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Script Analysis - Angles of the Letters

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18 January 2007

Script Analysis - Angles of the Letters

From my list of script analysis questions

"Measuring the angles of the strokes

Extend the angles of the entry and exit strokes of each of the letters, most importantly the O, to the nearest part of the baseline or waistline. You can mark the extensions of the strokes on tracing paper placed over the ductus rather than marking up the ductus itself. 3

Measure the angle of each line using a protractor or Katarina Helene's Analysing Guide which has the advantage of the lines coming right up to the edge


Look for any steepened or flattened angles, and any changes of angle designed to counteract inconsistencies of weight in the letter’s construction. 3

Make notes of any of these cases on the ductus


What is the dominant (most common) angle? ?3,4
This is pen angle of the script. Make a note on the ductus

Well, everyone knows that for Gothic Textura Quadrata. It's 45 degrees. What was a lot more interesting was where the strokes weren't at 45 degrees. Some were sneakily flattened. There's all sorts of stuff going on.

What are any variations of the pen angle, and in which letters? (for example a Z often has strokes with the pen at an angle of zero or 10 degrees)?2
Make a note of any of these cases on the ductus, including a note of the different angle


It wasn't easy to measure the angles of the letters. They varied a lot for the same letter.

The problem is illustrated by this piece showing varying angles from some Bedford Psalter script, from The Historical Source Book for Scribes (page 91)

I measured several examples of each letter, and used my general knowledge of the gothic textura quadrata script, and some common sense, to arrive at some answers.

The following extracts were relevant to my thinking :

from Harris, The Art of Calligraphy, page 52


Drogin, Medieval Calligraphy - It's History and Technique, page 141.

The relevant part starts half way down the first column, starting "It aided the design .." and continues to the end of the first paragraph of the second column.

Letters with only 90 degree angles

  • I,
  • version 1 of J (which looks like an I),
  • L

Letters with angles of 45 degrees only

The letters containing only 45 degree angles (other than vertical strokes) are :

I found it surprising that more letters didn't contain only 45 degree angles, but between the flattened angle of joining strokes that Harris mentions, and the flattened angles for letters that don't finish with a diamond, all the others have a mixture of angles.

I found, in fact, it was only when a stroke emitted from a diamond that the angle was at 45 degrees.

I'll talk about the note against some letters saying "slightly larger diamonds" another time.

Letters with flattened angles that don't finish in a diamond

According to Drogin, the angle of the bottom diagonal of the letters B, C, D, E, F, O, R, T, V, W, should be flattened (as explained in the excerpt above) with the possible except of C and E where the problem can be gotten around by shortening the upper stroke.

I found this to be partly true with the Bedford Psalter letters. I believe that the need to flatten the bottom diagonal is obviated in some cases by the use of the hooked serif. That serif fills the empty space - in the same way Drogin mentions a trailing line extending from the final stroke of the R in some G.T.Q. ductii.

Drogin doesn't say which of the bottom strokes should be flattened, (left or right or both) and I've got a mixture of left or right stroke flattening.

The C and E in this case didn't have flattened bottom strokes, nor shorter top strokes - they do have the serifs, instead.

The letters that I did find to have flattened bottom diagonals were :

The angles marked on the Ds are pretty hard to read. The ascender of version 2 (the first one, version d1 is in the pure 45 degree angle section) is at 30 degrees, the bottom left stroke at 20 degrees and the right bottom stroke at 45 degrees.

On version 3, the ascender is at 37 degrees (midway between version 1 and version 3).
The angle on the left bottom stroke has been cut off. It should be marked as "30 or 35 degrees" (I just couldn't decide which, after measuring lots of them. I'll work it out when I start using a pen to write them). The right bottom stroke is at 45 degrees.

Ooops, the angle marked for the left hand stroke of the V is cut off as well (so much for my Photoshop editing). It's 45 degrees. (And the pasting of pictures in Blogger is a bit of a nightmare)

The drawing of the slightly curved stroke that at the left of the bottom of the W is pretty bad.

That leaves C, version 1 of D, E, F, R and T out of Drogin's list that don't have flattened bottom strokes. But they all have serifs to make up for that empty space.

Flattened angles of connecting strokes

Harris talks about flattened strokes used as connecting strokes. This is relevant here for H, G, and Q

Other Flattened Strokes

Letters that

  • do finish in a diamond, but
  • contain flattened strokes as well,
  • which aren't connecting strokes
- are shown below.

- this isn't a very well drawn Half R

- Long S

- this is the ampersand

Letters that have angles greater than 45 degrees

Miscellaneous Letters

P has a 45 degree angle as a connecting stroke, and the zero degree angled stroke at the base

There is the same sort of situation with the T, except the 45 degree angle is the edge of the top of the letter formed with the crossbar, and it has a zero degree strokeas the crossbar

It's just the serif that sits at 45 degrees, otherwise it's a simple vertical. But getting the serifs at the right angle is important too, and the J version 2 has nothing else to put it in any other category,

The Hooked Serif

All of the letters than end in a vertical (with a diamond at the bottom) have a hooked serif to finish.

For example :

This serif extends from the bottom of the diamond at an angle of approximately 30 degrees (and then straightens out to the vertical).

This serif finishes just over half way up the height of the letter

I think I've got ahead of myself again, and answered a couple script analysis questions early. I will write out the whole document, all in order, when I've finished doing the analysis.

I've also not answered the script analysis questions directly - just shown the work. I'll write it out properly when I write out the whole document.

I became more familiar with the letters as I did this measuring and looking back at the original script, and realized that my reproductions (photocopies gone over with a pen) are pretty inaccurate.

I have two big pieces of information about each letter - the height of the ascender/descenders and the angles of the strokes, that's going to make for a very crowded ductus if I marked each letter up. I realized that it was a good idea to draw the letters on graph paper, where each square was the size of the nib width (working with 1.5 mm nib width), working with the information I've measured but referring back to the original script for examples of the letters. I'm choosing a 'nice' looking example of each letter, since they do vary a bit, even on the same page.

It's quite hard and slow to do - trying to get them right. The curved strokes at the top are just terrible. I'll do better when I'm working with a broad edged pen rather than pencil and biro.

It's a bit circular - trying to draw accurate representations so I can learn to write each letter, when I haven't learnt to draw the letter yet. I can't see myself doing a really good ductus until I've spent some time practising the script itself.

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