(i)Their repetitive structure must have taught the people around the great composer the essence of music.
(ii) Part of the answer is in the proposition, but the essence is in the meaning.
(iii) The implications of these schools of thought are of practical essence for the teacher.
(iv) They had added vanilla essence to the pudding.

Explanation

(i) the most important quality of something that makes it what it is.
(ii) the main part.
(iii) practical importance
(iv) liquid taken from vanilla that contains its smell and taste in very strong form.