As you can see above, the score features a third line, an 'inner stimme' which is not to be played, merely implied, in the accentuations of the two given accompaniment parts. Generally it seems that this move is either taken to be a part of the gradual diminishment of the voice in Schumann's work (related to his mental illness) or perhaps a tribute to Clara and one of her works. I'd also like to suggest a possible hidden reference, which is pure conjecture. The Humoreske was composed in 1839, and a few years previously the pianist Sigismond Thalberg was becoming incredibly famous (he was described in 1837 as the leading pianist in Europe), although his star was later eclipsed. Here is a quote from the Oxford Companion to Music:
The impact of Thalberg's playing largely depended on his 'three-handed technique', where a melody played by the thumbs in the middle register of the keyboard is swathed in ornate arpeggiated figuaration in bass and treble, creating the illusion that three hands are required.
Could Schumann have been influenced by, or even been referring to this 'three-handed technique'? I don't know, it's certainly possible. There is an example of Thalberg's technique here.
Now, Zizek describes the first section thus; 'one is thus compelled to (re)construct a third, "virtual" intermediate level [...] which, for structural reasons, cannot be played.' 'Virtual' here is Deleuzian; a set of real properties which have the capacity to be actualised. To me, this is interesting enough in a musicological sense, although I would perhaps suggest that we understand this 'implied' melody in spectral terms - a non-present presence. We can see this effect in hauntology - the memory music of the Caretaker involves a source recording taken to the very threshold of cognition, but it also occurs in jazz - Charlie Parker 'weaving' his way around a standard melody, suggesting it without ever playing it directly. Zizek isn't satisfied with this, however. He wishes to make an additional point, regarding the repeat of the same section later in the piece, this time with no annotated voice:
what is absent here is the absent melody, namely absence itself. How are we to play these notes when, at the level of what is in fact to be played, they exactly repeat the previous notes? [...] The true pianist should thus have the saviour-faire to play the existing, positive notes in such a way that one would be able to discern the echo of the accompanying non-played "silent" virtual notes or their absence ... This, then, is pure difference: the nothing actual, the virtual background, which accounts for the difference of the two melodic lines.
Now, disregarding the usual Zizek sloppiness (surely he means the difference of the two accompaniments?), we should judge this point on two fronts - does it stand up to musical scrutiny, and does it stand up to Deleuzian scrutiny?
pianist: Sviatoslav Richter, the two passages are at 5:29-5:59 and 8:31-8:48
Now, Richter cannot have read the performance notes, for this recording actually features the inner voice being played the first time! So much for the virtual! This is helpful however, so that we can hear what we are not supposed to, so to speak.
pianist: Soojin Ahn, 4:25-5:08 and 7:45-8:40
Here, Soojin Ahn avoids playing the 'inner voice', but she renders the two sections in such a radically different way that we cannot really point to any 'minimal difference' at work. The first section certainly renders the absence palpable, but the second is so slow and hesitant, anticipating the fermatas that occur in the following section, that any sense of 'voice' is lost.
Regarding the Deleuzian aspect of Zizek's point, it must be said that Zizek is on fairly safe ground here, utilising a section from Difference and Repetition that draws upon Lacan to discern what Deleuze calls the virtual object. Zizek takes the virtual object to be only perceived in what he himself describes as a minimal difference, a parallax, which corresponds to the anamorphic nature of the Lacanian Real. Deleuze:
Virtual objects are shreds of pure past [...] Although it is deducted from the present real object, the virtual object differs from it in kind: not only does it lack something in relation to the real object from which it is subtracted, it lacks something in itself, since it is always half of itself, the other half being different as well as absent. This absence [...] is the opposite of a negative.
The virtual object is never past in relation to a new present [...] virtual objects exist only as fragments of themselves: they are found only as lost; they exist only as recovered. Loss and forgetting here are not determinations which must be overcome; rather, they refer to the objective nature of that which we recover, as lost, at the heart of forgetting.
Deleuze here makes obvious use of Lacan; the Real, which is always in its place, is virtualised and becomes a condition of temporality itself. Deleuze notes that the Lacanian phallus is an erotic example of the virtual object as pure past, an always displaced fragment, that creates the condition for repetition: repetition does not manifest itself sequentially between two linearly arranged moments, but across distinct series of time that are related by the virtual field:
Repetition is constituted not from one present to the other, but between the two coexistent series that these presents form in function of the virtual object (object = x)
Now, Zizek wants Deleuze's virtual object to correspond to Hegel's eternal absolute - he takes a highly Lacanian passage from Deleuze and then translates it back into Hegelese, taking him back into his comfort zone. Here is his conclusion regarding Schumann:
the eternal absolute is the third un-played line, the point of reference of the two lines played in reality. It is absolute, but fragile - if the two positive lines are played wrongly, it disappears.
Now Zizek claims that the first of the sections is not enough - for him, the pianist cannot highlight the inner voice the first time to make it clear - it must be repeated again without the highlighted missing voice in order to make the absence palpable. But what is occurring the first time? What is the presence of the original inner voice? For Zizek's analogy to work, he needs there to be a repetition, in order for there to be a 'minimal difference' that both depends on and enables this repetition. Now for the listener, what are they actually experiencing? The first section stresses the absence of the inner voice - its fragmented appearance in the actually occurring music is enough to suggest its existence. The repeated section, rendered correctly, does not suggest any voice whatsoever. Rather than suggesting the echo of the notes, the repeat is a negative positing of the voice, the presence of the absent voice is removed, but in a destructive way. The virtual background is not what accounts for the difference of the two lines, but the occlusion of the space where the missing line was articulated. I suggest that the use of the term 'repetition' is the problem here. In the Humoreske, the missing line is not merely spectrally suggested but then is exorcised by repetition of the positive notes in an altered manner. This is, however, to conflate the musical repetition of a phrase with the repetition of which Deleuze speaks:
Undoubtedly the whole psychoanalytic [...] game of repetition is at issue here. The question is whether repetition may be understood as operating from one present to another in the real series, from a present to a former present.
Zizek's example, although interesting in and of itself, fails to correspond properly to the terms that he uses it to explain.
UPDATE- For the past few days, I have been unable to stop humming the non-existent 'virtual' melody to myself, which might well be a world first.