In introducing the concept of interval functions, several theorems concerned with simple necessary and sufficient conditions for Fechner's law, the power law, the linear law, and the exponential law are derived. The use of just noticeable differences and any form of Fechnerian integration is avoided, thus remaining in the safer "macroscopic" area. Implications of the difference model and the ratio model of scaling are considered, and the relations between these models are studies. Theorems concerning the logarithmic relationship between magnitude scaling and category scaling are derived, providing an insight into the distinction of prothetic and metathetic continua. Fechner's law and the power law both appear as interchangeable, so that any controversy about them misses the point. For the broad class of prothetic continua it is shown that ratio scales contain just as much information as interval scales; traditional claims of superiority of ratio scales are void. A simple differential equation may be regarded as a general psychophysical law.