partialdiff and eth

cuttlefish's picture

I've gotten in the habit of using the partialdiff (u2202) glyph as a base for eth. I'm concerned that this may be a bad practice.
In most fonts I've seen, partialdiff is in the form of a an italic or script delta, whether the font is italic or not. Is this necessary in a font that is not intended for setting math?

Jackson's picture

Briem has become the go-to source for how to construct an eth. You might find this easier and more successful than your partialdiff method.

cuttlefish's picture

I'm familiar with Briem's writings. I'm not putting a crossbar on partialdiff to make an eth; I'm making a correct eth without a crossbar and putting it in the partialdiff space, then referencing that to the eth space and adding the crossbar.

I guess it makes as much/little sense as using long s as the base for f.

Does anyone care what a partialdiff looks like in a font if it doesn't also come with a full complement of obscure math symbols?

hrant's picture


I make my eth from scratch, not canned ingredients.


nina's picture

"I'm making a correct eth without a crossbar and putting it in the partialdiff space, then referencing that to the eth space and adding the crossbar."
Dunno, I've seen that done before, and I must say it annoys me.* Yes, both these characters may seem pretty obscure, plus they're both a bit twiddly to make, so I understand the temptation. But to me this is one to resist; think about it – these characters come from completely different cultural backgrounds, from completely different contexts, they also appear in different contexts combined with different other glyphs, and last but not least they mean completely different things – now why should they share the same genes? Because they might look a bit similar on a surface level? :-\

"I make my eth from scratch, not canned ingredients."
I don't, but if you alter/tweak enough, at some point it doesn't matter what the original ingredients were.

[* Edit: I should maybe clarify that it annoys me from a potentially idealistic beginner's perspective that doesn't (yet) factor in ROI…]

Jongseong's picture

The partial derivative symbol shouldn't look like an eth without a crossbar. Its extender should be more bent and fill out the space more, and may well have a ball-like terminal. It should be italic in design, that is to say cursive and slightly inclined, because it is only used for mathematics. It is a letter-like symbol, not a letter. Therefore the design is very different from eth, which is a full-fledged letter and should harmonize with other letters of the Latin alphabet.

cuttlefish's picture

So, when you draw a partial derivative symbol for an italic font, do you have to skew it even more than the general italic slant of the font?

Jongseong's picture

I would use the same cursive and inclined glyph for the roman and the italic. Many letter-like (and non-letter-like) symbols used in mathematics, the partial derivative symbol included, are not meant to come in different forms for the roman and the italic.

Michel Boyer's picture

Here is a little question that may be relevant or not.

If we look at the unicode file, we can see that it contains the following characters (search for the word "partial"):


Now, here is a grab of the five last characters above taken from the chart "Mathematical Alphanumeric Symbols" to be found at the url

What should be filling the blank?


Michel Boyer's picture

Here is the partial symbol I get with the fourier LaTeX package when I choose the option "upright" (\usepackage[upright}{fourier}). That option gives upright capitals and upright greek letters in mathematical formulas, which is a standard in French mathematical typesetting.

Nick Shinn's picture

Why bother including math characters in a general purpose font?
You might just as well put your foundry logo in that slot, or a dingbat.
Wouldn't the only people who use a partial diff character be working in a math program with a specialist math font?
i.e., as Michel indicates, unless a font includes a set of upright Greek characters, it will not be used by mathematicians.
Also, I don't believe mathematicians buy commercial fonts.
Correct me if I'm wrong.

cuttlefish's picture

@Nick The partialdiff (u2202) glyph is part of the MacRoman encoding, and is therefore one of those things that is kind of expected to be there to make a font "minimally complete" even if nobody would ever use it. At least that's what I've been told. I don't know why it was included in the MacRoman encoding; so are a lot of other mysterious characters. It's also part of TeX-Base encoding, but that makes more sense.

tupper's picture

Also, I don't believe mathematicians buy commercial fonts.
Correct me if I'm wrong.

Some mathematicians do buy commercial fonts, but only very rarely for setting mathematics.

Jongseong's picture

Nick, you're probably not serious, but one should never ever put one's foundry logo or a dingbat in a slot reserved for a specific character. The partial derivative symbol is a fairly common technical symbol and should be expected to crop up often inline in general textbooks, for example, which would not normally be set in a specialist maths font and could benefit from using symbols that harmonize well with the main text.

