Scaffoldings

[Guest Ryan Murtha]

You might like this, the picture that got me started was Leonardo da Vinci's Bacchus, pointing with both hands - you only need two points to indicate a hexagon grid. Norwegian artist Odd Nerdrum confirmed analysis of two paintings. There are many, but I will attach a few good ones. 

 

In The Painter's Manual (1525) Dürer wrote:

Considering, however, that this is the true foundation for all painting, I have proposed myself to propound the elements for the use of all eager students of Art, and to instruct them how they may employ a system of Measurement with Rule and Compass, and thereby learn to recognize the real Truth, seeing it before their eyes.

Michelangelo thought Dürer's reliance on geometry excessive, and is reported by Vasari (The Lives of the Artists, 1550) to have said "It is necessary to keep one's compass in one's eyes and not in the hand, for the hands execute, but the eye judges."

 

“I began from the background, with the architecture. Once the lines were marked out, I called all my figures, one by one, and they came obediently to take their places in the perspective.” Ingres, quoted in Charles Blanc, Ingres, sa vie et ses ouvrages (1870)

 

When you want to draw on a wall, first level the surface and then attach pieces of wood to the legs of a pair of metal compasses, to make them as long as you want, and tie a brush to one end so that you can mark with color the proportions of the figure and describe their halos. When you have marked the proportions of the figure, take some ochre and draw first with a watery solution. - Dionysius of Fourna, Painter's Manual (1730-34)
 
With larger paintings, I wondered how it was done, and realized you would only need a piece of string and chalk; you would just mark the circumference, then chalk up the string and snap it on the canvas, probably on the floor, to get a grid.

[Kate]

This is SO synchronistic words fail me. I just logged in to post this image and saw that Ryan had just posted the above and this is a forum topic that has largely been unvisited for months - at least by any of us who regularly post. What are the chances?
 

Anyway the above is fascinating and I was going to write to say I take it all back about deciding there was only a slim chance, due to the printing press procedure, that they were using sacred geometry on the cover and dedication of the sonnets: look at this.

It’s in a book I just purchased today. It should/must be credited to Wooden Books and the author Adam Tetlow.

Here is where you can purchase your own copy of Harmonic Geometry and others in their amazing series.

https://www.amazon.co.uk/s?k=wooden+books&crid=1HRISVPB10R4M&sprefix=wooden+books%2Caps%2C67&ref=nb_sb_ss_ts-doa-p_2_12

 

This method dates to the 1200s! 

Edited June 28, 2022 by Kate
Grammar

[Guest Ryan Murtha]

14 hours ago, Kate said:

This is SO synchronistic words fail me. I just logged in to post this image and saw that Ryan had just posted the above and this is a forum topic that has largely been unvisited for months - at least by any of us who regularly post. What are the chances?

This method dates to the 1200s! 

The Villard Folio came up in my research-

The 13th-century folio of Villard de Honnecourt, an artist connected with cathedral builders in France, includes the following recipe:

Retain that which I will tell you. Take leaves of red cabbage, and of avens - this is an herb which one calls 'bastard cannabis.' Take a herb which one calls tansy and hemp - this is the seeds of cannabis. Crush these four herbs so that there is nothing more of the one than of the other. Afterwards you take madder two times more than any one of the four herbs, then you crush it, then you put these five herbs in a pot. And you put white wine to infuse it, the best that you are able to have, being somewhat with care that the potions not be too thick, and that one is able to drink them

 

Villard Folio.pdf

[Kate]

Thank you. It's long so I'll read properly later, but I see it begins with mention of 33 parchment leaves!

[Kate]

I finally got around to read it. Thanks for sharing, it is very interesting but I was slightly disappointed by the lack of  drawings, there is just reference to all but 4 of them. I went on a search and found this. It has all 33:

Facsimile of the sketch-book of Wilars de Honecort, an architect of the thirteenth century https://archive.org/details/facsimileofsketc00vill/mode/2up

 

[Eric Roberts]

5 hours ago, RoyalCraftiness said:

