Learn English – Pronunciation of “especially”

Both short and long i are acceptable. AHD gives the following usage note:

The pronunciation (-laɪvd) is etymologically correct since the compound is derived from the noun life, rather than from the verb live. But the pronunciation (-lɪvd) is by now so common that it cannot be considered an error. In the most recent survey 43 percent of the Usage Panel preferred (-lɪvd), 39 percent preferred (-laɪvd), and 18 percent found both pronunciations equally acceptable.

Wiktionary agrees with that usage. Other dictionaries (Wordnik, Dictionary.com) list both pronunciations without comment.

Personally, I almost always use the short i like in 'give'.

(I'd give the two pronunciations slightly different connotations, something like short-i = it was around for a short time and it's already dead/gone, long-i = it's still around but won't be for long.)

According to the section labelled "pronunciation" on Wikipedia, the musical instrument is pronounced /ˈkæli.oʊp/ and the Greek Muse is /kəˈlaɪ.əpiː/.

Oxford disagrees, listing only the latter pronunciation (or something approximating it). Merriam Webster lists both pronunciations for the musical instrument.