This is wonderful information, guys, thank you and pardon my uninformed knowledge of chemistry, I didn't know what to search for! I understand this is an experimental question and I appreciate the time.
Yes, a complete chemical analysis of a sample of air would be a very precise term for it. I imagine what I'm looking for would be gases exclusively, indeed. A sample of air in a moment in time. Ideally, I imagine the fullest spectrum possible with a focus on organic particles. I still need to do a lot of research into the human sense of smell, but as I understand it we are able to sense quite a lot of different chemicals, including non-organic particles, so these would be relevant as well.
I've been looking into the concept of the gas chromatograph mass spectrometer (GC-MS) and this appears to come very close to what I had in mind. I've got the impression that these tend to be mostly focused on certain chemicals as opposed to a fuller spectrum, so perhaps what I'm looking for could be a more 'neutral', specialised GC-MS? At the moment I'm just wondering what is possible to achieve and how far away it lies.
Frankly, I don't believe I can assure you. However, to provide a bit of insight, I'm a fine arts student and this subject is a part of an experimental project. Atm it is only research.