Gray tonal scales would correspond more to amplitude = volume, to spin off from your analogy.

However, practically speaking, doesn't one measure the density of a range of tones on paper, to establish what White is, what deepest black is, what the first noticeable gray tone just below white (call it W-) and the first just noticeable tone above black (call it B+)? Each step would one JND (Just Noticeable Difference) from the next. It is said that humans can distinguish about 200 steps on prints (glossy paper).

One can also divide the range from W- to B+ into ten zones. The exposure steps that would achieve that on different papers and different grades would be different.

Is your question not a technical one rather than an aesthetic one?