Relations among pure-tone sound stimuli, neural activity, and the loudness sensation

Both the physiological and psychological responses to pure-tone sound stimuli are used to derive formulas which: (1) relate the loudness, loudness level, and sound-pressure level of pure tones; (2) apply continuously over most of the acoustic regime, including the loudness threshold; and (3) contain no undetermined coefficients. Some of the formulas are fundamental for calculating the loudness of any sound. Power-law formulas relating the pure-tone sound stimulus, neural activity, and loudness are derived from published data.