Nothing accidental: Georges Seurat

You’ll often find this painting in use as an example of the golden section in art, although it’s by far the most ideal picture for the job. It isn’t ideal because the frame itself is not in golden section proportions. The key number for the shape of this painting is 1.487 as this is the outcome when you divide the length by the width. (A4/DIN paper is 1.414, and the golden section is 1.618). Still, it’s a beautiful painting so I can understand why makers of beautiful books would use it.

There’s little difference between .618 and .487 and the first two images demonstrate this respectively. They both have their similarities to the image and it’s difficult to tell which Seurat would have used, if either. I have wondered, though, if it is better, where possible, to use a ratio for proportions which is the same as the proportions of the shape you are working on. For instance, if you’re using an A4 page, could three typefaces which get larger by 1.414 be more pleasing to the eye than if it were by 1.618? In other words, is stringent consistency in proportion more worthwhile?

What’s clear from the images is the definite placement of the water level in the distance, and the heads/figures are usually set against some guiding line. The fifth image is the most interesting to me; the circles are in proportion with the frame and have shocking similarities to the content. The outermost circle follows the arch of the left figure’s back, trims off the top of the tree and passes across the front of the right figure’s face. The next circle in carves a portion out of the reclining man, chops off the left figure’s legs and leans on a distant figure’s head. On the other side, it also bends around the paddler’s knee and past the edge of the clothes on the bank.

How/why?? There are always two answers and it could be either every time. 1) The artist knows all about proportion and has done his/her ‘homework’. There is no such thing as coincidence in their work and the creativity lies in ‘what’ rather than ‘how’. Perhaps Seurat’s creativity was his scene and his skillful pointillism. 2) We risk giving the artist a little too much credit in their mathematical understanding and find that the whole thing was an accident. The composition was done by eye and, because s/he has a good eye for proportion, the artist has been able to conjure something so pleasing without maths. As my title will suggest, I usually hope these artists have actually devised some big plan for their work – an invisible secret behind it all. Who knows. Of course, there are always those times when paintings simply suck and no compositional flair is anywhere to be seen.

Five-point star alternative of first method

After a little review of my method I decided to use the finished star and see how it might relate to the rectangle in other ways. The images below show the most simple explanation I got.

I started by mapping out the simple golden rectangle with itself reduced three times in golden proportion. You have to do this all four ways (as in the second image) because the original shape has four edges. This is was is slightly misleading when you read about the golden section – the first image here is usually what you’ll find but the second image is the proper division of the rectangle.

The third image shows our key points. Those darkest rectangles indicate the edges of the pentagram (its width). So, we know already how long one line in the pentagram is: the distance from the edge of one dark rectangle to the edge of the other. With that, we know the length of every line in the pentagram because they must all be the same.

All we need, then, is a direction for the line to go from our red mark on the left in the third image. The answer is through the cross-over point of the two diagonals of the darkest rectangles. From there on in it’s just a case of using the same line length to get the remaining edges. If you want to be really geeky you can divide your first lines of the star by the golden ratio and you’ll have an intersection point for the other lines.

Incidentally, I did say in the other post that the size (size, not proportion) of the star did not seem to relate to the rectangle but, in fact, it does. If we say the length of the rectangle is x and the golden section is φ then the length of one line in the pentagram is (x/φ² + x/φ⁴). In other words, it’s the length of two of the smaller rectangles added together: so it does relate!…just really subtly…..

Five-point golden star: my method

This construction came from when I recorded how to get a golden rectangle from a horizontal line without extending the line (as shown in the post called Two Constructions). If you search for a golden rectangle construction method you’ll likely be told to create a square and extend it to a rectangle so I wanted to know how to do it in reverse as it were.

Anyway, the five-point star (pentagram) is the absolute necessity behind the use of the golden section throughout most of its history in the art world. Gothic architects devised a master diagram based largely on the five-point star, pentagon and decagon (the latter two are made by joining the five points/five points and points between).

My earlier pentagon construction is most often found in books on the subject but this one below is of my own making – I haven’t seen it elsewhere so far.

