# If we could see multiple octaves of light, would we perceive a cycle of colors?

1. Jul 24, 2008

### Blue_Jaunte

Similar to the cycle of notes we can hear? I read a similar question on another site about how we perceive red and violet as similar in nature even though they are far apart on the spectrum. I noticed that the frequency of violet light is almost double that of red light. Similarly, as you know, 880Hz and 440Hz sound like the same note (although an octave apart).

2. Jul 24, 2008

### Andy Resnick

Probably not. Audio frequencies are detected coherently- the phase of the wave in addition to the amplitude of the wave. This is how we can tell where a sound comes from. Light is detected incoherently-the phase information is lost- due to the much higher frequencies involved.

Coherent detection allows for effects like interference to occur. That's why we can synthesize sum and difference frequencies aurally (good barbershop quartets exploit this).

3. Jul 24, 2008

### m.e.t.a.

This is a great question!

Your analogy of the musical octaves is good. I think I see what you're getting at.

We perceive (for example) the notes A4 @ 440 Hz and A5 @ 880 Hz as having the same musical "feel" or "quality" to them. In other words, because one frequency is double the other, both notes trigger many of the same hair cells within the ear to vibrate due to resonance.

This causes A4 to sound very similar to A5, and also somewhat similar to A6, and so on. (Similarly, C2 sounds similar to C3 etc.) It's basic resonance that causes the effect. You wanted to know: what if eyesight worked this way?

http://www.webexhibits.org/colorart/i/cone-spectral-sensitivitie.jpg

(Above: diagram showing the approximate wavelength sensitivity curves for human rod cells and each of the three types of cone cells.)

The diagram does not extent into the ultraviolet or infrared. However, if it did, we would notice that these zones are devoid of both cone and rod sensitivity. The narrow 400 nm - 700 nm range is all we can detect. But yours was a "what if?" question, so let's imagine that our eyes, like our ears, are sensitive to a range of wavelengths which spans multiple octaves. Also, like the ears, let's assume that their sensitivity does not span an infinite number of wavelengths, but tapers off as it deviates from the normal 400-700 nm.

http://en.wikipedia.org/wiki/Image:Cone-response.svg

That diagram would look a little different with our hypothetical super-eyes: there would be a "bump" at every "octave" of 420 nm, 498 nm, 534 nm, and 564 nm. (The bumps would get smaller in height the further they are from the 400-700 nm zone.)

With such eyes, yes, I can only imagine that vision would be truly cyclic. Of course, the manner in which octaves of light would be perceived as "similar" is impossible to say. That would depend on the precise mechanism that these hypothetical eyes would use to sense into the deep UV and IR. I can't imagine how such a mechanism might work, so I can't tell you if your musical analogy would be appropriate here. (Would (monochromatic) 700 nm light look identical to 350 nm light? Or would there be a sense of "pitch", as with sound? 350 nm is a "low-pitch" red while 700 nm is a higher-pitched red? Would we be able to "see" temperature as part of the symphony of wavelengths that each object would glow with?)

Are you hypothesising that it is because violet (~400 nm) has roughly half the wavelength of red (~700 nm) that the two look similar? (We might imagine magenta as being the colour that should come halfway between them. I agree that they do not "feel" like they belong so far apart in the spectrum.)

If you are correct that there is a link between red and violet's similar appearance, and their closeness of having half/double each other's wavelength, then that would imply that both wavelengths trigger roughly the same cone cell response. But this is not the case! Red elicits a completely different cone response compared with violet. Red light triggers the long-wavelength cone cells with virtually zero response from the short-wavelength cells. With violet light, it is vice versa. There is only one "bump" per type of cone. Resonance, or anything mimicking it, does not come into play.

If I were to guess as to the real reason why violet seems close to red -- so close that we can draw a colour wheel, with magenta bridging the gap, even though their wavelengths are not close -- it would not be because of any kind of resonance effect. Instead, I would tentatively guess that it's probably something to do with the brain's search for symmetry. I did write a pretty long answer, but I've erased it because I don't think it made any sense.

I hope I was some help, anyway.

- m.e.t.a.

P.S. All that stuff about hair cells, and how the ear works -- I was only guessing, for analogy's sake. Don't take my word on any of it.

