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Producing Music can happen in many different ways, because music can be so many different things. If a band has a song that they’ve played live a hundred times, producing a record of that song is mostly a question of getting a good recording of a good performance by the band. Mixing and mastering are still important challenges, and the band may find new arrangement choices in the studio -- additional solos, background vocals, more complex instrumentation -- but the basic idea is to record the song that they already play.
Producing original music has evolved to include a lot of different approaches though, and much of what is recorded today is composed part by part in music production software, often with no reference to a live performance. Later, the artist may find ways to recreate the production in live shows, like when an act writes beats for a track and then has a drummer play them live later, but all of the decisions about what to leave in and what to leave out are made according to what makes the song -- and the production -- work the best.
Only recently has this approach really become practical with respect to classical instrumentation, and a lot of that is thanks to a truly amazing group of people in Vienna Austria called the Vienna Symphonic Library (www.vsl.co.at).