CONSTRUCTION: The first image shows the drawing I made to begin with. I’d learned my lesson from before with the circles so I checked this digitally straight away (and it works). So, as in the second image, you draw a golden rectangle any way you like and divide it in two. Then use the length of a half to extend lines from all edges. The end points, as in the third image, make the centre points of circles whose radii (weirdest plural form ever) will each touch two corners of the rectangle. Do this for every point and you get a pretty picture, as in the fourth image. I’ve marked in red the key points here which will inform the drawing of the pentagon (where lines overlap). The last image includes our pentagon. It’s relatively simple to draw when you know the following: each line in the star must be the same length; the first two lines should start at the top red mark and one should hit the the mark on the far left and the other, the mark on the far right; the cross-bar sits directly over the middle line of the guiding rectangle.

Et voila. This construction is a little different in that the rectangle you use to draw the star is not actually related by size. In more common constructions of the star, the length of the lines is equal to the length of the rectangle (they’re just pointed towards the centre so they look shorter). The star here is made of lines that, even when multiplied by 1.618 do not become equal to any measurement of the rectangle.

Golden circles construction

There are, of course, constructions already established for many shapes using the golden ratio (or the number 1.618) but it’s important, I think, for designers to draw these for themselves. I’ve actually been able to design my own constructions of various shapes and definitely understand a lot more about proportion in doing so.

This construction is of proportionally equal circles (reducing them in size by 1.618). The challenge is to do it all without measuring tools or calculators. Only a ruler’s edge and compass should be used; this way, you focus on the shapes and lines themselves rather than numbers.

I actually thought I‘d found a successful method in the drawing below but when I tried it digitally it was actually incorrect. BUT, in taking screenshots just now, I’ve figured it out!

The problem with drawing things out by hand is that your scale will be too small to check if a tiny miss-match of points is due to your compass or if it’s actually an error. Only on a digital version will you be able to be pin-point accurate and if your construction works it would be pin-point accurate on every point.

CONSTRUCTION: I started with a circle and protruding square. Then I extended lines from the centre of the circle to the corner and first quarter of the square. I then thought the two red dots (where the lines hit the circumference of the circle) would be the radius of a smaller circle (proportional to the larger). I was wrong though and, as the fourth image shows, the green circle (which would have been the correct outcome) is slightly smaller. The difference is miniscule but this is only because it’s a small scale. So, larger scale=big difference. As I said though, I’ve just figured out the correct radius to use, as shown in the last image. So one point is on the circumference and quarter into the square, and the other is defined solely by the square.

Often these constructions have relatively simple outcomes but only in drawing your way through them can you really understand it all.

Golden pentagon construction

I’m a little obsessed with proportions right now, as can probably be seen by my recent posts. I’m trying to tie down everything I know about type and layout by going back to the beginning and getting my head around what is basically the fun, or at least less dull, side of maths (geometry). I’m beginning to regret having done French at a-level…. Should have done maths! I made my own drawing of the pentagon/decagon construction but thought it could be done in another way and, surely, with more ease. I was right! So, in a later post, my own method will be shown.

Grid Systems/Raster systeme by Müller-Brockmann

I’m currently working through the book below, which I bought recently after it finally became in-stock on Amazon, and have to say it’s one of the best I’ve ever read on layout and typesetting. Readers may already be aware of most of what’s in it but it’s really handy to get something that keeps everything in one place. It’s a beautiful book too. If anyone is interested, it‘s on Amazon but you’ll have to be quick (it’s quite highly sought after), and don’t worry that it says it’s German – it has an English translation running beside the German right through. Fantastisch!

Also: I would steer clear of the ironically named Layout Book by Ambrose and Harris if you’re after something that actually teaches anything in detail about layout. It’s worth getting to adorn your bookcase but only for its varied examples of design work and its basic intro to all things typographic (like the golden section, typefaces and book page rhythms).

Two Constructions

Nothing accidental: Diego Velazquez

I chose to look at Las Meninas for this second post on compositions – again, I’ve analyzed the work with equally-proportioned shapes and have sought some kind of overall guide to the composition without assuming that the artist ever even intended to do so. I haven’t read the background of this work in detail so I’m unaware of how much time Velazquez spent considering the composition. If this was a sitting involving children (who are often restless and playful) I doubt the composition could be overly considered. Nonetheless, the point of this is merely to speculate on the layout of his work.

