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For example I want to say: ...the level of (fine-grained in noun) that is needed... I wonder if the word "grainery" will work.

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    We need some context. In certain cases, precision might fit, but your usage may require other terms. Granularity is a generic term that does not presume fineness.
    – bib
    Sep 18, 2014 at 18:03

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I think you're looking for "granularity".

Wiktionary's entry for granularity reads:

Noun

granularity (countable and uncountable, plural granularities)

(uncountable) The condition of being granular

(countable) The extent to which something is granular

And Wikipedia elaborates in its article on granularity:

Granularity is the extent to which a system is broken down into small parts, either the system itself or its description or observation. It is the extent to which a larger entity is subdivided. For example, a yard broken into inches has finer granularity than a yard broken into feet.

Coarse-grained systems consist of fewer, larger components than fine-grained systems; a coarse-grained description of a system regards large subcomponents while a fine-grained description regards smaller components of which the larger ones are composed.

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