About this exposition
Conversely, what music should you play that allows for identity (and freedom)?
In a similarly minimalistic genre, it would be decorrelated noise played through many speakers distributed aleatorically in the room.
The listening experience would be more or less the same independently of the listeners position and orientation. The residual variation would be quite predictable for the listener, in contrast to what happens with the sine tone. Interferences of the sine tone with its reflections from the surfaces of the room will change its level with the tiniest movement of the listener's head. The amount of the change will depend on the chosen frequency and the room, but there will always be such an effect, therefore the listeners will find themselves "... in a prison of permanent change" (Boris Groys, as quoted in Annie Abrahams' JAR2 exposition "Trapped to Reveal - On webcam mediated communication and collaboration").
Both propositions are paradoxical. On the one hand, the sine tone is the simplest, most redundant signal we can imagine, but its identity is very hard to experience in a room (a headphone would do). On the other hand, the noise represents the biggest amount of change we can imagine in a sound, but in the imagined situation it will create a liberating uniformity. The movements of the listeners will not disturb the experience of identity, they will feel immersed in a sea of sound, which doesn't change due to their agency.
This is an interesting reply, since I wasn't sure what to expect. In a sense you are right, but you promote this 'minimal' setting i.e. a certain radical formalism that looks at order/entropy.
However, what about a rhythm or a meldoy (i.e. a musical structure or 'content' even)? May one not argue that they offer two types of identity at the same time, in the material and the experience?
Within the formalistic approach I have chosen, the control of time was excluded from the composition, aiming at an abstract formulation, at a "weak gesture" in Groys' sense. Both rhythm and melody rely on some notion of time - rhythm as a sequence of time intervals and melody as a sequence of tones.
To answer your question I have to leave the chosen formalistic framwork - a choice I took in my experiments with the research catalogue format. I am interested in finding or creating examples of using the research catalogue as the medium for art works - sound art works in my case. I adopted a conceptual attitude in order to be able to write this piece in two sentences and publish it here as the abstract. The empty white page is for me an allusion to the prison scene in George Lucas' movie THX 1138 (something I became aware of once I looked at what I did).
But now to answer your question, if musical structure doesn't offer two types of identity at the same time, one as material and one in the experience. I think I agree with you, that it does and it doesn't need to be rhythm or melody, which are structures resulting from a particular way of thinking music. If you think music from the point of view of the sound, most probably other structures will be relevent. And I think your argument also applied to those - there is the possibility that they do offer two types of identity at the same time. But what is the relationship between these identities? Isn't this the important question from a compositional point of view? I think we cannot think them as isomorphic. Moreover, an identity on the level of the material may not offer an identity in the perception and vice versa.
How is your interest in identities motivated?
Answering your question will move the point away from your contribution here. It may be better to discuss what you are actually after in more detail, although I am not sure if I am the best person to do this -
In any case, I thought about the relationship between entropy and redundacy that I discuss in my PhD on p.40ff. The point is that we somehow operate between minimal and maximal redundancy (or disorder, for that matter) and that only because of this, structures are actually possible. My point is less that this may be due to the human etc. but rather that your model does not capture it (and that's why we are in a prison).
From the moment structures are possible, life/thought is possible. I tried to suggest with my previous comment that traditional music (or art) - but perhaps also other forms - may qua structure have introduced the possibility for life/thought. Going all the way to the other extreme as you suggest, closes that possibility again.
Why I am interested in it? - This is where I think I operate both in life and in art.