[Who is Sharaku?] Every line in artwork can be divided into arcs

"(from Wikipedia)  Toshusai Sharaku was a Japanese ukiyo-e print artist, known for his portraits of Kabuki actorｓ....Little is known of him....Neither his true name nor the dates of his birth or death are known. His active career as a woodblock artist spanned ten months....And his output came to an end as suddenly and mysteriously as it had begun."
"A poet from western Japan? A Noh actor? Hokusai avoiding the censors? Tracking down Sharaku's identity has occupied reseachers."
The arc-circle model can be applied for this problem.
Almost perfect arc-circle model can be made for any refined artwork as most of established folk music can be notated.
For the new readers I picked some examples I made before.

     (Okamoto Shinjiro/ Takahashi Shu/ Paul Klee/ Amedio Modigliani/ Hans Arp/ Pablo Picasso)


It seems that there is universal law for all artworks, which every great artist eventually find.
Now it is time to apply the grammar to traditional Japanese art.
Ukiyo-e was once very popular as reproduction art for the public.
Consequently the design became stylish, forming clear network.
I found this image of high resolution.

The lines are either separated or connected.
Each line which meets at points is a curved line( a straight line is a curved line of an infinitlly large circle).
The parts of any curves look like arcs.
The curved line is a sequence of arcs.
Firstly I prepared many concentric circles aside.
And extending each arc in the image to make a circle, find out the nearest circle in the concentric circle diagram to fit each arc.
Almost every curve can be replaced for the arc in the diagram.
I call this arc-circle model.

Arc model can be made, elasing the circles.

Even the detail is well structured.

The model shows the network has very architectonic strucure.
It is obvious that Sharaku made intricate plan for the engraver.
Sharaku had 'geometrical spirit': the same type which Giotto, Leonardo, Durer and Picasso had.
It is well documented that even Picasso mastered how to draw with perfect arcs in his late forties after long Cubist experiments.
As Shakespeare cannot be the uneducated local actor called 'Shakespeare', Sharaku cannot be amateur.
We can exclude the popular theory: Sharaku is the Noh actor.
(to be continued)

Paul Klee's Musical Structure

We can see the shape of musical notes and letters without ｕｎｄｅｒｓｔａｎｄｉｎｇ the meaning as sign.
We have innate ability of seeing shapes which I call Visual grammar.
Shapes have been used as sign because  we can distinguish each shape.
Artwork is the direct outcome of the grammar and music is its secondary application to sound.
Somehow the musical notation system was invented first.
As musical structure reflects shape structure, many artists got inspiration from music.
The reason why art theory equivqrent to music al theory has not been established is that the smallest element of art like musical note has not been located.

Although Kandinsky wrote about point, line and plane as elements, a visible point is a small black loop.
And the contour of a plane is also a loop.
A loop is a closed line and the parts of a line can be recognised separately as arcs like musical notes in a melody

I have chosen Klee's [Support for a shield] which I feel very musical among my cut out collection.

Though I found this digital work online too, I could only know two things: this is now in some German museum collection; this is used as illustration for the book ['in-between Painting and Music' or Thinking with Paul Klee and Anton Webern]


At first sight (without fixing view point, the size difference of the parts can be seen easily.
There are four dominant  curves and three loops.

We tend to see the center of each curve as the pole of a curve.
There are more noticeable points: the two ends of the line; the three intersections.

There are more gaze points on the line, which are noticeable because of position:
① the summits of convex
② the bottoms of convex

③ the right sides poles
④ the left sides poles
⑤ the changing points of bent.

All the gazing points can be connected to make a zigzag gazing point model.

The zigzag line can be converted into a curved line with the drawing tool.
Now the new curved line satisfies all the parameters.
Comparing this with the original, what this curve need is obvious.

What the mechanically drawn curve does not have is roundness.
A round curve can be constructed with arcs.

The coloured arc model can be made with eleven circles.
Erasing the circles, arc model can be made.

The arc model can be put together with the unit model.

I do not have to make circle models to select harmonious works.
It is innate ability to feel harmony.
Young Klee wrote in diary,
"When in Itary, I learned to understand archtectural monuments....
Even the dullest will understand that the obvious commensurabilty of parts, to each other and to the whole, corresponds 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."

I picked two more harmonious works: [Caryatid] by Modigliani; [Golden Ball] by Shu Takahashi.

Cubism is " arc-ism" ( Arc is atom of art)

An arc is so simple that we can easily picture it in the mind.
When we see the shape of a plate to draw it, we pay attention to several parts of the contour as arcs.
It is like touching an object in order to sense the shape in the dark.
Touching is the basic ability to sense an object and seeing on sense level is  its evolutionally advanced stage.
We self learn on this stage logically organisable structure of shape world around us.
The other abilities are moulded imitating the learned structure.

Cezanne painted almost every contour of the objects as a link of arcs.
And Picasso recognised Cezanne's excessive use of arcs very effective.
The other modern artists followed Picasso
This is the main reason why Modern art became great in a very short period of time.
Cubism was "arc-ism".

