Paul Klee's syntax

     Mountain Movement (in three and four time) 1928 / Bergblume 1933

I did not see this work [Mountain Movement] when I checked more than four hundred books about Klee in the National Library in Bern in the seventies.
Almost thirty years ago, I found this work on the auctioneer's catalogue which I bought at Strand in New York.
General public had chance to see the work first time when the catalogue was made after the death of the owner of the work; the reproduction is artwork: a sort of print.
I obtained the catalogue raisonne in early nineties
Coming back to Japan after long stay abroad for searching art books, I found the digital image of the painting online in 2011.
So far I have not used the books I collected for writing blogs.
When the photo of artwork becomes digital, it becomes digital artwork free to see anywhere any time.

It is not easy to guess how many digital image works there are online.
I did not find  [Mountain Movement] on image site pages.
Then I realised that I can search with English title since I have the catalogue.
I found the second work [Bergblume] not under the English title but the German title.

I always had desire to own the reproduction of the work in order to see it whenever I want.
The more I see his works the more I appreciate him.
I think the twenty century art criticism is totally outdated because there is no proper criticism possible without seeing and analysing the whole work.
I have convinced that all masterpieces have reason to survive: unique structure.
To understand such structure has been my passion for fifty years.

 Klee made many mosaic works with polygons.
this work [Mountain Movement] is a sort of cubist landscape; his interest in architecture made some compositional device.

The arch of a half circle can be seen as one evenly warped curved line and the centre of the half circle is easily spotted.
So I enclose the quarter circle with a rectangle.
The diagonal of the rectangle can be bent evenly in many ways and the quarter circle is one of them.
In this way any line segment can be expressed as a warped diagonal of a rectangle (diagonal is a curve with zero warp).
A horizontal line is a diagonal of a rectangle with zero vertical line and a vertical line is a diagonal of  a rectangle with zero horizontal line.
I call this unit the smallest unit of visible line: the element of artwork.
The diagonal model of Modern alphabet [B] and ancient Greek alphabet [B] is the same.
Both are made of six elements.

We can easily see that these two works are made of countable straight line segments.
There is a most noticeable point D(5) where five lines out from; the rest are four D(4) and fourteen D(3).
We call them polygonal mosaics, because each face is made of countable sides: a triangle is a tri-side.

Let me try to construct the design of [Mountain Movement] systematically.
As the subtitle suggests it seems that the triangle and the rectangle must be the two cores of the structure.

Firstly I extended one end of the four sides of the rectangle counter-clockwise to make a wind mill-like shape.

Extend each four side clockwise like a spiral to make a mosaic of five faces.

This is the first group.

Loosening the lines like string, stretch it on grid( string network model).


The second group with the triangle is more complicated.
Extend the three sides counter-clockwise.

Attach another triangle with one corner between the two corners of the first triangle.

Make a rectangle to fill the cavity.

With the same procedure make symmetrical pattern like this.

Move the horizontal side of the rectangle on the left.

String-grid model of this pattern is like this.

now we can see that the whole structure is made of three groups.

The spiral model can be extended; new spiral can be shooting out from each corner clockwise.

The extended spiral can bind the other two groups.

Though I picked two examples there are several more related works with polygons.


Goethe said, "(Painting ) lacks any established, accepted theory as exists in music".
Many syntactic devices in Klee's works suggest that Klee conceived such theory, though he did not have time to write down.
I expect that such total theory may be revealed when the analysis of his work progress.
The music theory largely relys on visible sign system, which means that we must have preceding innate ability to see the shapes of such signs, which I call visual grammar.

Klee's interest in syntax can be seen in his diary.

"When in Italy (in 1901), I learned to understand architectural monuments....Even the dullest will understand the commensurability of parts, to each other and to the whole, corresponds to to the hidden numerical proportions that exist in other artificial and natural organisms. It is clear that these figures are not cold and dead, but full of the breath of life; and the importance of measurements as an aid to study and creation becomes evident."

Klee knew every shape around him was artistic more or less..
He seemingly convinced that art theory formally must be one for all things he sees and that the measurable elements of structure are responsible to give us sense of beauty.
He also wrote, "I cannot be grasped in the here and now, For my dwelling place is as much among the dead as the yet unborn"
He can be grasped now; his works' dwelling place is on the Internet among the other masterpieces.