Sound is named in fancy ways. And although in music we may never forget the poetry involved, time and time again it appears to be difficult to characterize a sound in words.
A sound can be bold or broad, it can project, it can be centered, it can have an edge. A soprano can be straight and cutting or sweet; an alto radiant and clear or nasal or hollow, a tenor ringing or dark and warm, even a hint of acid has been mentioned, and a baritone can sound like a bomb. Metaphors enough. Just like the painter speaks of tone, so does the musician speak of colour and both explain something so obvious, don't they, that we don't have the proper words for it. At the same time, the physical approach often is neither possible nor clarifying.
I myself prefer to use a few concepts that are more or less verifiable and also relate to shape properties of the facing and the chamber:
Often you hear people speak about a focused or a centered sound. The hidden assumption is that everyone knows what that is. I came across only one attempt to define what the term means. The acoustician Arthur Benade defines a centered sound as one where the successive partials are indeed as harmonious as possible. In a wind instrument this is not automatically the case. Partials often have a tendency to be more or less, but not exact harmonics. Deviations in the bore profile can be one reason for this, inaccuracies in the correspondance between the truncated cone and the volume of the mouthpiece cavity another. This means that this property is partly outside the control of the musician and partly within it. According to Benade, a centered sound has a "singing" quality.
One more word of warning: the clarity of the sound plays a major role in how we perceive it: a sound with a lot of partials seems to sound louder than a sound with fewer. This has mainly something to do with the sensitivity of our ears, which is at its greatest for frequencies around 4000 Hz (and that is the area of the partials). That doesn't mean that the energy of the sound also increases. The tendency is to especially build mouthpieces in such a way that they produce a brighter sound – that does not mean that saxophones thus produce an ever more powerful tone!