4. Jul 24, 2008

### Blue_Jaunte

I'm pretty sure you got it right. Although I don't know how a hair cell, which responds to a single frequency (I think) would respond to exactly double that frequency (that is, whether or not there would be a bump in sensitivity due to sympathetic vibration). There's a really good book about sound by James Jeans called "Science and Music". I think I'll go back and read the chapter about hearing.
https://www.amazon.com/Science-Music-Sir-James-Jeans/dp/0486619648

For what it's worth, here's an ear sensitivity diagram:
http://www.audioholics.com/educatio...tivity-part-1/clip_image001.gif/image_preview
I suppose to make any connections to the eye diagrams, you would have to see a diagram of the sensitivity of individual hair cells and see if there is indeed a spike at octave frequencies.

I wondered the same thing. Theoretically, there would be some qualitative difference between a lower and higher octave of the same color, but you're right that it would be impossible to speculate what it would be like. I imagine we would be able to perceive temperature in that we already gauge the temperature of certain objects (the burners on a stove, for example) by the frequency and intensity of the light they emit. So perhaps different animals would glow at different colors based on their different body temperatures.

According to wikipedia, the peak wavelength of radiation emitted by the human body is 9500 nm, which is an octave of yellow-orange light (~590 nm).

As an aside, there's a good novel by Alfred Bester titled, "The Stars My Destination" in which one of the main characters can only see light in the UV part of the spectrum. There are some interesting descriptions of her perceptions.
https://www.amazon.com/Stars-My-Des...bs_sr_1?ie=UTF8&s=books&qid=1216942230&sr=1-1
Incidentally, that's where I got my screen name.

Yes, although calling it a hypothesis may be a little too generous. I was expecting either "wild speculation" or "the ravings of a mad man".

That's interesting. Could you elaborate a bit? Do you mean that red and violet are not actually similar in quality? But there has to be a reason why, if we mix a red pigment with a blue pigment, we perceive purple, right? Just as we perceive orange when we mix red and yellow (which aren't separated on the spectrum). I mean, other than a trick our brains play on us...maybe not. Maybe the whole analogy is evidence of my own brain's search for symmetry between hearing and vision.

5. Jul 25, 2008

### m.e.t.a.

Thanks for the recommendation; I just bought the book on Amazon UK. Like you, I don't know for sure whether hair cells are sensitive only to a single, fundamental frequency, or if they also respond to some extent to integer multiples of that frequency (the harmonics). (Also like you, I have a penchant for forcing unnatural long life upon my sentences through liberal use of commas and parentheses.)

When I decided that ear hair cells probably resonate in harmonic intervals, I hadn't thought my assumption through; nor had I done any research into the workings of the ear. Now that I have done a couple of hours' "research" (web browsing), I find that I'm almost none the wiser for it. It turns out that precise mechanism by which the various structures of the ear cooperate to detect pitch is not fully understood.

Needless to say, I made a gross over-simplification by modelling the hair cell as a simple oscillator. The true hair cell is a complex structure (see http://www.hhmi.org/images/bulletin/sept2005/inner-ear.jpg) and during my search I was not able to find out if an individual hair cell is activated by only one native frequency, or by that frequency and its harmonics as well. The whole subject is well beyond my level of understanding.

Yes, that's true. I did try to find such a diagram, but instead I got bogged down while trying to understand some really very technical articles which I hoped might contain the answer. Among the most promising of those articles is entitled: "Sound-Induced Motions of Individual Cochlear Hair Bundles" http://www.biophysj.org/cgi/content/full/87/5/3536#FIG3. I admit that I gave up around one quarter of the way through. YMMV.

I forgot to adequately link in the ear/hair cell/resonance analogy here. In my analogy I assumed that the group of cells tuned (for example) to the key of C3/130.81 Hz would respond most strongly to sound waves of that specific frequency, C3; and then less strongly to the key of C4, and even less to C5, and so on. I imagined this would be caused by sympathetic resonance of the cells at each harmonic level. (I didn't say so, but I also assumed that a hair cell would generate near-zero response to frequencies that are "far" from any of its harmonics.)