Michel, thanks for that contribution. I didn't know about the different styles of the partial symbol being encoded as separate characters in Unicode or the upright symbols being preferred in French mathematical typesetting. I will retract my earlier claim that a partial symbol needs to be italic.

I should point out that this does not mean necessarily that one should put an upright partial symbol in one's roman and an italic in one's italic in the same slot. No one is going to use upright and italic partial symbols in the same text. Rather, if you're designing all those variants, you should treat them as separate characters and use the assigned Unicode slots.

As for Michel's question about what should be filling the blank in that picture, I think that U2202 is the natural answer if we think of "roman regular" as being the default character. The form of U2202 itself may be italic and identical to U1D715, or upright according to stylistic preference. The other characters are there as stylistic variants, which tells me Unicode thinks of the upright form as the default, but it does not matter in the least if we choose italic as the default form and not provide an upright form at all, because no one is ever going to need the full stylistic palette of partial symbols for the same text.

jcrippen's picture

Because of its availability in less extensive fonts, I’ve seen partialdiff used as a phonetic symbol. Its use for this purpose depends on it being similar to other Latin letters in the font, so in this narrow case it should have the same center angle as other letters.

For the curious, I’ve seen it used as a replacement for schwa /ə/, as an interdental affricate /tθ/ or /dð/, and surprisingly as a voiced interdental fricative which is usually represented with just edh /ð/.

Michel Boyer's picture

Here are all the partial differential glyphs provided by the LaTeX Fourier mathematical font (based on Utopia) which comes with the MacTeX-2009 distribution.

The left square corresponds to the basic character (regular and bold, upright and italic), the right square to a variant, which is close to having that common ball-like terminal that Brian mentioned above. The first line are the glyphs we get when calling fourier with the upright option, else the glyphs we obtain are those in the second line (slanted).

That character is used for partial derivatives, where a slightly slanted version is indeed quite common. It is also used for a boundary operator in differential geometry, for which I personally prefer an upright version.


Jongseong's picture

Thanks Michel, I had forgotten about the use as a boundary operator (it's been a while). I don't know that I would prefer an upright version for that use, but I see how one might want to distinguish between different uses of the symbol. Another consideration may be that the symbol generally appears right next to italic letters (e.g. ∂S) and having an upright look recalls the similar use of upright letters as operators (e.g. bdS). But then as you mentioned with the French tradition, I guess different typographic traditions may have different preferences for upright and italic generally for mathematical typesetting.

James, thank you for mentionning the use in phonetic notation. Given how people have always tried to create phonetic symbols from what was available, this isn't surprising. In fact, I have noticed the partial derivative symbol being used for the schwa before, and probably for the eth also. This in my mind is as disgraceful as using a German Eszett for the beta. But using the partial derivative symbol for the dental affricate has a certain logic to it.

Michel Boyer's picture

I guess different typographic traditions may have different preferences for upright and italic generally for mathematical typesetting.

In this paper entitled "Typesetting mathematics for science and technology according to ISO 31/XI" (pdf), it is said: The main and possibly the only difference between "mathematical" vs. "physical" mathematics lies in the use of upright and sloping letters. Scientists and technologists (should) use upright letters much more often than mathematicians. I knew that some prefer to write dx (with an upright d) instead of dx for the differential, but I did not know where it came from.

Here is a grab of Hamilton equations taken from Nakahara "Geometry, Topology and Physics" where the partial sign does not look very slanted in spite (or because) of the use of nearby italic letters.



Nick Shinn's picture

The partial derivative symbol is a fairly common technical symbol and should be expected to crop up often inline in general textbooks, for example, which would not normally be set in a specialist maths font...

Could anyone post an example?

Michel Boyer's picture

Nick, the mathematics that this symbol belongs to is heavily used in natural sciences (physics, chemistry etc) and also in economics. I guess that most of the time, if figures in formulas that require an equation editor and thus a mathematical font. Yet, without it in standard web fonts, Martin Osborne could not have written

on his web page on mathematical methods for economic theory.


PS I had to use a grab, typophile does not support the <sub> ... </sub> tags.

Nick Shinn's picture

Thanks for digging up the example, Michel.


