Powered by OpenAIRE graph
Found an issue? Give us feedback
addClaim

Phantom beats in mistuned chords

Authors: J. L. Hall; M. V. Mathews; L. A. Roberts;

Phantom beats in mistuned chords

Abstract

Beats are heard in slightly mistuned musical intervals. For example, a mistuned fifth with frequencies f1 = 804 Hz and f2 = 1204 Hz will produce 4 beats per second. These beats have been attributed to interaction between the 3rd harmonic of f1 at 2412 Hz and the 2nd harmonic of f2 at 2408 Hz. However, 4 beats per second can be heard when the mistuned fifth is played with pure sinusoids which have no harmonics. A second hypothesis attributes these phantom beats to interaction between combination tones f2 − f1 at 400 Hz and 2f1 − f2 at 404 Hz. Experimental results supporting the second hypothesis are presented. If one combination tone is removed by a cancellation tone of appropriate amplitude and phase, the beats can no longer be heard. If tones are added to a perfectly tuned fifth so as to approximate the combination tones produced by a mistuned fifth, the resulting stimulus is difficult to distinguish from the mistuned interval. Similar results were obtained for mistuned fourths, attributable to interaction between combination tones f2 − f1 and 3f1 − 2f2.

  • BIP!
    Impact byBIP!
    selected citations
    These citations are derived from selected sources.
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    0
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    Average
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Average
Powered by OpenAIRE graph
Found an issue? Give us feedback
selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Upload OA version
Are you the author of this publication? Upload your Open Access version to Zenodo!
It’s fast and easy, just two clicks!