Octave stretching phenomenon with complex tones

The octave interval is one of the central concepts in musical acoustics. In a physical sense, it indicates a 2:1 relation between two tones, and it is common for most tuning systems. In contrast to the physically based frequency ratio, the frequency ratio that is subjectively perceived as octave has been found to differ from the physical octave. This phenomenon has originally been identified before the 20th century, and more studies have on this topic has been carried out particularly in the 1950s and 1970s. However, most of the research has been conducted from a psychoacoustical perspective with pure tones, whereas complex tones would represent natural instrument sounds more accurately. This paper presents results from a listening experiment where the subjects adjusted pairs of complex tones to match their perception on the subjective octave over a wide range of frequencies. The analysis compares the current outcome to the well-known octave stretching effect found in the conventional tuning of pianos.