הלכה על שבת 50:4

(starting at ועכשיו) We gather in shul and we say five chapters of psalms from Lechu Neranena (Ch. 95) until Hashem malach yirgezu amim (Ch. 99) because they are about the future redemptive days. Therefore (like Radak says), a person says to his friend “Let us sing to Hashem,” and then [the next chapter we sing] “Hashem reigns,” that is to say that we’ll fulfill that which is written (Zecharia 14:9) “On that day Hashem will be One and His Name will be One.” For Shabbat is a hint to this time, to “The Day that is Entirely Shabbat,” and then we’ll sing a new song (Ch. 96) to Hashem. For all songs are in the feminine, and the song of the future [redemption] will be in the masculine, like the Midrash explain. Therefore we say these chapters.