Any student of Modern Greek soon confronts — and is surely frustrated by — the myriad of ways of spelling the sound [i] (a high front vowel like the “ee” in feet), whereas the student of Ancient Greek looking at the modern language cannot help but be puzzled by this same fact.  As is well known, there are at least 8 Ancient Greek sources of the modern sound [i]:  ει, ι (long and short), η, ηι, οι, υ (long and short), and arguably υι as well (though it may be subsumable under υ and/or ι).  This convergence on [i] is referred to in the literature as “itacism”.

An obvious question to ask:  Why is this the case?

The facile answer is that all of the Ancient Greek sounds represented by these spellings were distinct in the Classical language but changed in their realization in the direction of [i].  But this did not happen all at once and various forces were at work to lead from the ancient system to the modern system.

The first to note is that the distinctive vowel length of Ancient Greek was lost during the Hellenistic period, so that ι (long and short) and υ (long and short) yielded simply ι and υ.  (This change affected long and short α as well as ο (omicron) and ω (omega), but that does not bear on itacism.)

Moreover, already in Ancient Greek, in dialects other than Attic-Ionic, there was movement in the direction of itacistic pronunciations; one finds, for instance, in Corinthian (a Doric dialect), that expected ει can be spelled ι, and even in Attic one finds χίλιοι ‘thousand’ (with long ι) where Corinthian has χείλιοι (and the ει represents the outcome of an earlier -εσλ-.  

In the Hellenistic and Roman periods (c. 300BC – 300AD), η came to be pronounced itacistically (though some modern dialects, especially Pontic, have -ε- from earlier η, suggesting competition in the Hellenistic and Roman periods between [ē] (to be shortened to [e] with the loss of distinctive vowel length) and itacistic [i] (most likely originally [ī]) as the pronunciation of η.

Among the last vowels to itacize were υ and the diphthong οι, which probably merged as [y] (a front rounded vowel like modern French < u >) by the end of the Roman period, and were maintained as such until approximately the 10th century, at which point they became [i].  Some modern dialects, e.g. the so-called “Old Athenian” dialect  (the Greek spoken in Athens prior to the mid-19th century when a Peloponnesian variety took hold), have [u] for earlier υ, suggesting a rounded pronunciation into post-Classical times.

The process lasted from 600BC to 900 AD; it begins with the transition of ει into  ι  in ancient Corinthian dialect to completion with transition of  η and υ into ι (Thumb 182). Still in 1914 some dialects retained  η and υ pronunciation as e  (Pontic) and u (Old Athenian dialect (Newton), cf. Mani dialectic)

As Horrocks mentions, and BDJ in Pros ta nea ellinika, ancient Boeotian vowels were relatively advanced.

Many spelling issues arise from this phenomenon. For example, κτήριο is correct since the noun derives from οικτήριον, but κτίριο is more common by analogy with κτίζω