What color is an octave above red?

I recently listened to an amazing Radiolab podcast on colors from a few years ago (check it out).

There are two very interesting questions that they didn’t address that I want to talk about.

The first question: “What’s up with pink?” will be a quick tangent. There is a great segment in the podcast where they talk about what different animals with different numbers of cones see when they see a rainbow, but pink never came up. So where’s pink (or brown, or grey for that matter)?  Electromagnetic waves (a.k.a. light) that are visible to us start with “red” at a relatively long wavelength of about 650 nm (nanometers) and ends with  “violet” with a wavelength of about 400 nm.

Wavelengths of Light

But  pink doesn’t have a wavelength: our brains just use it to bridge the gap between red and violet to create a smooth color wheel. To be clear, pink (and brown, and grey), is a real color, but “color” as interpreted by our brains is  more than meets the eye (pun intended). What’s crazy to me is that our brain is able to see a smooth connectioneverending staircasen from low wavelength red up to high wavelength blue, then “up” to low wavelength red. It’s the color equivalent of an Escher drawing  or a Shepard tone (listen here).

For a bit more info, check out this great Minute Physics video, and here’s a link to a Popular Science article from a few years ago about the color pink. She directly links to a post by Robert Krulwich (of Radiolab), so it’s safe to say they know something’s up with pink.

Now on to what I think is a far more interesting question:

“What color is an octave above red?”

Let’s back up and explain some musical terms. In music, two of the basic dimensions of pitch perception are pitch height and pitch chroma. Height refers  to the sense of high- or low-ness that we can hear. Go to a piano and drag your hand across all the white keys from right to left (a glissando), and you will hear in a very meaningful way that the notes are going down. If I played two random notes for you on a piano, you would be able to tell me which note was “higher”. Pitch chroma (Greek for ‘color’… coincidence? yea probably) refers to the thing that makes a ‘C’ a ‘C’ and an ‘F’ an ‘F’ and so on. On the piano (and in Western tonal music), we have a configuration of 11 unique chroma consisting of 7 white keys and 5 black keys before the pattern repeats. All C’s on a full-sized piano (there are 8) are the same chroma. Because it takes 8 white notes to get from one C to the next, we call it an octave (‘8 above’).

Piano

Both height and chroma correspond directly to the frequency of the sound waves produced at a certain pitch (frequency is inversely proportional to wavelength, so notes at the bottom of the piano have a low frequency in the same way that red on the bottom of the light spectrum has a long wavelength). Higher notes have a larger frequency, and every octave doubles the frequency. For example, Middle C has a frequency of 261.6 Hz (Hertz), the next C up has a frequency of 523.2 Hz, then 1046.5 Hz, and so on.

Music HelixThe easiest way to visualize this relationship is to imagine a spiral staircase. You start on C, and every step is a new note. On your eighth step, you are on C again but directly above where you started. This helix captures the fact that chroma is cyclical, while height is not. Here’s a piano for you to play around with if you don’t have one handy. Notice that there is something somehow the same about pitches of the same chroma. If you play Cs on the piano at different octaves, you’ll notice that they are somehow the same, even though they are also decisively different in terms of ‘height’ (here is a guitar version). This is a weird thing! Octave equivalency, a fundamental piece of music theory, is kind of bizarre if you think about it.

So what? Who cares? Well here’s the cool part: it seems completely plausible that there would be a similar concept of octave equivalence in light waves. So what does an octave above red look like?

stepupHere’s the problem. For sound waves, we can hear across a range of about 20-20,000 Hz. That’s pretty big. We can easily hear all the notes on a piano ( 27.5-4186 Hz), 8 octaves wide. A typical human eye will respond to light with wavelengths from about 700 to 399 nm. In terms of frequency, this corresponds to 430–770 THz (terahertz). If every time you double the frequency, you go up an octave, we would have to be able to see in the 860 THz range to even have a chance. So even though we can hear for octaves and octaves, it happens to be true that we can only see in a range just shy of one measly octave. That would be like if we could only hear sounds from Middle C up to the A above it! So the colors overlaid in the spiral staircase image above give the right intuition, but the staircase for light would go from red to violet, and just stop.

But what does the next step look like????

The more I think about this, the more I just WISH that we could see across a slightly larger range of wavelengths. Because I’m used to it, I can comprehend the idea that a high C is both somehow the same and somehow different than the C an octave below it, but I can’t wrap my head around the visual experience that could lead to a color that is somehow different than red and yet somehow fundamentally the same.

So what does an octave above red look like? Would we call it red ( just… a ‘higher’ red?) the way we do with musical notes? To be clear, the way our brains interpret color and sound is very complicated, and it’s completely possible that our perceptual understanding of octave equivalency in sound would not translate to octave equivalency in light.  Either way, there is definitely an interesting answer to this question, and we will probably never know. That bugs the crap out of me.

————————————–

Let me know what you think! We seem to have successfully given a third cone to two-cone-seeing monkeys and mice, and we know there are human tetrachromats, so maybe there’s hope. Unfortunately, it doesn’t seem like extra cones correlate to seeing a wider spectrum of light, just to seeing more shades of color within the visible spectrum.

One thought on “What color is an octave above red?

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s