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Many years ago, I remember hearing of a psychology experiment where participants were asked to listen to two sounds and choose which one was higher or lower.

The two sounds were a mix of pure tones. If we number the standard notes numerically, then one sound would be all the even numbered notes and the other sound would be all the odd numbered notes. So, the two sounds should sound almost identical but that's not how they were perceived.

I can't remember who did the experiment, where, or what conclusions, if any, were drawn from the results.

Hoping someone else remembers it. Thanks.

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    There are some published audio snippets which are even worse: a sequence of tones which repeats but the listener senses the sequence as falling or rising forever. See en.wikipedia.org/wiki/Shepard_tone
    – Carl Witthoft
    Commented Jul 7, 2020 at 13:52

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The experiment was a multi-octave (five or so) C followed by a multi-octave F# (or Gb). Actually, any augmented fourth or diminished fifth will work. Some people (supposedly) hear one tone as higher and one as lower. (I noticed a multi-octave tritone but couldn't tell which was higher; I don't have perfect pitch.)

I'm now sure why this should work unless one of the tones had the top or bottom missing (could skip a middle octave in the other so volume doesn't matter).

Tchaikovsky did use a similar technique in his Sixth Symphony. A melody is split between the First and Second Violin Sections; each section plays alternate notes of the theme. Some listeners find this disturbing. (I think that the recapitulation has the theme in the same section.) There's also a version that does not use the divided melody.

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  • I saw a fascinating documentary on that Tchaik melody once. They swapped the 2nds to where they would have sat at the time, on the opposite side to the 1sts, to show how the melody gets 'reformed' in your head from two independent sources.
    – Tetsujin
    Commented Jul 7, 2020 at 5:59
  • @ttw So 'multi-octave C' means just the note C, yes? Not the C major chord. And no even-numbers/odd-numbers. Is that right? In that case, as long as the third harmonic of C (ie the G a twelfth above the fundamental) and the second and fourth harmonics of F# (ie two F#s an octave and two octaves above the fundamental) were clearly audible in all registers it might indeed be hard to decide which was higher. It's rather different from what Tchaikovsky does though isn't it? (I'll look for a score of it. Which movement?)
    – Old Brixtonian
    Commented Jul 7, 2020 at 10:55
  • That's it, just two notes. It's different from Tchaikovsky. The effect is in the Fourth Movement. Also for another effect, see Shepard Tones.
    – ttw
    Commented Jul 7, 2020 at 12:25
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    This is called the tritone paradox en.wikipedia.org/wiki/Tritone_paradox . The person who researched it, Diana Deutsch, also discovered a bunch of other auditory illusions. Neat stuff.
    – awe lotta
    Commented Jul 7, 2020 at 14:51
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I think that the tritone paradox described by @ttw is what you are looking for. However, it might also be this experiment in which the researchers tested whether people perceived pitch by a sound's missing fundamental or based on the lowest note. Basically they created sounds with many pure tones that would imply a missing fundamental and tested whether a sequence of these sounds would be heard as ascending or descending, e.g. if the participants perceived the fundamental, they would say it was ascending but if they heard the actual lowest note, they would say it was descending. They found that the group could be divided into fundamental-hearers and overtone-hearers.

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