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I have been studying the different effects that happen to vowels when a preceding consonant becomes palatalized and i am having trouble figuring out the exact sound of и when there is a palatalized consonant preceeding it.

Examples: клавиатура and биржа , for both of these words they have the same IPA in the area of the и, yet sound completely different. Биржа = hard ee and клавиатура , soft e that sounds like клавеатура

IPA of each :
https://ru.m.wiktionary.org/wiki/клавиатура

https://ru.m.wiktionary.org/wiki/биржа

IPA System:
https://en.m.wikipedia.org/wiki/Help:IPA/Russian

Strictly formally

in биржа [и] sounds like it does in beer.

in клавиатура [и] sounds like it does in video.

The difference you perceive might stem from the vowel's being unstressed. In two these words one is stressed while another isn't.

Technically in isolation they sound identically. But without stress vowels tend to get reduced so their pronunciation is less distinct. The only formal rule for reduction of [и] in unstressed position deals with its reduction into [ы] which doesn't apply here.

I will agree that in клавиатура [и] gravitates towards [иэ] and in fact this is a syllable susceptible to mistake in writing of elementary and middle school children. Google lists 18,700 occurrances of клавЕатура.

It lists Бержа as well but almost exlusively capitalized and not in the sense of stock exchange.

The vowel sounds in Russian words get reduced depending on their position in relation to the stressed vowel. Here, 3 different positions are distinguished:

1. the stressed vowel;


2. the vowel in the syllable directly preceding the stressed syllable;


3. all the rest of the vowels in the word.

Vowels in position 1 are always pronounced as they are, and also they are loud, distinct, and long.
In positions 2 and 3 the result of the reduction is like this:

• the letters <а> and <о> become [ɐ] in position 2 and [ə] in position 3: барабан [bərɐˈban], молоко [məlɐˈko];


• as for the letters <у>, <е>, and <и>, each of them has the same sound in positions 2 and 3: for <у> it's [ʊ] – кусать [kʊˈsatʲ] (position 2), муравей [mʊrɐˈvʲej] (position 3).
  For <е> and <и> the reduced sound is always [ɪ]: веселиться [vʲɪsʲɪˈlʲit͡sːə], миллион [mʲɪlʲɪˈon].

Now, your words биржа and клавиатура.
You wrote:

Examples: клавиатура and биржа , for both of these words they have the same IPA in the area of the и, yet sound completely different.

You probably simply didn't notice the difference in the IPA symbols for <и> in these two words, but the difference is there, and the difference is important, although graphically it's just a mere dot over i.

In биржа, <и> is stressed, so it's pronounced like [i] and sounds very much like the English <ее> in meet or feel: биржа [ˈbʲirʐə].

In клавиатура, <и> is in the second syllable before the stressed <у>, so it is in position 3 and that's why it is pronounced as [ɪ] (note, there's no dot over it), that's the sound found in the English words sit, pin, or big: клавиатура [kləvʲɪɐˈturə].

IPA is a set of technical symbols, that's why all their graphic elements (like the presence/absence of the dot over i) are functional and cannot be neglected, or else inevitable confusion will arise.