Judgments of comparative loudness (e.g., loudness-ratio judgments or judgments of loudness relative to a reference sound) show a high degree of repeatability and loudness scales developed from such judgments have been found to be reasonably similar for different subjects. These scales, however, have typically been derived from a limited subset of a much larger matrix of comparative judgments. The scaling of loudness by the method of loudness doubling, for example, concentrates observations on only one side and close to the diagonal in the matrix of possible loudness-ratio judgments. A loudness scale obtained solely by the method of loudness doubling differs systematically from that obtained by loudness halving, and both scales differ from that obtained by loudness quadrupling. Thus, although the judgments are reasonably repeatable, the exact form of the loudness scale depends on which subset of judgments is used. In this paper, a general approach to loudness scaling based on a complete matrix of loudness-ratio judgments is developed and the results obtained from three separate implementations of the approach are discussed.