The Music of Snow Crystals

Snow crystals can be stunningly beautiful, thanks to their unique and complex symmetrical forms.  It’s no wonder that the “snowflake” has become a favorite visual icon of winter.  And given that snow crystal structures are so alluring to the eye, I found myself wondering whether they could also be made alluring to the ear.  Could we “play” snow crystals as music?  Of course, any image can be converted into sound in any number of different ways, but I had an idea that it might be possible to do something more interesting: namely, to translate the distinctive structures of snow crystals into recognizably similar musical structures, and hence to generate music that sounds meaningfully like snow crystals look.  I gave this idea a try, working with historical snow crystal imagery from winters of long ago—can we say these ephemeral forms were “frozen” for posterity?  I hope you’ll enjoy listening to some of my results below.

Let’s start with four typical images from Studies Among the Snow Crystals During the Winter of 1901-2 by Wilson “Snowflake” Bentley (1865-1931), who is celebrated today as the leading pioneer of snow crystal photography.

One more thing: as long as we’re going to be putting these images into motion as sound, we may as well put them into motion as pictures too, so that we’ll have something dynamic to watch while we’re listening.

Bentley #882, February 8, 1902 (audio threshold=0.5, scale=major)

Bentley #785, January 5, 1902 (audio threshold=0.4, scale=minor)

Bentley #594, February 15, 1901 (audio threshold=0.6, scale=minor)

Bentley #598, February 15, 1901 (audio threshold=0.3, scale=minor)

Bentley is supposed to have taken his first snow crystal photographs in 1885, but prior to that time a number of other people had recorded the forms of snow crystals they’d seen in other ways—by drawing them, say, or by cutting them out of paper.  The resemblance of these older images to actual historical snow crystals undoubtedly varies.  However, each of them at least reflects someone’s subjective perception of the structure of a snow crystal; and besides, for what I’m doing here accuracy may be less important than symmetry.  So let’s follow our crystalline thread a bit further back in time.

Despite a few rudimentary earlier drawings—see, for example, René Descartes, Discours de la méthode pour bien conduire sa raison (Leiden: Ian Maire, 1637), p. 227—snow crystal images seem only to have become significantly varied and intricate starting with plate VIII in Robert Hooke’s Micrographia (1665), a sample animation from which is shown at right.  A few other relatively early figures appeared in Johannes Jacob Scheuchzer’s Physica Sacra (1731) and in a 1692 work by Giovanni Cassini which I haven’t yet managed to track down (a couple of Cassini’s drawings are reproduced in Philip Ball’s Branches).

That said, the oldest truly serious collection I’ve encountered accompanies an article by John Nettis of Middelburg in the Netherlands, “A Method of Observing the Wonderful Configurations of the Smallest Shining Particles of Snow, with several Figures of Them,” which appeared in Philosophical Transactions of the Royal Society 49 (1755), on pages 644-48 and plates XX-XXI.  The text was read on May 13, 1756, but it describes experiments said to have been conducted in January and February of 1740.

Nettis #91, depicting a Dutch snow crystal of January or February 1740 (audio threshold=0.4, scale=major).

Another eighteenth-century source is an engraved plate accompanying the article “Observations on Snow,” published in the Columbian Magazine 3 (March 1789), on pages 180-181.  The snow crystal figures are credited to Thomas Bedwell and are said to have been recorded “at an early period of the late winter,” apparently meaning the winter of 1788-89.  The crystals had most likely fallen in Philadelphia, where Bedwell lived and where other observations are said to have been made later in the same winter.
Columbian Magazine, depicting a snow crystal observed by Thomas Bedwell, probably in Philadelphia, early in the winter of 1788-89 (audio threshold=0.3, scale=minor; no time blur).

Another sizable collection appears in An Account of the Arctic Regions (Edinburgh: A. Constable, 1820) by whaling captain William Scoresby, with several plates in Volume Two matching a description in Volume One including dates and associated weather conditions for each figure, keyed to italic letters.

Scoresby #66, one snow crystal among several recorded on May 6, 1817, during an otherwise disappointing whaling expedition: “Various and beautiful figures vastly profuse; deck of the ship covered several inches deep” (audio threshold=0.2, scale=major; time blur displacements=8). crystals were to become popular as a source of textile patterns in nineteenth-century Japan.  Doi Toshitsura, Daimyō of the Koga Domain, studied them with a microscope imported from the Netherlands and published an influential set of drawings of them in Sekka Zusetsu (雪華図説, 1832), a page from which is seen in motion at right.  A later book, Hokeutsu Seppu (北越雪譜 “Snow stories of North Etsu Province,” 1837) by Suzuki Bokushi, reprinted Toshitsura’s snow crystal figures, one example of which is presented below.