The first image is my first simple division of the frame (which is almost but not quite a square). Already, the diagonals in the bottom half seem to inform the angle in which the two girls are leaning. The dog is well framed by a triangle, and the half-way vertical and horizontal lines are undoubtedly used as a main guide; the horizontal cuts just above the tallest figure and the vertical, along the edge of the door in the background.

The second features a succession of proportionally-equal circles receding to the centre of the frame: that is, they are all reduced by the ratio of the frame length by frame width. It’s interesting that the skirt of the girl in the centre closely follows the edge of the first circle but apart from that nothing much is obvious.

The fourth image is basically the third with most of the edges of the shapes extended to the edge of the entire frame. These shapes are drawn in the ratio of the full frame and are reduced to their smaller size by the same ratio. Now we find lines marking the average height of the little girls, the start of the ceiling behind them, and the dog even looks disgruntled by the first guide in from the right.

The sixth image comes from the fifth – an extension of the grid lines to the corners of dupicates of the original frame sitting to each of the four sides. Here we find a line clearly resting on the heads of the three girls to the right – whose heights gradually lessen. The other lines, however, give away very little.

The final image is a collection of those marks which do inform the position of various points in the composition. It is most heavily based, therefore, on a grid that recedes to the centre. The upper corner of the room, interestingly, is hit by two diagonals and the dog sits nicely from the right edge of the frame. Closer to the centre, the panels of the picture frame and door frames can be likened to the difference between the two shapes over each of them (which are proportionally equal to the full frame).

Overall, in contrast to my hectic last image, the composition is actually rather straightforward. The frame is split into four by its mid-points. The four background figures are composed with the mid horizontal line and the five kids, with one clever diagonal and a couple of smaller rectangles receding to the centre. After all, as long as the main components are pleasingly positioned for the eye, other areas can go without the same treatment.

James Horner James Horner James Horner

I just saw The Boy in the Striped Pyjamas and, while fighting back the waterworks, became a little disappointed with the soundtrack. Braveheart and Enemy at the Gates both feature great soundtracks and yet, if you listen out for it, they (along with The Boy in the Striped Pyjamas) include the same riff which, in Enemy at the Gates for instance, is played each time there’s a dramatic turn of events (like when someone gets papped by a rifle). Come on Horner, mix it up a little!

Nothing accidental: François Millet

This is the start of a little series I’m writing about the composition of paintings; I’ve read a lot about the golden section and proportional geometry in general and have wondered where the balance lies. Is a well-composed painting the result of an artist with a great eye and natural flair? Or is it the result of a mathmetician with a brush in their hand? Maybe we need both characteristics as, after all, both composition and mark-making are scrutinized in the end.

I’m not sure of the exact wording but Jan Tschichold (at least, I think it was him) said that a design is only well composed when you can take any item away and balance remains. I find this true in painting but on a slightly different level. If you divide the frame into smaller proportionally-equal panels, each one should be pleasingly composed in itself. That’s not to say a panel can’t be empty – that would be the equivalent to ‘1’ if art were maths.

I saw this Millet painting reduced to mere restaurant decoration one night and, although I thought the content was a little glum, I knew the composition was ideal. So, in the images below, I’ve come to understand how the artist composed it – if, indeed, he set out to be so clinical in the first place! Who knows? Either way, I find it amazing that the human eye can see equal proportions in shapes so readily.

I found straight away that the frame is pretty much a root 2 rectangle – which is the nerdy term for DIN paper proportions (A4/A3/A2) i.e. a rectangle that can be split into two similar rectangles of equal proportion (fold an A4 in half and you get a smaller rectangle of equal proportion). Incidentally, a root 3 rectangle can be divided into 3 smaller similar rectangles, as a root 4 can be divided into…you guessed it, 4. The golden section, I’ll explain later when I use it to analyze another image.

