The same universal syntactic technique that was used for Ukiyo-e and Modern art

                                        Modigliani  [Caryatid]  pivot-line model 
Art making is not  sketching an object  but  designing a shape.
When he draws a curved line he is conscious that the line is made of several line segments each of which has different curvature.
Each curve becomes an arc.
The arc can be extended to a circle.
Using the circles he can adjust the balance.
Some artists were aware that the intersection of the circles can be fixed for balanced structure.
When I made the model of Modigliani's [Caryatid] I noticed a straight line going through more than three intersections(pivots).


This time I am going to check all the models I have made.

                               Modigliani  [Caryatid]  pivot-line model
Modigliani is generally known as a portrait painter.
But some people consider that [Caryatid] series is the most important.
The model supports such taste judgment.

                              Matisse  [Dance Ⅱ]  pivot-line model
We enjoy played music.
The effect is due to the structure which is expressed on the musical note.
Matisse painted [DanceⅠ] spontaenously.
Then he constructed [DanceⅡ] with unit arcs.
He chose a few circles to make a scale.
Matisse used the device to fasten the circles: to make the whole structure he intersected the circles on several spots, most of which are lined.

               Picasso  [Woman with a flower]  pivot-line model
Searching Picasso image online we find many imitation Picassos.
The reason why we can easily find out real Picasso is
the quality difference.
And the quality judgment can be supported by the model.

                             Klee  [Support for a shield]  pivot-line model
This masterpiece is not well known.
The reason may be because there is not so much to say in this picture of string on sign level.
The model reveals how the harmony is generated.
Now we know all the greatest modern artists used the same syntactic device.

                   Sharaku(Hokusai)  [Yamashita Kinsaku]  pivot-line model
Many people believe that Sharaku was Noh-actor and only early half body portraits are significant.
It seems that they see only facial expression and fail to see the whole body.
I consider that Sharaku style is the result of Hokusai's interest in early ukiyo-e.
The quality is equal to the best early ukiyo-e painters like Totorii Kiyonobu.

            Kaigetsudo Ando  [Tatibizinzu]  pivot-line model
I have chosen Kaigetsudo because his style is most distinct among early ukiyo-e painters.
Wikipedia says about Kaigetsudo, "it is probable that many of the works attributed to him were painted by his disciples".
The taste judgment can tell us which are by Ando himself and the pivot-line model can confirm the judgment.
The study of Ukiyo-e painting can be started with structural analysis of  works.
The pivot-line model shows us how artwoks are balanced and harmonised.

Cezanne's intuitive syntax and Modigliani's intentional syntax

                                  Hokusai [Ryakuga haya-osie]
                                  Cezanne [Six Bathers]/ Modigliani [Caryatid]
For these works, the same type of harmonizing syntax was used.
Painting, ornament, sculpture and archtecture are based on the same syntax.
As we can see in [Hokusai Manga], Hokusai knew that painting and ornament are designed in the same way.
Renaissance artists were experts of all the types of art.
There is no such thing as pure art but artwork is made for some practical purpose.
Art survived even after the practical purpose outdated or forggoten because the shape remained like a shell.
We get artistic sensation by seeing visibly perceivable geometric characteristics.
We perceive them quantitatively.
Artist is an inventor of new syntax.
Most people are accostomed to see shapes on iconic level.
In figurative painting the outline is not noticed as geometric because the line is a sequence of arcs.
Unlike painting , ornament has easily recognizable symmetric structure of circles.
A good listener can only perceive the effect of the musical note but the composer  can　use the musical syntax.
A good viewer can only perceive harmonious effect  of shape but the artist can use the syntax of shape.
Klee wrote in his diary,
"I learned to understand archtectual monuments....the obvious commensurability of parts, to each other and to the whole, corresponds to the hidden numerical proportions that exist in other artificial and natural organizms.....the importance of measurement....becomes evident."

                Cezanne [Six Bathers] lithograph
This drawing above seems to have been drawn after the lithograph below.
Althogh the legs are missing the foot is in proper position.
The curvature of the lines is very clear.
Arcs are the smallest elements.
The sequence of arcs becomes a melodious line.
The closed or almost closed line is a motif.
Ornament has pivot structure for balance and harmony.
At least Cezanne knew that deliberately drawn line becomes a curve with single curvature though he was not aware that the composition was forming  pivot structure.


