Apply something cool to your head before reading on.
There can be several distinct copyrights in a piece of music. It arises naturally as soon as a work is fixed in physical form. Regardless of what you may see people say, you don't need to take any special steps to secure copyright protection; though there are certain benefits to registration in the USA (uniquely I think) if you're planning on suing someone.
In the UK:
- Copyright in a literary or artistic work endures for 70 years from the year of death of the creator (or if there's more than one, the last of them). Addressing your BQ - Rachmaninoff died on 28th March 1943, so his music will enter the public domain on 1st January 2014. Konstantin Balmont, the librettist of Rachmaninoff's The Bells, died on 23rd December 1942, so his writings will enter the public domain on 1st January 2013.
- Copyright in a printed score endures for 25 years after first publication. That's for the benefit of the publisher who produced it.
- Copyright in a recording endures for 50 years from the date it was made; or from the date of release if it remained unreleased for more than 50 years. That's for the benefit of the record label and performers. There's been a recent EU proposal to extend the former of those terms to 70 years; I'm not sure of its current status.
I'm not an expert on US law, but know that artistic copyright now lasts for 70 years from the creator's death, and that the position with recording copyright is complicated - it used to vary from state to state. The main international copyright treaty is the Berne Convention, originally drawn up in 1886 but since revised several times. The US only signed up in 1988, so the position with works created outside the US before then is complex.
[EDIT] Just noticed your username ...
http://www.youtube.com/watch?v=JZ4Q9_bDwLY
nicht wahr?