Because this is a root 2 rectangle, the number 1.405 (which has been rounded up) is important as it determines the proportions. 295mm, for instance, is the length of an A4 page. 295/210 (length/width) is 1.4047… so I can use this number to further smaller rectangles with the same proportion. 210/1.405, for example, gives 149mm so I make a rectangle 210x149. This is what I’ve done in the images below to create the white guides and, low and behold, all sorts of coincidences turn up.

The first rectangle in on the first image shows a clear bounding box for the whole of the three women. The second shows some similarities with the angles of the arms and torsos and the dotted lines, which are made by the overlapping diagonals, also  serve to frame the figures. The third and fourth images clearly show why the horizon is at such a comfortable point in the frame and again squares off the figures. You could crop the image with any one of these guides and I’m certain there would still be a balanced composition. Finally, the last two images show what I think Millet might have planned. The panels are proportional to one another and the page, and clearly frame each new vertical slither of a figure or landscape from left to right.

Polish Film Posters

I came across the world of Polish film posters when I was researching Piotr Dumala and his jaw-droppingly atmospheric animations for a bit of work during my Foundation year. There are, of course, thousands of Polish film posters but there seem to be a certain bunch from the 80s that achieve the strongest visual form. I’m referring to those that combined a good concept with a great drawing and a limited colour palette. I suppose they are, in some ways, incredibly ugly but it’s their shamelessness and consistency in that respect that must make them lovable at the same time. The first one here is definitely my favourite of all. In my mind, Starowieyski was to Polish posters what Klimt was to the Secession…indispensable

Dirk Rudolph

I’ve known of this designer for a few years now and I still have never heard any mention of him in design literature. Not sure why that is but I reckon he deserves a bit more of an audience. His image-making skills are second to none but he even has time to do the odd bit of clean typography, which is probably why I like him. His book, Spark, is going cheap on Amazon (too cheap for my liking! I spent £30 on it) if you fancy seeing more of his work – it’s purely images of his work. Just noticed my review of it is still on there. I’m starting to think I’m the only one who ever bought it…

Moonraker

Sort of stumbled into this while working on something else. Happy accident, maybe. Could have made a good DVD title for the film with this concept.

Pocket watch

Here’s the pocket watch I got for Christmas. I love it. It’s shiny, and that’s all that matters.

The other day, however, I came across a watch as I was looking to see what ‘niello’ was and I saw a really nice art deco one but it’s sold! Noooooo! Niello, incidentally, is a black compound of metals that would get pressed into ready-made grooves on metal objects (usually swords or armour) and it’s since made its way into other objects like that watch…which is sold…bah

I wanted to see how my camera would fare with a little macro-setting test. Not bad for a completely digital camera. I love shooting in macro – there’s so much to explore all around us, only on a tiny scale. Just look at Willard Wigan: he has worked on sculptures that you could inhale if you got too close! I like the end of Men in Black where the universe is portrayed as a marble being tossed about by some massive alien creatures. Makes you wonder…

Notes on Renaissance calligraphy

Since Greek antiquity the distinction between uncial (all caps) and cursive (joined minuscules) hands was that the former was used for literary works and the latter, for correspondence. The surviving Roman minuscule cursive hand came to be known as Carolingian minuscule. The Renaissance humanists revived this form to replace Gothic medieval calligraphy.

The ‘roman’ typeface, then, came from a combination of the Carolingian minuscule and Roman majuscules, and was first seen in 1465: German printers in Italy, Arnold Pannartz and Konrad Sweyheym, published an edition of Cicero’s De Oratore using a roman typeface.

From 1495 Francesco Griffo worked with the main printer of Venice, Aldus Manutius, and developed cursive typefaces for him including Bembo. He is also recorded as the inventor of the italic form.

In the 16th century Francis I brought Italian calligraphers to Fontainbleau to assimilate the common Italian form of correspondence, cancelleresca corsiva, into the Gothic French hand, cursive française, to create ‘ronde’. ‘Ronde’ had three forms: financière (upright), bǎtarde (inclined) and coulée (script). This was the French national hand for centuries later.

MESRINE

The two-part film follows Jacques Mesrine from his early 20s right up to his death after a long life of robbery, murder, and numerous sentences in prison from which he usually escaped. I heard that none of his alleged murders have actually been proven even to this day.

