Harmonographs

One of my favorite series in print comes from Wooden Books. They are beautifully designed and printed books on various esoteric topics. My favorite in the series is Anthony Ashton's Harmonograph, a visual guide to the mathematics of music. The harmonograph was a popular 19th-century parlor pastime that created art similar to a Spirograph, but with a much wider range of variables. Ashton purchased one and illustrated his book with it. He also gives a history of math and music dating back to Pythagoras, and includes schematics for building your own harmonograph. You can generate them by computer these days, but there's something hypnotic and amazing about watching one in action. The Wooden Books website lets you browse the series for free for 20 minutes a day, but if you're like me, you will want to experience the tactile pleasures of these lovely little pieces of art. The whole series is first-rate!

Wooden Books website (2nd image via Wikimedia Commons)

• [Anonymous]

  I got myself Buckard Polster’s Q.E.D., Beauty in mathematical proof from that collection and it is indeed a real pleasure. Precise, clear and and the drawings are exquisite.

• [miss_poppy]

  The asymmetrical harmonograph resembles a swarm of starlings. I wonder if a swarm of birds produces a sound that drives the patterns of the swarm. In any case, the sound in the swarm must be amazing.

• [kenahoo]

  The Wooden Books look cool, but I was trying to find a photo of one of them – are they actually wood, or is that just their name?

  • [Andrea James]

    @kenahoo: They are paper books. I believe the name was chosen because the books have a very old-school feel, like hand-set artisan printing and engraving. Very lovely craftsmanship.

• [Anonymous]

  This reminds me a lot of the “3d spectral analysis” in a software synthesizer called Metaphysical Function (which is an instrument that works inside Native Instruments Reaktor 3).

  See if you note some graphic similarity :

  http://www.youtube.com/watch?v=H7hqdet2ZuE

• [Art Carnage]

  I owned one of these machines as a child. The same company (Hasbro) that made the Spirograph toy also made Spiro-Man. After putting it together, it resembled a small, narrow 4-legged table. It was about 3 feet tall when assembled. Two poles were gimbled at the table. The top of one pole was a 2-D cut-out of a profile of a man (the Spiro-Man) holding a pen in an outstretched hand. On top of the other pole is the platform for the paper that the pen will write on. Two large plastic “donuts” were filled with water and attached at the end of the poles. These provided the weights needed to turn the poles into free-swinging pendulums. The pen-holding pendulum could only swing back and forth, but he paper pendulum could swing in any direction. I remember it came with a number of different pens, each in different colors. You could let it create a design in one color, and switch pens and add to the existing design in a new color (like Spirograph). I was about 10 at the time, which puts in the late 1960s.

  Picture: http://drawingtoy.com/images/spiro_box.jpg

• [Anonymous]

  The site is cool, and they publish some awesome books. In fact, I was browsing and adding books to my shopping cart left and right- until the store kicked me out and said no more browsing until tomorrow.

  That’s a pretty hostile approach to take towards potential customers. I think I’d rather just go down to the local physical bookstore, where I can look at as many books as I like before buying. Who says internet bookstores spell the death of local, physical ones?

  • [CastanhasDoPara]

    Completely agree on the hostile-ness of the site and it’s ability to make me want to go down to the book shop so I can browse at my leisure. Though I would not really be so hot about buying any of them, the site is that big of a turn-off for me. Well, okay the few I have already sort of balances that out but still what the hell?

    Daud Sutton’s Platonic Solids is pretty choice especially for the unfolded examples in the back. Great resource for paper craft or modeling.

• [wizardofplum]

  Ah! Yes Miss Poppy@1 Nature’s symmetry at work.You are probably aware of the same phenomena with shorebirds such as plovers,lapwings and snipe. We old fogies would call a ‘swarm’ of starlings,a murmuration or chattering [the latter is more appropriate perhaps?] The shorebirds would be[in order]congregation,deceit and wisp.Sorry to go off topic, just an old man yearning for “sights and sound so well remembered” A symptom of D.D.T.’s to whit,Decadal Degenerative Torpor.

• [mzed]

  Jason Martineau’s book on the Elements of Music, part of this series, is also very good. Smart and elegant.

• [Anonymous]

  I tried ordering a PDF file from this site but the link does not work though I paid for it. Who knows, maybe someone will write me back (?).

  The site is very nicely done though.

• [Anonymous]

  There is an online Harmonograph at the following site:
  http://www.sequences.org.uk/harmonograph/harmonograph_site/harmonograph.html

  Requires Shockwave. No instructions. But just click stuff. I got it to work.

• [Anonymous]

  I attribute my love of fractals, especially of the flame variety, directly to playing with a spirograph as a child. I would’ve had a blast with a harmonograph.

• [Michael Croucher]

  If you want to generate these pictures on a computer then you might find my blog post useful

  http://www.walkingrandomly.com/?p=151

  It includes the equations needed along with some Mathematica code.

• [Anonymous]

  My latest toy generates a continuous stream of moving epicycloids: http://www.youtube.com/watch?v=-DdJHVn8rnQ It’s a bit like having a four foot oscilloscope hack on your wall.

• [Anonymous]

  This is also similar to how guilloche patterns were traditionally etched onto currency plates, finer jewelry, or ceramic vessels.

• [teufelsdroch]

  Reminds me of Dmitri Tymoczko. His web page has some cool software to try out the idea.

• [Anonymous]

  Here’s another harmonograph simulator, this one in JavaScript using the HTML5 canvas element:
  http://typethinker.blogspot.com/2010/03/harmonograph-in-javascript.html
  Requires a recent browser that is not IE.

• [addaminsane]

  very exquisite drawings indeed

• [Anonymous]

  It looks like the Wooden Books site got boinged to death. Poor internetz.

  509 Bandwidth Limit Exceeded

• [bellebouche]

  Excuse me while I let out a long, slow, weary sigh.

  Download the PDF e-book. £4.99

  Buy the tangible, physical papery book from Amazon who will pack it up, transport it and deliver it to my door where it will land with a resounding thud on the doormat for just £4.47.

  That aside, looks excellent. Ordered, from Amazon.

• [KaiBeezy]

  .
  reminded me of the excellent
  2006 album of the same name
  by singer-songwriter
  boo hewerdine
  .
  cover art is a nice spiral
  .
  standout song is
  “girl who fell in love with the moon”
  featuring moonshot radio clips
  and backup singers i envision
  as a disembodied trio of
  female robot heads
  .

• [alberto]

  The Wikipedia page only includes one image of an harmonograph that does not show how it works.
  There are several videos in YouTube:
  http://www.youtube.com/results?search_query=harmonograph

  The clearest one I’ve found is this one, of a DIY harmonograph in action:
  http://www.youtube.com/watch?v=H4YQonwQUDs

• [Anonymous]

  Artwork created using a pendulum. For peace and harmony.

  http://www.youtube.com/watch?v=X8rT9hZIXtw