Day 29: Madness-inducing Interval Graph Paper

Day 29: Madness-inducing Interval Graph Paper

Interval Graph Paper After doing all the survey analysis late last night, I fell into a fitful sleep. ETP users who wanted double-sided pages were going to get their notebook, but the significant minority of single-sided page users would not be satisfied. They wanted their dot grid on the blank side, but it would have to wait.

I dreamed that there was a magic graph paper that went far beyond dot-grid paper in its mystic properties, but in my vision the paper was blurred and I couldn’t get a good look at it. When I awoke, I thought I would see what I could come up with. I based the design on ratios from 1/1 to 1/12, foggily thinking that maybe some secret of music theory would be revealed if I sketched on it for a long time.

Interval Graph Paper

I took a basic interval and divided it into 12 equal steps, thinking that this would be somewhat equivalent to 12-tone scale as people perceive it. From my thin grasp of music theory, though, I know that an octave is actually a doubling of frequency, and that the divisions between notes are actually (checking Google) the 12th root of 2 on an equal-tempered scale. Which is not exactly right either, because it’s not the distances that matter, but the consonances and dissonances between frequency relationships, but they’re close enough to allow transposition of keys. OR SOMETHING LIKE THAT. At that point I decided to just draw dots.

To see what would happen, I divided the basic interval in 11ths, 10ths, 9ths, and so on down to 1/1. Then I repeated and reflected it to see what it would look like. A pleasing pattern, I think, emerged. I put stronger dots down so I could see the basic blocks more clearly, printed the PDF out, and then tried writing on it. Perhaps a MAGIC INSIGHT would occur to me, like in my dream. Or I would go MAD trying to resolve the shapes patterns with what I was doing. I ended up writing (see photo), but that put me in in a non-visual mode (mostly) and I was able to ignore it.

So what good is this? I don’t know. Maybe it will spark an idea or a discussion. What if it was a type of fractal pattern? Or a subtle Escher-esque pattern that influences our subconscious patterns? My takeaway is that I should continue to make bizarre graph papers to bend the mind…it’s an interesting line of inquiry!

You can download US Letter and A4 below if for some reason you want to play with it:

Adobe Acrobat Reader is recommended for printing. The built-in "Mac OS X Preview" and "Chrome Browser" PDF viewers do not always draw dotted lines correctly.


Groundhog Day Resolution Posts for 2014

I am challenging myself to create a new product every day for the month of February 2013. The Challenge Page lists all the products in one place. Check it out!


  1. penny 10 years ago

    oh dave… i could see use for this with my knitting design.

  2. Author
    Dave Seah 10 years ago

    Penny: oooo…that is a cool idea. Maybe I should make some Lagrange pattern graph paper. I never understood the point of it in school, maybe it will come to me as a pattern!

  3. To my eye, it looks like graph paper for explaining General Relativity: everything travels in a “straight line”, as defined by moving from point-to-point. But because space is warped, the path ends up curved.

  4. Author
    Dave Seah 10 years ago

    Amanda: That would be cool…space-time curvature graph paper! Could have a big black hole in the middle.

  5. Ben 10 years ago

    Maybe these need to be boxes instead? They actually remind me of the grid examples in web grid systems.

    In western chord theory many if not most chords are built on stacks of minor and major thirds — in your scheme three and four dots. There might be some fun interactions to be explored there.

  6. Ilze 10 years ago

    I approve of the direction! I actually like the larger pattern, how it’s showed in the preview image, better than the more condensed version of the actual download. The peacock tail-shaped pattern seems inspiring for notes like wishlists, brainstorming ideas etc.

  7. TesTeq 10 years ago

    Interesting idea but I see no difference between US & A4 versions. Both links seem to point to the same US file.

  8. Author
    Dave Seah 10 years ago

    Ben: A chord stack would be interesting to try!

    Ilze: That is a great suggestion…maybe a larger structure! I’ll try that.

    TesTeq: I double-checked the links and the files, and they are indeed different.

  9. TesTeq 10 years ago

    Thank you. Maybe there was some glitch in my iPad. Now I can access A4 version of the file. I will give it a try. There are some Europeans interested in your very interesting work!