I found the film a little segmented: his friends and girlfriends seem to all appear in groups rather than by coming and going. For instance, he has a wife and his two French gangster buddies at first, then a French-Canadian pal and a bonnie-like (from Bonnie and Clyde) girlfriend, and then a gold-digging girlfriend and his mate the prison-escape artist. The daughter from his marriage appears towards the end when she’s grown up but I didn’t think she was used enough in the second film. The contrast between the characters of Mesrine and his father was really interesting and I think they could have balanced the second film out a little more by exploring the relationship between him and his daughter further. Blow is a film that looks into the main character’s gangster lifestyle and family relationships in equal proportions.

I thought Mesrine was a little like how Johnny Depp is said to have described Bush’s America: a big dumb dog. He seemed to have learned how to rob banks and then never looked back. For instance, the scene where he discusses his interest in going after ‘the system’ and attacking the max-security prisons; his ex-Algerian-freedom-fighter partner points out that he has more or less funded the MSAs by spending the money he steals in the shops.

Still, the variety in characters and actors is fantastic and I was really glad they didn’t try to make Mesrine some sort of hero; instead, they relied on his lovable humour and reckless unpredictability to entertain the audience right to the end. Well worth getting.

Moiré video

I found a really cool video recently that shows how moiré can be used as a device for animation too. http://killsometime.com/videos/3851

Study Playlist

This is a playlist I set up to listen to while studying/working. Lots of good stuff in here including moody soundtrack titles like Perfume and Hannibal, the ever-calming Chopin nocturnes and lots of hand-picked tracks too. I put some favourites in bold.

