A student and I recently worked on a realization of a portion of Stockhausen's Studie II (1954), as a way of getting into the piece in a more concrete way. Like many pioneering pieces of electronic music, it is best known in its original realization, with the then-state of the art resources of the WDR Studio for Electronic Music in Cologne. Although I have heard that Stockhausen preferred his realization to other, later versions made by others — a thought I will come back to —, the limits of the equipment available are obvious and, if we are to take the score of the work (Universal Edition 1956) at its word that "it provides the technician with all of the information necessary for the realization of the work", then questions about the faithfulness of that first realization to the requirements of both the score and the composer's stated conceptions of the work provide some incentive for trying, with contemporary resources, to hear what, precisely, a more faithful realization might sound like.
For example, by using multi-layered recording of individual sine waves, Stockhausen was unable to synthesize his tone complexes in a way that fused as one supposes he had intended and the pitch accuracy of his plan was seriously compromised first by rounding off to the next Hertz in the score and then accepting whatever amount of resolution error the oscillators then had. Today, neither fusing of composite wave forms nor the accuracy of pitch resolution are significant issues; the score can readily be realized on a home computer, whether in recorded form, via something like CSound, or as live synthesis. (We happened to be trying the latter, using PD, a program authored by Miller Puckette, who has admirably used PD in his teaching to re-create a number of works of "classical" electronic music.) Despite these improvements, in trying to realize the score, issues of authenticity in performance practice were persistent.
For example, the tuning: without having an equipment limitation of a one Hertz resolution, should the realization use the notated frequencies, or should they be a better approximation of Stockhausen's intended 25th-root-of-five tuning scheme? If we chose a one Hertz resolution, with digital accuracy to several decimal places, strictly speaking the piece will then be realized in a kind of expanded just intonation (without getting into an argument about the definition of just intonation, which is something for another time...) and, aside from the interval 5:1, that is not what the composer was after. Should we realize the score with a more accurate representation of the 25th-root-of-five tuning? It's certainly worth trying out both options.
Or this: Stockhausen combined his sine waves by overdubbing and then played back and re-recorded the composite tones in a reverberant room to get a better fused and what might be described as a warmer tone. We can now begin with a better fused composite tone and add reverb electronically or acoustically. (For that matter, we can realize the score directly with the specified sines and eliminate the middle step of creating a library of composites.)
Or, how about dynamics: Stockhausen's score differentiates dynamics over a 31-step scale, in which each step represents a difference of one decibel. Should we instead take a bit of psychoacoustics in consideration and adjust this scale to compensate for the Fletcher-Munson curve? I suspect that such a consideration would be taken into account in the equalization of a playback of the recording, but it's nice to have the option to build this into the realization itself. The original attack envelopes were made by hand, by raising a pot, but we can now do this with precision. On what basis do we decide how to shape and time these envelopes?
Finally, Studie II is a monophonic piece and, arguably, all of the tones and composites in the work belong, conceptually, to a single scale/spectrum. Is our realization limited to a single channel of sound, or might it be useful and musicial to project the sound onto multiple channels; if we do use additional channels, on what intutional or analytic basis would such a project be made?
Stockhausen's preference for the first realization deserves some thought. While a purely mechanical reading of the score could have been made, I suspect that the series of musicianly interventions made necessary by the equipment produced a result which while necessarily introducing inaccuracies, ultimately created a more approachable, even endearing sound. Likewise, in the 13th hour of his final compositional project Klang, Cosmic Pulses, a work with 24 layers of looped melodies with tones connected by portamenti, the actual speed of the portamenti was done by hand, perhaps a similar expression of preference for a human intervention in the surface of an otherwise through-calculated process.