The syllable structure of the word "narrator" depends on the pronunciation. If the word is pronounced with the stress on the first syllable (NA-ra-tor), then the first syllable is an open syllable, and the second and third syllables are closed syllables. An open syllable is a syllable that ends with a vowel sound and is not followed by a consonant sound. A closed syllable is a syllable that ends with a consonant sound.
However, if the word is pronounced with the stress on the second syllable (nar-RA-tor), then the first syllable is a closed syllable, and the second and third syllables are open syllables.
For example:
NA-ra-tor (open-closed-closed syllables)
nar-RA-tor (closed-open-open syllables)