Fig. 17.1
Percentages of pitch-matched F0 relative to the overlap-and-add frequency
The response distributions were discrete: most of matches were concentrated near 0 cent or −1,200 cents (an octave below). The frequencies of the octave below matching tended to increase as the scaling factor moved away from the original, i.e., 1.00. An asymmetry was observed between the contraction (<1.00) and dilation (>1.00) sides. The tendency of the octave downshift was more prominent for the dilation side than for the contraction side.
For each scaling factor, a test of the homogeneity of the distribution compared to the reference condition was performed by counting the number of responses in three bins; (a) −100 to +100 cents, (b) −1,300 to −1,100 cents, and (c) others. The null hypothesis of homogeneity was rejected for all scaling factors except for 0.95 and 1.04.
2.6 Discussion
The results demonstrated that an octave down pitch shift occurred when the scaling factor exceeded a certain amount. The distribution of pitch matching was discontinuous along the F0 axis, i.e., it was quite rare to match an F0 that would correspond to the perception of a different chroma. This observation suggests that the pitch shift caused by alternating the two wavelets is one with no change in chroma. The familiar change in pitch used for musical melodies is accompanied with chroma changes and accomplished by changing the F0. Contrastingly, a pitch shift with no chroma change can be achieved by attenuating the odd harmonics (Patterson et al. 1993). In the second experiment, the pitch shift of the SAWSs was investigated by matching to a harmonic complex tone whose odd-numbered harmonics were attenuated.
3 Experiment 2 (Odd-Harmonic Reduction Pitch Matching)
3.1 Purpose
The purpose of the second experiment was to measure the pitch shift of the scaling alternating wavelet sequences in terms of the attenuation level of the odd harmonics of the harmonic complex tones.
3.2 Stimulus
The test stimuli were the SAWSs generated as in Experiment 1. In Experiment 2, they were generated for five Japanese vowels, “a,” “e,” “i,” “o,” and “u.” The overlap-and-add period was 8 ms. The other details were the same as in Experiment 1. However, the scaling factor 1.09 was not tested because of a bug in the experimental configuration.
The important difference from Experiment 1 was the way of making the comparison stimulus. One can shift the pitch of the original harmonic complex an octave “upwards” by attenuating the odd harmonics. On the other hand, an octave “downward” shift was expected by alternating the scaled and original wavelets. To generate appropriate comparison stimuli, vowel sounds, i.e., harmonic complex tones, with 16 ms base period were generated as a first step, and a series of comparison stimuli were generated with the attenuation factor up to −40 dB in 1-dB steps. The odd-harmonic attenuation was accomplished by adding the delayed version of the original waveform with the required amount. The delay necessary to attenuate the odd harmonics was 8 ms for this experiment.
3.3 Procedure
The experimental procedure was the same as in Experiment 1 except for the number of the test stimuli. The total number of pitch matches required for a listener was 120. The experimental session took 1 or 2 h per listener.
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