Geometry, Application of Greek Dynamic Symmetry, Michael Price

Painting Formats and the application of Greek Dynamic Symmetry

An elemental part of the artist's compositions is the format, i.e. the proportion of the height to the width of
the rectangle. The format the artist opts for is a direct application of Greek dynamic symmetry. This means
that rectangles are built up of different geometrical units - either a golden rectangle, a √2 (square root of 2) or
√5 (square root of 5) rectangle, or a combination of these rectangles with or without a square. Theoretically,
these combinations can be varied ad infinitum and will always provide a harmonious proportion of height to
width. One can actually work either very spontaneously within such a format as the artist mostly does now, or
in a more calculated manner as he did during the mid to late 1980’s. The placement of the figures or other
compositional elements within the rectangle can be in harmony with the structural units or at variants
according to the required compositional tension.

Golden rectangle, root 2 and root 5 rectangles

Below, the construction of the basic units from a square:
1. √ 2 rectangle
2. A golden rectangle
3.√ 5 rectangle

The following diagrams show the relationship between the golden rectangle, the pentagon and the
golden section, or golden ratio. The golden section or the divine proportion is given the ratio of
1:1.618. These diagrams are from the artist's controversial and still unpublished research into charcoal marks
and compass holes found in the infra-red examination of Tintoretto's Bamberg "Assumption of the Virgin
Mary". The artist is well aware of the importance of the work done by many intellectuals with regards to
sacred geometry and finds the following publication the most adequate answer to date.
From Footnote 19 of the artist's research on the Tintoretto painting.
Peter H. Richter/Hans-Joachim Scholz, Der Goldene Schnitt in der Natur. Harmonische Proportionen und die Evolution,
Munich and Zurich 1987, p.211.
'The remarkable fact that the golden ratio characterizes the last ordered motion before complete takeover by
chaos, is not only true for the double pendulum. It is one of the amazing universal features of complex
dynamics that computer experimentation has brought to light in recents years'.
'Der Goldene Schnitt...ist in wohldefiniertem Sinne das irrationalste aller Zahlenverhältnisse und charakterisiert somit in
Geometrie und Dynamik den Gegenpol zu Kommensurabilität und Resonanz'. For further information regarding recent
research into the golden ratio see, Richter/Scholz, 'Das ebene Doppelpendel' (The Planar Double Pendulum), Film C1574,
Publikationen zu Wissenschaftlichen Filmen, Sektion Technisch Wissenschaften, Series 9, Number 7, Göttingen 1986, p.34.

The Diagonal DB of Golden Rectangle ABCD gives the pentagon BEFGH when the inscribing radius =AB of
the Golden Rectangle ABCD

1989. Michael Price.
Study for Transcription after Tintoretto.
Oil paint on canvas.
198 x 122.5cm. (Rectangular format with an
inscribed semi-circle).

1989-1998. Michael Price.
Tintoretto Transcription, Bamberg "Assumption of
the Virgin Mary".
Natural & mineral pigments in oil on canvas.
198 x 123 cm. (Stretcher frame built with arch).

An Analysis of "The Assumption of the Virgin Mary" by Jacopo Tintoretto - Michael Price
Images courtesy of the Doener-Institut, Munich, Germany.

The following images, both infrared and X-ray images provide and outline of the artist's on-going research into a
curious puzzle surrounding Tintoretto's "Assumption of the Virgin Mary" in Bamberg, Germany. A few infra-red
images showed compass holes and very sharply incised charcoal lines that indicated the use of large stencils to
position some of the figures on this very large painting. The figures are life-size.
The investigation is centred around the following important discoveries:
1.Two infrared images showed compass holes, one of which is very clear.
2. One infrared image shows a small charcoal cross for the position of one of Maria's hands.
3. Another infrared image reveals incised lines to position the foot of an angel at the top of the painting.

Tintoretto's "Assumption of the Virgin Mary"
during restoration showing the painting
removed from its stretcher

A composite of the x-ray images of the
painting showing hardly any changes to the
original disposition of the figures

The X-ray images revealed hardly any compositional changes for a painting that had to be executed using a
scaffold.
The question is did Tintoretto use geometry as a compositional tool for the disposition of the
figures?

The author's approach to answer this question is to try to find the exact position of the compass holes in relation
to each other and to the format of the painting. Unfortunately, the author was introduced to the unsolved puzzle
after the Tintoretto painting had been restored and returned to Bamberg.
Since one cannot use photographs of the painting due to a considerable distortion of the format through a camera
lense, the author decided that using the series of available X-ray images on a 1 to 1 scale would provide the most
accurate method of measuring the distance between the compass holes and the distances between the compass
holes and the edges of the painting.
1.The right edge of the painting has been cut by a few centimeters. This creates the difficulty of calculating the
original format, but based on the evidence of the width of the loom to produce the roll of canvas used for the
painting, the cut-off piece was estimated to be about 4cm.
2. Piecing the X-ray images together requires a lot of patience especially where there are overlapping images.
Details of this are recorded below.
The following four infra-red images provide the most compelling evidence for the use of geometry and stencils
for the disposition of the main figures in the composition.

Infra-red image of the ankle and foot of the angel at the
very top of the painting. The precision of the incised line
indicates the use of a stencil.

This infra-red image shows a Charcoal cross marks the
position of Maria's right hand on the centre of the painting.

Infra-red image showing a mark in the middle of Maria's
head indicating a compass hole.

Infra-red image showing a clear light hole in the middle of
the appostle's head vertically below that in Maria's head
indicating another compass hole.

The Use of the X-ray images to provide the necessary measurements to assess if geometry
was used for the disposition of the figures.

The following X-ray images produce a full size replica of the "Assumption of the Virgin Mary" by Tintoretto.
The final measurements were made on the author's visit to the Doerner-Institute in Munich (December 2004).
The main difficulties of putting the X-ray images together on a large light wall are:
1. Lining up any overlapping of the images
2. Deciding where the edge of the painting is when the canvas is badly frayed
The measurements taken will require some time to evaluate.

X-ray images of "The Assumption of the Virgin Mary"by
Tintoretto showing the life-size figures mounted on the light-wall
at the Doerner-Institute. The step ladders help indicate the scale.

A close up view of the apostle far right who is directly below the Virgin Mary. The distance between the centre of his head and the left
and bottom edges were required.

The three following X-ray images show the left edge of the painting and some of the difficulties in assessing where the painted edge
finishes. On the full sized images one can see where the bare canvas begins which was nailed to the wooden strainer or stretcher.

The dark area shows the occasional
overlapping of the X-ray images,
but the matching up is not affected.

together with the ladder to help indicate the scale.together with the ladder
to help indicate the scale.

Close up of the X-ray image of the Virgin Mary's
head.

The measurements within the painting
have to be compared to those of the
'original' format. The preliminary results
have shown the distance between the
two compass holes equal the length of the
side of the inscribed pentagon which is
the same as the main golden section of
the format.

Golden
Rectangle

Square

Golden Rect.

Golden Rectangle

√ 5 Rectangle

√ 2 Rectangle

√ 2 Rect.

1. √2 Rectangle
AC=AE=1.
DiagonalCE=CD=√2

2. Golden Rectangle
GF=1, FE=2, GE=√ 5, GD=√ 5. CD=1+√ 5

3. √ 5 Rectangle

AC=AE=EF=1.
AC=1, AF=2, DiagonalCF=√ 5
CF=CD=√ 5

Examples of the artist's formats based on research into Greek Dynamic Symmetry

Geometry - Michael Price
Research into the Application of Greek Dynamic Symmetry
in the Construction of the Format of a Painting.