Finding the X Height


Greetings!  It has been almost exactly two weeks since my last blog post.  I had a busy weekend, recovered from that, then everyone in my home became sick.  I still am but the doctor says that I will be just fine.  Thanks for being patient!

FINDING THE X HEIGHT


A reminder first, the “x” height is the height of the main body of any letter.  It is generally measured in nib widths or how many pen widths it takes to get the main body height.  Remember when I talked about Pen Ladders?  Today we are going to talk about reverse engineering that.  Or in other words we are going to look at some writing and figure out how high the pen ladder should be.

I did some quick calligraphy for you.  I purposefully varied the lettering heights and shapes so that you will better see how this system works.  As always click on the picture to get a larger view of it.  All pictures will open in a new window when clicked on.

The same pangram written in three hands in three different sizes

The same pangram written in three hands in three different sizes

And so we have Gothic Textura Quadrata, Uncial and Carolingian Minuscule.  So how do you figure out the “x” height?  First get out your tools.

You will need:

Dividers look like a compass without any graphite in it.

Dividers look like a compass without any graphite in it.

A pair of dividers.  Dividers are used for measuring things.  You can also quickly multiply out the measurement simply by turning the dividers end over end along a straight line.

AND/OR

Simple ruler with both inches and centimeters.

Simple ruler with both inches and centimeters.

A ruler

Now that you have your tools, where do you measure?  You want to try to measure the thickest part of the line.  The thickest part of the line is the width of the nib.  Unless the pen angle is flat (90 degrees) you don’t want to measure any vertical line in the letter.  Here is why:

put the points of the divider exactly on the outside of the line.

put the points of the divider exactly on the outside of the line.

Okay so you place the points of the divider on each side of the vertical line of the “h” and you get a measurement of?

That's 2mm inside the divider points.

That’s 2mm inside the divider points.

2 mm.  Not bad but is it accurate for determining the width of the nib?  No.

Lets take a measurement of the thickest part of the line.  How do you determine where that is?  You have two options really.  One, just look at it with the naked eye and put down your measuring device and when you get the thickest part, that is the width of one nib.  The second option works a bit faster.  Look for the flat angle of the letter. This will tell you the angle the pen was at when the letter was drawn.  Find the part of the letter that is at opposite that angle, that should be the thickest part of the letter.  

Like here:

The angle at the top of the "i" works nicely for us.

The angle at the top of the “i” works nicely for us.

And what is that measurement?

Looks a bit bigger than the previous measurement.

Looks a bit bigger than the previous measurement.

Well that is 3 mm in width.  So what?  After all it was only off by 1 mm.  Well yes, but since the “x” height is a ratio of the width of the nib think about it this way instead.  The wrong width was 2 mm. The correct width was 3 mm.  A difference of 150%.  I think we can agree that 150% is very significant especially if you’re going to be multiplying it!

Okay so now we have the width of the nib at 3 mm.  That is only part of what we need to do.  Next we need to see how tall the “x” height of the letter is.  Remember the “x” height is only the main body of the letter without ascenders or descenders.

The letter "q" for your viewing pleasure.

The letter “q” for your viewing pleasure.

We can see from the picture that the letter “q” is about 16 mm in height.  But we don’t want all of that height.  We only want the “x” height.  In this case that means we want to ignore the “tail” of the “q”.  Wen we do that we see that the letter “x” height is about 10 maybe 11 mm.  Do some division and we see the following:

10 mm divided by 3 mm equal 3 1/3 nib widths. (10mm/3mm = 3 1/3 nib widths)

Okay but how tall should capitals be?  Glad you asked.  I would hate to have taken all these pictures for no reason.

What is the height of the Capital?

What is the height of the Capital?

22 mm is the height of the capital.  So we do math again.  22mm/3mm = 7 1/3 nib widths

But what about those squished letters we saw?

That is considerably shorter.

That is considerably shorter.

The “u” and to some extent the “m” next to it are both about 8 mm in height.  The math says 8mm/3mm = 2 2/3 nib widths.

And then you get funky letters like the “f” where the “main body” of the letter is somewhat difficult to determine.

So what is the measurement here?

So what is the measurement here?

The crossbar on the “f”, is that above or below the “x” height.  Having a good solid knowledge of the script your working with is of great help to answer that question as the placement of the crossbar differs from script to script.  For a moment though we need to ignore that and focus on what is in front of us.  After all, the scribe could have decided to write the letter differently than the norm for the script being used.  This is when you look around for clues. The letter next to the “f” in the same word is the letter “o” which is an “x” height letter.  By the way after the “o” is the “x” and that is the letter this whole system is named after.  So what do the clues tell us?