Well known way to draw an oval is to connect two arcs of a small circle and two arcs of a large circle.in the way above.
The four arcs are easily recognizable:  top and down arcs and right and left ones.
Let me show how we see a plate.
Though we see innumerable oval shapes from various angles we recognise it as oval.
This way of seeing is sign-seeing: we know that the plate is a circle.
We fix a viewpoint to see an object.
In this photo image the outline is not symmetrical: the circle of the left arc is larger than the circle of the left arc; the left side of the top arc is more curved than the right side; the right side of the bottom arc is more curved than the left side.

The outline of refined artwork becomes a smooth line and the smooth line is a link of arcs.
Artwork is easily recognizable pattern for an ideal seer as musical note is for a musician.
It can be said that Cezanne's work was in the mid way of becoming purely clear pattern.
This is similar process as a folk music sound becoming pure musical sound.

There are some prints by Renaissance painters showing a device how to draw still life objects, which means that it was even for them difficult to get photographic view overcoming three-dimensional illusion.
Cezanne did not have interest to use such device; his composition is not realistic; the only realistic factor is volume, which, Picasso eventually realised, is not essential.
Then what was his advantage of not being realistic?
Cezanne could simplify the whole pattern.
As every contour became a link of arcs the whole network was easily manipulated like Cubist method
As the first Cubist Cezanne painted unrivalled harmonious artwork.

Although we see mathematical curves beautiful, we do not find such beauty in nature so often.
There must be some other factor in the beauty of artwork.
I reason that pure artwork is made of harmonious links of arcs.

Before I defined that the smallest unit of artwork is an evenly warping curve and it can be enclosed by a rectangle.
In this illustration the maximum curvature is represented as a quarter-circle and straight line is a curve of a infinitley large circle.
The other curves are arcs between the two.
Any shapes can be re-constructed with arcs
Refined artworks tend to be made of a fewer arcs.

The advantage of defining the unit as arc is that every unit becomes a part of circle and the radius is defined.
There are infinite curves between the quarter circle and the straight line.
A small portion of a large circle becomes almost straight line.
The link of them can express any line of any artwork.

Clear image of a shape in the mind can be expressed with smooth lines and a smooth line drawn by hand tends to become a link of arcs.
This is the last version of Picasso's bull series, which is considered to be the good example of perfect abstraction.
It looks being made of arcs and straight lines only.
Once I imagined that I could draw all the lines using circular cardboard cut-outs as rulers.
Living long enough to be able to use Microsoft Drawing Tool, I could draw almost round circles easily.
The quasi-circles are good enough to make my point because we see a quasi-circle as a circle.

More realistic Modigliani can be drawn in the same way because he understood Cubist method well.
He painted the oil paintings as applied art for making a living.

Hokusai was a one of forerunners of cubist( arc-ist).
He knew that shapes are made of arcs though he disguise the outline for practical purpose.

                                    Matisse Monsieur Loyal
This Da Vinci sketch tells us that the outline is further separated into line segments and the proportion of each part becomes measurable vertically and horizontally.
As Da Vinci drew it for his own interest he did not bother to refine the line and Hokusai needed to draw realistic outline for readers; the final quality of executed line depends on the practical use.
They were the same kind to Picasso: analytical artist.
Ferdinand de Saussure distinguished parole and langue and studied the latter,
.Likewise the visual grammar seeks ideal models underneath individual works.

Most of modern abstract paintings are made of straight lines and arcs.
And Surrealists' works are made of curves which are links of arcs.
Formally every artwork is made of arcs.

                                    Albert Magnelli

                                   Giacomo Balla

                                   Piet Mondrian

In this work by Magnelli arcs make polygons with curved lines.
The second one by Balla and the third one by Mondrian are made of overlapped arcs.

In the works of Modigliani and Arp they may look different type as we tend to see the works on iconic level at first sight.
Besides, the arcs are hidden in the outline, which is why the contemporary critics failed to see the common denominator of these works: arcs.
As they could not see that all the modern artists were  Cubists, they classified Modern art on sign level, inventing the isms.
It was chaotic like the time of discovery of the numerous subatomic particles in physics without recognising the parameters.

There are eight possible connections out of two different arcs.
Imagine they are made of wire, their shapes can be easily recognised in the dark, which means that sense-seeing is as fundamental as tactile ability and that colour-seeing is different.

This Arp can be made of three two-arc unit.

   I call this quarter circle model.  

   The number of unit can be increased.

Now I can introduce another model: circle model.

The arc model and the unit model can be put together.

Modigliani's  significance is underestimated because of popularity of his less important portrait paintings.
His Caryatid series is as advanced as Webern's serial works.

It was unfortunate that the best formalist Clive Bell used the term  "form" not only for shape but for colour, which is the cause that prevented unification of all art.
Even Picasso took sometime to realise that colour and tone is not essential factors.

Visual grammar is the most basic cognitive faculty based on sensing shape.

