As a linguist, I have a good idea of what linguistic properties of a sound can be: be they describable in terms of distinctive features or whatever. But what, then, are spectral properties? It's not clear to me if they are distinct from or partially overlapping with linguistic properties.
'Spectral properties' are, essentially, acoustic properties. The term 'spectrum' is usually used in reference to frequency, especially when looking at relative intensities across a range of frequencies (e.g. peaks in the spectral envelope or 'formants').
I guess 'spectral properties' is a subset of 'linguistic properties' but there are some spectral properties (e.g. the intensity of the 12th formant) that are most likely irrelevant to linguistics. Despite this I guess there's no reason why even such properties couldn't be studied as part of phonetics (NB I'm not meaning to suggest that phonetics is not part of linguistics).