The litograph can be reconstructed with five circles as he had excellent sense of harmony.
The modern artists could easily recognize Cezanne's scale method.

                Cezanne [Six  bathers] arc model
The circle-arc model I made before was to show that the largest and the second largest circles make the basic composition.
This time I add the smaller circles to show that each motif is well balanced.

                Cezanne [Six Bathers] pivot model
This model shows that same colored arcs are grouped at specific parts, which suggests that he paid very much  attention on the arcs of the same circle.
To make the point clear ,I enlarged two parts.

               Cezanne left Bather
The three pink circles overlapping the body are the main structures with pivots(intersection of more than three circles).
The highest circle which is the extension of the bottom thigh has six pivots.
The middle circle which is the extension of backbone has four pivots.
The lowest circle which is the extension of the front part of lower limb has also four pivots.
When a designer trys to balance the closely grouped arcs, the extended circles of the arcs tend to form pivot structure like ornamental design.

                            Cezanne right bather in [Six bathers]
The largest circles (green) which make the arm parts is the basic.
The second largest circles (pink) are not used as a whole circle but covering partially from both sides.
Many of the smaller circles intersect at the pivots.


The holes of ancient flute are made to sound scaled tones.
A musician of flute makes scaled music.
The document says that Cezanne was very fond of visiting The Loubre and enjoyed to draw marble statues.
Cezanne's sense of harmony further developed as he painted  the same motif  for sevral months.
Cezanne discovered the harmonizing device unintentionally.
Modigliani learned Cezanne's technique of harmony.
It is almost unbelievable that Cezanne used pivot structure consciously but surely Modigliani used it
deliberately.

                              Modigliani [Caryatid] pivot model
There are  three distinctive syntactic devices in the model.
1) It is made of six circle scale.
2) The second largest circle(green) is the base of the pivot structure.
3) There are eleven lines with more than three pivots and six of them intersect at a point(pivots on radial lines).


As nobody studied  artwok syntactically, the development of Modern art stood still.
Universal Art is a masterpiece based on unique syntax.

               


          

Picasso and Matisse belong to the same school called Cezannism

It is commonly said that  Abstract Art is the final stage of  Modern Art.
But some artists like Kandinsky and Kupka are not directly connected to Cezanne.
Picasso and Matisse are direct heir of Cezanne though they are not abstract artists.
Picasso said,
 " There is no abstract art.
You must always start with something.
Afterward you can remove all traces of reality."
The classification by isms is superficial ; it is based on sign level and fomal art is based on sense level.
The re-classification by the structure of artwork is necessary.
I show the common element of Picasso and Matisse,
.  
        Cezanne  Five Bathers / Matisse  Pink Nude / Picasso  Woman with Flower


Until the last time I showed that the pictures on the left and the center are made of arcs and that the circles of the arcs are structured with pivots .
    Cezanne  Bathers(litho)  pink and green circle-arc model
This lithograph is composed with lines only.
And Cezanne must have thought the composition satisfactory, as it was signed.
Therefore we can expect the work represents his syntactic idea .


Matiss spent several months to finish this painting and he left 22 photos of each session.


In the thirties Picasso made many  harmonious paintings.
I chose [Woman with Flower] to make the circle-arc model and the scale diagram.

Matisse  Pink Nude  circle-arc model / concentric scale diagram



    Picasso  [Woman with Flower] circle-arc model   scale diagram


The largest yellow green circle is dominant in [Pink Nude].
The third largest light blue circle is dominant in [Woman with Flower].
I used lighter blue for the two circles with many pivots; the right circle with five pivots and left circle with four pivots.
The concentric circle scale diagrams show that [Pink Nude] is more harmonious than [Woman with Flower] because of two reasons.
1) the number of circles in the scale in [Pink Nude] is five and the number of the circles in the scale in [Woman with Flower] is eleven.
2) the proportion of the circles in the scale of [pink Nude] is very even and the proportion in [Woman with Flower] is uneven.


Unlike a book a blog should be readable without refering the previous blogs so much.
So I show some pivot structure models from the past writings.

