Below, the construction of the basic units from a square:1. √ 2 rectangle2. A golden rectangle3.√ 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 These diagrams are from the artist's controversial and still unpublished research into charcoal marks and compass holes found in the infra-red examination of Tintoretto's Bamberg "Assumption of the Virgin Mary".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 PriceImages 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
Infra-red image showing a clear light hole in the middle of
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 images2. Deciding where the edge of the painting is when the canvas is badly frayedThe 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.
The montage 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
 The complete analysis is presented in "Renaissance Mysteries, Vol. I, Natural Colour and Vol. II, Proportion and Composition".For further details go to:renaissancemysteries.com
Golden
Rectangle
Square
 Square
Golden Rect.
Golden Rectangle
√ 5 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 formats based on research into harmonic rectangles
A
B
E
C
F
D
A
E
 B
C
G
F
 D
A
E
F
B
C
G
H
D
 Geometry  -  Michael PriceResearch into the Application of Harmonic Rectangles for the Format of a Painting.
 Page 6
 Painting FormatsThe following is a brief presentation of the application the geometry of proportion - (see Volume II) from the two volume book:"Renaissance Mysteries, Vol. I: Natural Colour and Volume II: Proportion and Composition".For further information go to: renaissancemysteries.com