A high pitch (>2 kHz) will be perceived to be getting higher if its loudness is increased, whereas a low pitch (<2 kHz) will be perceived to be going lower with increased loudness. Sometimes called "Stevens's rule" after an early investigator, this psychoacoustic effect has been extensively investigated.
With an increase of sound intensity from 60 to 90 decibels, Terhardt found that the pitch of a 6 kHz pure tone was perceived to rise over 30 cents. A 200 Hz tone was found to drop about 20 cents in perceived pitch over the same intensity change.
Studies with the sounds of musical instruments show less perceived pitch change with increasing intensity. A perceived pitch changes for around 17 cents for a change in loudness from 65 dB to 95 dB. This perceived change can be upward or downward, depending upon which harmonics is predominant. For example, if the majority of the intensity comes from harmonics which are above 2 kHz, the perceived pitch shift will be upward.