What do the accents (acute/grave/circumflex) of Ancient Greek sound like?

From what we can work out, including the evidence from the ancients, and as consolidated on Ancient Greek accent – Wikipedia:

• If the syllable was short: an acute meant High pitch, and a grave meant Low pitch. (In reality, it meant neutral pitch.)
• If the syllable was long, break the syllable up into two Morae. An acute meant Low pitch on the first mora, and High pitch on the second. A circumflex meant High pitch on the first mora, and Low pitch on the second. A grave is still neutral pitch.

When accents were first invented, graves were written on every syllable that was not accented: ἄνθρὼποὶ ántʰrɔ̀ːpoì. That’s the evidence that the grave was in reality a neutral pitch.

Chinese as a tonal language has a tone on every syllable. Greek was a Pitch accent language, the way Serbian and Swedish is now: a polysyllabic word has one accent, but that accent involves different levels of pitch, as well as different levels of loudness. The other syllables in the word are unstressed, and have neutral pitch.

That means that the tone contours of Ancient Greek would not have sounded as up-and-down as Chinese: there’s a lot more neutral syllables than in Chinese. Moreover, a single mora was either high or low; it wasn’t rising or falling. The rises and falls were there on long syllables, but they were spread out over the two morae. Which means that pitch changes were slightly more gradual than in Chinese.

The four tones of Mandarin don’t quite match:

• Acute, short: High pitch — corresponds to First (high–level) tone.
• Grave, short or long: Low pitch — corresponds to Neutral tone. Maybe Third (low, dipping) tone, without the dipping.
• Acute, long: Low-to-High pitch — close to Second (rising) tone, maybe slower rise.
• Circumflex, long: High-to-Low pitch — not close to Fourth (high–falling) tone, which falls quickly; more like First then Third (low, dipping) tone.

So if I were to transliterate “But welcome, O wise people”:

καλῶς δὲ ἤλθατε, ὦ σοφοὶ ἄνθρωποι
kalɔ̂ːs dè ɛ́ːltʰate, ɔ̂ː sopʰoì ántʰrɔːpoi

into Mandarin, it’d be something like this:

galōǒs dě eéltade, ōǒ sopǒy āntroboy