It is well established that musical sounds comprising multiple partials with frequencies approximately in the ratio of small integers give rise to a strong sensation of pitch even if the lowest or fundamental partial is missing—the so-called virtual pitch effect. Experiments on thirty test subjects demonstrate that this virtual pitch is shifted significantly by changes in the spacing of the constituent partials. The experiments measured pitch by comparison of sounds of similar timbre and were automated so that they could be performed remotely across the Internet. Analysis of the test sounds used shows that the pitch shifts are not predicted by Terhardt’s classic model of virtual pitch. The test sounds used were modelled on the sounds of church bells, but a further experiment on seventeen test subjects showed that changes in partial amplitude only had a minor effect on the pitch shifts observed, and that a pitch shift was still observed when two of the lowest frequency partials were removed, so that the effects reported are of general interest.
References
[1]
Terhardt, E., Stoll, G. and Seewann, M. (1982) Pitch of Complex Systems according to Virtual Pitch Theory: Tests, Examples, and Predictions. Journal of the Acoustical Society of America, 71, 671-678. https://doi.org/10.1121/1.387543
[2]
Terhardt, E., Stoll, G. and Seewann, M. (1982) Algorithm for Extraction of Pitch and Pitch Salience from Complex Tone Signals. Journal of the Acoustical Society of America, 71, 679-688. https://doi.org/10.1121/1.387544
[3]
Software Implementation of the Terhardt Virtual Pitch Algorithm; the C Code Was Originally Available from Richard Parncutt’s Website
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https://github.com/IntersectAustralia/hcsvlab-psysound/tree/master/AudioAnalysers/%40VirtualPitch/private
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Terhardt, E. and Seewann, M. (1984) Auditive und Objektive Bestimmung der Schlagtonhöhe von Historichen Kirchenglocken. Acustica, 54, 129-144. (English Translation Included in [2] and at http://www.hibberts.co.uk/terhardt.htm)
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Lehr, A. (1986) Partial Groups in the Bell Sound. Journal of the Acoustical Society of America, 79, 2000-2011. https://doi.org/10.1121/1.393208
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Walpole, R.E., Myers, R.H., Myers, S.L. and Keying, Y. (2002) Probability and Statistics for Engineers and Scientists. 7th Edition, Prentice Hall, New Jersey.
