One can see that the acquired interval sizes may not exactly match between the input (the Invention No. 1 in F Minor is one of the forebears of this work and the recomposed output). This is because Cope usually uses MIDI data, in which there is no scope for discriminating diverse enharmonic spellings (F^#/G^b) of sounding pitches. One will notice that some acquired figures may be inverted, because EMI is interested more in the size of intervals than in their direction. Finally one may see that EMI is mode-blind and freely transforms strings originating in one 'ality', as Cope calls the general class of phenomena including modality and tonality, to another.

The EMI B^b-Major Invention     

David Cope, On Algorithmic Representation of Musical Style, in: Understanding Music with AI:Perspectives on Music Cognition, ed. Mira Balaban, Kemal Ebcioglu and

 Otto Laske, Menlo, CA 1992, pp. 354-363

and its variant

presented by D. Cope 1993; this piece is included in the enclosed Compact Disk.

Soundsample online

both pose a performance problem for pianists trained in the classical style which proscribes the use of the thumb on a black note. Fluid fingerings that do not violate this rule are difficult to image. EMI's inventor offers a surprising response: this invention is not in B^b Major, he claims. It is tonally neutral, since, unlike its natural parents, the artificial progeny consists purely in a set of intervallic relation ships that can be channeled, at output time, to any key the user selects.

It is because EMI isolates attributes from events that it so closely parallels the genetic approach to understanding human traits. The dissociation of attributes that occur simultaneously in the previously indivisible musical event leads not only to virtual tonality, virtual meter, virtual instrumentation, and virtual articulation but ultimately also to virtual authorship and virtual composition. For cultures such as ours that value the written artifact above the improvised performance, this sphere of activity poses profound questions about the future roles of composers and performers, as well as music theorists and historians. Since we may soon witness a welter of user-defined, made-on-the-fly experiments in sound engineering, we may wish to ponder what use future generations of musicians will have for the idea of a canonical repertory and for the notion of a composition as 'fixed' by its composer?

At the same time, the work of both Cope and Ebcioglu inadvertently reveals that among the uncodified elements of musical practice gestural factors merit considerable attention as a source of constraint on musical composition. In this respect, the biological paradigm can go only so far. Human factors physical, cognitive, and emotional remain to be accommodated.

The Mathematical Paradigm as a Paradigm of Perfection

In Bach's age the equation of mathematical and musical processes was indebted to a common capacity to express the idea of perfection. The search for spiritual perfection