Diplacusis is a hearing disorder in which the two ears hear the same sound as different pitches. Suppose we know that someone with diplacusis has one normal ear and one ear that is slightly off. Using simple sine waves sent through headphones, it is possible to have the person adjust the pitch being sent to one ear until the sound is identical in both ears, which would tell us by how much the ears are offset (at that frequency). But is it possible to devise a test which could detect which ear is normal?
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1$\begingroup$ "which ear is normal" cannot be decided, human ears are not gauged to a absolute frequency scale, but hearing gives a subjective pitch. There is no way to tell which pitch is "the right one". $\endgroup$– Sebastian RieseCommented Nov 30, 2015 at 17:20
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1$\begingroup$ @SebastianRiese - what if multiple pitch offsets are considered? For example, suppose the person is a musician. If a scale is played that sounds perfect in one ear, but in the other ear one or more pitches sound like they are slightly off the scale, then that could be an indicator. Or perhaps the same note 4 octaves apart played simultaneously that sound like the same note in one ear but out of tune in the other. I guess this would depend on how pure the offset curve is... $\endgroup$– TTTCommented Nov 30, 2015 at 17:35
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$\begingroup$ In such cases this could certainly be possible, I guess. This is, however, not pure pitch offset between the ears, but also inconsistency of the pitches reported by a single ear. The doubling of the frequency corresponds to the change of pitch by one octave quite exactly. But even then you cannot specify, that the pitch one ear produces for a 440Hz sine wave is the correct one. $\endgroup$– Sebastian RieseCommented Nov 30, 2015 at 18:25
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$\begingroup$ Why would you want to even if you could? All you need is a frequency-shifter applied to either ear (assuming the offset is constant) to make the subject hear "properly." $\endgroup$– Carl WitthoftCommented Nov 30, 2015 at 20:42
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$\begingroup$ @CarlWitthoft - if you know which ear is the problem, it could help with diagnosing the cause. $\endgroup$– TTTCommented Dec 2, 2015 at 17:51
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2 Answers
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From a physics perspective: No. Relative differences can be detected as you point out, but in order to test which ear is normal, you need a reference. In the case of pitch difference, you can use one of the ears as reference for the other. In your case, the absolute reference scale is missing. And you can't get it from another person, because perception is subjective (is the pitch I perceive the same as the one you do? Why don't we have the same frequencies we don't like?). Maybe there is something objectively wrong with one of the ears or the brain tissue processing the signals - but for that, I guess you'll need to ask physicians and not the physicists. But note: "objectively wrong" here means that it is different from the majority of ears of the human population. Now you have a reference!
The underlying problem you are facing lies at the heart of experimental physics: For most experiments, you are trying to measure something on a (for all practical purposes) continuous scale: You might be measuring a frequency, a time, a distance, etc. All of this is only possible by comparison with a reference scale. In a continuum, there is no absolute scale until you fix one. This is why it is so very important to have good definitions of units: we need good absolute scales which we can compare our experiments with. Luckily, nature is in many ways discrete and has some fundamental constants that are dimensionless - and we can use that to define our scales objectively (time is defined by number of oscillations of a Caesium atom, mass will probably be defined by the number of atoms in a crystal at a specific temperature).
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$\begingroup$ I'm not 100% convinced that there is no way to get an absolute reference, but I agree that if one exists it is the physician, not the physicist that can answer that. My current line of thinking is to learn more about how cochlear implants work. Perhaps someone who is deaf in one ear and has a cochlear implant, and can hear fine in the other ear would be able to tell us if this is possible. If the implant needs to be tuned to the user's preference, then perhaps the electrical signal is not absolute. Seems like a stretch anyway that the signal would be interpreted the same way by everyone. $\endgroup$– TTTCommented Dec 1, 2015 at 17:25
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$\begingroup$ @TTT: Even if you can extract a reference in the case of a cochlear implant, that wouldn't be much help for any other case. I have no idea about medicine, but a priori, there can be two ways for the pitch shift to occur: There is a failure of the mechanical parts of the ear to transmit the frequencies faithfully (if this is the case, if you'd replace the bad ear by a cochlear implant, you'd notice), or there is failure of the brain to process the information correctly (in which case a cochlear implant can't tell you whether the other ear is "normal"). But we agree, that's not physics. $\endgroup$– MartinCommented Dec 1, 2015 at 20:45
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$\begingroup$ I fully agree. I'm making the assumption that the failure is (usually?) mechanical rather than the processing. I suppose this is true of eyes as well. Now that I think about it, this question could be entirely repeated for eyes instead of ears. Many people see slightly different colors or shades in each eye. I would assume the answer would the same. $\endgroup$– TTTCommented Dec 1, 2015 at 21:06
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When the afflicted subject listens to a single tone, he will hear one pitch in one ear and another pitch in the other ear. The difference between the pitches will be clear, but for the answer to be "yes", the subject would need some other piece of information to discriminate between the two. Otherwise, they won't know if their left ear is incorrectly shifted up, or their right ear is incorrectly shifted down.
So, for the great majority of the populace who cannot listen to a single tone and tell whether it's "right" or "wrong", there's no way to tell which ear is wrong. But, those with absolute pitch CAN listen to a single identified tone and tell whether it's wrong. So, an unfortunate musician with this condition may be able to play $A$ on a piano and tell whether one ear is wrong, and which one.
As an aside, about ten years ago I had an ear infection which gave me exactly this problem. Everything sounded like dissonant chords, which (as a musician) was a serious bummer. (I knew which ear had been infected, so I knew which one was mis-hearing.)
As a software engineer, I decided to measure the condition, and so wrote a simple Macintosh application called ToneTester. It played a pitch in each ear and let you adjust the two until they seemed to match. I couldn't play the pitches simultaneously, since audio leaks from one ear to the other and you could hear the tones beat against each other and tell that they were wrong. So, my app alternated playing one tone in one ear and the other tone in the other ear. Using this I found that one of my ears would hear pitches about one and a half semitones higher than the other.
Over the following year my ears adjusted, and I once again heard clearly. I haven't updated ToneTester in a long time, and it won't run on anything later than OS X 10.6.8.
answered Nov 30, 2015 at 22:01
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$\begingroup$ Interesting point about playing the tones simultaneously and having beating. $\endgroup$– TTTCommented Dec 1, 2015 at 17:34
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1$\begingroup$ I think you're making a big leap about perfect pitch and how the brain processes it. You're implying that somehow the brain "knows" that the bad ear is "reporting" a different value than the good ear. It would be interesting to track down someone who's got both perfect pitch and diplacusis to see what happens, but my bet is they'll recognize pitches just fine with either ear. $\endgroup$ Commented Dec 1, 2015 at 18:13
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$\begingroup$ @CarlWitthoft Nope. Someone with real absolute pitch (not me) can listen to a note and tell you whether it's an A or an A flat. If they play an A, and hear A in the right ear and A flat in the left, then they'll know the left ear is hearing wrong. $\endgroup$ Commented Dec 1, 2015 at 20:49
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$\begingroup$ @DanielGriscom, that assumes that the person had perfect pitch before getting diplacusis, otherwise they would never have been able to learn which ear was correct to begin with. $\endgroup$– TTTCommented Dec 1, 2015 at 21:02
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$\begingroup$ I doubt people are born with diplacusis; otherwise their brains would never train to hear pitches differently in each ear. Wikipedia supports this, although not explicitly. $\endgroup$ Commented Dec 1, 2015 at 22:03