The document discusses the history of linear hearing instrument fitting methods from the 1930s to present. Initial attempts to create fitting formulae involved "mirroring" the audiogram by providing 1 dB of gain for every 1 dB of measured hearing loss. However, it became clear this did not account for the reduced dynamic range and loudness tolerance of sensorineural hearing loss. Half-gain and other prescriptive fitting formulae based on hearing threshold measurements were developed instead. Finding the optimal gain remains challenging due to variability in input signals, loudness perception, and individual communication needs.