For an ascending "r" look at the original metal Cheltenham.

hhp

Where the ball of the “r” is placed at the tittle?

Or the beak of the "r" could extend rightward
and the stem of the "i" could be short.

Or (as I once did to mock Steile Futura as being
too sterile) you could just put a dot above the "r". :-)
There might even already be a Unicode for that!

hhp

OT: it’s the second time I hear of Cheltenham’s ascending r, but I was unable to find a sample, and I have an hard time trying to visualise how it could be shaped.

I'll try to find something.
(But probably a few people will manage
to whip out samples sooner than I can.)

hhp

Thank you Hrant :-)

Back on topic, here’s a very quick and rough sketch on how a didone r_i ligature could (or couldn’t) work:

I am constantly reminded about how many variables there are worth accounting for!

I'm am specifically looking for something where the tittle of the 'i' and the shoulder (terminal?) of the 'r' are the same/united. Riccard's example is not quite on the mark. I admit that in the traditional style of didones, this may be sacrilege but who knows.

Also wanted to say that I wasn't able to find a metal sample of Cheltenham, (though there are some half-decent flickr pictures up, but nothing of substance.)

Not the Chelt yet, but I did find this:
http://typophile.com/node/9775#comment-62340
http://www.themicrofoundry.com/other/steile.gif

hhp

Hah:
http://typophile.com/files/Pivit_Logo_Comp.jpg

hhp

http://www.archive.org/stream/ATFBookOfAmericanTypes1934/atf-1934-book-of-american-types-hathi-mdp-39015061016286-png#page/n111/mode/2up

Cheltenham

Toldja. :-) Thanks Gillian.
But there might be an even more "dramatic" one.

hhp

Swashy Bookman! (I know, not Didone, but neither is Chelt)

Now that's what I call letterforeplay. In contrast to full
ligation, most graphically illustrated in the "The" of the
"The Coffee Bean & Tea Leaf" logo...

hhp

http://new.myfonts.com/fonts/nicksfonts/emfatick-nf/regular/glyphs.html

Close to a Didone: the "ri" is in the currency position, and is automatically placed when dlig is activated.

From today's FontShop newsletter: New swashier Bookman! With specific r built for an i plus entirely 6 other variant r designs.

Wow, cool. And that last one can probably reach over the
next letter to ligate with an "i"! What would that be called? :-)

hhp

That would be Mark Simonson’s Bookmania:
http://www.ms-studio.com/FontSales/bookmania.html

Oh yeah, sorry! Forgot the most important piece of info...the link!

No, I mean what would one call a ligation that
happens with a "neutral" letter in between?

hhp

Perhaps they’re not so uncommon in certain swashed styles, but usually they involve a capital and happen under the “neutral” letter. We could call them under-ligations or over-ligation (or maybe über-ligation ;-)

Leapfrog ligation!