Music is the under pinning for any video production, whether it be promo, music video (obviously), training video or feature film. It's inportance for setting the mood for the visuals cannot be understated and provides the tempo for the whole production.
Copyright for music is a complicated business. During the course of our work producing video, we would normally recommend to client's using one of the terrific sound libruaries like Audio Network to provide broadcast qualify generic music. For custom music, there are PLENTY of eager musicians/composers eager to produce interesting work for the video producer.
Unless you have bags of money and time, one way NOT to do it is to rip a track from your CD collection, unless you retain a copyright lawyer who will contact the publishing company with what might be a very expensive and long, drawn out negotiating process. There are at least three different copyrights you will have to gain rights to for any piece of commercial music: composers’ rights, performer’s rights and synchronisation rights.
Generally, if the composer has been dead for more 50 years, the music enters the public domain (no more composer’s copyright.) Because Vivaldi has been dead more than 50 years, you may use his music without paying for the composer’s rights. However, if the performance you have chosen of his music was played by say, the London Philharmonic Orchestra, then you will still have to pay the publisher performance rights so that the musicians get their fair share.
Here's an example of a video we produced for Remeha which features Spring from Vivaldi's Four Seasons.
If you just must use a specific piece of music, you will have to jump through these hoops and pay the price. Do not try to get away without paying copyright charges. The legal ramifications are serious! Even if your program is a “not for profit” film festival entry, you must investigate the copyright. Sometimes a publisher will grant you the rights for free (or very little cost) for festival films, but not always.