Hokuetsu Seppu, drawing by Doi Toshitsura of a Japanese snow crystal of the early 1830s (audio threshold=0.4, scale=major, time blur displacements=8).

The mid-1850s English snow crystal studies of Cecilia and James Glaisher have been well documented in an online exhibition of the Fitzwilliam Museum in Cambridge, England, where much of their work is preserved.  Among other things, the exhibition summarizes a line contemporaneous speculation into the value of snow crystal forms as sources of artistic patterns for dinner plates, fabrics, mosaics, and so forth.

Glaisher(C)/4/9/1, “Arctic Crystal” (audio threshold=0.4, scale=major, time blur displacements=8).

I’ll skip over Israel Perkins Warren’s Snowflakes: A Chapter from the Book of Nature (Boston: American Tract Society, 1863), because all of its snow crystal figures seem to have been copied from earlier publications.  That brings us to Cloud Crystals: A Snow Flake Album (New York: D. Appleton & Co., 1864), which was the creation of Frances Knowlton Chickering of Portland, Maine, although the title page simply reads “collected and edited by a lady.”  The images in it are reproduced from paper cutouts which Chickering made to record her observations.

Chickering, cut-paper image of a Maine snow crystal of the 1860s, from a plate online here (audio threshold=0.5, scale=major).

So how did I go about doing this?

The animated GIFs are pretty straightforward.  All the snow crystal images I’ve chosen have a sixfold radial symmetry, so I set them in motion using the simple technique described here, with a sixty degree clockwise rotation per frame.  This kind of display isn’t just a visually attractive gimmick; it’s also legitimately informative.  I’ve described it elsewhere as a “symmetry test” because it allows the eye quickly and easily to assess rotational symmetry.  Most snow crystals are largely symmetrical, but they’re never perfectly so, and animations of photographs of them can illustrate this point vividly.  The same is also often true of handmade representations of snow crystals, depending on the approach the artist has taken to them.

For the audio, I take a snow crystal image, such as this one (Bentley #895)—

—and I transform its polar coordinates into rectangular ones, with the center mapped to the bottom.  The x axis running from left to right now corresponds to a counterclockwise rotation of the crystal.

I’ve always tried to center the snow crystals before carrying out this transformation, and for all the pre-Bentley examples presented above, I think I did a pretty good job of it.  However, I can’t say the same for the Bentley photographs, which were the first images I experimented with.  My technique for centering snow crystal images in Photoshop has been to crop the vertical and horizontal dimensions to the same even number of pixels, to create horizontal and vertical markers at the halfway points, and to line the middle of the crystal up with the point where the two markers intersect.  But I hadn’t quite figured things out yet when I was working on the Bentleys, and through some mix-up or other I ended up mistakenly transforming them all off-center to a greater or lesser degree.  Hold that thought for the moment; I’ll come back to it later.

For the initial conversion into audio, I repeat (or “loop”) the image horizontally a few times and then interpret it as though it were a sound spectrogram for additive synthesis.  I used to use ImageToSound for this purpose, but I’ve since coded my own “spectrophone” in MATLAB so that I can have more control over what it does and how.

The process is algorithmically identical to paleospectrophony, but the source in this case doesn’t represent sound until we make the connection arbitrarily ourselves.  A snow crystal picture isn’t a preexisting “picture of sound” like a spectrogram, a barrel organ programming diagram, or certain kinds of medieval musical notation.  That means we’re free to associate our vertical and horizontal axes—corresponding in the original crystal to distance from center and radial position—with whatever values we like.

For all the examples shared above, I’ve associated the vertical axis with an exponential frequency scale running from 10-8000 Hz, with 10 Hz corresponding to the center of the crystal and 8000 Hz to the outer boundary of the original source image, cropped however made sense to me at the time.  And I’ve associated the horizontal axis with a duration of twenty seconds per rotation—or eighteen degrees per second, if you want to think about it that way.  If the crystal is bright on a dark background, I tie amplitude to brightness; otherwise, to darkness.

