The communality of a variable represents the degree of its generality acrossn − 1 behaviors. Domain-sampling principles provide a fundamental conception and definition of the communality. This definition may be alternatively stated in eight different ways. Three definitions lead to precise formulas that determine thetrue value of the communality: (i) from thek necessary and sufficient dimensions derived by iterated factoring, (ii) from then − 1 remaining variable-domains, and (iii) fromk' multiple clusters of then variables. Seven definitions provide approximation formulas: (i) one from thek dimensions as initially factored, (ii) one from then − 1 remaining variables, and (iii) five from a single cluster. Rank of the matrix is not a desiratum in some definitions. Using an example designed by Guilford to illustrate multiple-factor analysis, applications of the formulas based on the three precise definitions recover the true communalities, and five approximation formulas each gives values closer than thead hoc estimates usually employed in factor analysis.