fineness

(′fīn·nəs)

(mathematics) For a partition of a metric space, the least upper bound on distances between points in the same member of the partition. For a partition of an interval into subintervals, the length of the longest subinterval. Also known as mesh; norm.
(metallurgy) Degree of purity of gold or silver in parts per thousand.

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noun

The quality of being exceptionally good of its kind: excellence, superbness, superiority. See good/bad.

n

A means of grading alloys with regard to gold content. The fineness of an alloy is designated in parts per thousand of pure gold, pure gold being 1,000 fine.

goldsmiths A measure of proportion, against a maximum of 1 000, notably to express purity of gold. Thus a fineness of 995 indicates 0.5% impurities.

IN BRIEF: n. - The quality of being very good indeed; The quality of being beautiful and delicate in appearance; Having a very fine texture; The property of being very narrow or thin.

Tutor's tip: You won't create calligraphy of surpassing "fineness" (the state of being fine or of superior quality) if you don't learn how to use a brush with great "finesse." (an artful or skillful performance)