I'd like to use a music based on Beethoven's Piano Sonata in my short movie. I'm planning to ask a violin player to work with the score and use the recorded music for my movie. How can we deal with the rights and payment?
Beethoven's Piano Sonata is public domain
There will be copyright in the performance but as you are specifically hiring the musician to perform the piece for you to record, you would own the copyright in that as a work for hire provided this is stated in the contract.
Sound recordings (the term used in US copyright law is "Phonorecords" or sometimes "phonograms") of music potentially have two separate copyrights. The first is on the musical composition. The second is on the particular performance and the recording of it. (Note that a performance that is not in some way recorded has no performance copyright.)
There can also be a separate copyright on the sheet music. Performing from copyrighted sheet music can infringe that copyright mutopia and similar sites offer public domain sheet music. However, if the sheet music is essentially just a copy of sheet music first published before 1924 (in the US) or otherwise out of copyright, the copyright on the sheet music may not be enforceable.
If the music is a derivative work, such as an arrangement or adaptation, there could be a separate copyright on the arrangement or other derivative work, even if the base work is out of copyright. This will be owned by the author (creator) of the derivative work, or whoever the author may have sold or transferred the copyright to.
Beethoven is in the Public domain
Beethoven's Piano Sonata, and all other published works by Beethoven, are long since in the public domain under US law, and also under the law of every other country that I know of. Unlike a more modern composition, there is no need to secure rights from the composer or the composer's heir. In US law, all works published before 1924 are now in the public domain. The exact date will be different in other countries, but i don't know of any where a work more than 200 years old would still be in copyright. (See this chart for more detail.)
Copyright on the Recording
The recording will have its own copyright as soon as it is made. If it were a pre-existing recording by someone else, rights to use it would need to be secured. But when the recording is being made for the purpose, the matter can be handled by contract with the performer(s). There are three somewhat different ways in which this can be handled.
Under 17 USC 101, a work that is:
a work specially ordered or commissioned for use as a contribution to a collective work, as a part of a motion picture or other audiovisual work, as a translation, as a supplementary work, as a compilation, as an instructional text, as a test, as answer material for a test, or as an atlas, if the parties expressly agree in a written instrument signed by them that the work shall be considered a work made for hire.
is a work-made-for-hire, and the person paying for the work will be legally the "author" and will own the copyright from the moment that it is created.
Note that a musical recording is only eligible to be a work-made-for-hire if it is created for use in a movie or video. A pure musical recording may not be a work-made-for-hire.
See also this copyright office circular (PDF) and this Wikipedia article
The contract between the performer(s) and the person paying for the work (whom I will call "the producer") could specify that the work will not be a work made for hire, but instead that the copyright will be transferred to the producer after the work is complete. This offers greater protection to the performers, because they can refuse to execute the transfer until after they have been paid, and the performers retain the right to terminate the assignment after 35-40 years.
The contract between the performers and the Producer could instead provide that nthe performers retain the copyright, but license it to the producer, giving the producer permission to use it. Such a license could be permanent or for a limited term, and could be exclusive or non-exclusive. The terms may be whatever the parties agree on. If the license is non-exclusive, the performers may also permit others to use the recording, or may market it themselves, subject to any limitations in the agreement. Obviously this arrangement most favors the performers, and least favors the producers, and so might involve a smaller fee.
Fees and Terms
The fee paid by the producer to the performers can be whatever they agree on, lump sum, fixed installments, or on a royalty basis. Whatever it is, it should be spelled out clearly. Similarly, the contract should specify under what conditions, if any, the performers get the rights back -- for example, if the producer goes out of business with fees owing to the performers. (If it is a work made for hire, it would be unusual for ther performers ever to get any rights back.)
It is common for such a contract to specify whether and how the performer(s) will be credited for their work.
To add to David Siegel's answer:
There's a third copyright - the sheet music. While all of Beethoven's musical works are in public domain for musical composition, most of the sheet music of Beethoven's works would not be in the public domain. That sheet music would, unless created prior to 1923 (USA - other countries vary), be protected by copyright.
I'm not sure if performance of non-copyright music from a copyright score requires permission, but it looks like it may do:
There are, however, websites that make available sheet music which is in the public domain. One example would be http://ibiblio.org/mutopia which contains a collection of modern editions, arrangements and new music which is in the public domain. All of the musical works on the Mutopia Project may be freely downloaded, printed, copied, distributed, modified, performed or recorded.
The Mutopia Project offers sheet music editions of classical music for free download. These are based on editions in the public domain
Unless you specifically purchase sheet music that comes with a public performance license -- which is considerably more expensive in many cases -- your use of the sheet music is limited to personal use. The copyright holder maintains exclusive control of public performance, and it’s typically not granted in most sheet music sales. Purchasing sheet music allows you to perform the song in your home and to friends and family, but if you plan to perform them in public, you must purchase a performance license from a rights-management company
If the sheet music copyright holder does enforce their copyright then a performance licence may be required, a recording licence will be required, and a separate synchronisation licence will be required for incorporating the music into a movie. Using public domain sheet music would appear to sidestep those requirements.