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Why is the combination of two light waves (red, yellow) percieved as the same color as the arithmetic mean of their frequencies (orange) while we percieve two musical notes at the same time as just those two waves stacked on top, and not the mean of those frequencies?

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    $\begingroup$ The perception of two musical notes is not that simple - if the frequencies are close, a noticeable beat frequency can be heard. $\endgroup$ – Not_Einstein Oct 22 at 15:16
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    $\begingroup$ A musical note is not an analog to a frequency of light. A single musical note is made up of many audio frequencies that have a relationship to each other. In fact, if we present two related frequencies to a listener, the ear and brain will combine them and perceive them as a single musical note. A chord is made up of notes, not frequencies. You can't compare musical notes to colors of light - they are not analogous either in their physical properties nor in their effects on human perception apparatus. $\endgroup$ – Todd Wilcox Oct 22 at 22:57
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    $\begingroup$ 'why' as in 'for what purpose' or did you mean ''how" as in 'by what mechanism'? Cephalopods have the means to perceive colour much like we do chords, because they use that information to disguise themselves by changing colour, how they do that is via pupils which diffract different frequencies to different parts of their retinas. $\endgroup$ – Pete Kirkham Oct 22 at 23:56
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    $\begingroup$ You may be interested in how we perceive colour as well as how we perceive sound and its 3d position. $\endgroup$ – user21820 Oct 23 at 5:05
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    $\begingroup$ @smcs If we played three sine waves with just intervals like a chord, then they would likely not be heard as a chord but as a single note. The reason why we hear three notes played on real instruments as chords is because each note is composed of several sine waves. There are actually some instrument sounds that a close to sine waves and when chords are played with those instruments it can lead to auditory illusions that make the chord sound more like a single note. $\endgroup$ – Todd Wilcox Oct 23 at 17:02
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Because 16,000 is greater than 3.

We only have 3 sorts of detector (called cones) in the eye, sensitive broadly to red, green and blue light. So a mix of red and green light excites the red and green cones. But yellow light, in between red and green, also excites the red and green cones, and the brain can't tell the difference. So it's not the mean of the frequencies - a red-blue mix is different from green - but there is some averaging going on.

But the ear has 16,000 hair cells each sensitive to a particular frequency, so the brain gets a whole lot more information. A 256 Hz C will excite the 256 Hz hair cell, but a mix of 242 Hz B and 271 Hz C# will excite those two receptors and not the one in between.

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    $\begingroup$ And with so MUCH frequency data available, but no POSITION data, the brain and perceptive system evolved to make the most of that data. $\endgroup$ – Ross Presser Oct 22 at 23:28
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    $\begingroup$ Actually there is overlap between frequency responses of the hair cells, but as you write, there are many of them and the bands are nevertheless relatively narrow in comparison to hearing frequency range. The overlap improves pitch recognition, at least for trained musicians. @RossPresser yes, there is position data: most of us have two ears, and the brain can do quite amazing things with them. Obviously though, two is much less than millions of cones in the eyes. $\endgroup$ – user1079505 Oct 23 at 0:30
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    $\begingroup$ @RossPresser There happens to be quite a bit of position data available, which is how we can identify the source of sounds. The position data just so happens to be extracted from the frequency data $\endgroup$ – TheEnvironmentalist Oct 23 at 0:46
  • $\begingroup$ @user1079505: A human's normal undamaged hearing system can pinpoint the direction of a sound in 3 dimensions with reasonably high resolution, so it doesn't really make sense to compare the number of ears to the number of cones... Look up interaural cues. $\endgroup$ – user21820 Oct 23 at 5:12
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    $\begingroup$ @TheEnvironmentalist: You have two ears. That's adequate for direction finding in a plane (2D.) With additional frequency information, your brain can do 3D direction finding. The frequency content of a sound is modified by the physical shape of the head and ears depending on the direction the sound comes from. The human direction finding ability is a combination of 2D direction finding (basically, time of arrival of the sounds) together with the evaluation of the different frequency content due to the direction. Not one, not the other. Both. $\endgroup$ – JRE Oct 23 at 8:19
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Why is the combination of two light waves (red, yellow) percieved as the same color as the arithmetic mean of their frequencies (orange)

Simple: no, it isn't. This is not how color perception works. (If you're inclined to disagree, ask yourself: how does your model account for the fact that changing the relative intensity of the two light sources changes the perceived color?)

But in any case, there is no a priori reason why the human eye and the human ear (and the associated psychophysical processes for color and sound perception) should work the same way.

