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HearTomorrow

Psychoacoustics lab

Here is your opportunity to explore the fascinating aspect of human hearing. Keep your ears and your mind open while you experiment.

Note: If your sound card has digital processing options such as reverb, chorus, or "3D-wide", please make sure to disable it, as they would hinder proper operations, especially of the binaural (stereo) samples.

 

PURE TONES

Let's start by listening to individual pure sine waves. The first is a central A (440Hz), while the second is a perfect fifth above that (E=660Hz). Both tones are monaural, so they appear to be sounding right in the middle of your head (if you are wearing headphones), or directly in front of you (if you are listening through loudspeakers).

440Hz (A) sine wave

440Hz sine wave


660Hz (E) sine wave

660Hz sine wave


 


SUMMING AND MIXING

The first summing experiment we'll try is what we call "stereo summing". The A tone (440Hz) is applied to the left channel, while the E tone (660Hz) is applied to the right channel. You probably hear each tone individually. However, you may also perceive the two notes as a musical interval, or two-note chord. In this rather limited sense, your brain is summing the two notes arriving by separate channels into each brain hemisphere.

Stereo summing 440/660Hz

Stereo summing 440/660Hz

Incidentally, this file is good for checking your stereo separation. In some of the experiments that follow, a reasonably good approximation of true binaural (independent left and right channels) is necessary for best results. Listen to just one earphone at a time (cover the other one with your hand), you should hear only one tone in each earphone, with very little interference.

Now let's sum the two tones into a single monaural signal (left and right channels identical, this is called "monaural or true summing"). Acoustically, we've just summed the two tones. As the frequency domain graph below demonstrates, it contains only the two frequencies 440Hz (A) and 660Hz (E). However, this is where the "psycho" in psychoacoustics comes into play.

Mono summing 440/660Hz

Mono summing 440/660Hz

It is quite common if you sometimes hear two distinct tones, much as in the case of the stereo summing experiment. Other times the lower tone may predominate, with the higher tone only adding "colour" or timbre to the sound. After looping a number of times, the higher tone may "disappear" completely, leaving only the lower tone with a somewhat harsher, almost bassoon-like timbre. This is not surprising, since the higher tone is harmonically related (albeit indirectly) to the lower tone. The brain appears to synthesize the higher octave of the E tone (at 1320Hz), then chooses to perceive it as the third harmonic of the fundamental tone.

On rare occasions, it seems that a lower octave of the A tone (at 220Hz) is also present. If this occurs to you, it demonstrates the illusion of "phantom bass". This effect may also be noticed when listening to stereo sets with small speakers incapable of reproducing low bass. The ear will quite often "fill in" the missing frequencies, as if the little speakers were doing a better job than they actually do.

This time we'll actually mix the two signals by applying a non-linearity. The function used was an "RMS filter", which essentially squares each point on the summed signal.

Summed signal

The result is in the sound sample below, along with its spectrogram. The two original frequencies are shown in bold lines, note that there is now a lower tonic (difference frequency) at 220Hz (A), as well as sum frequencies every 220Hz above that.

Mono mixing 440/660Hz

Mono mixing 440/660Hz

The higher tone (660Hz) has apparently disappeared completely, being absorbed in the wash of harmonics created by the mixing process. Isn't it just sounding somewhat like a kazoo or maybe an oboe on steroids?

The sound now has a distinctly "major" tonality, because of the presence of the sums which add the major third to the fundamental and perfect fifth tones. If you can't quite hear what we are talking about listen to the next sample sound, obtained from the previous one by applying a sharp low-pass filter, with a cut-off frequency just above 1100Hz, and emphasizing the difference signal (A=220Hz) and perfect fifth (E=660Hz):

Mixed and filtered

Mixed and filtered


 


PHANTOM NOTES

Now for one possible explanation of the phenomenon known as "phantom notes": it has been reported, especially by woodwind players, that two instruments playing different pitches together can result in an unrelated, but clearly audible higher note. The usual interpretation is that the phantom note represents the sum of the frequencies of the two "real" notes.

What is most probably happening is that "shared harmonics", to coin a term, are responsible for the phantom notes effect. Let's say that we have a sound with its fundamental at A (440Hz), and a strong 9th harmonic content (9 * 440Hz = 3960Hz, which is close to a major 16th, or an octave higher than a major 9th). Now let's take a second note at E (660Hz), and assume that it has a prominent 6th harmonic (a perfect fifth an octave up). This would calculate out to 660Hz * 6 = 3960Hz again. In such a case, the two different harmonics could augment each other, particularly if stereo imaging were involved.

Here's a demonstration. As it turns out, the "oboe" sound from a popular synthesizer suits the above requirements (strong 6th and 9th harmonics) very well. Let's see if we can hear a phantom high B when an A (440Hz) and E (660Hz) are played together. First, the two notes separately. The spectrogram of the A sound is also shown below.