        Sharaku(Hokusai)  [Otani Hirotugu]

    Sori(Hokusai)  [Namiura first version]

    Kaigetudo 

The same pivot structure was used by some Ukiyo-e painters.


The present problems in art criticism are due to the careless use of the term 'art' for many different meanings.
'Art' should be used for one meaing.
In my writing it means formal art which is universal (regardless of when and where).
Some time before I started conceiving three problems  to think over.
1) What is modern art? (hundred year problem)
2) Who is Sharaku? (two hundred year problem)
3) What is fine art? (ten thousand year problem)


For long time I had the notion that abstract art is made of lines and curves,
When I wrote about Matisse's [Pink Nude], I realised that I see the contour of any shape as a chain of curves.
Abstract art and figurative art became the same type.
Any consciously drawn curve has single curvature which is an arc.
After defining that the smallest element of art is arc, I could solve the second problem.
Establishing the grammar  and finding syntactic devices like pivot structure, 
the other two problems may be solved .
The examples of syntactically similar works form a group of jigsaw pieces like an island and many islands may be connected to become one.
I further expect to find the pivot structure in other styles of art like ancient Chinese Jade design, early mediaval miniature, early renaissance painting and so on, which makes unification of art.


Universal artwork is the shape of the image projected on retina.
Digital image online is ideal artwork.
As any shape is geometrically analysable,
All artworks should be classified into one system.

Harmonious scale in Matisse's Pink Nude

Any painting has a structure on formal level.
Everyone knows that painting is not always artwork.
Only masterpieces deserve to be called pure art which can tell us what art is.
As the taste judgement can find masterpieces immediately,
there is no difficulty to find interesting works among ever increasing digital images.
I expect that making models can help to think why great artworks are so distinctively attractive.
The principle of visual grammar is that redrawing the same shape makes the lines more smooth, almost  chains of arcs.
Here is a good example of such case.
Matisse spent almost six months to paint Pink Nude and twenty-two photos were taken for each sesession.

                                         Matisse [Pink Nude] and the photo of the first version


Firstly I make the circle-arc model of the final painting.

                   Matisse  Pink Nude  circle-arc model
There are seven pivots (intersection of more than three arcs), and
five circles are enough to make the whole structure.


Now I arrange the circles concentrically.

                                   concentric diagram of scale for Matisse's Pink Nude
The diagram shows that the circles  have very regular intervals.
The regular scale creates  sense of harmony.


I use these cicles to make circle-arc model of the first version of the painting.

                   Matisse Pink Nude  the photo of the first version
Surprisingly all the clearly drawn lines of the nude can be replaced with the circles in the scale.
It means that the five circles already had become the main motifs at the first stage.


I made the circle-arc models of all the versions to see the change of scale.


    Matisse Pink Nude arc models


I used only thirteen circles to make all the models.
The largest yellow green circle became dominant at the last stage.
This way of using the largest circles for unity is the same technique Hokusai used for [To-Megane].
It can be said that the twenty-one versions were painted to search the right circles for the unclear parts of the nude in the first painting.




I have made more than a dozen of circle-arc model for personally interesting artworks.
So far thirteen circles were enough to make all the models.
This number suggests that our ability to distinguish the difference in curvature of arcs.
It is not coincidence that musical scale has twelve tones.
Our sense is not analogue but digital.
Our sense organ is so primitive that twelve or thirteen scale is enough to express our perception.
Visual perception develops firstly and then we start thinking logically on this level.
The other abilities are constructed based on this structure.
This is the reason why every cultured world valued art.
It seems that art is not considered important anymore as education.
Such educational system fails to produce potential geniuses.

Matisse's DanceⅡhas ingenious syntactic structure for harmony [Rethinking modern art] Ⅱ

The second drawing  after the first tends to have very clear curvature.
We can pay attention on one curvature of one part at one time.
Therefore the curve becomes a chain of arcs when we draw it.
When we try to valance many arcs we are conscious of the extention of the both sides of the curve: circle.
As a result the circles almost start forming a pivot structure(with more than three circles  intersecting at a point).
Many genius noticed that this structure can be constructed to make balanced composition.
The good example of this process can be seen in Matisse's Dance Ⅱafter DanceⅠ.
The left  illustration is the first version.
Only the nude in the left is drawn with clear line.
It is obvious that Matisse intended to draw all the nudes in the same style in danceⅡ.
The right picture is made of round contours and looks more rhythmical and harmonious.
The outlines can be easily replaced with arcs of a few circles
.I used only six circles which function like a musical scale.              Matisse     DanceⅡarc model
Extending the arcs, the circle-arc model can be made.


