Octave stretching phenomenon with complex tones of orchestral instruments

Abstract

For decades, the phenomenon of subjectively enlarged octaves has been investigated using sinusoidal and synthesized complex tones. The present study elaborates the topic with samples of real orchestra instruments in successive tone listening experiments. Compared to previous research, this study also included a substantially larger number of subjects (N ¼ 36). Examined instrument tones were categorized into five groups based on their acoustic principles. In addition, each group was assessed at three dynamic levels (pp-mf-ff). Collected data were analyzed with tuning stretch curves by applying generalized additive models in the manner of the Railsback curve used to characterize piano tuning. Although the tuning curve modeled for the orchestra instruments was observed to differ slightly from the Railsback curve and typical Steinway D grand piano tuning (Steinway, New York), the stretching trends were qualitatively similar. Deviation from a mathematical equal-tempered scale was prominent. According to statistical analyses, dynamics or musical background of the participant did not affect results significantly, but some instrument groups exhibited differences in the curve extremities. In conclusion, the stretched scale is natural for a human listener and should be used as a reference scale in tuning machines instead of the mathematical equal-tempered scale. V

Why is the perceptual octave stretched? An account based on mismatched time constants within the auditory brainstem

“…The stretch is typically larger at higher frequencies than low, at least for the melodic octave (Demany and Semal, 1990;Ohgushi, 1983;Jaatinen et al, 2019) although, as mentioned earlier, for a harmonic octave the ability to notice mistuning breaks down in the upper range. The stretch is also larger for high amplitude stimuli than low (Sundberg and Lindqvist, 1973;Bonnard et al, 2013).…”

“…Mistunings are easier to detect for positive than negative excursions for both harmonic (Demany et al, 1991;Bonnard et al, 2013) and melodic octaves (Ohgushi, 1983;Demany et al, 1991;Hartmann, 1993). The stretching is observed for pure tones as well as complex tones and sounds of musical instruments (Sundberg and Lindqvist, 1973;Jaatinen et al, 2019). It is however unclear to what degree the stretch is specific to the octave, as a similar stretch has been reported for intervals of minor sixth or greater, while smaller intervals typically are compressed (Rakowski, 1990;Burns and Ward, 1999).…”

“…This paper proposes a potential explanation for octave affinity, and for the perceptual stretch of harmonic and melodic octaves that has long puzzled scientists (for reviews see Burns and Ward, 1999;Jaatinen et al, 2019;Demany et al, 2021).…”

Uncertainty in tuning evaluation with low-register complex tones of orchestra instruments

“…In a previous experiment [7], we observed that the perceived pitches of the low-register orchestra instruments at C1 (32.5 Hz) differed notably from each other, although the fundamental frequency and harmonic overtone frequencies were identical. In particular, the contrabass clarinet was perceived even one semitone lower than all other bass instruments.…”

“…The focus is on how perceived differences in pitch can be attributed to differences in the spectrum envelope. The study was motivated by a phenomenon observed in an earlier experiment [7], where the pitches of contrabass clarinet tones were perceived to be lower in pitch in comparison with other bass instruments. The presented approach, combining a listening experiment using stimulus tones from orchestral instruments with a principal component analysis on the spectral differences between the evaluated stimuli, has not been reported earlier.…”