It's not the umlaut which is sitting lower, but the i-dot which is sitting higher. No pun. In most typefaces the umlaut is in line with other accents.
The i-dot may sit higher for aesthetic reasons, but I am not sure if this is a must. (I think Mr Gaultney raises the issue in his essay on diacritic design, and following it I have tried to drop the i-dot a bit but found the result unpleasing. At least in German, the combination of i and umlaut-letter doesn't occur often -- if at all.)

Karsten

I am of the school that says the diaeresis should always sit at the same height as the dot on the i, along with the dot on ċ ė ġ ż ȯ ṁ ṅ ṗ ṡ ṩ

Of course, this presumes that the dot on the i isn't in the stratosphere. For a language like English, of course, the dot on the i can be virtually any height, since there are almost no accent marks to be concerned with. But as soon as you have a language with a rich diacritical set you want the height of the dot on the i to be constrained to a reasonable height. In a typically proportioned text face, I usually align the top of the dot somewhere close to the cap height.

I concur with Mr Hudson, and I also align my dot and diaeresis/dieresis/umlaut accents. One of the oddest dot location things I have ever seen is in the text face used in The New Yorker, where the dots on the i and j are at slightly different heights. Looks very odd in a word like "Nijinsky".

I usually make my dieresis dots a bit smaller than the i dot, for two reasons:

1. So that, compared with other accents, it (the dieresis) is not too heavy -- it has to have "single accent" weight, and not look like two 'i' dots.

2. Because of the f, as Hrant says, but also because of ascenders that may follow, such as b, h, k and l.

I line them up along the bottom, with the i dot.
I sometimes vary the width betwen the dots, depending on the width of the character.
A lot of little "cheats".

...national peculiarities which get evened out as character sets grow.

Not necessarily even -- it seems that the more demanding languages are paid more attention in the mega-language font; for instance, when some languages have proponents who are quite adamant about having steep acute accents, and others traditionally have a flatter angle, and no strong voice arguing for that in the type design community, then the steeper accent will predominate.

> align them to the bottom

Optically or mathematically?

BTW, when you wrote "the diaeresis should always sit at the same height as the dot on the i" I assumed you meant their entire bodies should look to be the same height (which would mean aligning the centers, not the bottoms).

hhp

> The doubling of the ї is not unusual either

I'd missed this...
Well, well, Mana's kerning pair for її wasn't that anal after all! :-)

> I don’t see a difference between optical
> and mathematical in this instance

It's probably small, but probably more than 1/1000 em.
Not that I adjust stuff below 2 em myself generally,
except to combat grid coarseness (like in an italic).

Anyway, I really don't know, since I've only
made the diaresis visibly lower (and smaller,
dotwise). Probably with the Baskerville I'll
have to be more Modernist though.

> If you align the centres, the diaresis tends
> to sit too high relative to other accent marks.

Even the ones with a lot of vertical span?

hhp