I've tought myself to read the Greek alphabet, and it is still confusing to read and identify "h" sound in the ancient Greek. For example, Athena talks about Calypso that she has "αἱμύλιοι λόγοι" in Odyssey(1, 56). It seems 'aimylioi logoi' to me, because α has no diacritical mark on, but I have seen that is read as 'haimylioi logoi' elsewhere. Which one is right, and why? Is it to do with the Homeric Greek, or does ἱ after α affect the pronunciation? Thank you!
All words beginning with a vowel are marked with a 'breathing.' This looks like a single inverted comma. When the breathing is 'rough' (aspirate) it is c shaped < ;when the breathing is 'smooth' the inverted comma is reversed > . In the case of αἱμύλιοι the aspirate, the rough breathing, has been placed over the second letter of the vowel pair αἱ.
The other diacritical marks are tonal accents:
αἱμύλιοι is proparoxytone;
λόγοι is paroxytone. perispomenon and properispomenon are only found on long vowels and diphthongs, and can be, barely, heard as a rising-falling tone.
fdb is absolutely correct (+1), but to address this part of your question:
does ἱ after α affect the pronunciation?
The answer is, yes, it absolutely does!
In (most dialects of) Ancient Greek, there were fourteen vowels (*):
- α, ε, η, ι, ο, ω, υ are written with single letters
- αι, ει, οι, υι, αυ, ευ, ου are written with double letters
The vowels in the second group are conventionally called "diphthongs", even though not all of them were actually diphthongs in the linguistic sense (ει and ου were monophthongs).
But even though they're written with two letters, these diphthongs act as single vowels. So the convention is, whenever you put an accent or breathing mark on a diphthong, it goes on the second letter.
So when you have a word like αἱμύλιοι, it has four syllables, each with one vowel: αἱ-μύ-λι-οι. The first vowel is αι, marked with a rough breathing, and transcribed hai in the Latin alphabet.
(*) Some dialects had more, some had less. In Epic, there were also three long diphthongs that disappeared before Classical Attic (ᾱι ηι ωι), and three long monophthongs that weren't indicated in writing (ᾱ ῑ ῡ). Other dialects had a distinction between ει and ε̄, and ου and ο̄, which Attic didn't—but I don't know if Epic is one of these.
EDIT: As fdb points out, the long diphthongs were still written in Classical Attic. My bad.