There necessarily also exists a group of cells whose native frequency is C4, and another group whose native frequency is C5. These other C groups are necessary for distinguishing the notes of C4 and C3, even though the C3 group can detect those higher notes by itself. Without the higher C groups it would be impossible to distinguish (with C3-sensitive cells alone) the difference between a quiet sound at frequency C3, and a loud sound at frequency C5. This would be something like if the eye possessed only rod cells. Except -- the eye would still be sensitive to a broad range of wavelengths. An ear with only one variety of hair cell would be deaf to virtually all sound except one certain wavelength (or, if we still follow my analogy, that one wavelength plus its harmonics). You would be able to hear C3, C4, C5, C6 and so on...but they would all sound the same.

Ear hair cells are so wavelength-specific -- the range of wavelengths that triggers any given cell is so narrow -- that a large number of them are needed for acoustic sensitivity across a broad wavelength band. This would not be the case if hair cells had a bell curve-like sensitivity to different wavelengths -- as do cone and rod cells in the eye -- but they don't; they are much more specific. (If they do generate a bell-curve response, the rim of the bell is narrow indeed). If ear hair cells operated like cone and rod cells, then only a handful of different types of them would be required. The brain would calculate the frequency of sounds the same way that it calculates the colour of light -- by comparing the amplitude response of a couple of different kinds of sensor cell. However, it seems to me that with such a system it would be impossible to hear more than one frequency of sound at a time. Multiple simultaneous frequencies would blend into a single perceived frequency -- just as our eyes "blend" the red-green-blue light from the pixels of a television screen into a myriad perceived colours. We're tricked into seeing colours that aren't really there because the eye can't tell the difference between, say, pure 610 nm orange light and a mixture of 680 nm red and 500 nm green (as random examples).

I've gone so far off track now that I'll need to quote you again:

Theoretically there could be, but it would depend on the how the light-sensitive cells work, and what types are present. For example, the super-eye might possess the optical equivalent of a group of frequency-specific "hair cells" for each of many (narrow) "sub-bands" of the visible band of the EM spectrum. 500 THz red and 250 THz infrared would therefore be detected by two different types of light-sensitive cell, each of which would accordingly send a unique signal to the brain, enabling the brain to see, and distinguish between, the two octaves. With this system multiple octaves of light could be detected and distinguished between, but we would not necessarily perceive octaves as "similar looking", since no resonance takes place.

Alternatively, the super-eye might have only a few types of light-sensitive cell, much like the cone and rod cells of a normal human. The difference is that the super-cells would be sensitive to multiple octaves of the cells' "fundamental frequency" (I use the term "fundamental frequency" in a purely hypothetical sense). The 400 nm - 700 nm (750 Thz - 430 THz) band of light that we are sensitive to with our normal eyes would then be "multiplied" over and over if we had the super-eyes. We would be sensitive to 800 nm - 1,400 nm; 1,600 nm - 2,800 nm, and so on (diminishing in sensitivity as we travel far from the "normal" wavelength range). And that is only if the three types of cone cell "vibrate" at their "fundamental frequency" in the 400-700 nm band -- their fundamental frequency might be much higher. In the ultraviolet, perhaps. Then we would be sensitive to light in the 200 nm - 350 nm; 100 nm - 175 nm, and so on. With this system multiple octaves of light could be detected, but every octave would look the same -- they could not be distinguished between. There would be no way of telling apart dim 500 nm light from very bright 5,000 nm light.

A third possible setup for the super-eye would to have it exactly the same as a normal human eye, except to "stretch" the wavelength sensitivity range of each type of cone and rod cell. The sensitivities of each type of cell would remain the same relative to each other, but their range of detectable wavelengths would be scaled up. (Doubled, say.)
This would transform the 400-700 nm range into something like 250-850 nm while keeping the number of types of cell the same. With this system multiple octaves could be detected and distinguished between; but, again, octaves would not appear "similar".

Finally, you could theorise a hybrid of my first and second suggestions. (The first suggestion involved many types of cone cell, each covering a narrow band of the spectrum. The second suggestion proposed that some kind of resonance might take place within the cone cells such that they can detect harmonics of their native frequency.) The hybrid super-eye would have a specialised cone cell family for each wavelength (actually, for each narrow band of wavelengths) within the visible band. Each of these cells would sense not only its native wavelength of light, but harmonics of that wavelength too. This system would work exactly like the ear (I just copied the workings of the ear, after all). Multiple octaves would be detectable and distinguishable as different "pitches". Similarity would be felt between octaves due to resonance triggering many of the same cones.

