Weber–Fechner law

The Weber–Fechner law states that perceived sensation grows approximately with the logarithm of stimulus intensity. It links this relation to Weber’s finding that just-noticeable differences are roughly proportional to stimulus magnitude.

Weber's law: Weber's law states that the just-noticeable difference between stimuli is approximately proportional to their baseline intensity. Its proportional-threshold rule supplies the step that Fechner integrated into a logarithmic sensation scale.
Ernst Heinrich Weber: Ernst Heinrich Weber was a German physiologist whose experiments quantified sensory discrimination. His observations about proportional difference thresholds supplied the law's empirical starting point.
Sound intensity: Sound intensity is acoustic power transmitted per unit area, commonly measured in watts per square metre. Auditory loudness judgments are often compared with physical sound intensity to test logarithmic scaling.
Stevens's power law: Stevens's power law models perceived magnitude as a power function of stimulus intensity. Its modality-specific exponents often fit magnitude estimates better than a universal logarithmic relation.
Weber–Fechner law in hearing: The Weber–Fechner law in hearing describes proposed logarithmic scaling between auditory stimulus strength and perceived sensation. Auditory loudness provides a test case where frequency and sound level shape the fit.
Just-noticeable difference: A just-noticeable difference is the smallest change in a stimulus that can be reliably detected. Fechner treated successive detectable changes as roughly equal increments of sensation.
Gustav Fechner: Gustav Fechner was a German physicist and philosopher who founded experimental psychophysics. He derived a logarithmic sensation scale from Weber's threshold findings.
Decibel: The decibel is a logarithmic unit expressing a ratio of power or field quantities. Its logarithmic scale resembles sensory compression, but it is a measurement convention, not a direct sensation scale.
Signal detection theory: Signal detection theory separates sensory sensitivity from decision criteria when detecting signals amid noise. It analyzes detection performance without treating thresholds as direct measures of sensation magnitude.
Weber–Fechner law in vision: The Weber–Fechner law in vision describes proposed logarithmic scaling between visual stimulus intensity and perceived brightness. Visual adaptation and luminance range make the law's domain of validity especially clear.

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