Great topic. This is an area I have spent a great deal of time studying. Commenters often don't know what to call these reference lines. The lines that come out of a rectangular frame which relates to the corners and to the intersections of lines from them to define points (and their projection to the sides to give ratios) are what is called, boringly, armatures. An armature need not be just that. Armatures produce what is termed "dynamic symmetry"  of the sort you show. That was extremely desirable to produce works which contain multiple elements that are fixed upon points of high coincidence. The more coincidence there was in points, the more importance those points had to guide the planning. In fact, much of the game of Art in this period is to try and produce works emulating nature which display the underlying relationship to pleasing geometric symmetry. The use of circular armatures was common. There are pentagonal (star shaped) ones in many examples of Baroque art. The fledgling appreciation for Euclid's works in Europe also meant that basic geometric constructions started to appear as armatures in the composition of works. The "flower of life" design will get used as armature. It will keep on going into Golden spirals and anything which the creator will want to employ to guide his composition. It was a bit of a game played by some to try and detect what was guiding the composition of some paintings. Add to that the fact that one can place at a point of highest coincidence an element loaded with symbolism of its own. Because much of art was of the religious kind, it makes the use of geometry in it be referred to as "sacred geometry". There isn't anything particularly sacred about it. Much of it is arrived to by basic construction methods. It is the additional "theology of number" of the Pythagoreans, for example, that imparts meaning to art that is often exploited.

Here's an example of a study I made of a work by Rembrandt depicting St James, the brother of Jesus. The rectangular frame is divided in a 4x3 array of rectangles with obvious suggestion of 12. James was one of 12. The elements in the painting are arranged around a series of concentric circles (9 of them) evenly spaced which have a center which coincides with the bottom corner where the Bible is placed (the object of focus is the point of most coincidence). There's an esoteric meaning to the 9 levels. Part of that suggestion is an idea which relates to the mystery hidden deep within the vault under the 9 levels  (arches) in Enoch's prophetic story.  However, Enoch isn't a Biblical story. Those legends were scrubbed out of the Christian corpus at the council of Nicea. The content of the vault are said to be only attainable by adherence to the word of God. The artwork suggests as much. It is worth taking a minute and looking at how the paintings' scant elements are made to fit in the rectangular frame and be guided by the circle arcs. The hands, wrist, fingers, nose, etc. All find a place in the composition based on the guiding effects of the lines.

There's a lot of this in one of Bacon's works which I have studied profusely, Sylva Sylvarum. There are multiple armatures guiding the composition in that one. All seem to have a pertinent relationship to philosophical ideas which we current at the time.

Hi R.C. -  If we measure the distances between the concentric arcs on this slightly enlarged image, using the yellow vector and working from the inside outwards, there is quite a bit of variation, i.e. the arcs aren't equidistant: 22mm, 24mm, 26mm, 28mm, 24mm, 25mm, 25mm (approx. just using a ruler). The application of circular geometry to classical and renaissance paintings is very interesting, especially in this case where the arcs are centred on the Bible as you pointed out. Also the vertical and horizontal division of the panel into twelve rectangles is brilliant! But to be fair, perhaps the arcs should be redrawn more precisely? 🙂

[Eric Roberts]

On 7/2/2022 at 11:06 PM, Kate said:

I finally got around to read it. Thanks for sharing, it is very interesting but I was slightly disappointed by the lack of  drawings, there is just reference to all but 4 of them. I went on a search and found this. It has all 33:

Facsimile of the sketch-book of Wilars de Honecort, an architect of the thirteenth century https://archive.org/details/facsimileofsketc00vill/mode/2up

 

Hi Kate. What an interesting and charming find. Had no idea there was a master mason's "sketchbook" in existence. You are full of rich surprises. Thank you.

[RoyalCraftiness]

8 hours ago, Eric Roberts said:

Hi Kate. What an interesting and charming find. Had no idea there was a master mason's "sketchbook" in existence. You are full of rich surprises. Thank you.

The art of composition : a simple application of dynamic symmetry : Jacobs, Michel, 1877-1958- : Free Download, Borrow, and Streaming : Internet Archive

Is an excellent resource for anyone looking to deduce composition in a work suspected of containing it.

[Light-of-Truth]

15 hours ago, RoyalCraftiness said:

The art of composition : a simple application of dynamic symmetry : Jacobs, Michel, 1877-1958- : Free Download, Borrow, and Streaming : Internet Archive

Is an excellent resource for anyone looking to deduce composition in a work suspected of containing it.

This is a fascinating book. Some of the concepts I learned in Graphic Arts and other visual design classes, but not to this level. It can be applied to Elizabethan artists for certain.

[RoyalCraftiness]

On 4/5/2023 at 10:14 AM, Light-of-Truth said:

This is a fascinating book. Some of the concepts I learned in Graphic Arts and other visual design classes, but not to this level. It can be applied to Elizabethan artists for certain.

