It is my understanding that algorithms (not their concrete implementations) are not copyrighted. Musical scores or productions usually have a copyright.
Some music is constructed from a small set of rules, for example Spiegel im Spiegel, by Arvo Pärt
Is it a violation of copyright to publish a computer program that exactly produces such a piece, without containing the piece itself in the program?
Edit: I found actual examples of what I am described here and here
Is it a violation of copyright to publish a computer program that exactly produces such a piece, without containing the piece itself in the program?
Yes. A program that reproduces a particular work is functionally a derivative work and is a copyright infringement.
A program that composes music not tied to a particular work would be patentable, but the algorithm would not be protected by copyright, although derive works based on the code implementing the algorithm might be protected by copyright.
Of course, this assumes that the person devising this algorithm knows about the original work that it will produce. If the person devising and the person using the algorithm are ignorant of the existence of the prior work that it produces, it is not a copy or a derivative work and is not infringing.
The source of the creation of an allegedly infringing work in relevant in copyright law even thought it is not relevant in patent and trademark law. Copyright protects independent inventors of the same work from infringement liability, although this may be hard to prove.
In theory the burden of proof to show copying is on the personal bringing the lawsuit alleging infringement. But, a copyright infringement plaintiff can meet their burden of proof in a copyright case by inferring that copy was made from the circumstantial evidence of the allegedly infringing work's similarity to the allegedly infringed work without direct evidence of copying or deriving the work from the original work.
There has been a few questions by people assuming that a computer program, doing things on its own, may be treated as if it were a sentient being.
It is not. Certainly, there are no laws which would treat it as such. A computer program is a device. It enjoys no more rights than a fountain pen.
Whoever operates the device produces a certain outcome, as they would when using any other tool. The fact that the device is sophisticated, or that the outcome is sophisticated, does not change it.
A computer program, the running of which would produce a certain specific melody, is a tool just like a mechanical piano, modified to play a certain melody when prompted to do so.
But a program, the running of which would produce a melody not known to the person running the program ahead of time, is just like a regular old piano. The fact that the person operating it may not know its internal workings does not change the fact that it's just a tool and that it is the person using the tool who is responsible for the produced outcome.
