacted in training can be understood as the emergence of a molar, hierarchical structure built from accumulations of general types (scales, chords etc.) and particular instances (individual works that make up a given repertoire), a process of progressive differentiation that qualitatively forms the player via a given repertoire. What these diagrams seek to express is pedagogical practice as a progression of symmetry breaking transformations that actuate privileged zones of activity within polarities established by repetition (De Landa, 2002).

To illustrate the mechanisms of these symmetry breaking transformations I will introduce two types of differential relations: a bijective function a one-to-one correspondence of one codomain mapped onto its domain, and an surjective function where every element of a codomain is mapped to at least one element of a domain, thus certain elements are subject to omission (Academy, 2009).

We could view the initial domain as the instrument/performer assemblage in its beginner stage, the instrument as pre-differentiated, ontologically symmetrical, pure potential. Via the teachers imposition of a pedagogical filter on the students activities, every lesson and practice session applies a surjective function to the instrument/performer assemblage, creating a codomain that in strengthening certain elements necessarily omits others. ¹ Through repetition, applications accumulate over time producing successive domain to codomain relations, gradually constructing the conceptual screen that informs our engagement with instruments. Pedagogical practice, in determining the nature of differential relations, plots the points of attraction that progressively differentiate a given instrumental space. Pedagogues can impose answers, prescribe rote practice without offering understanding, promote performance practices without regard to the cultural context in which they exist or inspire curiosity, invoke critical questioning, and unveil the potentials of a given instrumental surface to a student. I would propose an ontology of instrumental surface that while perhaps cannot be said to be flat, is at least bumpy (Harman, Speculative Realism, 2013).

These deformations imposed by pedagogy, depicted on keyboard surfaces in the diagrams are irreversible. Without some procedure to step outside of our cultural conditioning a flat ontology is not possible for us. One cannot perceive an instrument outside of a given conceptual/pedagogical constellation that binds points of attraction into a neighborhood. As such I will need to introduce one more term to illustrate this reality, that of an ordinal series. Unlike a cardinal series (one, two, three&), which is defined in terms of bijective functions and quantitatively defines the nature of the elements it orders, an ordinal series (first, second, third&) implies asymmetrical relations between abstract elements;, it orders elements without defining them quantitatively, only requiring that a given element be in between two other elements (De Landa, 2002). Via the surjective differential relations employed by pedagogical practice, ordinal distances establish the neighborhoods that for us define instrumental surface. ²

This analogy of recurrence to size is a way of illustrating the virtual contortions a conceptual screen imposes on instrumental surface via desire. The diagrams point to a danger in certain narrow pedagogical approaches that tend to emphasize one repertoire at the expense of all others. Overemphasis of a particular set of neighborhoods over time risks hardening the interface between performer and instrument, effectively turning instruments into stone. Aided by the diagrams, one can imagine what such an instrument would look like. These are the instruments that we allowed to petrify, to calcify in their fixity. It is not the instrument that turns to stone but ourselves.