         Matisse  DanceⅡ  circle-arc model
To see better the pink circle network stretching the entire surface, I make pink circle-arc model.



    Matisse  DanceⅡ  pjnk circle-arc model
The crosses show the intersecting points of more than three circles which are named pivot.
The pivots are systematically arranged.
There are two pivots on the green vertical line.
There are four pivots on the upper horizontal line and three pivots on the lower horizontal line.
There are two perfect circles; left one with four pivots and right one with three pivots.
There are six pivots on the light pink circle on the lower right.



The most dominant circles are shown in light blue.

    Matisse  DanceⅡ  blue circle-arc model
The largest pink circles make the base network, then  the network of the second largest blue circles overlap.
As the most of the arcs are the parts of the networks, the whole effect becomes  harmonious like the musical tones on the musical note.


Formal art history can be written as the history of inventions of such devices.
I wonder how many syntactic devices have been invented until now.
The present art world does not have the good atmosphere to produce artists.
I believe that the digital images are the medium of art in our time.
The painters for the gallery system are already outdated like chess masters.

Soon  the grammatical knowledge about art will be established online.
Then AI artist can be created.
As David Cope's Emmy composed almost-Bach, it will be possible for AI artist to paint almost-Picasso.
Besides brand new art styles may be invented as the AI chess master found many unexpected new moves.

Rethiking Modern art]Ⅰ Syntactic device in Cezanne's [Basel Five Bathers]

Any smooth curve is a chain of arcs.
Arc is a part of a circle.
An arc can be differeciated from another arc of a different circle.
Arcs can make a scale like tone scale of music.
Some artists with such notion  balanced arcs in a composition by handling the circles of the arcs.


Cezanne rediscovered the scaling system for composition.
What cubism was influenced by is a historical problem.
What Picasso and Matisse learned from Cezanne's  [Bathers] is a formal problem, which is quantitatively answerable .
I have shown that Sharaku (Hokusai) used syntactic device (pivot structure) intentionally.
We can find the syntactic use in art  everywhere and everytime as it is universal.
It is ovbious that modern artists were inspired by Cezanne's syntactic device.
 I should be able to find the use of syntax in specific Cezanne paintings.
I chose this square brownish painting called [Basel Five Bathers].




    Cezanne  [Bazel Five Bathers]　1885-87


To see how the motifs are extended arc model is useful to start with.
As the contour is simple and mostly enclosed by black lines,
the arc model is easily made. 

Though most of  his paintings with bathers look representational with full of green and blue, this painting is strangely un-natural: the space has no illusion of classical perspective;
 the light is not natural;
 many parts of the bodies are outlined with black
and the impression of the whole is brownish like Cubist painting.
This painting must contain something which attracted Picasso and Matisse.
The garment in the lower left reminds me of [Avignon].
And Matisse's [Dance] has similar borderline of sky and ground.


There is a related sketch on the facing page of this reproduction in the exhibition catalogue [Bathers].
We can see that the position of the body parts in the painting are following the gridded sketch.
This square painting is very schematic; each shape of the nude in the sketch is a motif to be extended.

To see how the motifs are extended arc model is useful to start with.
As the contour is simple and mostly enclosed by black lines,
the arc model is easily made.
   [The Basel Five Bathers]  arc model      


Extending the arcs, the circle-arc model can be made.
     Cezanne     [Basel Five Bathers]  circle-arc model


Next,  I make the blue circle-arc model to see the pivots better.
        Cezanne     [ Basel Five Bathers ]  blue circle-arc pivot structure model
 


The intersecting points (pivots) are shown with yellow crosses.




