October 27, 2008


On the Harmony of Light

Because I've done a lot of work in music analysis and color perception, I frequently get asked about the possible analogy between harmony in music and visual perception. Here's a series of well-put questions and my answers:

Q: I have always been interested in the fact that our (color) vision spans but one octave, like a Fisher-Price piano, a single frequency doubling, within which all the colors are unfolded. What I would be interested in is to be able to observe the effect of analogous frequency (light) collections, at similar ratios to musical pitch classes, that is, to observe the kinds and interactions of the color combinations thus derived. I am not familiar enough with Albers' theory to know whether he used any interval scalings, either integer ratios or "equal temperament" (2 to the 1/12 power=1 half-step) in figuring better or worse combinations, and whether these are related to the quantifiable consonance/dissonance of musical intervals and trichords.

A: Yes, I see the attraction of this: I assume you are familiar with the Pythagoreans: it is truly an ancient and honorable quest!

Q: For example, take a perfect fifth, 7 semitones, or approximately two frequencies at a ratio of 3/2. How do different pairs of colors at this same ratio relate to the eye?

A: Well, as I understand it, the analogy with music is tenuous at best. Color is only tangentially related to wavelength: in fact most colors are "non-spectral," that is, they don't correspond to a particular wavelength (frequency). The most obvious example is magenta which is a mix (chord?) of red and blue light (low and high frequencies), yet is perceived as single, distinct color that is neither red nor blue. It's as if an interval was perceived as a pure tone, not a mix of frequencies. (It's also interesting that musical pitch is not perfectly related to frequency: if you haven't heard "Shepard tones" or the "tritone paradox" they are worth a quick web search. I wonder what those with perfect pitch make of them?)

Q: For me to test this with your color combination page, I would need to be able to determine a color by inputting each respective actual frequency. For example, a major third (such as C-E) is approximately a 5/4 ratio. So, if we start at say red-hydrogen, what would be the effect of another color at 5/4 times that frequency's color distance?

A: Unfortunately, pretty much every color on your computer screen is non-spectral, being a mix of red, blue and green pixel colors (which are themselves not particularly spectrally pure). So I can give you hue, but not wavelength. When someone invents a tuned-dye-laser display, that might be possible, but also note that different combinations of wavelengths can result in effectively identical color perceptions. Fortunately, this makes it possible to get a reasonable (if far from perfect) color gamut without the expense and mess of tunable monochromatic lasers.

The relation between perceptual color and wavelength is pretty well expressed in the CIE chromaticity diagram, which I think is fascinating, and worth your time. Any color of light is a point on the diagram, and the color of any mixture of two will fall on the straight line between them: http://hyperphysics.phy-astr.gsu.edu/hbase/vision/colper.html
Wavelength runs around the outside for the spectral colors. There are some interactive versions of that which may approach what you are looking for, e.g. : http://www.cs.rit.edu/~ncs/color/a_chroma.html

Q: I'd like to be able to arrange colors somewhat specifically by various frequency intervals, and then ponder the relative qualities of the differences, as if sitting at a piano and listening to pairs or groups of tones. Like Newton, I don't have a hypothesis, it's just an aspect of the phenomena (visible light) which I haven't seen anyone address, and which I have a hunch there is some information there that might be worth finding out (or not).

A: Well, there may well be interesting things going on, but it's pretty clear our perceptual apparatus just doesn't have the frequency resolution to --literally -- see what's happening. The human eye is only sensitive to three primary colors; all other colors are merely a mix of those. It's like your ear only being sensitive to three notes, and all music -- all sound -- would be perceived as mixtures of the three. And that's a pretty strained analogy, which indicates to me that there's a limit to how far it goes.

I'm personally interested in the boundaries of color perception: I've made an artwork that uses near-infrared LEDs to produce a very dim but noticeably red glow. Unfortunately, it doesn't look any more red than red -- we -- or at least I -- just don't have spectral sensitivity any lower.

As fas as "visible octaves," I've heard that the retina (or more specifically the blue-responding cones) really are sensitive to well into the high 300 nm ultraviolet, and it's only the lens of the eye that is filtering it out. Apparently people who have had their lenses surgically replaced with synthetic ones see rich and vivid violets they have not perceived before.

(As an interesting sidebar, there is evidence that some women are tetrachromats -- they have an extra optical pigment and so are are sensitive to four primary colors. Honeybees can see not only well into the ultraviolet, but polarization axis as well -- what must the world appear like to them?)

Fascinating an exactly right on all counts. Only a couple of minor points to add...

The phenomenon of two tones in a musical interval merging to form a single percept was investigated by Carl Stumpf in the late 19th century: he called it "tonal fusion" (Tonverschmelzung). See here for more details. Tonal fusion seldom occurs with music, but does happen, so perhaps that's the closest analogy to our non-spectral perception of combined colors as a single percept like "aquamarine" or "magenta."

As well as spanning only a single octave of frequency range, our human eye-brain system has remarkably poor noise sensitivity. The signal-to-noise ratio of a typical analog TV is only about 35 dB, for example. The human ear/brain system boasts a far greater noise sensitivity: we can easily hear noise that's 60 dB down (this is the S/N ratio of a typical cassette deck, whose hiss we easily hear) and only when we get above about 80 dB S/N ratio do we hear sound as truly noise-free. The 35 dB noise sensivitity of our eyes is about 1/300 the 85 dB noise sensivitity of our ears.

Moran and Pratt in a 1926 article in the J. Exp. Psych. determined that there exists a fairly wide range within which we hear musical intervals as defined categorically. See Moran, H., & Pratt, C.C. (1926). Variability of judgments of musical intervals. Journal of Experimental Psychology, Vol. 9, pp. 492-500.

For example, Moran & Pratt found that the range within which listeners heard a musical perfect fifth sounding like a perfect fifth ran from about 680 cents to 720 cents. This goes along with observations from ethnomusicologists that some non-Western cultures divide the octave into 7 equal parts (more or less), which gives you around 680 cents for a perfect fifth, while other musical cultures around the world divide the octave into 5 equal parts, which gives you 720 cents for the perfect fifth. The conventional Western perfect fifth sits in between, with 700 cents. The just 3/2 ratio is only slightly different at 701.955 cents.

SO it doesn't make sense to identify a musical interval with a single frequency ratio. Each musical interval (major 3rd, perfect fifth, etc.) seems to correspond to a range of frequencies. Anything within that range gets heard as a perfect fifth or a major 3rd, etc. This may provide an analogy with the fact that we very seldom encounter pure colors in everyday life, unless we happen to be looking at a fairly exotic light source like an emission line from some excited spectral source, or a laser, or something like that.
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