Pitch circularity produced by varying the amplitudes of odd and even harmonics

Abstract

Pitch circularities have been produced using tones whose components stand in octave relation (Shepard, 1964; Risset, 1969). This paper describes two circular pitch scales produced by a new algorithm. Each scale consists of a bank of harmonic complex tones, each tone 500 ms in duration. As the scale descends in semitone steps, the relative amplitudes of the odd‐numbered harmonics decrease in 5‐dB steps, so that at the bottom of the scale they are 55 dB lower than the even‐numbered harmonics. The entire bank of tones is then low‐pass filtered. The lowest tone of such a scale is therefore heard as though its fundamental frequency were displaced up an octave. For each scale all possible (i.e., 132) ordered tone pairs were presented, and 15 subjects judged for each pair whether the second tone was higher or lower than the first. The data derived from these pairwise comparisons were subjected to Kruskal’s nonmetric multidimensional scaling (MDS). For both scales, two‐dimensional plots yielded approximately circular configurations; Stress1 values for the two scales were 0.016 and 0.034. When the tones were presented in semitone steps, the impression of infinitely ascending and descending scales was obtained. These circular scales are demonstrated with sound examples.