The lithograph of [bathers] in 1887-89 is a better example to recognize arcs.
     Cezanne  [Bathers]  lithograoh  1887-89


It is easier to make arc model because all the contours of the nudes are drawn in line.
I used only seven circles.
     Cezanne  [Bather  lithograph]  arc model


Next I extend each arc to make a crcle
     Cezanne  [Bathers  lithograph]  circle-arc model


We can see the largest green circles and the second largest pink circles make basic structure
      Cezanne  [Bather  lithograph]  green circle-arc pivot structure model


There are three crosses on two deep green circles.     Cezanne  [Bathers lithograph]  pink circle-arc pivot structure model




The pink arcs are grouped in two areas: lower left and middle right.
When the the circles form a pivot structure the circle-arcs are balanced with a sense of harmony.


The greatest accomplishment of Cezanne is that he rediscovered the long forgotten visual- grammar, specially the scaling of arcs.
And the modern artists further developed their own syntax.
Next time I am showing that Matisse used the pivot structure deliverately for Dance Ⅱ.

[Who is Sharaku?] Ⅵ Sharaku (Hokusai) used unique compositional device.

It is well known that Hokusai was very ingenious artist.
When Hokusai called himself Sharaku he was already very inventive.
His pictures look like being  made of arcs drawn with prepared circular stencils.
I have shown the examples of okubi-e (portrait of the half of the body).
This time I show that more complcated picture ( two portraits of the half of the body) has new compositional device.
I picked [Sawamura Yodogorou and Bandou Zenji] because of its high resolution.

                                               Sharaku  [Sawamura Yodogorou and Bandou Zenji]

Firstly I made the circle-arc model then enlarged the detail of the right person's head.

                             Sharaku  [Sawamura Yodogorou and Bandou Zenji]  the detail
We can see easily that the curling hairs are drawn one by one.
It is obvious that the painter used some device like stencil or circular rulers.
I colored each circle-arc in six colores: yellowish green, red, blue, green, bluish green and orange.
In the detail the blue colored circle-arcs are distinktively used: not only the contour of the head, but also the ridge of nose, the cheek, the right shoulder and the collars.
These circle-arcs are used as the main motifs to
construct  the whole picture.
Now let me show the whole model.

                      Sharaku  [Sawamura Yodogorou and Bandou Zenji]  Circl-arc model
It is obvious that each motif is used as a group at specific part.
The yellow green circle-arc is used to express drooping long hairs, the hanging sleeves and the left person's loose collars.
The curled hair tips in red are the same as the left person's long sideburns and the round parts of  collar.
The right person's belt is also made of this circle-arcs.
The round blue circle-arcs are more expressive in the head of the left person; the head cap, the outline of the shaven hair, the whiskers , the cheek and the chin.
In this way the whole network is organised according to the degree of curvature.


This technique was used more obviously in [osiokurihatoutusennozu], which I explained in the previous blog.

                                   Hokusai(Souri)  [The big wave]  arc model
The four circl-arcs which construct the boat in the lower center are the main motifs to express various waves.
Each circle-arc functions as a group at various spots.


A portrait and a landscape are comparable, not on symbolic level but on technical level.
As a double portrait this picture needed new device to harmonize the two motifs.




[Nakutenanakuse tomegane] which I introduced last time is also a double portrait.
As I used only the detail I show the whole image to explain another device.

                               Hokusai Souri  [Nakutenanakuse tomegane]
We can see the trace of stencil on top left side of the margin.
It looks that each rib of the umbrella is made of two identical curves.
I extended each  arc to find the whole circle.
This circle turned out to be the same as the outline of the opened umbrella.
The arm lines also look like having the same curvature.
So I tried to draw all the slightly curved lines as the part of the circle.
Surprisingly many lines can be drawn as the part of the circle.
The circle is the largest in the model of the picture.
The rest of circle-arcs, being smaller, are easier to recognise the curvature.
I call this composition the largest circle-base method.
One way of seeing a line is moving the eyes along the line, then seeing the lines with the same curvature must give the viewer a sort of sense of unity.


People in general see an image as sign as the result of education.
They lose the natural ability of seeing the shape as it is.
This is why only the early style of Sharaku's works are valued.
His fame is as the great portrait artist as people see the surface meaning.
Wikipedia writes that Sharaku's later styles are "artistically inferior".
This type of neglect by the authority reminds me of the cases of Cezanne's bathers and Klee's later drawings which I will reevaluate later with the aid of analytic method.
The later styles of Sharaku seem to be great experiments after the study of early ukiyo-e, which is another undervalued style.