- Satie: Gnossiennes - 1. Lent
- Handel: Harpsichord Suite In D Minor, HWV 437 - Sarabande With Variations
- Spiegel im Spiegel. Angela Yoffe & Vadim Gluzman
- "O giusto cielo!" from Lucia di Lammermoor, Act 2. Anna Netrebko, Claudio Abbado, Coro Sinfonico di Milano Giuseppe Verdi, Mahler Chamber Orchestra & Romano Gandolfi. Sempre libera.
- Symphony No. 2 in C Minor, Op. 17 "Little Russian": III. Scherzo. Berliner Philharmoniker & Herbert Von Karajan. Tchaikovsky: Symphonies Nos. 1-3
- Chopin: Nocturne #1 In F Minor, Op. 55. Claudio Arrau
- Chopin: Nocturne #2 In E, Op. 62. Claudio Arrau
- Chopin: Nocturne In C Minor, Op. Posth. Claudio Arrau
- Chopin: Nocturne #2 In E Flat, Op. 9/2. Claudio Arrau
- Chopin: Nocturne #7 In C Sharp Minor, Op. 27/1. Claudio Arrau
- Chopin: Nocturne #10 In A Flat, Op. 32/2. Claudio Arrau
- Dante Symphony, S. 109: Magnificat. Daniel Barenboim. Liszt: Dante Symphony, Dante Sonata
- Into the Forest. Danny Elfman, Corpse Bride.
- Edward Scissorhands: Main Title - Ice Dance. Danny Elfman , Edward Scissorhands.
- Die unsichtbare Front. Gabriel Yared & Stéphane Moucha, The Lives of Others (Original Motion Picture Soundtrack)
- Die Sonate vom guten Menschen. Gabriel Yared & Stéphane Moucha, The Lives of Others.
- IM "Martha". Gabriel Yared & Stéphane Moucha, The Lives of Others.
- Symphony Of Sorrowful Songs, Symphony No.3. Gorecki.
- Dear Clarice. Hans Zimmer, Hannibal (Original Motion Picture Soundtrack).
- Avarice. Hans Zimmer, Hannibal.
- Virtue. Hans Zimmer, Hannibal.
- The Burning Heart. Hans Zimmer, Hannibal.
- To Every Captive Soul. Hans Zimmer, Hannibal.
- Eastern Promises. Howard Shore, Eastern Promises (Original Motion Picture Soundtrack).
- Tatiana. Howard Shore, Eastern Promises.
- London Streets. Howard Shore, Eastern Promises.
- Sometimes Birth and Death Go Together. Howard Shore, Eastern Promises.
- Trafalgar Hospital. Howard Shore, Eastern Promises.
- Slavery and Suffering. Howard Shore, Eastern Promises.
- Anna Khitrova. Howard Shore, Eastern Promises.
- Eagle and Star. Howard Shore, Eastern Promises.
- Nine Elms. Howard Shore, Eastern Promises.
- What Are You Asking Me? James Newton Howard, The Village (Soundtrack from the Motion Picture).
- The Bad Color. James Newton Howard, The Village.
- Will You Help Me? James Newton Howard, The Village.
- The Shed Not to Be Used. James Newton Howard, The Village.
- Goldberg Variations, BWV 988: XXII. Aria. Jenö Jandó, Bach: Goldberg Variations, BWV.
- Fauré: Requiem, Op. 48 - In Paradisum . Jeremy Summerly: Oxford Camerata
- Vide cor meum - Rhys Meirion Vocal (Rhys Meirion Vocal), Katherine Jenkins.
- Satie: 3 Gymnopédies - Lent Et Douloureux. Klara Kormendi.
- Splendeurs Nocturnes. Les Chœurs De L'armée Rouge. (Red Army Choir).
- Sailing to Byzantium. Lisa Gerrard & Patrick Cassidy, Immortal Memory.
- Abwoon (Our Father) . Lisa Gerrard & Patrick Cassidy, Immortal Memory.
- Masquerade: Waltz. London Symphony Orchestra & Yuri Ahronovitch.
- Iconography. Max Richter, The Blue Notebooks.
- Vladimir's Blues. Max Richter, The Blue Notebooks.
- What Have They Done? Max Richter, Waltz With Bashir (Soundtrack).
- Lullaby from the Westcoast Sleepers. Max Richter, 24 Postcards in Full Colour.
- Found Song for P. Max Richter, 24 Postcards in Full Colour.
- The Artifact and Living. Michael Andrews, Donnie Darko (Soundtrack from the Motion Picture).
- Puccini: Madama Butterfly - Act 2: Humming Chorus. Miriam Gauci, Etc.; Alexander Rahbari: Slovak Radio Symphony Orchestra, Slovak Philharmonic Chorus.
- Debussy: Suite Bergamasque, L 75 - 3. Clair De Lune. Moura Lympany.
- Main Titles. Pete Anthony, Red Dragon.
- Threats. Pete Anthony, Red Dragon.
- There, Far Away, Beyond the River. Red Army Band; Red Army Choir.
Moscow Nights.
- The Girl With the Plums. Sir Simon Rattle/Berliner Philharmoniker, Perfume - the Story of a Murderer (Original Motion Picture Soundtrack).
- Grenouille's Childhood. Sir Simon Rattle/Berliner Philharmoniker, Perfume.
- The 13th Essence. Sir Simon Rattle/Berliner Philharmoniker, Perfume.
- Moorish Scents. Sir Simon Rattle/Berliner Philharmoniker, Perfume.
- The Method Works! Sir Simon Rattle/Berliner Philharmoniker, Perfume.
- Laura's Murder. Sir Simon Rattle/Berliner Philharmoniker, Perfume.
- Awaiting Execution. Sir Simon Rattle/Berliner Philharmoniker, Perfume.
- The Crowd Embrace. Sir Simon Rattle/Berliner Philharmoniker, Perfume.
- Epilogue (Leaving Grasse). Sir Simon Rattle/Berliner Philharmoniker, Perfume.
- Wake. Thomas Newman, Road to Perdition (Music from the Motion Picture).
- Just the Feller. Thomas Newman, Road to Perdition.
- Road to Chicago. Thomas Newman, Road to Perdition.
- A Blind Eye. Thomas Newman, Road to Perdition.

Moiré Kaleidoscope

Well my computer managed to get through it without dying – the Moiré looks pretty good here. I like the really subtle change in detail in the first one: the orange and green triangles at the circle centres. These would have to be used in small doses being as detailed as they are.