The Zohar teaches that every day, the Levites' song corresponded to that thousand-year period: On Sunday, it stood for the first; on Monday, the second, etc. Thus:
Six Thousand Years of Creation
The first day corresponds to the earth's first thousand years, when the earth was complete in its "fullness;" this was the time until the flood, when humanity enjoyed the full benefit and pleasure of the earth's bounty. Therefore the Levites sang "The earth is the L-rd's, and the fullness thereof."
On the second day of the week, the Levites sang "Great is the L-rd, and highly to be praised in the city of our G-d, in the mountain of His holiness." For it was during this historical period that Mount Moriah was chosen by G-d to rest His holy presence amongst mankind forever.
The third day's song was "G-d stands in the congregation of G-d; He judges among the judges."
For it was in the world's third thousand-year period that G-d presented the Torah to Israel, and rested the Divine Presence in their midst.
On the fourth day the Levites sang "O L-rd G-d, to whom vengeance belongs; O G-d, to whom vengeance belongs, shine forth!" For this day corresponds to the epoch when the Temple was destroyed, and the Holy One has vowed to bring His vengeance against those who were responsible.
The fifth day's song was "Sing aloud to G-d our strength: make a joyful noise to the God of Jacob." For during this entire thousand years, Israel was without the Holy Temple; no means of serving G-d remains for her save singing.
On the sixth day, G-d alone will reign, and the kingdom will be His. And the holy Sabbath which is sanctified by G-d and sacred to Israel is an allusion to the 7,000th year - the future rectified world.
These songs, and the lore surrounding them, deserve to be examined in greater detail, for they constitute an entire treatise for study in their own right. While this is not the place for such a treatment, we can already sense that they are replete with meaning and significance, and that each song is inexorably connected to its corresponding day by an intricate web of thought and symbolism.