Adiscussion of audio tones in the physics classroom will include mention of their frequency. The frequency of a periodic signal is a well-defined quantity that can readily be measured. A concept related to frequency is that of pitch. Pitch is a perceived quantity that cannot be measured directly and is most important when listeners characterize periodic acoustic signals. The distinction between frequency and pitch is often simplified or even overlooked entirely. Several examples are presented here that clearly illustrate that pitch and frequency are not always simply related.

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4.
There are many such audio editors available. One that was used for demonstrations described here is Audacity (http://www.audacityteam.org). For that editor, each pure tone is generated in a separate track, then the tracks are combined on output. The quality of the audio playback electronics and speakers/headphones can influence the results for some of the examples described here. For the examples here, it is immaterial whether sines or cosines are used in Eq. (2).
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Throughout, the “listeners” are assumed to include only those considered to have normal hearing.
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12.
There are many examples of Shepard tones available on the internet, not all of which are executed effectively. One that is recommended is the video by David Huron currently available at https://vimeo.com/34749558.
13.
Readers can find the following materials at TPT Online, http://dx.doi.org/10.1119/1.5135796 , under the Supplemental tab: (1) An Excel spreadsheet file with frequencies and amplitudes that can be used to make Shepard tones using Eq. (2) and an audio editor. (2) An MP3 audio file containing a simple tune made using amplitude modulated noise. All notes are made to have equal duration, with longer notes divided into multiple shorter notes. The notes are separated by an interval of pure noise.
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19.
All the notes of the song are made to have the same duration so that rhythm cannot be used as a cue. Longer notes may be played as repeated shorter notes.

Supplementary Material

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