Between two Regimes of Madness
The diagrams of piano keys resized according to frequency of usage in Beethoven's Piano Sonatas presented in David Pocknee's article, found elsewhere in this journal, are the result of a contraction, via a bijective function – or one-to-one mapping – of time onto key size. The diagrams represent a condensation of singularities, an accumulation of proximities and tactile relations, of former presents collected and flattened into simultaneity. The diagrams do not – and cannot – depict with complete fidelity the diachronically contingent field of difference (IToE) that is a subject of this article. If sound can be considered to exist within a smooth space, an intensive spatium or multidimensional continuum, our diagrams rely on the striation of this continuum into discrete, countable sets – the individual keys of the piano. In addition, time must be quantified with a cardinal metric in order to make a bijective association with spatial displacement. Quantity, countability, spatiality, and distance are all characteristics of the extensive magnitudes that occupy striated space (Yu & Bunnin, 2004). On the other hand, affect, for example, does not lend itself to analysis via a bijective relationship. Affect and sensation, along with those matters of quality such as pitch and hue manifest within an intensive continuum, which is occupied by the intensive magnitudes that characterise smooth space (Castellano, 2004, 2007). While intensive properties can lend themselves to a metric, these metrics are ordinal, generally accumulate by orders of magnitude, and do not divide without changing in nature (Deleuze & Guattari, 2005). So the diagrams, while entirely extensive in their expression of complex relations between magnitudes, refer to an accumulation of the intensive magnitudes that characterise listening and performing. Musical discourse relies on some striation of the intensive spatium, of extensity’s capacity to explicate intensity, while in practice intensity feeds back and envelopes extensity (Deleuze, 1994, 230). The violinist sees a notehead on the fourth line of the treble clef and makes a one-to-one association with a precise position on the neck. A lifetime of practice and habit – the accumulated moments of concentration, contemplation, and physical effort that are ingrained into the cognition and musculature contracts the finger within two decimals of a centimetre, and the pitch is accurate to within a cent. What does the performer then do?Vibrato. Like a child playing with his or her food, the performer recoils from the rigidity that characterizes bijection in order to pull the sounding result back into some resonance with the intensive reality of his or her own internal states. Extensity exteriorises while intensity interiorises, and it is between these two poles that the instrument/performer assemblage oscillates and contracts. Each revolution opens an extensive space on the instrument’s surface and projects an intensive reality onto instrumental surface, and as such defines a zone of indiscernibility proper to becoming (Deleuze & Guattari, 2005)
 For example, the discomfort we feel in extreme heat is not linearly proportional to the number of degrees above room temperature (Castellano, 2004, 2007).