The requirement for an infinite length was a rhetorical one, to fit your contrived use case.
I'll see your "contrived use case" and raise you your own comment:
An example might be to create a software program that outputs every possible combination of notes permissible under the rules of standard musical notation, then file copyright on it.
I'm not the one changing the scenario around; you are. I arbitrarily limited the scenario to be "all 4 minute, incredibly simplistic song representations".
Your arguments against a static copy are torpedoed by the contrived requirements you assert as being extant: 4 measures of 4:4 time would at most, at fullest extrapolation, be a few gb in size.
O Rly. Let's take your cited scenario:
You can narrow it down a bit if you make some simplifications, such as, 4:4 time, with maximum 8 notes per chord, 16 chords per measure.
I presume you will agree that there is more than 1 octave available in music. I chose 8 octaves, which I believe is a reasonable number, but it doesn't really matter (as you will see presently). 8 octaves * 12 notes = 96 available notes. Fine. Now, 8 notes per chord: 96 choose 8 == 132,601,016,340 possible chords. Forgive me for switching to logarithmic notation at this point, because the numbers are just too enormous to post here. Apply this to 16 chords per measure, 4 measures.
(96 choose 8)^16^4 == 10^(log(96 choose 8)*16*4) ~= 10^712
Congratulations, you have narrowed the space to 10^712 permutations. This disregards the explosion of permutations that would happen if you *also* allowed chords of smaller than 8 notes or allowed silence for one or more beats.
Feel free to insinuate this isn't what you meant by saying that you could fit static copies of this data into a few GB, but we both know the truth. Much like 10^1200, 10^712 is also a very good approximation of infinity.
A complete but truncated example of that space (every possible combination of 4 measures) can be experimentally interesting to see what proportion of that space humans would consider music.
Sounds useful! Just grab all 7 billion people on Earth and have them listen to your samples for ~10^703 years. FYI, the ultimate heat death of the universe (after all the black holes have evaporated) is scheduled for ~10^100 years, so you might have to develop some new physics to finish your experiment.
If I made such a study for money, would I not be correct in pointing out the obvious utility that copyright would offer to finance additional research? Also, by giving such a test case, do I not essentially torpedo your claim that the sequence has no intrinsic merit for which copyright would apply?
Well, given that your copyright would have expired before you could even begin to scratch the surface of that particular experiment...
The idea behind copyright is to promote the progress of science/art for society as a whole. I'll rebut your claim that I am appealing to unnamed authority (ie. without citing legal precedent) with a counterpoint that you are asserting without proof that having the USPTO grant you sole copyright over all copyrightable material would serve to promote the progress of art and science in society.
Because, for all the changing of your proposed attack vectors, that is your stated goal: to own all copyright and somehow foment massive changes to US intellectual property law. It is patently obvious that it doesn't serve the public interest to grant this kind of meta-copyright and so it won't be allowed.
I am not even going to engage in a futile search for case law on this, because it is so absurd. I will leave you with an adage from US jurisprudence: "The Constitution is not a suicide pact" . If even the US Constitution can be set aside in certain circumstances for the common good, what do you think your semantic games on a $35 online copyright registration will count for when weighed against the potential for destroying all intellectual property production for 75 years? Again, this doesn't cover the arguments that you know lawyers could come up against this, even based on extant law & regulations.
Your meta-copyright would be first mocked as frivolous, then retroactively rejected if you ever managed to get it granted and subsequently tried to assert it. By all means give it a shot, but don't forget I told you what was going to happen.
Don't mistake my claim that your attack is unworkable as support for the status quo in the US IP regime. In fact, the polar opposite is true: I am almost to the point that I believe that all copyright should be abolished. I just don't believe your approach is tenable in the legal system.