Logarithmic parameters

Some physical parameters, that are positive by definition, appear often as reciprocal pairs, like an electrical resistivity ρ and the electrical conductivity σ = 1/ρ , or a frequency ν and the period T = 1/ν . Theoretical arguments suggest that behind these pairs there are more natural parameters: their logarithms. This paper suggests a terminology that could bring those logarithmic units into normal use. Although perturbing long-term established habitudes, the defined logarithmic units, if adopted, could simplify measuring practices: if the instruments were manufactured using these units, changes of scales (say from Ω to kΩ and to MΩ when measuring an electric resistence) would be suppressed, and the simpler algebra of absolute uncertainties would replace that of relative uncertainties in most measurements. The suppression of the arbitrary accumulation near the zero value when not using the logaritmic units (for instance, near the frequency zero in one case or near the period zero in the reciprocal case), may be important conceptually. As an example of use of the logarithmic units one may consider the tuning of a musical instrument where a new, slightly modified musical scale can be defined. The oddly defined decibel unit can be clarified using the proposed definitions.