Sometimes when writing I find myself looking for a word to describe something in the “³⁄₂th” place — exactly between first and second. I would like to ask, does there exist an easy expression for this? If so, does it generalise to other “in-between” places as well?
(I mostly encounter this problem when writing mathematics, where I wish to write the “³⁄₂” order derivative, and normally have to endure clumsy or imprecise expressions (“Taking the fractional derivative. . . .”).)
Best Answer
The word you are looking for is the sesquialter, sesquialteral, sesquialterate, sesquialteral, or sesquialterous element.
You can also use sesquialter as an ordinal noun, for the midpoint between first and second:
That’s because sesquialter means “one-and-a-halfth”,1 but is substantially easier to say.2 It is one of those sesquipedalian terms surpassing both in erudition and utility alike. Per the OED, it means:
Here are a few of its more recent citations:
And its etymology is:
The sequi- prefix is today most familiar in terms like sesquicentennial, for the 150-year anniversary of some event. It gives rise to a delightful multitude of derived terms.
The OED provides not only senses 1b through 1d, with which we need not here concern ourselves, but also the operative sense 2a:
Sense 2b also gives several nice words for harmonic situations:
As you correctly perceive, having a word that means ³⁄₂th is exceedingly convenient at times, which no doubt why are ancestors invented sesquialter way back in the 16th century. This is the first citation given for the term in the OED:
Footnotes:
Regarding the productivity of the -th suffix for creating ordinals from cardinals in English, see this question.
Insofar as words that have end in -fth or -xth are often considered difficult to pronounce by non-native speakers, like fifth, sixth, twelfth, and if they find twelfth tough, they seem likely to find halfth tough as well.