Is pitch a smooth function of frequency? Evidence from octave adjustments

In a classic article on the perception of the melodic octave, W. D. Ward [J. Acoust. Soc. Am. 26, 369-380 (1954)] reported two main findings: (1) the frequency ratio R_oct defining perceptually a perfect octave between successive pure tones is not fixed but varies rapidly, in an irregular and listener-specific manner, with the reference frequency; (2) on average, R_oct is slightly larger than 2:1. Ward's second finding, now referred to as the "octave enlargement" phenomenon, was confirmed multiple times. However, his first finding needed to be verified with a more rigorous methodology. This was the aim of two experiments reported here, in which overall more than 4000 octave adjustments were performed with pure tones at 65 dB SPL. They show that R_oct can be significantly different for two reference frequencies only 50 or even 25 cents apart. If R_oct defines a constant distance on the pitch dimension, then the results imply that, contrary to common belief, pitch is not a smooth function of frequency. A third experiment supported the idea that the octave enlargement should not be interpreted as a deliberate bias intended to make an adjusted octave more brilliant and therefore pleasant, rather than optimally accurate.