He called her, emailed her, texted her, tweeted her—all to no use.
Strictly speaking, I would need to write texted her and tweeted her, but I'm omitting and to convey a rhythm and sense of urgency. What do you call this kind of construction, and is it accepted grammar (at least for creative writing, if not in an academic context)?
It's a rhetorical device called asyndeton, and you can find its definition (as well as those of other rhetorical figures) here.
Asyndeton consists of omitting conjunctions between words, phrases, or clauses. In a list of items, asyndeton gives the effect of unpremeditated multiplicity, of an extemporaneous rather than a labored account: On his return he received medals, honors, treasures, titles, fame.
I was taught that omitting the 'and' in such a situation was completely acceptable, especially in creative writing. The rhythm is much better without it. Leave it as is.