I left the "special math characters" empty in my legacy format fonts, after the Adobe model, assuming that they would be substituted from default fonts.

However, since OpenType I have been including glyphs for all those characters in both standard and OpenType fonts.
In most fonts, it doesn't really work to make partialdiff by cannibalizing the eth. Another chore for the reputable foundry.

Michel Boyer's picture

Another chore for the reputable foundry.

Maybe you could find inspiration from another reputable foundry, Adobe. Here are Rosewood's mathematical operators (a grab from their pdf Glyph complement sheet)

I wonder why they did that instead of leaving the characters undefined.


Thomas Phinney's picture

When Adobe converted their type library to OpenType, they filled all the alphabetic fonts out to Adobe Western 2, which is a slight superset of WinANSI and MacRoman. For Adobe Originals where the added characters were at all relevant given the design, they got all the glyphs custom made. For non Adobe Originals, and Adobe Originals for which such glyphs were not very relevant (e.g. Rosewood), they had most glyphs automatically synthesized from a generic MM font.



Nick Shinn's picture

Maybe you could find inspiration from another reputable foundry, Adobe.

I follow the FSI practice of custom designing the glyphs to the font, not automatic synthesis--which is really the old "odd sorts" practice of providing little used characters from a different font. Long ago, for instance, Italic fonts didn't even have their own capitals or figures, these being borrowed from the roman.

I first did custom math operators for Fontesque, although I thought it unlikely that it would ever be used for setting calculus.

The principle of covering every possible eventuality is, IMO, a best practice for font producers, because it is more productive to assume that anything is possible than to spend time trying to figure out what isn't.

Michel Boyer's picture

I downloaded from Will Robertson's experimental LaTeX package, called unicode-math, intended to be an implementation of unicode maths for LaTeX using XeTeX (and later LuaTeX) typesetting engines.

On page 10 of his unicode-math.pdf document (dated 2009/11/01) he writes, concerning the partial differential U+2202 and the math italic partial differential U+1D715:

At time of writing, both the Cambria Math and STIX fonts display these two glyphs in the same italic style, but this is hopefully a bug that will be corrected in the future — the ‘plain’ partial differential should really have an upright shape.

If we take into account that the package will offer the following math-style options,

that makes sense.


cuttlefish's picture

So would it be safe to regard Will Robertson as an expert authority with regard to math typography? If so then U+2202 should indeed be an upright partialdiff glyph (unless the font is its self italic/oblique?). In that case, does it take the form of lowercase Greek delta, or similar to a reversed 6 as in the italic form?

Michel Boyer's picture

One thing is clear: everyone I know that typesets mathematics does it with LaTeX. Even papers on economics that I have found on the web and that use mathematics were written in LaTeX. Martin Osborne, that used a partial on his web site on economics (of which there is a grab above) has even written a package for LaTeX. Have a look at his web page.

In fact I am using pdflatex, because that gives me access to Type1 fonts (which was an improvement over previous metafont fonts). What do you think will happen when Opentype fonts become easily available to LaTeX users? That is what XeLaTeX and LuaTeX will provide. Will Robertson is the person working on the math packages for XeLaTeX. When those packages become functional, users like me will expect to get the functionality that they announce.

I think Michel Bovani did it correctly for the Fourier font (grabs above). Here is again a citation from Robertson:

Table 7: The various forms of the partial differential. Note that in the fonts used
to display these glyphs, the first upright partial is incorrectly shown in an italic


PS I have books with partial diff glyphs that vary a lot in the last 60 years. I may post a few pictures if that can be useful (and when I have time).

Michel Boyer's picture

Hmm, it seem to be enough to have a look at the fonts you must already have. Here is Arno Pro regular, semibold, bold, italic, semibold italic and bold italic:

and the same with Utopia

cuttlefish's picture

I don't have a current collection of Pro-grade fonts right now; thank you for your time in pointing these out.

So, from all this, I conclude that partial derivative sign at U+2202 should be an upright form, and legacy fonts with an italic form in this position are wrong.
The partial derivative sign resembles a reversed six, but it is neither a reversed six nor an eth without a crossbar. The arm from the right should be overarching to the left and may end in a heavy terminal.

Thank you all for enlightening my ignorance.

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