SHAPE: In most ancient city-states style of alphabets Eta had the form , which developed into H.
This shape also produced (by being diminished to its upper corner, only) the two breathing marks e.g. .

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SOUND: The history of 'H' is quite adventurous!
Original pronunciation of this letter was /h/. This sound started disappearing very soon: HEΛΛAΣ [hel`las] = Greece became EΛΛAΣ (today pronounced [e`las].
During classical times the symbol H was pronounced as a long [ε:] especially in the ionic Asia Minor dialect. But others, dropped the /h/ very soon. They had no use for it anymore.
After hellenistic times it was uttered as today's [i], but has always played the role of a 'long' vowel in grammatical rules. The reminiscence of the /h/ sound was represented by alexandrian scholars of hellenistic times as the daseia < breathing mark.
Today: It is interesting that erasmic pronunciation of ancient greek preserves this old /h/ sound, as well as all the greek-deriving words of latin and the european languages, while in greek it is not heard at all. Erasmic pronunciation uses the classic [ε:] for Eta, hence it is also called an 'etacistic' pronunciation, while we pronounce it as [i] ('iotacistic' pronunciation see Iota). The term 'Etacistic' (ger. Etazismus) implies not only the 'tendency to preserve [ε:] and the variety of similar sounds, but also, any scientific attempt to reconstruct the classical pronunciation.
Transliteration: Both greek letters E and H are transferred in latin and european languages as 'E'. e.g. λλην → hellen.

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NAME: ETYMOLOGY: from northsemitic (phoenician): hêt' = door (also check Epsilon).
NAME: SPELLING: The polytonic hellenistic accents for eta's first letter are psile and perispomene: τα

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COMBINATIONS: DIGRAMMES: rare HY [if] or [iv] erasmic [eu]
Rare archaic long diphthong HI ηι also written: subscript or adscript (for capital H) Hι.

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MORE GREEK WORDS STARTING WITH ETA
•ήλεκτρoν=amber/electrum - ηλεκτρόνιo=electron, Hλέκτρα= Electra •ηθικό=ethical
H with daseia < breathing mark: •ήλιoς=sun - ήλιoν=helium •ηγεμoνία= hegemony •ημι...=semi...half - hemisphere •ηρωικό=heroic