What does the é in Sméagol do to the pronunciation?

I've read Lord of the Rings, and I don't seem to understand what the accent is supposed to do to the pronunciation, I don't know how I'm supposed to lay pressure on the e, neither how JRR thinks there isn't enough pressure to say the name Smeagol. I know that JRR made his own language, but I can't speak it, if somebody knows why there is an accent I'd be happy to get an answer.

From Appendix E on writing and spelling:

In Sindarin long e, a, o had the same quality as the short vowels, being derived in comparatively recent times from them (older é, á, ó had been changed). In Quenya long é and ó were, when correctly2 pronounced, as by the Eldar, tenser and ‘closer’ than the short vowels.

2 A fairly widespread pronunciation of long é and ó as ei and ou, more or less as in English say no, both in Westron and in the renderings of Quenya names by Westron speakers, is shown by spellings such as ei, ou (or their equivalents in contemporary scripts). But such pronunciations were regarded as incorrect or rustic. They were naturally usual in the Shire. Those therefore who pronounce yéni únótime ‘long-years innumerable’, as is natural in English (sc. more or less as yainy oonoatimy) will err little more than Bilbo, Meriadoc, or Peregrin. Frodo is said to have shown great ‘skill with foreign sounds’.

And to show that the above doesn't just apply to Sindarin and Quenya:

In names drawn from other languages than Eldarin the same values for the letters are intended, where not specially described above, except in the case of Dwarvish.

From Appendix F, specifically in relation to the name you're asking about:

The Stoors of the Angle, who returned to Wilderland, had already adopted the Common Speech; but Déagol and Sméagol are names in the Mannish language of the region near the Gladden.

Tolkien's phrase "as is natural in English" involves awareness of the influence of French on (British) English pronunciation. Most Englishmen, at least educated ones in Tolkien's time, would be aware that é in French is pronounced something like a shorter version of the English "ei" (as in the common loanwords café and résumé), and therefore would err on the side of pronouncing it as such in any unfamiliar word (é not being a naturally occurring letter in English, but French being the most common second language in England).

Therefore, I think the accent on the third letter in Sméagol indicates that the name should be pronounced more like SMAY-a-gol rather than SMEE-a-gol. It's not about stress, as such, although I know that accents can be used to indicate stress in some other languages (such as Russian). It's actually more like the accents used in languages like Czech and Hungarian, which are used to indicate a "longer" vowel rather than a "shorter" vowel (my "smay" versus "smee" above is an approximation of this, not exact, but an approximation which would commonly be used by "rustic" speakers such as most of the hobbits with the possible exception of Frodo).

In addition to Rand al'Thor's very nice answer I'd like to offer another route. I'm not completely sure how solid the sources I found are, so I invite everybody to find better sources to underpin (or disprove) my line of argument.

The name Sméagol is derived from an Old English word:

As for Sméagol, Tolkien explains in Guide to the Names in Lord of the Rings, “Sméagol’s name is derived from Old English sméah, an adjective meaning “creeping in, penetrating.” This word is related to the word smial, which was applied by the Anglo-Saxons to Cain, who slew his brother Abel, establishing a connotative link between Sméagol, who murdered his cousin Deagol to steal the ring.

Where Did Gollum Come From?

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The name, Sméagol, comes from Old English smeagan (“to burrow”).

'Gollum' at Wiktionary

For smeagan, Wiktionary lists "smēan, smēaġean, smēġan" as alternative forms.

So we need to look at the Old English pronunciation of "éa" (or "ēa"). And according to The Encyclopedia of Arda

The name Sméagol name derives from Old English, and in that language the vowel combination éa was a diphthong, pronounced approximately like 'ai' or 'ay' in modern English. So, strictly speaking, the name should be pronounced as if it were spelt 'Smaigol' or 'Smaygol', but the alternative pronunciation as 'Smeegol' is rather more natural to speakers of modern English, and is also very common.

The names Sméagol and Déagol are noted in Appendix F part II On Translation to be formed on the basis of Old English words as a parallel to the names Trahald and Nahald.

Having gone so far in my attempt to modernize and make familiar the language and names of Hobbits, I found myself involved in a further process. The Mannish languages that were related to Westron should, it seemed to me, be turned into forms related to English. The language of Rohan I have accordingly made to resemble ancient English, since it was related both (more distantly) to the Common Speech, and (very closely) to the former tongue of the northern Hobbits, and was in comparison with the Westron archaic. ...

[There follows a paragraph discussing the way Tolkien "modernized" some forms in Rohan, e.g. Dunharrow.]

