Pick up that little section of lead pipe; feel it in your hand. It’s heavier than you might’ve thought, maybe? It’s dense, in other words, right? Right.
Now, pick up that chunk of pumice, about the same size. What do you call that, in comparison to the pipe? Light? True, it is lighter than the pipe, but it could be just as heavy, if only it were bigger. Airy? Maybe, but even in a vacuum it would feel like it had the same weight, most likely. Sparse? No: It’s not a forest in your hand, after all.
The question is, when we’re talking about material objects, what’s the opposite of dense?
The answer, at the moment, is less dense, unsatisfactory because of our habit of using paired descriptions for physical properties (heavy/light, soft/hard, wet/dry, and so on). Once upon a time, though, dense had an opposite. Until the mid-19th century, the word was rare.
In fact, the earliest meaning of rare in English was precisely this one. The OED notes the word’s meaning as “[o]pposed to dense,” and provides the following example (from around 1420), among others:
The londis fatte, or lene, or thicke, or rare.
I don’t know what a londis is, and I’m intrigued by thicke as a stand-in for dense (as in a thicket, perhaps). But mostly, I’m thrilled to find rare used in this way.
One can imagine how, in the less dense Britain of the 15th century, a word like rare could move from describing a single object (as in, for example, “this rare piece of pumice”) to describing a collective object (“this rare forest”) to describing the likelihood of encountering individual objects while wandering through the realm (“the rare African swallow”).
Still, I propose we resuscitate rare‘s original meaning. I’ve looked for such a word many times, and so have others. To inspire you, I close with more examples from the OED:
Cvcumber in this mone is sowen rare. [C. 1420]
The Assemblie was so rare that they were not exceeding the number of nineteen Commissioners. 
A projectile would travel a far greater distance through a rare medium like air, than through a dense medium like water. 
Who wouldn’t want a word that can as readily describe cvcumbers as Commissioners, projectiles as londises? The chance to improve our language by looking to antiquated usage is (forgive me) a rare one.