Demonstrations of
Auditory Illusions and Tricks

2nd Edition

Contents Introduction Chapter 1 Chapter 2 Chapter 3 Chapter 4
Chapter 5 Chapter 6 References Archives Demo Index Top Page


V. Dynamic Pitch


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<20> A Continuously Ascending and Descending Series of Pitches Shown by Complex Tones Whose Spectral Components are Spaced at Non-Octave Intervals
Shepard (1964) generated a set of complex tones with the same spectral envelope, with decreased levels of very high and very low components in order to obscure the frequency boundaries of the spectra.   Each tone consisted of spectral components spaced at one-octave intervals and had a clear tone chroma.   When these complex tones were presented in repetition in the circular order of the tone chromas, (as in C, C#, D, D#, E,..), the listener often perceived their pitches ascending or descending continuously for a long time.   This phenomenon was considered to prove the circular order of tone chroma.   Burns (1985), however, showed that the same kind of continuously ascending or descending series of pitches can be perceived even when complex tones without clear tone chromas are employed.  

The tones in the present demonstration have spectral components spaced at 1400-cent (7/6-octave) intervals.   The figure below shows the first complex tone.   Thirteen other tones were generated by shifting all the components upwards in steps of 100 cents (1 semitone).   These tones are presented in repetition in this order.   The listener typically hears a continuously ascending series (a) or descending series (b) of pitches.   He/she may perceive a sudden fall or rise of pitch occasionally, but this is often vague and less frequent than the circular repetition of the tones.  

Shepard, R.N. (1964).
Circularity in judgments of relative pitch.   Journal of the Acoustical Society of America, 36, 2346-2353.

Burns, E.M. (1981).
Circularity in relative pitch judgments for inharmonic complex tones: The Shepard demonstration revisited, again.   Perception & Psychophysics, 30, 467-472.

Fig.20

Animation Figure Wave File AVI File
(a) (56 KB) (1.26 MB) (2.16 MB)
(b) (56 KB) (1.26 MB) (2.16 MB)







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<21> A Continuously Ascending or Descending Series of Pitches Shown by Complex Tones with Spectral Periodicity and Quasi Spectral Periodicity
Nakajima et al. (1991) generated complex tones, which are similar to those in Demonstration <20>, and had spectral periodicity of 1400 cents.   Because each spectral period had two components at intervals of 600 cents and 800 cents, the tones also had quasi-periodicity of 700 cents.   These tones are typically perceived as continuously ascending or descending pitches when presented in repetition to cover the spectral period of 1400 cents in steps of 100 cents as in (a) or (b).   The same tones are presented in different order corresponding to the quasi-periodicity of 700 cents in (c) and (d).  

Nakajima, Y., Minami, H., Tsumura, T., Kunisaki, H., Ohnishi, S., & Teranishi, R. (1991).
Dynamic pitch perception for complex tones of periodic spectral patterns.   Music Perception, 8, 291-314.

Fig.21

Animation Figure Wave File AVI File
(a) (68 KB) (1.26 MB) (2.19 MB)
(b) (68 KB) (1.26 MB) (2.19 MB)
(c) (68 KB) (1.26 MB) (2.19 MB)
(d) (68 KB) (1.26 MB) (2.19 MB)







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<22> A Continuously Ascending or Descending Series of Pitches Shown by Complex Tones without Spectral Periodicity
Murakita et al. (1997) generated complex tones of 15 components, which had no spectral periodicity.   That is, a spectral range of 3 octaves was divided into 15 section of 240 cents each, and one component was placed randomly within each section.   Each spectral component move upward in steps of 100 cents, and when a component moved beyond the upper spectral boundary, another component appeared from the lower boundary keeping the number and the density of the components the same.   These tones are typically perceived as a continuously ascending series (a) or descending series (b) of pitches.  

Murakita, Y., Uesako, N., & Nakajima, Y. (1997).
An endlessly ascending or descending scale consisting of pseudo-noises (in Japanese).   Trans. Tech. Com. Psycho. Physio. Acoust., H-97-93.

Fig.22

Animation Figure Wave File AVI File
(a) (192 KB) (1.59 MB) (2.98 MB)
(b) (192 KB) (1.59 MB) (2.98 MB)





Contents Introduction Chapter 1 Chapter 2 Chapter 3 Chapter 4
Chapter 5 Chapter 6 References Archives Demo Index Top Page