It is now worth saying a few words on how accents must have been pronounced by ancient Greeks; this is intended to provide accuracy and completeness of information and, to a lesser extent, to bring up the issue of historical pronunciation in reading Greek.
We must remember that the ancient did not use to mark accents on vowels, except for rare instances where adding an accent proved useful to avoid ambiguities. Evidence has been provided by the study of papyri and epigraphs. The same was true also for breathing marks and punctuation marks as well as for spaces between words. Systematic marking of accents on each word originated from μεταχαρακτηρισμός, i.e. from the transcription of classical texts in Byzantine Era. Such transcription was carried out purposely according to the criterion of establishing what could still be considered certain about the way words were pronounced in the classical age, thus avoiding doubts deriving from the fact that pronunciation had become markedly different over the centuries.
It is no wonder that all Greek words, except enclitics and proclitics, now carry an accent. In fact, also in other languages, each word is pronounced stressing one of the syllables, even though such stress is not marked in writing. In Italian, for example, accents have to be marked only on truncated polysyllabic words (e.g.: città, perché, andò, etc...), but all words are pronounced stressing one of their syllables. It is sufficient to mention the difference between áncora (noun - anchor) and ancóra (adverb - again), whose pronunciation is quite different even if they do not carry any accent mark.
As to the sound of accents when pronounced, several clues make us think that they must have sounded as follows:
The acute accent (in Greek ὀξεῖα προσῳδία)), as its name implies, must have been pronounced with a rising tone, pitched higher than unstressed syllables. To get an idea, click on the word ἄνθρωπος and listen. It sounds strange to our ear, to say the least. Such impression depends on the way we pronounce stressed syllables, which is different from that of the ancient: the intonation of the stressed vowel is less important to us, since we usually, though unwittingly, lengthen stressed syllables. In Italian for example, if we mispronounce the word tavolo by lenghtening the syllable vo, we feel we have stressed such syllable; voice intonation in pronouncing Italian syllables is irrelevant. By contrast, the ancient made a clear distinction between stressed syllables and lengthened syllables; when pronouncing or hearing syllables they could distinctly perceive long accented syllables, long unaccented syllables, short accented syllables or short unaccented syllables. For this reason, we may feel as if we were shifting stresses from their natural positions, when we recite Greek poems metrically, i.e.: keeping syllable length and making long syllables heard even if they are not stressed. Indeed, the ancient did not share such feeling of ours, by which we are doomed to sense the ancient's poetical language as both artificial and unnatural.
The circumflex accent (in Greek περισπωμένη προσῳδία, closely meaning pulled around accent) was pronounced with a high-low pitch contour on the accented syllable: a rising tone over the initial part followed by a falling tone over the second part of the stressed vowel. To this purpose, remember that only long vowels can take the circumflex accent, for their length is equivalent to two short syllables. On the other hand, a circumflexed vowel is ultimately the result of contraction either between a stressed vowel and an unstressed vowel or between a stressed vowel and a diphthong. To get an idea of how circumflexed
vowels must have been pronounced listen to this example: δῆμος.
As far as the grave accent (in Greek βαρεῖα προσῳδία) is concerned, it must be remembered that such accent is compulsorily placed only over final syllables, provided they are not immediately followed by any punctuation marks. Probably, it is just a different way of writing the acute accent. As a matter of fact, it is hard to determine whether the different mark originated from a change in pronouncing the stressed syllable. From a practical point of view, keep in mind that both dictionaries and grammar books always mark the last syllable of oxytone headwords or entries with the acute accent. In texts, however, all oxytone words are written with the grave accent, unless they are immediately followed by a punctuation mark. For this reason the most frequent Greek word, i.e.: the conjunction καί = and is almost always written with the grave accent: καὶ.
Finally, bear in mind that when the accent falls on a diphthong, the accent mark is written over the second vowel, but it is pronounced over the first vowel.