The vowels in
Minas Tirith are all short, as long vowels in Sindarin are marked with an acute accent or a circumflex.
But the matter of Sindarin short i seems a bit confused according to two accounts published by JRRT himself.
In The Lord of the Rings Tolkien first explained that the sound should be like that in English machine:
'irrespective of quantity' -- in other words, as I read it anyway, the same quality as the i in machine, whether short or long. But a bit later Tolkien also noted that Sindarin long a, e and o had the same quality as the corresponding short vowels -- noting that he did not say the same about i and u here. Shouldn't Sindarin long i have the same quality as the corresponding short vowels too, if the earlier 'irrespective of quantity' is true?
Later in
The Road Goes Ever On Tolkien wrote:
'The intended pronunciation is given in Appendix E to Vol. III but not perhaps with great clarity, so I offer a few notes.' and with respect to short i, here he said that it
'may be rendered as in English sick.' I'm no expert but this seems to be a difference of quality, and perhaps this explains why i was not noted as having the same quality, in at least one part of the Appendix (which might also be what Tolkien referred to, at least in part, with his comment about being unclear in Appendix E).
In my opinion then (so far): Sindarin short
i should be rendered as in English
sick -- except with
ir if it occurs finally or before a consonant -- as this is also noted in Appendix E, where the example 'eer' appears instead. This differs from the film (I think) where it seems to have been decided to follow the example of 'machine' irrespective of quantity.
A bit confusing in any case

Tolkien did record his version of
A Elbereth Gilthoniel: I can't remember at the moment, but if the information from
The Road Goes Ever On is in play (and if I undestand things correctly), the short i in words like
Gilthoniel, silivren, linnathon should have the sound as in sick, but
míriel and
palan-díriel should have the quality of the i in machine, and be long.