The dove is a bird related to the pigeon, with a soft cooing cry. It is often used as a symbol of peace, and thus is sometimes shown with an olive slip in its mouth, as in the arms of the Worshipful Company of Tallow Chandlers, 1456 [Bromley & Child 237]. In heraldic art, the dove is distinguished by a small curled tuft on top of its head. The dove’s “proper” coloration is white, with pink (some sources say gules) beak and legs; its default posture is close.
“Descending” is a special term applied to doves, equivalent to “migrant to base”. A “paraclete” is a dove portrayed as the Holy Spirit: descending and with a halo.
Francesca of Bright Angel bears: Azure, a dove displayed, head elevated argent.
Serena Fabrizio bears: Sable, three doves volant contourny argent.
James de St. Germain bears: Purpure, upon a chevron argent beneath a paraclete descending proper three crosses of Lorraine sable.