My thoughts/interpretations as a partial answer that might help others:
Period could mean a few things, Menstrual Period, a length of time, a specific time period (like B.C. or A.D.), or the punctuation mark. Contraction could mean 2 words combined, coming down with something (like contracting a disease), becoming smaller or contractions that happen during pregnancy.
With Hen, nest, periods and contractions, it's sending us on the though path of eggs (uteral and chicken). But as the title says, that aspect may all be a red herring. I've tried thinking of this in all of those aspects: Eggs, pregnancy, birth, etc, but nothing seems to fit.
Wow typing all this out has got me thinking and I think I just figured out the answer. ACCENT!
Periods in periods result in my contraction.
In various time periods, some phrases or words become popular and are turned into a shortened-slang form where an accent is placed at the end like: nothin´ . This could also refer to various periods in time where foreign alphabets were created and they have accents over the letters themselves, like i's (can't replicate it on this keyboard).
One of which appears in the expanded starting fraction.
Accents are developed when small groups splinter and live somewhere isolated and then their community grows and develop until they have their own way of pronouncing words. (Like England versus Ireland)
I am often confused with that is taken from "in d'nest".
The accent punctuation symbol [´] can look like an apostrophe but it's not.
To exhibit explicit qualities is how you'd use me best.
To show someone is from a specific area or have a specific upbringing, they speak in an accent, or you write them and change how words are spelt in writings to reflect that accent.