The word θάλασσα thálassa "sea" is spelled in various different ways, with different letters replacing the sigmas: some dialects had a tau, for example, while others had a theta.
Do we know (through loans and cognates, for example, or transcriptions into other languages) what underlying sound these various letters were representing?
We can only speculate about the exact underlying nature of the "foreign phoneme"; on the other hand, its surface realization is obvious, [tt] or [ss].
Below is my summary of the most relevant research on this problem.
Everyone agrees that θάλασσα is Pre-Greek (i.e. not IE), one of the reasons being that there were no geminates either in the PIE or in Pre-Greek (Beekes, Brixhe etc.).
As Stephen Colvin (Colvin 2007) writes, "the prehistory of these clusters [i.e. obstruent +y, Alex B.] is complex and much disputed" (p. 26). That being said, the communis opinio seems to be that the underlying consonant to be a palatalized velar, e.g. *-χyᾰ (Lejeune 1972, §98d) or *kʲᾰ (Beekes, kya in his notation); cf. Macedonian (?) θαλάγχα(ν).
Bubenik 2017 offers a very clear and a rather compelling account of how this might have happened. He writes that dental and velar palatalization, with subsequent affrication, happened in Proto-Greek:
*tj > *t'j > *t's'j
*kj > *k'j > *t's'j (in his notation).
The palatal glide was later lost, the palatal affricate was depalatalized and merged with Proto-Greek *ts.
This cluster, Bubenik writes, "could be subject to progressive assimilation ts > tt (in Boeotian, Attic and Central Cretan) or to regressive assimilation ts> ss (in other dialects)' (p. 647). Thus, he classifies all the dialects into the following groups:
He speculates that tt "could have belonged to the Aeolic basilect, surviving in Boeotian (and extended to [Western?] Attic), but eliminated partially in Thessalian and wholly in Lesbian" (p. 648).
cf. "geminate tt in Attic is a reflex of part of the palatalization isogloss shared with Boeotian and Euboean, corresponding to the geminate ss of Ionic and other dialects: cf. lexical forms like thálatta ‘sea’, glôtta ‘tongue’ vs. Ion. thálassa, glôssa, or verbal formations like *eret-jō > eréttō ‘I row’ (cf. erétēs ‘rower’), *kāruk-jō > kērúttō ‘I announce’ vs. Ion. eréssō, kērússō" (Angeliki Malikouti-Drachman, “Phonology (Survey)”, in: Encyclopedia of Ancient Greek Language and Linguistics, 2013).
If you are interested in more dialect data, feel free to peruse Thumb and Scherer or even Meister.
There have been various theories about the phonetic value of ττ and σσ, but it`s often held that they were pronounced as might be expected, i.e. as [tt] and [ss]. The philologist Sidney Allen argues as follows:
These facts have led some scholars to suppose that both the ττ of Attic and the σσ of other dialects represent different attempts to write such an affricate without the use of a special symbol; and that the pronunciation as a double plosive or fricative is a post-classical development, based in part at least on the spelling. But apart from the improbability of spelling influence on colloquial speech in antiquity, it is scarcely credible that the existence of an affricate sound would not have been revealed in any inscriptional spelling outside those mentioned above (e.g. as τσ), nor the tradition of it survive in the account of any grammarian. On the other hand it is perfectly feasible for both [tt] and [ss] to develop from an earlier affricate, and there seems therefore no need whatever to assume that the ττ of Attic or the σσ of other dialects mean anything more than they appear to. (Sidney Allen, Vox Graeca, A Guide to the Pronunciation of Classical Greek, pg.58)
Geoffrey Horrocks also attributes the values [tt] and [ss] to ττ and σσ.
[I]t was noted that many of the adopted place names and vocabulary items borrowed from the pre-Greek languages of the Aegean basin had undergone dialectally diagnostic sound changes. The almost certainly borrowed word for ‘sea’ , for example, has the following forms:
both of which reveal the dialectally standard products of the palatalization of an original voiceless dental or velar by a following semi - vowel. 3 Consider the example in (6):
Allen (1958) explains this divergent dialectal development on the assumption of a generalized heavy palatalization of /t/ in Boeotian: the Attic reflex is then probably due to close contact with Boeotian at the time of the change (on which see further below). But the fact that loanwords such as that in (5) undergo developments identical to those undergone by native vocabulary (even though we cannot, of course, discover the exact form in which such words were first borrowed) strongly suggests that the division of Greek into the historical dialects attested in literature and alphabetic inscriptions had only taken place after all its future speakers had become established in the Aegean area. (Geoffrey Horrocks, Greek, A History of the Language and its Speakers, pg.19)
Additional information:
Although your question doesn't deal with the following, I thought you might be interested:
But, like many literary languages, literary Attic was subject to influences from outside the restricted area of the spoken dialect, most particularly from Ionic. And one of the most characteristic features of this influence is the substitution of forms with σσ for the ττ of 'pure' Attic as exemplified by the inscriptions. In fact in tragedy, and in prose works up to and including Thucydides, the ττ of Attic is almost entirely avoided. Even though normal Attic grammar was used, and Attic phonology generally adopted, it seems that the ττ was felt as something of a provincialism by contrast with the σσ of most of the rest of the Greek-speaking world—all the more to be avoided as a characteristic of the speech of the 'συοβοιωτοί'; and even false Ionicisms (notably ἡσσᾶσθαι as against Attic ἡττᾶσθαι and Ionic ἑσσοῦσθαι) were liable to be perpetrated in avoidance of this shibboleth. (Sidney Allen, Vox Graeca, A Guide to the Pronunciation of Classical Greek, pg.11)
