How to assess what optical size(s) a given type style is intended for?

I'll like to join!

Quote from Simon's article:
"for a given design, there should be some kind of relationship between the stroke contrast, spacing, vertical metrics, and parametric values such that when we measure these values, we can work out the “natural” optical size for the design... ... but if we, as a whole, believe that certain things make a design more suited to text and other things make it suited to display, shouldn’t those “things” be, at least roughly, measurable and reproducible?
...
...
we can try to work this relationship out.
(Spoiler: I haven’t got there yet, and would appreciate input"

About nine years ago, I explored ways to create a script that could determine the “gray value” of each font. My goal was to sort all the Google Fonts from lightest to darkest. (At that time, there were about 100 fonts, most of them single-style.)

The first approach was to measure just the stem width.
Obviously, that didn’t work—stem width is only one factor. Some fonts were more condensed, others wider. And many other variables come into play.

Eventually, I gave up—but the unsolved problem kept nagging at me.
Then one day, while practicing calligraphy, I stumbled upon a surprisingly effective solution… a bit of a eureka moment. The solution revealed itself while I was practicing with various nibs of different widths, using the practice sheets that calligraphy books recommend for each nib size and style.

What I noticed, basically, was that there was a relationship between the nib size and the guidelines on the practice sheets. 

Not sure how to explain it using words, so i will make a quick sketch...
This are the typical proportions used in calligraphy for normal text:
– 5 nib widths for the x-height
– 1 nib for the stem
– 3 nibs for the counter

 

In the second sketch is more display-oriented, the proportions are:

– 3 nibs for height
– 1 nib for stem width
– 1 nib for the counter

What’s interesting here is that these measurements aren’t absolute and they’re not based on any standard unit. Instead, they’re all relative to the nib size. And while there are many other proportions that can be measured, these three are the key ones, they define most of the visual relationships in the texture of the text.

With this insight, I was able to write a Python script that measured the proportions and calculated a value using <b>x-height</b> × <b>stem width</b> × <b>counter width</b> across all the fonts I fed into it.
That way, I got a “darkness” value for each font, and I could sort them from the most compact and heavy to the lightest and most open.

The script isn’t perfect—it doesn’t account for serifs, for example—but overall, the results were pretty solid.
It’s not a definitive method, but the idea of multiplying x-height by stem width by counter width might be a good starting point if you want to refine it and improve the concept.

Here is the old script FL5 script. It also normalizes the values according to the EM units.
https://github.com/impallari/Impallari-Fontlab-Macros/blob/master/IMP Measures/All Darkness.py

John Hudson said:

...Sometimes, a change in Darkness value is only going to reflect a bolder or lighter design, not one whose proportions are more or less suited to small optical sizes or display type...

Yes John, not only ligther/bolder designs but also wide/condensed designs, as well as lower/higher x-height designs. But all those things considered, that simple darkness formula does a nice job averaging all those variables.
The best way to evaluate it will be to feed the script a bunch of fonts (both similar and extreme ones) and generate a test page to see the results visually, sorted by darkness. It may provide a better understanding of what's good and what's bad about it, and ideas for improvement... or maybe applying the general concept of using the nib as reference for a totally new and different formula.

One of the things we discussed last night was the idea that we find a good optical size by equalizing grey; David Berlow showed that a very simple optical size adjustment for fonts without an opsz axis is to simply change the weight of a setting as the point size changes, so that the settings have equal optical grey. I wondered if this could give some insight into working out the natural optical size of a family - set the font at various sizes in the same area of text box, and see which size gives you a similar grey value to a reference font. I haven't quite fully fleshed that out, but I wrote a simple web tool which sets the same weight across different sizes, and then measures the grey so you can see how it changes by size.

I'm not entirely sure how to interpret the results yet other than "browsers seem to do something weird with 6pt text". But here it is: Colorimeter. The "blur" feature works best on Firefox (due to a Chrome bug it becomes insanely slow if you use it a few times), and the "Rendering strategy" feature works best on Chrome. It's fastest in Safari, but neither of those features work. So try a few browsers.

Simon Cozens said:

Craig Eliason said:

I'm curious as to why these new proposals for calculating "color" are superior to the more intuitive and simple idea that the word could describe the ratio of black areas to white areas in a font.

That is exactly what I'm talking about when I talk about measuring grey, though.

Why, then, would a single static weight at different sizes show up as having different levels of "color" in that sense? (Aside from the difference in characters that appear in the sample.) Does rasterization distortion tend to push the overall grayness one way or the other?

Note that what Mark is talking about wouldn’t impact the measurement we are discussing.

Edit: Ah, Craig makes an excellent point below. Fair. Once you reduce the cap size to the x-height, you have effectively introduced more white space.