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Most instruments have a lot of subtle variations in tone; you need a lot of different samples to capture that variation in a realistic manner.
A piano is probably the simplest case. A piano doesn't just get louder when you hit the keys harder, the quality of the note also changes. A modern piano sample library will include a minimum of eight recordings of each key, from very soft to very loud. That adds up to at least 704 stereo WAV files. Those recordings at different levels are blended together to give a realistic response to the player's touch.
You'll also usually get at least five different microphone positions, from close microphones right under the piano lid to a broad stereo pair capturing the ambience of the room. A single piano can therefore add up to several thousand samples, taking up a few gigabytes.
A violin is probably the most complex case. There are a huge variety of ways to play a violin. You can pluck the strings (pizzicato), you can play with the bow close to the bridge or close to the fingerboard, you can play with the back side of the bow or with a mute on the strings, you can blur the notes together smoothly (legato) or play crisply separated notes (détaché).
For each of these possible playing styles (articulations), you need separate samples of each note at multiple volume levels. The sample playback software (Kontakt) allows you to switch articulations using the keys on the left of the keyboard, playing the notes with the right hand. Again, you'll usually want a variety of microphone positions to give you control over the room ambiance. My preferred solo violin library has 38 different articulations, adding up to over 24,000 unique samples.
Multiply that across all the instruments of an orchestra and you've got a shitload of samples. The VSL Symphonic Cube orchestral library includes 764,000 samples, hence the 375GB installed file size. Most composers have multiple sample libraries covering an entire orchestra, each of which has a different sound based on how the instruments are played and how they are recorded. VSL is very traditional and is ideal for orchestral works. Spitfire Albion is quirky and modern for Hans Zimmer style atmospheric cinematic arrangements. The EWQL Hollywood Orchestra does exactly what you'd expect, giving you that epic John Williams sound.
We don't just want an orchestra of course, we want modern instruments like guitar and bass, world instruments, historical instruments and so on. We also want a variety of each - I currently have 94 different drum kit libraries installed, from a vintage 1930s jazz kit to a modern heavy metal kit.
This meticulous approach to sampling gives us an astonishing degree of realism. You probably don't realise it, but the overwhelming majority of music you hear on film, TV and video games is produced on a computer using sample libraries. Some productions have the budget and the timescale to go out to Eastern Europe and record with a real orchestra, but most of the time it's just one bloke in a home studio with a ton of software.