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I am working with my teacher on recognizing notes played harmonically. She plays two notes together and I need to sing them back to her. The problem is I sometimes hear notes she is not playing, and they sound louder than the notes she is playing.

For example - she will play F4 and C5 and I will hear a very loud A4 and my mind will get stuck on it and make it impossible to hear the other notes.

Does anyone else have this problem? What are some effective exercises to get over it?

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    I have this problem. I think it’s common to hear the other notes but it seems like most people with trained ears can tell which notes are actually being played versus phantom notes. I have not developed that skill.
    – Todd Wilcox
    Commented Oct 19 at 22:10
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    I don't hear most of these tones, but from physics, we know that 2 simultaneous notes actually have 4 notes - the principals, a frequency subtraction and a frequency addition note. That means you should hear something like an additional a5 and f3
    – user121330
    Commented Oct 19 at 23:10
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    Does this happen with specific intervals or all intervals?
    – Aaron
    Commented Oct 19 at 23:36
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    @user121330 My question was for the OP.
    – Aaron
    Commented Oct 20 at 0:51
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    @Aaron We noticed it with perfect fifth, where I am adding a major third above the lower note.
    – HNHN
    Commented Oct 20 at 5:15

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What comes to my mind is summation tone, which is a type of combination tone.

When two notes are played, combination tones occur at the frequencies equal to difference of the two tones, and sum of the two tones. For two notes at a fifth ratio (3:2), the differential tone occurs primarily at an octave below the lower tone (1:2). The summation tone is primarily an octave + a (just) major third above the lower tone (5:2).

There is a separate question, why do you hear these tones? In typical situations, the combination tones are not heard. I even found in HANDBOOK FOR ACOUSTIC ECOLOGY by Barry Truax, 1999 a sentence "there is doubt that they [summation tones] occur at all".

Combination tones are attributed to some kind of non-linearities in the ear, and they are heard for rather loud sounds. If I remember correctly, Tartini discovered them when listening to the sound of the violin he was playing, thus close to his ears.

Maybe your ears have more non-linarity than typical? Or you are more sensitive to small details?

Some steps to produce combination tones artificially, in Audacity:

  1. Generate a tone, e.g. 200 Hz at the amplitude of 0.5.
  2. On another track, generate another tone, a fifth above, i.e. 300 Hz, at the same amplitude.
  3. Select Tracks/Mix and Render, to sum the two sounds. At this stage you will likely hear just a perfect fifth.
  4. From Effect select Distortion and Modulation/Distortion. Experiment with various settings. For me, with maximum distortion and "Even Harmonics" algorithm, the extra major third (+octave) was quite audible.
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  • For what it's worth, which is probably not very much, the difference tone in equal temperament is theoretically about 6 cents lower than an octave below the lower tone, and the sum tone is about a cent flat of a just major tenth above it. Is it possible that the 500 Hz tone is a difference tone between the second harmonic (400 Hz) of the lower tone and the third harmonic (900 Hz) of the upper?
    – phoog
    Commented Oct 20 at 20:09
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    I don’t know what having non linearity means. I do know that sounds other people consider normal volume are very painful to me.
    – HNHN
    Commented Oct 20 at 20:13
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    @HNHN non-linearity means that response of a whatever system is not proportional to the input. E.g. a small laptop loudspeaker producing buzzing sound when put at maximum volume. This doesn't refer to any specific biological process. The fact you're more sensitive to loud sounds might be related, but at this point I must recommend you to visit a doctor, an audiologist, rather than searching for information in the internet. A doctor can check your ears, and give advice responsibly. For example, possibly you need to protect your hearing more than general population.
    – user1079505
    Commented Oct 20 at 22:20
  • @phoog yes, of course harmonics add additional possibilities of intermodulation. Various effects may reinforce each other.
    – user1079505
    Commented Oct 20 at 22:20
  • I don't understand the quoted comment about "not being heard...." As you wrote, a simple audiogram will show the AM (amplitude modulation) at the sum and difference frequencies, so the overtone is most certainly there. You might as well claim that the signal output from AM radio is "not really there" . Furthermore, if the OP's teacher is using a piano or other acoustic stringed instrument, the instrument itself will generate sympathetic vibrations, so most certainly the frequencies exist.
    – Carl Witthoft
    Commented Oct 22 at 16:57

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