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In Malory's Le Morte d'Arthur, all the knights of King Arthur's court swear an oath—it was the code of chivalry, as Malory describes:
The king...charged [the knights] never to do outrageousity nor murder, and always to flee treason; also, by no mean to be cruel, but to give mercy...and always to do ladies, damosels, and gentlewomen succor...Also, that no man take no battles in a wrongful quarrel for no law, ne for no world’s goods. Unto this were all the knights sworn of the Table Round, both old and young. And every year were they sworn at the high feast of Pentecost. (Le Morte d'Arthur, pp 115-116)
Chivalry was a code of conduct that developed for the most part to control the behavior of knights during the Crusades, wars against the Muslims (holding Jerusalem/the Holy Lands). Trying to dissuade the knights from barbaric behavior in these battles, they were called upon as servants of the Church to a higher standard.
Christianity had a modifying influence on the classical concept of heroism and virtue, nowadays identified with the virtues of chivalry.
In terms of the symbolism of Pentecost being a time of "knightly renewal," we should look at the significance of Pentecost. There are two references in the Bible as to why this time was so important. If one is familiar with the Old Testament, he/she will recall that this was a day to honor Moses' return from the mountain with the Ten Commandments—from God, to the Israelites:
Pentecost...commemorates God giving the Ten Commandments.
In that the law had been passed on to the knights regarding their moral code (to protect women, avoid murder and treason, and grant mercy to any who asked it), the renewal of a knight's code of honor on Pentecost might symbolize the acceptance of God's laws—even as the Israelites were to be ruled by the Ten Commandments.
In the New Testament, Pentecost was a time when the Holy Spirit descended upon the disciples and a multitude of righteous people from different cultures who spoke in tongues—meaning, regardless of their "mother tongue," all spoke words that everyone else understood, even if from a foreign location: these people were "of one accord." It was considered a miracle.
The movement of the Holy Spirit had been foretold by Jesus before he left his disciples; this event took place after the Resurrection. This is also often referred to as "the Birthday of the [Christian] church. Symbolically, this holy day might refer to the posture of the Apostles that day, drawing a comparison to the gathering of Arthur's knights. The Bible records:
And when the day of Pentecost was fully come, they were all with one accord in one place. (Act 2:1)
Being "of one accord" meant that all the Apostles were in agreement. This would be the desired situation of Arthur's knights on Pentecost, reaffirming their vows—of chivalry, being all of one mind—in agreement—and gathered together for the purpose of good—serving God, according to their oath.