Oboe sound, A (440Hz), mono

Oboen-Sound, E (660Hz), mono

Oboue sound

If you have a good musical ear, you might pick out the 9th harmonic (high B) in the A sound. However, it's unlikely that you'll hear it in the E sound, because of the perfect fifth's tendency to "hide" in the fundamental, as in the mono summing example given earlier.

Incidentally, there is another illusion at work here. Because of the extremely strong second and fourth harmonics in this sound, it may appear that the fundamental frequency is an octave, or even two octaves higher than it really is. Compare with the pure sine wave sounds at the beginning (tracks 1 and 2), and you'll see what we mean.

Finally, listen to both notes played together. The A sound is placed somewhat left of center in the stereo image, while the E sound is panned to the right. Do you hear that high B dead-center in the stereo field? That's the phantom note!

Phantom note


 


BEAT FREQUENCIES

Another interesting phenomenon is that of "beat frequencies", which is often explained as a psychoacoustic mixing process. The reality of beat frequency perception is undeniable, as this experiment will demonstrate. Again, however, this phenomenon can be explained without the necessity to postulate non-linearity (mixing) in our perception of sound.

So far we have only experimented with sounds whose difference frequency (also known as beat frequency) is quite high. What if the difference between the two is very little, resulting in a beat frequency of only a few Hertz? The two sound samples below are 440Hz and 443Hz - this represents a difference in pitch of about 12 cents. If you listen to the samples a few times in succession you'll hear the slight pitch difference.

440Hz sine wave

443Hz sine wave

Now listen to the two tones, summed together into a mono signal. You will have no trouble discerning the beat frequency.

440Hz + 443Hz, mono

So what's going on here? Are the ear and brain using nonlinear mixing to perceive the 3Hz difference frequency? Maybe not. For an alternate explanation, let's first have a look at what the waveform looks like in the time domain:

 Waveform in the time domain

If you don't quite understand what's going on here, have a look at an "expanded" version below. This is what the wave would look like if the summed frequencies were 50Hz and 53Hz.

Waveform in the time domain

Note that the wave has a distinct "envelope", or repetitive wave-like fluctuation in peak amplitude. In a sense, it behaves as a single tone frequency, modulated by the 3Hz envelope. What happens is that the ear perceives that single tone in the frequency domain, but the envelope in the time domain.

This theory is set by the observation that as the difference between the two signals increases, the beat of course gets faster and faster, ending up in with a sort of "warbling" quality. At a certain point, corresponding to about a quarter of a semitone, the sound morphs from the single modulated tone into two discrete, out-of-tune notes.

At no point does the ear perceive a low bass frequency. A sample is provided below; this is an A (1760Hz) summed with 1860Hz. You'll probably hear it as a single tone, modulated by 100Hz, or as two dissonant tones. However, no matter how you try, you won't be able to perceive a discrete 100Hz (low bass) note. While there are definite illusions relating to hearing, they are not caused by non-linear response in the ear, nervous system, or brain.

1760Hz (A) + 1860Hz, mono

FLet's do another experiment, which is now probably the most surprising. You'll definitely need headphones for this one, as it is a binaural experiment. As before, we use an A (440Hz) and a 443Hz tones, except that this time each frequency is isolated in its own channel - 440Hz in the left ear, and 443Hz in the right ear.

440Hz (A) + 443Hz, binaural

The amazing result is that you will hear very little, if any, "beating". Instead, you'll hear two discrete and slightly out-of-tune notes, or you may perceive it as a single tone "smeared out" across the stereo field. Any residual warble you perceive is most likely due to imperfect stereo separation in the processing chain from recording to reproduction.

This indicates that the brain does not even do any summing, let alone nonlinear mixing, on purely binaural signals (input to the left ear completely independent of input to the right ear). As a practical side-note, if you use the beating effect to tune instruments to each other, you will hear a more distinct beat if both instruments are close together directly in front of you (simulating a mono signal) than if they were positioned directly to the right and left of you (approximating a binaural signal).


 


RESULTANT TONES

We'll end off this series of experiments with a highly interesting one. Can we demonstrate an organ "resultant" in the electronic medium? Here's an mp3 of an imitation of a pipe organ diapason. About two seconds of a low C are played (lowest frequency is about 65.5Hz, i.e. 16' pipe range), then the G above it is played. Can you hear a 32' pipe (very low C sound at 32.75Hz)?

Organ diapason sound, mono

Just for reference (and for the fun of it) here is a sonogram of this sound. A sonogram is another way to plot sounds in the frequency domain. It shows changes in a sound as it plays out, and can therefore be viewed as a kind of "voice-print". Time is plotted horizontally, while frequency is shown vertically. The color indicates the intensity of that frequency component at any given time.

As you see in the sonogram, there is not even a hint of any lower octave as the perfect fifth starts playing. Confirmation once again that what you hear (if you hear it) is your human brain at work, and not a "physical" phenomenon.

Sonogram

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