Variance, n.
Etymology: [L. variantia.]
1. The quality or state of being variant; change of condition; variation.
2. Difference that produce dispute or controversy; disagreement; dissension; discord; dispute; quarrel. That which is the strength of their amity shall prove the immediate author of their variance. Shak.
3. (Law)
A disagreement or difference between two parts of the same legal proceeding, which, to be effectual, ought to agree, -- as between the writ and the declaration, or between the allegation and the proof. Bouvier. A variance, in disagreement; in a state of dissension or controversy; at enmity. "What cause brought him so soon at variance with himself" Milton.
Shades of meaning
Fernald lists variance only as an antonym, under harmony.
He lists it without comment; the entries above explain its neighbors.