I admit that in my above examples I did cross into the realm of the highly theoretical. But, despite the fact that none of it was realistic, I hope that I offered at least one idea which was not ridiculous.

Earlier I said that the eye blends whatever spectrum of light frequencies it sees -- however complex -- into a single perceived colour. (Or rather, I should say, a tiny area of the eye containing a handful of each type of cone blends whatever spectrum of light frequencies it sees...etc. Clearly we can simultaneously see different colours at different points on the retina -- but only one colour per point.)

There are short- (S), medium- (M) and long- (L) wavelength cones, whose sensitivities peak at blue, blue-green and yellow-green respectively. (See http://www.diycalculator.com/imgs/cvision-how-works-01.jpg. That's a very good site.) They are present on the retina in the ratio 1:10:20. The eye-brain system is obviously geared to compensate for this unequal distribution. Once the compensation has been made, a perceived colour can be thought of as a code comprising the normalised percent-response of each type of cone (where 100 is "maximum response" i.e. very bright light). (I'm ignoring the rods because they don't play a part in colour vision.) Note that any colour is "as compared to white". We are programmed to think of "white" as the colour of sunlight -- the normal, everywhere colour against which all others are compared. Our idea of white does change dynamically depending on ambient lighting conditions, but I'm ignoring this effect for now.

So, an object emitting vivid blue-green monochromatic light might have the (S, M, L) code: (0, 80, 60). The same object in lower light might give (0, 40, 30). A red laser pointer might give (0, 5, 20).

Of course, we rarely encounter monochromatic light sources. Most substances emit light across a range of wavelengths in roughly a bell/mountain shape, with the longer-wavelength tail tapering off more gradually. Whites, greys and blacks would have all three of their code numbers the same (after white balance compensation): (n, n, n). You might be thinking: "But I can tell whether something is white, black or grey just by looking at it! There must be a qualitative difference in the eye's response." I don't believe this to be the case. A camera, for example, when exposing a piece of white paper in shadow alongside a black shoe in full light, might easily record both in the same range of greys. For further evidence that the eye can't tell the difference, either, see this famous illusion: http://lh3.ggpht.com/_JaZhbCdgtHM/R...d+H.+Adelson.+checkershadow_illusion4full.jpg. (I didn't that mean to sound so patronising, by the way. It's a side effect of explaining a thing that I'm bound to "explain" concept that you already understand better than I do.)

Anyway. Red/violet. When determining what colour is being viewed, the only information that the eye/brain has to go on is an (S/M/L) code. There are an infinite number of ways of superimposing different wavelengths at different intensities that would appear to us in each case to be the same single colour. However, most emission spectra do conform to a bell-shaped curve...and...um... Ok, I walked away and then came back a few hours later and now I've completely lost the plot. I have no idea what I was talking about. Reading it over again, it seems like I wasn't approaching any kind of an answer to the red/violet/magenta puzzle. So, sorry about that! Perhaps if you figure it out you could tell me? To avoid confusion I should delete the last few paragraphs, but I can't bear to erase what took me so long to write.

I wish I could be of more use. Thank you for a very interesting discussion!

- m.e.t.a.

Last edited by a moderator: May 3, 2017
6. Aug 11, 2008

### Kalirren

Hm. It seems to me that the "octaves" idea actually wouldn't work, and here's why I think so;

The rhodopsin-based pigments work because a cis-trans double-bond isomerization in the rhodopsin center causes a conformational change in the protein, which gets converted into a membrane potential change somewhere downstream in the pathway (I don't remember exactly how). In any case, the sensitivity profile of the double bond, as modulated by the immediate biochemical surroundings of the rhodopsin molecule embedded within the polypeptide side chains, creates the unique absorption spectrum of the pigment.

In this way, rhodopsin is unlike fluorescent absorption by a metal center or the like, where absorption occurs at energy levels corresponding to integer multiples of some quantum. There are only two possible states, cis and trans. So I don't think we'll get "octaves of vision," because the structural machinery of the visual detection mechanism essentially reduces the stimulus to a binary input.