If you apply the dynamic symmetry principles to Bacon/Rawley's Sylva Sylvarum you will begin to understand how the image was put together. For example, the circles/arcs in that image are all nested in between diagonals. Locating the squares that at the basis of the framed rectangle containing the image yields important lines also.

The height of the practice of this was in the Baroque period from the early 1600s to the 1750s. It is one of the features of Western esotericism. It went so far as to suggest that all great art was based in these considerations. The art had much to do with the geometric considerations, because the Royal Craft also did (God as a geometric architect). That is to say that unless your work was steeped in this sort of consideration it wasn't really great art.  In time there were movements that sough to destroy this idea, but artists like Picasso, for example, still relied heavily on it. The dynamic symmetry of reoccurring squares is a relevant aspect of cubism.

Edited April 6 by RoyalCraftiness

[RoyalCraftiness]

On 4/5/2023 at 10:14 AM, Light-of-Truth said:

This is a fascinating book. Some of the concepts I learned in Graphic Arts and other visual design classes, but not to this level. It can be applied to Elizabethan artists for certain.

I located a precise study I did with Geogebra which shows a few things about Sylva Sylvarum's illustration composition. It's showing the main diagonals and armatures as dotted lines. The large rectangle ABDC contains a small base rectangle BKLA. Using its corners you can locate the squares ABNP and ABOQ. OQ is a segment on which the biblical text is placed. On NP there is A1 on the central divider which is the tip of the ray of light. TU is the water line.  From A on line AO one can project an arc which connects with point C, informing us the length of the chosen large rectangle was selected carefully. Point W on the main divider is located on the horizontal joining the armatures. It's the center for the circular stereographic projection in the image. BVA is an interesting triangle made from joining the base corners to the mid point above. Its sides are tangent to the circle centered at W. Point V is also a circle center for circle with tangents given by the main armatures. This actually just the beginning of it. The amount of careful placing of features in the illustration goes far beyond a simple consideration. There is a very complex circular armature configuration in the image which one can show. If you recall, I previously showed that the ancient Greek geometric demonstration for the building up from a point to a pentagon (the vase of life construction shown below) is used to inform the composition too. One can also say a lot about the placement of the columns. Safe to say the image was not thrown together by fortuitous elegance. It is not unlike the Droeshout portrait that way. Someone spent a lot of time planning these images. The reason is that one can extract a symbolic meaning from it which is very closely tied to a philosophy and a cosmology of the Universe.

The pentagon here is mapping onto the central circle. Point K on this image corresponds to the midway point on the base. 

 

Edited April 8 by RoyalCraftiness

[Light-of-Truth]

8 hours ago, RoyalCraftiness said:

The reason is that one can extract a symbolic meaning from it which is very closely ties to a philosophy and a cosmology of the Universe.

Good to know. 🙂

I hope to get a moment to look into Sylva Sylvarum's illustration composition. Maybe even on Easter Sunday if I am lucky.

I read a quick article in passing today that might be a cool curiosity for some.

"At Long Last, Mathematicians Have Found a Shape With a Pattern That Never Repeats"

It is actually a very basic pattern as far as the pieces; a hexagon cut in six equal parts, arranged to make the "Einstein" 13 sided shape. It never repeats, as opposed to our favorite repeating numbers. 🙂

 

 

[Eric Roberts]

36 minutes ago, Light-of-Truth said:

Good to know. 🙂

I hope to get a moment to look into Sylva Sylvarum's illustration composition. Maybe even on Easter Sunday if I am lucky.

I read a quick article in passing today that might be a cool curiosity for some.

"At Long Last, Mathematicians Have Found a Shape With a Pattern That Never Repeats"

It is actually a very basic pattern as far as the pieces; a hexagon cut in six equal parts, arranged to make the "Einstein" 13 sided shape. It never repeats, as opposed to our favorite repeating numbers. 🙂

 

 

Hi Light-of-Truth. Thanks for sharing this computer generated non-repeating tile pattern. However, it is a 4-colour pattern and relies on colour to avoid repetition. If restricted to black and white, it is repetitive. 

Although it has nothing to do with sacred geometry, the 13-sided irregular tessera is very versatile in the various ways it combines with itself. Thanks again. 🙂

[Light-of-Truth]

24 minutes ago, Eric Roberts said:

If restricted to black and white, it is repetitive. 

I'm curious what the articles mean by "repeating". You show that in small groups of shapes you get the same patterns, but the neighboring areas may or may not repeat from one to another.