At this point, the result doesn’t yet sound very “musical.”  Here’s a single rotation of Bentley #882:

But then I apply my melodization algorithm.  This filters the individual octave into sub-bands (twelve for a chromatic scale), evaluates the relative intensities of those sub-bands across all octaves within each analysis window (here I’ve chosen a window of 20000 samples, or a little under half a second at 44.1 kHz), and chooses the top n values (here I’ve chosen three) consistent with a specified scale (here I alternate between F major, or “major,” and F minor, or “minor,” although these are equivalent to D minor and D major, so this is really just a means of obtaining some tonal variety), barring any simultaneous notes that are closer together than n steps (here, two semitones).  I also have the option of filtering the sub-bands widely (preserving more of the original sound quality) or narrowly (isolating the pitches more strongly).  For all the examples above, I filtered things down to 2% of the width of each band.

In most cases I make one final adjustment.  I want transitions between notes to occur at points that sound right—at moments that could pass for, say, striking a note on a musical instrument.  Thus, I choose the “intensity” option for melodization, which reassigns window boundaries to local amplitude peaks and retains the previously detected notes whenever the amplitude fails to rise above a designated threshold value (which I vary here between 0.2 and 0.6 of maximum amplitude; the higher the value, the more resistant pitches are to change).  Even so, transitions occasionally come out sounding a bit abrupt or wrongly-placed.  To try to mask that problem, I usually apply my time blur algorithm to “blur” the transitions a little bit (default settings: Displacements=15, Interval=50, Iterations=1).  This creates something like an echo, but with no fade-out over time.  Every now and then I find that the time-blur obscures some feature I’d prefer to keep, in which case I might leave this step out or reduce its intensity.

Each of the sound files presented above was created as I’ve just described, with variable settings as indicated and a duration of six rotations over two minutes.  The same snow crystal image ends up being “played” six times, but the reference points line up differently each time due to the interplay between the 20,000-sample window cycles and the twenty-second, 882,000-sample rotational cycles. Thus, the melodizer isolates different combinations of peak frequencies with each iteration, and we don’t get exact duplicates of the same audio.

The visually distinctive pattern of the snow crystal comes out most clearly in the rhythmic structure of the music, which passes through a cycle of six repetitions with minor changes due to the crystal’s asymmetry.  On the other hand, the source of the permutations of melody and harmony is less transparent: these are derived by algorithm from a statistical analysis of the source, but in a more roundabout way that doesn’t have any obvious relationship with what the crystal looks like.  The result is something like a Rorschach test for chord progressions and resolutions.  It might be interesting to have people listen to the music long enough to get it stuck in their heads, and then try to repeat it from memory afterwards.  What order would they “remember” out of the chaos?

Now back to this matter of centering.  Carrying out a polar-to-rectangular-coordinates transform on an off-center crystal image doesn’t alter the rhythmic structure all that much (although it has some effect), but it does introduce a lot more variation in frequency, which translates into more variation in musical notes after melodization.

When I discovered that I’d messed up the centering of the Bentley photographs, I went back and reprocessed them with the crystals more carefully centered, but I found that the results didn’t sound nearly as musically compelling as they had before.  So I’ve stuck with my original versions of the Bentley examples for presentation above, and I have to say I’ve become pretty attached to them.  At the same time, I’m a little bothered that they owe some of their appeal to a chance mistake on my part.

But should I be?  It’s not altogether clear what ground rules ought to pertain here—where it’s okay to take liberties, and where it’s important not to.  There needs to be some basic respect for radial symmetry, I think; without that, the logic of the whole approach falls apart.  And my instinct is to take it just as seriously here as I would if I were working with a gramophone disc.  But with the snow crystals, does accuracy trump aesthetics if the two happen to come into conflict, or is it the other way around?  Can we even speak of “accuracy” when we’re transducing patterns into sound that don’t represent sound in the first place?  The linkage between the music and the form of the snow crystals is crucial, but does it have to be strictly objective, or is it enough for it to be causal and recognizable?  The audio could be understood as an attempt to sonify historical documents faithfully, but it could just as well be understood as aleatoric music governed by a set of self-legitimizing instructions: take any image of a snow crystal, rotate it around some point of your choosing, and translate the radii into sound using this algorithm, setting a few parameters however sounds best to you.  After all, if we think of our use of snow crystal forms mainly as a matter of “rolling the dice,” then what’s wrong with tilting the table a bit?  The trouble is that I don’t just want to “roll the dice” if I can help it.  I want to translate beautiful visible structures into corresponding audible structures so that we can experience them in a new way.  Nudging snow crystals arbitrarily off-center doesn’t feel consistent with that goal.

Still, there wasn’t any problem with the centering of the older snow crystal images by Nettis, Bedwell, Scoresby, Toshitsura, Glaisher, and Chickering, so my reservations don’t apply to the audio I got from those.  And as for the audio from the Bentleys—well, I guess we can just enjoy it for what it is.


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