A quantitative equation for umami evaluation of food and condiments based on the Weber-Fechner law

Here, a quantitative equation for Overall Umami Strength (OUS) in foods and condiments, based on sensory evaluation, was defined using the Weber-Fechner law. Sensory evaluation was conducted utilizing objective questions grounded in triangulation tests and paired comparisons to accurately determine the absolute and difference thresholds for monosodium glutamate (MSG). These thresholds were employed to define various levels of umami strength, which facilitated the creation of an umami sensory difference strength curve. Subsequently, the OUS equation was constructed through a well-fitting function, represented as “$\mathrm{OUS}=9.6828\times {\log }_{10}\left(C_{\mathrm{MSG}}\right)+34.8$” (R² = 0.996). Once the relative MSG concentration of the sample is determined, it can be converted into the OUS value under the thresholds scale mentioned above for quantification. To validate this quantitative equation, multiple samples, including fish, mushrooms, and soy sauce, were evaluated using the paired comparison test to obtain relative MSG concentration. The OUS value calculated by relative MSG concentration was compared with the existing method to verify its correctness and effectiveness. The results demonstrate that both foods and condiments, even from different species origins, can be reliably quantified for overall umami intensity using the proposed sensory quantitative equation.