The frequency-pitch mapping was established before models of pitch existed

Evidence

The earliest work on pitch perception consisted of connecting scientific observations with acoustics. Musicians, physicists, and otologists understood that there was a strong relationship between the acoustic quantity of frequency and the psychological quantity of pitch and that increases in frequency were associated with increases in pitch. This knowledge formed the beginning of our understanding of the relationship between pitch and stimulus frequency and led to models of pitch perception that are still accepted by modern scientists. — Jennifer Lentz, Psychoacoustics- Perception of Normal…, 1236