Art theory needs notation system (Art cannot be explained in words alone)

 What is common in these images?
All of these images are made of curves and straight lines.
Each line can be seen as a chain of different curves like a melody.
We have ability to distinguish the degree of curvature, though we may not exactly see the division of each curve.
The visibly smallest part  is a curve of the same curvature and this can be enclosed with a rectangle on grid, which is like a musical note.
When the same work is made repeatedly for practical purpose, the shape line becomes smooth.
And usually the design becomes simpler, which means that the shape is made of smaller number of units.
Each line becomes a chain of simple curves like a melody with pure sounds of instrumental music.
A typical example is Matisse's two paintings called [dance]; Dance Ⅱ has more smooth lines than Dance　Ⅰ.

The contour of each apple in this Cezanne's still life is almost a chain of arches, each of which was enclosed by a rectangle on grid.

  

How only Cezanne could see the unit curves is his way of seeing.
It is said that he watched the motif until the apples became rotten.
To see the same thing all the time means that he neglected ever-changing natural lighting: shade and colour.
What he saw all the time is the shape.
Cezanne's oil painting of still life is the evidence of his way of seeing the object.
And his drawing is the result of his understanding about art.
Each of Picasso's early Cubist painting was the experiment to examine the unique structure of Cezanne painting.
Picasso eventually succeeded to  invent Cubist method: the composition with curves and straight lines.

These three works show his stages of understanding what art is.
The individual work must be analysed for proper understanding of his idea.
He deducted unessential factors from his painting little by little.

In the first painting, what he eliminated are chromatic colours and naturalistic proportion.

In the second painting, the contour is still expressed by tones but the volume and shading are not natural and the outlines are more emphasized.

Finally he drew contour lines.

Pablo Picasso



Artwork has four layers: code level; symbolic level; iconic level; formal level.  
And each can be seen separately.
Seeing this Arp reminded me that Arp is considered to be surrealist. I call this level art of code(or index or reference).

We may associate from this something like animal with two eyes. This level is art of symbol.

Each seer may associate different thing but a black shape with two holes is anybody with common sense sees. This is art of icon level.

Seeing a loop with two smaller loops inside is the level of art of shape, which is non-associative sense activity.

Hans Arp


Unlike Picasso Matisse did not conceive any model beforehand; he never adopted Cubist method.
But he reached the same realization from Cezanne's Bathers that artwork is made of lines ,as seen in DanceⅡ．
This shape was cut by scissors; cutting each curve must be more　conscious than drawing a curve; for each curve the scissors must be re-adjusted.

Henri Matisse


In calligraphy we should distinguish the difference between executed line and model line.
It is like the difference between played music and written music.
The model line is definitive though the outline of the touch may be accidentally shaky.
In general the executed line can be various, depending on a used tool for making a line, as a melody sound various , depending on what type of musical instrument is used.
When the practical purpose requires making many products, the line becomes more polished.

Brice Marden


This Kelly's work is a green shape with characteristic contour.
The shape is so simple that we become aware of  the way of seeing; to see the unique shape is to see the contour.
The contour is a ring of various curves, each of which can be recognized separately because of   the difference of curvature.
Practically any curvature can be expressed as a part of a circle.
We can see an oval having very gradually changing curve, but this is not the way of seeing a shape when we see an artwork.
We tend to see it as a ring of a few arches.
Cezanne gradually became aware that our way of seeing is not analogue but digital, as we see a plate shape in his still life changing from oval to more distorted shape with a fewer curves at later stage.

Ellsworth Kelly


This ancient Chinese jade is usually treated as artefact and the historical background is little known. (code or referential level)

As a consequence the practical use is unknown. ( symbolic level)

We can see this stone artefact with a hole is standing. (iconic level)

This image is a loop with a smaller loop inside. (formal level)

Ancient Chinese jade


This is a typical case out of many neglected formal artworks without which a sound art theory is impossible to establish.
The western academic art world regarded ancient Greek sculpture as ideal.
Consequently painting was considered to be the most advanced style of art.

When our curious mind tries  to see every  artefact on the formal level, we may be surprised to realise that much grammatical  knowledge have been already known by the ancient.
Actually Cezanne's discovery of formal art was rediscovery.

Attributed to Hokusai


This is an old Japanese game one person play; the rule is the player must draw the picture using the ten letters on top taken from the poetry on the left side; while reading the poem the drawing must be finished.
I picked one letter "no"which was handwritten variously.
The way of seeing the contour of Cezanne's apple is the same to seeing the letter.

As a sign five units are enough to make "no" letter,
As calligraphy the meaning is irrelevant and the shape matters; the number of unit can be increased.

Alfred Bar's famous diagram says that modern art developed into two types: geometrical art and non-geometrical art.
But every shape is geometrical; the difference is degree of complexity: the number of units.
If we once realise that semiotic level of art is irrelevant and  every shape is made in the same way, art theory becomes very easy to be established.

Art criticism is for those who want to talk about art; they talk what words can express.
Artwork as image is for those who want to see it for enjoyment; they know words alone cannot explain why they get artistic sensation.