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    $\begingroup$ how ... changing the relative intensity of the two light sources changes the perceived color? Simple: weighted average. And the a priori reason that sound and light perception would work the same way is that they're both waves, and - as anyone who has taken a basic physic course can tell you - both sound and light are made of waves, and waves of different frequencies combine in a particular way. -- Not that I actually believe any of that, but I feel this answer is overly dismissive and content free. $\endgroup$ – R.M. Oct 23 at 15:11
  • $\begingroup$ @R.M. OP explicitly specifies the arithmetic mean of the frequencies (i.e. with no weighting) so your point is moot. This answer is dismissive because the question is poorly written and poorly researched -- and because this was written before the question made it on HNQ and without a broader audience in mind. I'm not particularly interested in expanding this -- if anything needs to change, it's that this thread needs to be removed from the HNQ list. $\endgroup$ – Emilio Pisanty Oct 23 at 16:20
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Colour perception isn't as simple as you think

Roger Barlow has already described why sound perception is different (you have enough receptors to distinguish bot a wide variety of notes and their strength at the same time).And the eye has only 4 receptor types.

But human colour perception is also different for another important reason. It is not a matter of creating the perception of the mean frequency. It is also possible to create colour perceptions that do not exist as single colours in any spectrum.

The reason is that the sensitivity of colour receptors are broad and overlapping. Making sense of that in the brain isn't as simple as "averaging" the signals. Also, we would overload our optical nerve capacity if we tried to transmit a large signal containing data from all the pixels so a lot of pre-processing is done before the signal gets to the brain. But the overall process for colour is far more complex than averaging.

On reason is that the signals from the receptors are pre-processed to give pairwise differences between receptor signals (especially the red-green pair and the difference between the red+green and the blue). This is one reason for common colour blindness as, if the red-green receptors overlap too much, it bugger the ability to distinguish the two colours (completely missing receptors is a far less common cause). The brain then synthesises perceived colours from these difference signals.

A consequence of the complex processing is the ability to see non-spectral colours like magenta: a colour that never appears in a single wavelength spectrum. The brain doesn't average a signal containing red and violet light (that would average to green): it synthesises a new colour. This shows the brain is creating colour perception is a more complex way than "averaging" would suggest.

In short, colour perception is necessarily different to sound perception. Colour is a complex thing synthesised from just 4 signals (roughly brightness + the three colours though brightness only matters much in low light). there are thousands of sound receptors and they can all send signals at once so we can perceive many simultaneous sounds (with little spatial detail) but only one perceptual colour (for each region and with far more spatial detail).

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The answer to any human perception question is "its complicated."

We evolved for maximum fitness (for some fitness function). The way we hear sound and the way we hear light are the most effective ways we have found to deal with the signals.

If we try to read into it further, however, its worth noting that its useful to be able to identify "individual" sources of sound. You can do a lot once you have individual sounds isolated from each other. Virtually all sounds we hear in the natural world have a harmonic character to them. You never hear a 440Hz sine wave in the forest. You always hear 440Hz mixed with others (such as 880Hz and 1760Hz), and the relative amplitudes of these frequencies are reasonably fixed because they're defined by physics.

There's little advantage in being able to hear each frequency and then to do some heavy duty processing deeper in the brain. Instead what we have found it its most valuable to take sound and basically split it up into a fundamental frequency and a sound "color" which captures the associated overtone amplitudes. Its this color which is why a trumpet sounds different than a flute, even if they play the same note.

Indeed, if you split up the signal in this way, you can do some remarkably processing. Our ears "color" the sound based on direction, emphasizing different frequencies depending on which direction the sound approaches the ears. If our brains can identify the "color" of the sound, we can actually back out this frequency-dependent response and figure out the direction of any given signal (even if there's a bunch of other sounds going on).

For a fun aside, there's a trick in the electronic music community where you leave off the fundamental on your low bass notes. Leave it off completely, and only have the harmonics above. Our brain will recognize the "color," and fill in the fundamental for you. This is great because it can take a lot of subwoofer power to reproduce the fundamental, and quite a lot less power to reproduce the harmonics. If the musician can rely on the human brain to fill it in, their music will sound better on weaker sound systems!

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    $\begingroup$ Concerning your last parapgraph: that technique isn't restricted to electronic music, it has been used in pipe organs for a long time.... ei.tum.de/fileadmin/tueifei/mmk/Personen/Terhardt/ter/top/… $\endgroup$ – piet.t Oct 23 at 7:47
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    $\begingroup$ @piet.t Nice! I love it when I find out that I underestimated how old a technique is by a few centuries! $\endgroup$ – Cort Ammon Oct 23 at 7:48
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    $\begingroup$ @CortAmmon And re your last paragraph,that is almost exactly how bass guitars work. The fundamental on a bass guitar is actually very weak (because of the scale length), so it's not uncommon for a mix engineer to "beef up" a bass guitar by adding a sine wave fundamental so that it does work on sound systems with a decent low end response. $\endgroup$ – Graham Oct 23 at 11:31

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