Another interpretation regarding the Gittite. Isaiah said (Isaiah 5:16) "And the LORD of hosts shall be exalted in justice". When will the Lord be exalted? When he executes judgment on the nations of the world.
What is written above this (Isaiah 5:15)? "And the mean man shall be brought down, and the mighty man shall be humbled". At that time, the Lord of hosts shall be exalted in judgment. Similarly, it is said (Ezekiel 38:18), "And it shall come to pass at the same time when Gog shall come against the land of Israel..." and Joel says (Joel 4:9-11) "Proclaim ye this among the nations; prepare war; stir up the mighty men; let all the men of war draw near; let them come up.
Beat your plowshares into swords and your pruning hooks into spears; let the weak say, I am strong. Assemble yourselves, and come, all ye heathen, and gather yourselves together round about: thither cause thy mighty ones to come down, O LORD." (Joel 4:2) "And I will also gather all nations, and will bring them down into the valley of Jehoshaphat, and will plead with them there for my people and for my heritage Israel, whom they have scattered among the nations, and parted my land."
What is the valley called Jehoshaphat? It is the valley in which the Lord will judge the nations. Similarly, it is said (Joel 3:14), "Multitudes, multitudes in the valley of decision: for the day of the LORD is near in the valley of decision." The multitudes refer to (Jeremiah 25:33) "And the slain of the LORD shall be at that day from one end of the earth even unto the other end of the earth".
And then (Joel 4:17), "So shall ye know that I am the LORD your God dwelling in Zion, my holy mountain." When will the Lord be seen upon Gath? Similarly, it is said (Micah 1:10), "Declare ye it not at Gath, weep ye not at all: in the house of Aphrah roll thyself in the dust." At that time, victory will be given to Him.
"To the chief Musician upon Gittith" - there are four Gittiths: for the sons of Korah (Psalm 8), "For the Chief Musician upon Gittith", "Come down", and "For the Chief Musician, set to the Gittith" (Psalm 81) "Sing aloud unto God our strength, make a joyful noise unto the God of Jacob." This one is "upon Gittith."