Can a song be made entirely of samples?

Of course.

For example, say I sample a single middle-c piano note. My understanding is that a DAW sampler can then change the pitches of this one sample so I could potentially get all the notes across the piano from just this one sample.

So far, you're right to an extent - simplistically-speaking, the piano is one of the instruments that can be reproduced quite accurately* with samples. However, it can't be done at all accurately by sampling a single middle-C note and repitching that one note. This is because the way the timbre of each note evolves is very different at different points on the keyboard - and also different when the note is struck at different velocities. So a convincing piano multisample will need to consist of at least dozens, and probably hundreds, of individual samples. This can take hundreds of megabytes, or even a number of gigabytes, of RAM to store - which is one of the drawbacks of sample-based synthesis.

(*And even then, some aspects of the sound of a real piano come from the way the different strings resonate with each other - which would possibly take even more samples, plus some clever programming, to emulate).

Similarly I could use samples for all harmony, beats, and melodies across all instruments.

Well, all instruments is where it gets really tricky.

Let's step away from music for a minute and imagine that you want to make a sampled version of your own human voice. You could just record yourself saying each word in the dictionary, and then construct any phrase, perfectly realistically, out of that, right?

Well, of course you couldn't - the way humans use their voice, they never quite say the same word twice - it depends on the way they are expressing and intoning the sentence due to the meaning and context, how it joins on to the words that come before and after, the emotions, how tired you are... there's a lot of variation.

Now something like a violin perhaps doesn't quite have as many input parameters as the human voice does - but there are still all sorts of ways of bowing, articulating notes and joining each note to the next - so many so that building a truly realistic sample-based instrument and programming the ways the samples were selected would be an incredibly complex proposition. A synthesized physical model of a violin would have the advantage here.

And of course - you can only sample instruments that exist. One of the great things about synthesizers is that they can create sounds that couldn't exist acoustically.

why use synth instruments then?

• Because they don't use oodles of memory
• because they can be programmed to react to multiple, constantly-changing parameters much more easily
• because they can create sounds that can't easily be created acoustically

Can a song be made entirely of samples?

Of course.

For example, say I sample a single middle-c piano note. My understanding is that a DAW sampler can then change the pitches of this one sample so I could potentially get all the notes across the piano from just this one sample.

So far, you're right to an extent - simplistically-speaking, the piano is one of the instruments that can be reproduced quite accurately* with samples. However, it can't be done at all accurately by sampling a single middle-C note and repitching that one note. This is because the way the timbre of each note evolves is very different at different points on the keyboard - and also different when the note is struck at different velocities. So a convincing piano multisample will need to consist of at least dozens, and probably hundreds, of individual samples. This can take hundreds of megabytes, or even a number of gigabytes, of RAM to store - which is one of the drawbacks of sample-based synthesis.

(*And even then, some aspects of the sound of a real piano come from the way the different strings resonate with each other - which would possibly take even more samples, plus some clever programming, to emulate).

Similarly I could use samples for all harmony, beats, and melodies across all instruments.

Well, all instruments is where it gets really tricky.

Let's step away from music for a minute and imagine that you want to make a sampled version of your own human voice. You could just record yourself saying each word in the dictionary, and then construct any phrase, perfectly realistically, out of that, right?

Well, of course you couldn't - the way humans use their voice, they never quite say the same word twice - it depends on the way they are expressing and intoning the sentence due to the meaning and context, how it joins on to the words that come before and after, the emotions, how tired you are... there's a lot of variation.

Now something like a violin perhaps doesn't quite have as many input parameters as the human voice does - but there are still all sorts of ways of bowing, articulating notes and joining each note to the next - so many so that building a truly realistic sample-based instrument and programming the ways the samples were selected would be an incredibly complex proposition. A synthesized physical model of a violin would have the advantage here.

And of course - you can only sample instruments that exist. One of the great things about synthesizers is that they can create sounds that couldn't exist acoustically.

why use synth instruments then?

• Because they don't use oodles of memory
• because they can be programmed to react to multiple, constantly-changing parameters much more easily
• because they can create sounds that can't easily be created acoustically

Having said all that - there isn't necessarily an abrupt line separating sample-based instruments and synth instruments. Many sample playback instruments are "sample + synthesis" - providing some extra processing on top of the basic sample playback - and many 'pure' synths still make use of some basic wavetables which are played back much as a recorded sample would be.