The measurement of loudness

Abstract

No new scale of loudness is proposed, nor are those already proposed examined completely. The object of the paper is to examine proposed scales from one point of view only, and to determine only whether any one of these is distinguished from the remainder by being founded more firmly on facts and being more free from arbitrary convention. We are not concerned primarily with such questions as convenience or practicable accuracy. In § 1 the facts (a)-(f) implied by all adequate scales of loudness are stated in a manner that does not (like most statements) imply that any scale is possible. It is concluded that these facts are not sufficient to distinguish from each other the infinite number of scales that might be or have been proposed. If one scale is to be distinguished from another by facts, some other facts must be introduced which are not so intimately involved in the meaning of loudness. There is an important difference in this respect between scales for tones of the same frequency and scales for all sounds. In § 2 proposed scales for a single frequency are considered under the following headings: (i) mental estimates; (ii) equal relations; (iii) just-perceptible differences; (iv) thresholds. The presumed facts (g)-(k) are involved in these scales and in part determine them; but the facts as known at present are not sufficient to force on us the selection of one particular scale, though they may force us to reject some. In § 3 the problem of sounds in general is considered. Here again it is concluded that the facts, though they may limit further the choice of scales, do not determine one scale uniquely. On the other hand, if a scale for a single frequency could be agreed upon, work on the lines of Fletcher and Munson's latest publication would solve the problems peculiar to complex tones so far as it is soluble at all. In § 4 some more general questions are treated briefly. It is urged that the arbitrary element in all scales may be advantageous as well as disadvantageous, for it permits the use of different scales for different purposes. To the question whether a scale uniquely determined by facts can ever be set up, we reply with a guarded negative; such a scale is conceivable, but all evidence available at present indicates that it is no more than conceivable.