The basic principle of the ® CODE BACH consists of using graphic elements specific to the language of visual arts (colors, patterns, etc.) to symbolize distinct figures.

For example, the holes located to the right of the “BW Resilience” paintings (see image) correspond to the numbers 0 and 1.

The number 0 is symbolized by a small hole, while the number 1 is symbolized by a large hole.

These numbers 0 and 1 allow you to encrypt a message hidden in this painting.

In addition to the blue background color and black splatters, there are two main colors on this painting: red and yellow. These two colors will symbolize the two numbers of the binary system, 0 and 1.

The two points located at the top of the table in the center (in a small piece of lattice) indicate to us, by their order of appearance from left to right, that red (the first point) will symbolize the number 0 and that yellow (in as the second point) will symbolize the number 1.

This painting is number 33 (more precisely 33bis since it was produced in two different ways) from the series “SMALL BW PORTRAITS”, painted by Jean-Claude Bossel in 2018.

The number 33 is symbolized on the painting by the small vertical lines (these are slits painted in red or yellow) located in the right part of the painting.

The order of the colors of these vertical lines is:

red - red - yellow - red - red - etc

If we translate these colors into numbers 0 and 1, we obtain the sequence:

0 - 0 - 1 - 0 - 0 - 0 - 0 - 1

In binary code (in base 2), this corresponds to the number 00100001, which we write in a simplified way 100001. Once converted to a decimal base (the usual base of numbers in our usual counting system) we obtain the number 33.

At the bottom of the painting, there are small colored dots in the mesh of a metal mesh.

By reading the columns of five points, from bottom to top, going through them from left to right. we obtain sequences of five successive colors:

1) red - yellow - yellow - yellow - yellow

2) yellow -red - red - yellow - yellow

3) red - red - red - red - red

4) red - yellow - red - yellow - yellow

5) etc.

By converting colors into numbers as shown in part 1-a above, we obtain five-digit numbers in binary writing (also called “base 2”).

1) 0-1-1-1-1 (corresponds to 15 in decimal code)

2) 1-0-0-1-1 (corresponds to 19 in decimal code)

3) 0-0-0-0-0 (corresponds to 0 in decimal code)

4) 0-1-0-1-1 (corresponds to 11 in decimal code)

The beginning of the ENCRYPTED MESSAGE is therefore:

15-19-0-11-etc

To be able to decipher this message, we will have to use a matrix of order 2 (a table of four figures, called Hill matrix), which will be provided to us by the colors of the small sticks placed at the top left of the painting.

We read the colors of the sticks again from bottom to top and again from left to right.

We then obtain four color sequences:

1) red - yellow - yellow - red - yellow

2) yellow - red - yellow - yellow - red

3) yellow - red - red -yellow - red

4) red - red - red - yellow - yellow

As in part 1-b above, we will convert these color sequences into sequences of numbers 0 and 1:

1) 0-1-1-0-1 (corresponds to 13 in decimal code)

2) 1-0-1-1-0 (corresponds to 22 in decimal code)

3) 1-0-0-1-0 (corresponds to 18 in decimal code)

4) 0-0-0-1-1 (corresponds to 3 in decimal code)

The decryption matrix (denoted D) will thus be formed of the four numbers 13, 22 (first line) and 18, 3 (second line).

We can now begin to decrypt the hidden message, by multiplying the matrix D by the numbers constituting the encrypted message, using these numbers two by two in the form of vectors.

We therefore start by multiplying the decryption matrix D by the vector formed by the first two numbers of the encrypted message 15 and 19.

The new numbers thus obtained (613 and 327) must be considered as representatives of two classes of remainders modulo 32 and must therefore be reduced to a number between 0 and 31 (613 then becomes 5, and 327 then becomes 7).

The image shows these calculations, carried out manually with a simple calculating machine (which requires knowing the basics of matrix calculation in mathematics).

The CLEAR MESSAGE appears before our eyes, first in the form of a cipher sequence

5 - 7 - 18 - 1 - 16 - 31 - etc

Which corresponds (taking the order of the letters of the alphabet and considering that 31 is a word separator, noted /) to the CLEAR MESSAGE (this time perfectly readable and understandable): EGRAP / etc.

Note that EGRAP is an abbreviation for the workshop-studio-showroom in which Jean-Claude Bossel has worked since 2015 and in which he has been developing his artistic work based on the ® CODE BACH.

If we arrange the paintings in this series one after the other, we discover that the small messages contained in each of the paintings can form, if we juxtapose them, a more important text.

There we find in particular an assembly of several fragments of poems by Baudelaire, from his collection “Les Fleurs du Mal”:

“To my destiny,
From now on my delight,
I will obey
Like a predestined,

Docile martyr,
Innocent convicted
Whose fervor
Stir up the torment,

Because I have everything
Extracts the quintessence,
You gave me your mud
And I made gold out of it.”

