Three doves seems to be the least common number surrounded in head of Jesus Christ in Trees of Jesse. Saint Gatien’s Cathedral in Tours, France was rebuilt following a fire in 1166 during the 20-year sporadic war between King Henry II of England (and Normandy, Poitou, Aquitaine, Gascony, Anjou, Maine, Touraine, with control of Brittainy and Auvergne) and Henry VII of France. Reconstruction of the cathedral started about 1170 and continued intermittently for almost 400 years. At the east end of the church in the choir clerestory is a childhood of Christ and Jesse Tree window. (Window #202 per Painton Cowen). The central vertical panel contains the Jesse Tree. It was made in the third quarter of the 13th century.
Jesse Tree and childhood of Jesus window from the Cathedral of Tours. The bottom three panels are the donors. The central panel is the Jesse Tree with a recumbent Jesse. Above him are two kings, perhaps Kings David and Solomon, then the Virgin Mary. The kings are not identified by any symbols such as scepter or harp, for example. Christ is seated at the top with his right hand held in blessing and his left hand holding a book, presumably the Gospels.
Detail of the Christ panel of the Jesse Tree. Note the three doves above the head of Jesus
Three doves recall the Trinity: Father, Son and Holy Spirit. In addition there were other medieval stories that feature the number three referencing the Trinity.
One such story is the Holy Rood legend(s) dating perhaps from the 11th century and found in a 12th century vernacular Old English manuscript at the Bodleian Library (Bodley 343), Oxford.  The story starts with Moses finding three rods/trees in the desert after the Red Sea crossing. He was asleep and three rods sprung up during the night. One was at his head and one was at his right and left. The trees are cypress, pine, and cedar. At first, Moses is afraid of the wood. Another version has Moses recognizing the three wands as a symbol of the Trinity. After Moses discovers that the rods have to power to sweeten bitter water, he takes the three rods with him. David carried the trees to Jerusalem where they were placed in a pool of bitter water. The three become one mighty tree that grew in David’s garden, and, on which, David hung 30 silver hoops. Solomon cut down the tree to use in building the Temple but the wood was always the wrong length. The wood would get longer or shorter than what was needed. So the tree was put in the Temple. The thirty silver hoops were made into thirty plates that hung in the temple. The silver eventually came to Judas, the betrayer of Jesus, as 30 pieces of silver (Matthew 26.15). The tree remained in the Temple in Jerusalem and many miracles were associated with it. Eventually Caiaphas ordered that three hundred men get the tree to make the cross for Jesus. None of the three hundred men could move the tree. So, a section of wood was cut from the tree for the cross for Jesus.
Three hundred years later the legend picks up with Helena, the mother on Constantine, coming to Jerusalem and finding the wood of the True Cross as well as the crosses on which the robbers were hung. She divided the wood from the true cross, leaving some in Jerusalem. Then she carried some of the wood to Constantinople. When Helena entered the city, a dead man was brought to her, and he was made alive by the wood from the true cross. The story ends with Helena making a bridle for her son from the five nails used for the crucifixion. The bridle sped the spread of Christianity.
The Vita Adae et Evae (Life of Adam and Eve) dates from the 10th century. It was originally a Jewish legend. When Adam was old and in pain, he sent Eve and his son Seth back to the gates of Paradise to beg for oil from the tree of Mercy to anoint himself and ease the pain. The angel Michael met them and did not give them the requested oil. Instead they were given a branch and sweet smelling spices. Adam died and his children mourned him. Then Seth saw the hand of God give the body of Adam to the angel Michael. The angels Michael and Uriel buried Adam and his son Abel in Paradise. Six days later Eve died. Seth and his brothers and sisters mourned her for only six days because of the instruction from the angel Michael. The story ends as Seth makes tablets, writing down the story. Another version of this tale has Seth looking into Paradise and seeing in a large tree at the center of the garden the Virgin and infant Jesus. Upon Seth’s reporting this sight to his dying father, Adam exclaims, “Blessed are you, O Lord, for now I know truly that a virgin will conceive a son who will die on the cross, whence we shall all be saved.”