This assimilation also provided a convenient way of representing the peculiar local hobbit-words that were of northern origin. They have been given the forms that lost English words might well have had, if they had come down to our day. ... Sméagol and Déagol are equivalents made up in the same way for the names Trahald 'burrowing, worming in', and Nahald 'secret'.

Note here that contrary to this note, the forms Sméagol and Déagol do not seem to be modernized, but to represent Old English intact (the outcome of Old English éa being spelt ea in Modern English with no accent), just as the unmodernized Rohirric names.

The most straightforward interpretation is that Sméagol and Déagol are meant to be modernized forms, with the use of the accent throughout the text (and the appendix) being merely stylistic (albeit etymological), and we should follow the prescription at the start of Appendix E Part I Pronunciation of Words and Names that special words should be pronounced as in English.

The Westron or Common Speech has been entirely translated into English equivalents. All Hobbit names and special words are intended to be pronounced accordingly: for instance Bolger has g as in bulge, and mathom rhymes with fathom.

In that case, we should pronounce these names as we would pronounce an unknown English word Smeagol or Deagol with no accent, i.e. with the first vowel as in beat, that is Received Pronunciation /smiːɡɒl/ & /diːɡɒl/, Standard Southern British English /smɪjɡɔl/ & /dɪjɡɔl/, or General American /smiɡɑl/ & /diɡɑl/ (or there equivalents with the final vowel reduced to a shwa). In my experience this is also the typical pronunciation.

The alternative reading, is that Tolkien is being slightly sloppy in his comparison and does not intend to suggest these names follow the same model as Hobbitish words, but instead that they are unmodernized Old English as used to render Rohirric, in which case they should clearly be treated identically to Rohirric words rendered in the same way.

In that case, we should follow the note in Appendix E Part I Pronunciation of Words and Names that in Rohirric éa is pronounced as a diphthong (rather than two distinct vowels, as this would be pronounced in Quenya or Sindarin), and assume that this exception given only for Rohirric should also have covered them.

The 'outer' or Mannish names of the Dwarves have been given Northern forms, but the letter-values are those described. So also in the case of the personal and place-names of Rohan (where they have not been modernized), except that here éa and éo are diphthongs, which may be represented by the ea of English bear , and the eo of Theobald...

This is a rough approximation of the Old English pronunciation (typically reconstructed as /æːɑ̯/, a long smooth glide from the a sound in Modern English cat to the a sound in English father) of that sequence in the Received Pronunciation of Tolkien's day (although would be less accurate in today's Standard Southern British English).

This would lead to pronouncing Sméagol and Déagol as /smeə̯ɡɒl/ & /deə̯ɡɒl/ (in Received Pronunciation) or /smɛːɡɔl/ & /dɛːɡɔl/ (in Standard Southern British English).

Unfortunately this sound only occurs in instances where there was a former r, and so does not translate well to rhotic accents (such as General American). There is no remotely satisfactory approximation to Old English éa in such accents, but the a of father is probably the least wrong option. The closest I could get would be something like /smɑɡɑl/ (with the vowel of English cot in both syllables), rather than /smerɡɑl/ which would be the actual equivalent to the British pronunciation .

A pronunciation of the names as three syllables (so with éa read as two syllables) seems unjustifiable.

Sméagol is a translation of his original name Trahald.

Similarly smial (or smile) ‘burrow’ is a likely form for a descendant of smygel, and represents well the relationship of Hobbit trân to R. trahan. Sméagol and Déagol are equivalents made up in the same way for the names Trahald ‘burrowing, worming in’, and Nahald ‘secret’ in the Northern tongues.

The rules, as described in the "Pronunciation of Words and Names", should apply to Trahald, but they don't apply to Sméagol any more than they apply to all the Old English or English names in the books.

The Old English names aren't expressly excluded from the rules, as are the translated Westron names.

The Westron or Common Speech has been entirely translated into English equivalents. All Hobbit names and special words are intended to be pronounced accordingly: for example, Bolger has g as in bulge, and mathom rhymes with fathom. - Appendix E.

See that the reason why the Hobbit names and special words do not subject to the rules is that they are supposed to be "translations". They are supposed to follow the rules in the target language(s).

If we can agree that Théoden, Éowyn etc. are Old English names and should follow Old English spelling, they are not subject to the rules in Appendix E, 'cause they are simply not compatible.

Sméagol is a translation into a (relatively) modern language, not transcribed from one of "ancient [Third Age] scripts". It's likely Old English, 'cause there's no other plausible options, from sméag "creeping" + -ol, parallel to déagol "secret" < *déagan "hide" + -ol. It's supposed to be pronounced however you/Tolkien pronounce(d) translated Rohirric names -- It doesn't have to be perfectly reconstructed Old English pronunciation, parallel to the Hobbits calling him with a 500 year old name with a modern accent.