They tell us that the cross bar is below the “x” height line.  And if we measure from the bottom to the top of the “o” we see the “x” height is about 12 mm.

12mm/3mm = 4 nib widths, which is somewhat standard for this script.

So what do you do if your dividers don’t go small enough like this?

Now that is some small writing.

Now that is some small writing.

You switch over to an alternate method.  The clear ruler.  By the way if you’re working with manuscripts they won’t let you have a divider so bring a clear ruler so you can take measurement just like what you are about to see.

Well that is less than 1 mm

Well that is less than 1 mm

Sometimes you have to estimate what the measurement is, especially if you do not have a magnifying lens with you.  Or you can just bring with you a measuring device that is pinpoint accurate for everything.  Such measuring devices exist but for our purposes this clear ruler and some estimating work just fine.  When you are guessing make sure to check more than one letter for the nib width.

I used the thickest part of the "v"

I used the thickest part of the “v”

The two of these letters show us a nib width of about 3/4 (0.75) mm.  And that is a fairly small nib to be writing with.

Does it work with large nibs too?  It works with all sizes of nibs.  That is why this system is so wonderful.  In fact lets test it.  The last script is Carolingian Minuscule and I put a ladder at the beginning of the line.  So let’s first measure the thickest part of the letter…

Nice and thick part of the stroke.

Nice and thick part of the stroke.

We leave the dividers where they are and we transfer them over to the ladder which we know each step is exactly the width of one nib.

Got it!

Got it!

And we see that the widest part of the letter is indeed the exact width of one nib.

So that is how you figure out the “x” height of the letters you are looking at in a manuscript or anywhere else.  Measure the thickest part of a single stroke which gives you the width of the pen (nib) used to draw the letter.  Then you measure the “x” height of the letter.  Divide the “x” height measurement by the width of the pen (nib) measurement and you find out how many nib widths high the letter is.

One method I did not show in pictures is to take the dividers place them at the base of the “x” height and then “walk” them up a straight line and count how many times you turn the dividers over.  This method only gives you a rough estimate which for some things is just fine.

I hope you have enjoyed learning how to determine the “x” height used in manuscripts.  Please remember to rate this post and please feel free to leave comments.

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ADDENDUM

Richard D. was kind enough to make a comment about another way to find “x” heights and e-mailed me his pictures of the work.  I am adding them here so that you too may have another way to determine “x” heights.

Hello, very interesting article and I must compliment you on your attention to detail. However, the procedure can be simplified. This procedure was based on what E Johnston did and wrote about in his book. It is also explained very clearly in “The Historical Source Book for Scribes”, British Library by Dr Michelle Brown and Patricia Lovett.

All that being said, First draw horizontal lines from the top and bottoms of the letter bodies, Then, using the same pen angle of the original letter, compare nibs at the thickest part of a well made o bowl or a solid minim. Once you find the closest nib (or cut your quill to the same sizw, if using quills) then you have found the pen used by the original scribe. Use a ladder to measure the distance between the two horizontal lines you drew from the body heights. This is the x height.

Richard D "x" height example

Richard D “x” height example

I use this method when I have to analysis scripts from historical government mss to make corrections or add lines and pages. The method is more than accurate enough to match the beautiful variations found in historical documents.

I did a quick example on paper this morning when warming up but not able to attach to this note..

Richard D's example on a script.  Works for most Roman alphabets.

Richard D’s example on a script. Works for most Roman alphabets.

Cheers
Richard D

*****************************************************

Thank you Richard D

3 responses to “Finding the X Height

  1. Pingback: Lining Your Project | scribescribbling·

  2. Hello, very interesting article and I must compliment you on your attention to detail. However, the procedure can be simplified. This procedure was based on what E Johnston did and wrote about in his book. It is also explained very clearly in “The Historical Source Book for Scribes”, British Library by Dr Michelle Brown and Patricia Lovett.
    All that being said, First draw horizontal lines from the top and bottoms of the letter bodies, Then, using the same pen angle of the original letter, compare nibs at the thickest part of a well made o bowl or a solid minim. Once you find the closest nib (or cut your quill to the same sizw, if using quills) then you have found the pen used by the original scribe. Use a ladder to measure the distance between the two horizontal lines you drew from the body heights. This is the x height.
    I use this method when I have to analysis scripts from historical government mss to make corrections or add lines and pages. The method is more than accurate enough to match the beautiful variations found in historical documents.
    I did a quick example on paper this morning when warming up but not able to attach to this note..
    Cheers
    Richard D

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