The term "sound money" means different things to different people. Some stress the stability of purchasing power over time. Some stress the money's ability to facilitate exchange. Some stress the money's ability to promote macroeconomic stability. And, at least historically, some have stressed the sound a money makes when clinking against a glass or dropping to the table—perhaps to assess the metallic content of that money. For me, the important aspects are the ability to facilitate exchange—which any money will do but some might do better than others—and the degree of macroeconomic stability enabled by that money. When comparing monies along these margins, then, we must establish a benchmark. In what follows, I'll try to establish a benchmark for the second of those aspects: namely, the degree of macroeconomic stability enabled by a money.
My view is informed, in large part, by George Selgin's work, Less than Zero. I have also discussed the relevant issues in a comment with Alex Salter. In brief: a good money is one that expands to offset increases in money demand and contracts to offset decreases in money demand. Let's start with a very simple equation: MV = PT. M refers to the stock of money; V is the transactions velocity of money—that is, the number of times money changes hands over a period of time—and is equal to 1/Md, where Md is the demand for money; P is the price level; and T is the real value of transactions conducted over a period of time. The equation just states that the amount of money changing hands (left hand side) must equal the total amount spent/received in transactions (right hand side).
We know that prices convey important information about relative scarcity. Likewise, P conveys important information about the relative scarcity of goods transacted over time. If we become more productive, and the value of transactions T increases, the price level P should decrease to reflect that goods, in general, are less scarce today than in the not-so-distant past. On the other hand, when the value of transactions T decreases—perhaps because a natural disaster or policy change that reduces productivity—the price level P should increase to reflect that goods are more scarce today than in the not-so-distant past. Another way of stating this is that the left hand side of the equation should be held constant, allowing any change in T to be offset by a change in P. Alternatively, we could say that any change in V should be offset by changes in M, so as to keep MV constant. And, since V=1/Md, we can say that the money supply should vary to offset changes in money demand.
The implicit model employed above is quite simple. We could employ a marginally more complex model by including expectations and allowing for a gradual increase in prices over time. We might then conclude that the growth rate of M should vary to offset changes in the growth rate of velocity. Still, the underlying idea is left more or less in tact. And it provides us with a convenient way to express how an ideal money should behave. That's good news, since such a benchmark is required for considering alternative monetary systems.