Godfrey of Viterbo, an Italian or German cleric, diplomat, and secretary to the Holy Roman Emperor Frederick I Barbarosa tells the another version of the tree woods becoming one in Pantheon or Universitalis libri qui chronici appellantur, (c.1180-90), a history of the world.. Ionitus, an apocryphal son of Moses, plucked three fruits from three trees, a cyprus, palm, and fir. When planted they grew into one tree which David recognized as a symbol for the Trinity. Solomon cut down the tree to use in building the temple but the wood proved unsuitable since it kept changing length. Solomon set up the tree in the temple to be worshiped. A sibyl saw the Messiah in the tree. Solomon recognized that this portended the fall of Israel, and the Jewish kingdom. He threw the tree into the Pool of Siloam. The wood was retrieved from the pool to make the cross. When the wood was used to make the Cross, three colors of wood could be discerned.
The Legenda Aurea (or Golden Legend) compiled about 1260 by Jacobus de Voragine is another well-known source for legends about three becoming one as a symbol of the Trinity. The Golden Legend is a seven volume work that tells the lives of the saints (hagiographies), many of them fanciful. It was compiled about 1260 and published about 1275. It was another medieval “best seller” that circulated widely and was well known to those who designed and constructed Jesse trees.
The Life of Adam in Volume 1, tells a slightly different version of the death of Adam. As he was dying, Adam sent Seth, his son, to Paradise to obtain the oil of mercy. Instead Seth was given three grains or seeds or kernels of fruit. Adam died and Seth placed the three seeds under his father’s tongue before Adam was buried at Hebron. Out of these three seeds grew one tree on which Jesus Christ was crucified.
“Life of Adam” in Volume 1 and the “Invention of the Holy Cross” in Volume 3 tell different stories about how Seth was given the raw material from which would come the wood of the cross. In the Holy Cross version, the angel Michael gave Seth a branch of a tree to plant on Adam’s grave where it grew until the time of Solomon. Solomon found the tree and cut it down. Eventually the tree was buried in a pit that was a piscina, a pool for washing sacrificial animals. The tree floated to the top of the pool and was recovered to construct Jesus’ cross. Wood of the cross was not three types but four: palm, cypress, cedar and olive.
 Painton Cowen, <http://www.therosewindow.com/pilot/Tours/images/w202_comp_30224b.jpg>
 Painton Cowen. <http://www.therosewindow.com/pilot/Tours/images/w202-ABC-6b-IMG_6478.jpg>
 A. S. Napier, ed. History of the Holy Rood-Tree : A Twelfth-century Version of the Cross-legend with Notes, EETS, OS 103 (1894) London: Kegan Paul, Trench, Trübner. 2-32. <http://archive.org/stream/historyofholyno10300bodluoft#page/n6/mode/1up>
 Richard Morris. Legends of the holy rood : symbols of the passion and crosspoems : in Old English of the eleventh, fourteenth and fifteenth centuries / ed. from mss. in the British museum and Bodleian libraries (1871) London: Pub. for the Early English text society, by N. Trübner
 R. H. Charles. ed. Apocrypha and Pseudepigraphia of the Old Testament in English. Oxford, Clarendon Press, 1913. <http://www.ccel.org/c/charles/otpseudepig/adamnev.htm > See also: Brian Murdoch. The Apocryphal Adam and Eve in Medieval Europe : Vernacular Translations and Adaptations of the Vita Adae Et Evae. (2009) Oxford, Oxford University Press. 27 ff. See also University of Virginia’s online version of The Life of Adam and Eve at <http://www2.iath.virginia.edu/anderson/vita/english/vita.lat.html.>
 This interpolation is to be found in London, British Library, MS Arundel 326, said by Mozley to have derived from a manuscript of the thirteenth century, and its close copy, London, British Library, MS Sloane 289, dated to the fifteenth century. See J. H. Mozley, Documents: The Vita Adae, Journal of Theological Studies. (1929) XXX-os, 123. <http://jts.oxfordjournals.org/content/os-XXX/January/121.citation > Given the presumed late date, perhaps it was the Jesse Tree window design itself that was the basis for the legend.
 As retold in Barbara Braent and Lee Pready. A Heritage of Holy Wood : the Legend of the True Cross in Text and Image.(2004) Leiden ;Boston : Brill. 292-3.
 <http://legacy.fordham.edu/halsall/basis/goldenlegend/GoldenLegend-Volume3.asp#invention of the Holy Cross>