The canvas presented in image 2-a uses a certain number of graphic processes already used in example 1 above, adding others (always encrypted using the ® CODE BACH) which are displayed under other graphic aspects.

We notice dots of orange or red color, but also lines of color (the same colors orange and red), sometimes oriented in an ascending manner (read from left to right), sometimes in a descending manner.

This will provide us with a double possibility of symbolizing the numbers 0 and 1.

Red color = number 0
Orange color = Number 1

Descending line = number 0
Ascending line = number 1

This painting is filled with cryptic messages. We find some

• in the points located in the lower middle of the canvas (each vertical sequence of five points provides a number with five binary digits, therefore a usual decimal number between 0 and 31),

• in the strips of lines located in the upper part or in the lower part of the canvas, in the form of ascending or descending lines (each vertical sequence of five lines provides a number with five binary digits, therefore a usual decimal number between 0 and 31),

• in the very top and bottom ends of the canvas, with colored staples, also providing encrypted messages,

• in the two small paintings stuck on the canvas, which provide the parameters of the decryption matrix, this time in graphic and musical form,

• etc.

We are not going to decrypt all of the messages here and will therefore content ourselves with explaining one of the decryption processes used in this table, as an illustration of how the system ® CODE BACH works.

Let's focus our attention on the lines located in the upper part of the canvas. This is an ENCRYPTED MESSAGE that we will first translate into numbers by reading it from top to bottom (sequences of five colors), from left to right.

Note that if we read the orientation of the lines (ascending or descending) instead of the colors, we would obtain another message (also encrypted), which we are not going to decrypt here.

Considering the color sequences, we obtain:

1) red - orange - orange - orange - red

2) red - orange - orange - orange - red

3) orange - red - orange - orange - orange

4) orange - orange - red - orange - red

5) etc.

By converting colors to numbers as shown in part 2-a above, we obtain five-digit numbers in binary writing (in base 2)

1) 0-1-1-1-0 (corresponds to 14 in decimal code)

2) 0-1-1-1-0 (corresponds to 14 in decimal code)

3) 1-0-1-1-1 (corresponds to 23 in decimal code)

4) 1-1-0-1-0 (corresponds to 26 in decimal code)

The beginning of the ENCRYPTED MESSAGE is therefore:

14-14-23-26-etc

The text of the CLEAR MESSAGE (this is the name of the character “FRANZ GURTNER”) was previously encrypted by Jean-Claude Bossel so as to become an ENCRYPTED MESSAGE (therefore incomprehensible) on the painting.

This is what we see on the model presented in image 2-c.

This encrypted message is a sequence of numbers starting, as we saw above at the end of part 2-b, with

14-14-23-26-etc

(see the line labeled “code” in image 2-c)

To be able to transform this ENCRYPTED MESSAGE (which is therefore the sequence of numbers described above starting with 14-14-23-26-etc) into a new sequence of numbers allowing the MESSAGE to be read IN CLEAR, you must know the matrix of decryption (a Hill matrix of order 2, therefore four numbers to know).

We can then repeat the same type of matrix calculation as in point 2-d above (remembering that the results of the calculations must be converted into classes of remainders modulo 32, therefore be presented as numbers all between 0 and 31).

The four numbers constituting the decryption matrix are obtained using the two small tables glued to the large canvas (see one of them in the 2-d image).

The process of reading these numbers requires converting musical notes into the numbers 0 and 1 (see image 2-e below).

COMMENT ABOUT
FROM IMAGE 2-e

To encrypt a message in a painting, we saw in the examples above that it was possible to use different colors (for example 0 = black and 1 = red) or different hole diameters (for example 0 = small hole, 1 = large hole).

To encrypt information within a musical score, we can proceed in a similar way, agreeing for example that the number 0 corresponds to a duration of a “half” note (= two beats) while the 1 corresponds to the duration of a “black” note (= one beat).

We can observe this way of doing things in image 2-e, where we see, noted on a small canvas, the beginning of the famous theme from Beethoven's Heroic Symphony.

If we focus on the rhythmic values, we obtain a sequence of ten values ​​(the // indicate the bar changes):

IN THIS CONTEXT BLACK (TRANSLATED FROM FRENCH SOLFÈGE) MEANS QUARTER NOTE, AND WHITE (TRANSLATED FROM FRENCH SOLFÈGE) MEANS HALF NOTE.

white - black // white - black //
black - black - black //
white - black // white.

By transforming this musical notation into binary digits we obtain the sequence:

0 - 1 // 0 - 1 //
1 - 1 - 1 //
0 - 1 // 0

The first five digits correspond to the number 01011 (in binary code, therefore in base 2), which corresponds to the number 11 in our usual decimal system.

The next five digits correspond to the binary number 11010, therefore the number 26 in our decimal counting system.

The two numbers 11 and 26 provide here the first two numbers of a Hill matrix of order 2 (these two numbers correspond to the first row of this matrix).

Click on the image.