[Eric Roberts]

5 hours ago, Light-of-Truth said:

I'm curious what the articles mean by "repeating". You show that in small groups of shapes you get the same patterns, but the neighboring areas may or may not repeat from one to another.

https://topdrawer.aamt.edu.au/Patterns/Big-ideas/Repeating-patterns/Two-dimensional-repeating-patterns

You're right, of course. There is no "unit of repeat" in the pattern you posted. So it is nonrepetitive according to the definition of a repeating 2-D pattern.

Edited April 8 by Eric Roberts

[Eric Roberts]

15 hours ago, RoyalCraftiness said:

I located a precise study I did with Geogebra which shows a few things about Sylva Sylvarum's illustration composition. It's showing the main diagonals and armatures as dotted lines. The large rectangle ABDC contains a small base rectangle BKLA. Using its corners you can locate the squares ABNP and ABOQ. OQ is a segment on which the biblical text is placed. On NP there is A1 on the central divider which is the tip of the ray of light. TU is the water line.  From A on line AO one can project an arc which connects with point C, informing us the length of the chosen large rectangle was selected carefully. Point W on the main divider is located on the horizontal joining the armatures. It's the center for the circular stereographic projection in the image. BVA is an interesting triangle made from joining the base corners to the mid point above. Its sides are tangent to the circle centered at W. Point V is also a circle center for circle with tangents given by the main armatures. This actually just the beginning of it. The amount of careful placing of features in the illustration goes far beyond a simple consideration. There is a very complex circular armature configuration in the image which one can show. If you recall, I previously showed that the ancient Greek geometric demonstration for the building up from a point to a pentagon (the vase of life construction shown below) is used to inform the composition too. One can also say a lot about the placement of the columns. Sage to say the image was not thrown together by fortuitous elegance. It is nor unlike the Droeshout portrait that way. Someone spend a lot of time planning these images. The reason is that one can extract a symbolic meaning from it which is very closely ties to a philosophy and a cosmology of the Universe.

The pentagon here is mapping onto the central circle. Point K on this image corresponds to the midway point on the base. 

 

Hi CJ. It would be interesting to see your geometry scaled and fitted to the engraving...

[RoyalCraftiness]

10 hours ago, Eric Roberts said:

Hi Light-of-Truth. Thanks for sharing this computer generated non-repeating tile pattern. However, it is a 4-colour pattern and relies on colour to avoid repetition. If restricted to black and white, it is repetitive. 

Although it has nothing to do with sacred geometry, the 13-sided irregular tessera is very versatile in the various ways it combines with itself. Thanks again. 🙂

Nothing to do? Respectfully, that's woefully wrong. Sacred Geometry is simply geometry, and tessellation certainly involves geometry. It's a geometry of symmetry groups. The "sacred geometry" of Islamic art is full of tessellations. The last chapter of a very well known work on sacred geometry I am looking at today concerns tessellation and symmetry groups. Shall we contact the author and demand they recant? 

 

Edited April 8 by RoyalCraftiness

[RoyalCraftiness]

10 minutes ago, Eric Roberts said:

Hi CJ. It would be interesting to see your geometry scaled and fitted to the engraving...

Don't be too disappointed there Eric. It is interesting, yes. Give it a shot. I have such overlays. You likely won't be disappointed in your efforts. I'm satisfied with mine, but it takes some consideration to give it your best shot. You' ll face the same limitations I faced. The rectangle in the SS image used is deformed ever so slightly. You' ll have to modify the image using a perspective tool functionality in editing software to account for the slightly non-parallel sides. Ultimately, we are dealing with images on mediums that are prone to small degrees of movement, but that does not mean we are left with nothing today.  You' ll also have to settle on a degree of certitude which accounts for line widths for your dimensions. I've used pixel counts to generate the rectangle in Geogebra based on average line widths. Ultimately, this sort of planning with dynamic symmetry is only just a guide for an artist anyway. There is no requirement that it ought to satisfy the mathematical rigorousness of any rigid constructs we impose with our tools. That being said, it is a very pleasing result.

The features I was most interest in locating in relation to the frame at the time were the circular stereoscopic Earth projection in the middle and its corresponding circle center. The circle is itself slightly deformed in the image shown. It's center is offshore, just East of Brazil on the projection map. This is the suggestion of the eclipse location of 1651 again.  You know, the eclipse George Stirk ended up chasing as a result of studying the alchemical literature.  I suspect Bacon was just as interested in it. It's part of the empirical aspect of what he has played with in his Geo-metric consideration of the globe.

I know you like these types of studies. Why don't you look into it? It would be more productive to compare findings than to have me show you what I have produced. The absolute worst thing is to be contaminated by the bias of what someone else thinks he is seeing. I can guarantee you that you will see relationships I don't. I've not dived so far into this that I can account for all the typical armatures one would consider. I've gone into this critically, and it is worth knowing what else others might think we ought to also worry about in trying to work things back to a planning.

It's unclear exactly why the main frame would be chosen to have the dimensions it does, but one can assume that there is a desire to have some angles come out of the mix. The large isosceles triangle pinching the center circle here is 71.31 degrees at the base. It may have been intended for it to suggest 72 degrees and for it to relate to an internal pentagonal geometry. The angle of the wedge which is given by the dropped arc is the compliment of the angle of the arc suggested by the Droeshout portrait when one uses the tips of the points of the collar and the arc they form in that image. That is to say that the angle BAO here is suggesting that same angle (a curious similarity in the construction of the images that doesn't necessarily have a meaning). I'm talking of the pairing of 42 and 48 here. 48 is an interesting number as far as its references to knowledge in the Jewish esoteric tradition. These are things we can consider and wonder about subjectively, but the frame itself is subject to a more empirical study.

 

[Kate]

On 4/4/2023 at 1:44 PM, Eric Roberts said:

Hi Kate. What an interesting and charming find. Had no idea there was a master mason's "sketchbook" in existence. You are full of rich surprises. Thank you.

A little off topic but I noted that in the Coronation invitation, Charles has had this 'green man' incorporated. He undoubtedly has read Honecort's book. I've superimposed the Green man on a page from the book. The full coronation invitation can be seen at https://www.royal.uk/coronation-invitation

[Light-of-Truth]

9 hours ago, Kate said:

A little off topic but I noted that in the Coronation invitation, Charles has had this 'green man' incorporated. He undoubtedly has read Honecort's book. I've superimposed the Green man on a page from the book. The full coronation invitation can be seen at https://www.royal.uk/coronation-invitation

Tudor Rose?

May 6? Here is a Line or two from May 6 in the Sonnets:

http://www.light-of-truth.com/pyramid-GMT.php#Day126

The Rose lookes faire, but fairer we it deeme
For that sweet odor,which doth in it liue:

I have always enjoyed gazing at this page with all its secrets busting out like flowers in early May:

 

 

 

 

[RoyalCraftiness]

14 hours ago, Light-of-Truth said:

Tudor Rose?

May 6? Here is a Line or two from May 6 in the Sonnets:

http://www.light-of-truth.com/pyramid-GMT.php#Day126

The Rose lookes faire, but fairer we it deeme
For that sweet odor,which doth in it liue:

I have always enjoyed gazing at this page with all its secrets busting out like flowers in early May:

 

 

 

 

There's a theme that can extracted from Sonnets 27, 54, 81 and 108 about love, the symbolof love (the rose), the dying of the beloved and what is lasting. There is also a sort of building up to a conclusion about what remains after death for eternity. When the Rose dies there is still a sweetness that is not about its show. When the poet dies there is still a memory of him, but not so of his beloved. His words of love for his beloved are always new. They are like an eternal prayer for the living. We can forget about the principal actors and always find something in the words of love of the poet which rings true to everyone. It is a roundabout way to say that we will always long for reunions after death, and that is the promise of the Rose of the bloody red cross.

 

[Light-of-Truth]

5 hours ago, RoyalCraftiness said:

There's a theme that can extracted from Sonnets 27, 54, 81 and 108 about love, the symbolof love (the rose), the dying of the beloved and what is lasting. There is also a sort of building up to a conclusion about what remains after death for eternity. When the Rose dies there is still a sweetness that is not about its show. When the poet dies there is still a memory of him, but not so of his beloved. His words of love for his beloved are always new. They are like an eternal prayer for the living. We can forget about the principal actors and always find something in the words of love of the poet which rings true to everyone. It is a roundabout way to say that we will always long for reunions after death, and that is the promise of the Rose of the bloody red cross.

 

Sonnet 1 begins a theme about Rose which includes Love as well, right?

FRom fairest creatures we desire increase,
That thereby beauties Rose might neuer die,
But as the riper should by time decease,
His tender heire might beare his memory:

"His tender heire" is Bacon's Sonnets collection, at least in my mind. 😉