Study Rosh Hashanah folio 31A with parallel Hebrew-English text, traditional commentary, and modern study tools. Free access to Babylonian Talmud online.
שאני התם, דשירה דיומיה היא.
The Talmud rejects this argument. It is different there, as in any case “Sing aloud” is the psalm of the day, either because it was an ordinary Thursday or because it was Rosh HaShana. However, there is no proof from here that in all uncertain cases they would recite the psalm for an ordinary weekday, as it is possible that they did not recite any psalm at all.
תניא, רבי יהודה אומר משום רבי עקיבא: בראשון מה היו אומרים — ״לה׳ הארץ ומלואה״, על שם שקנה והקנה ושליט בעולמו.
§ The Talmud expands on the topic of the daily psalms recited by the Levites. It is taught in a baraita that R' Yehuda said in the name of R' Akiva: On the 1st day of the week, Sunday, what psalm would the Levites recite? The psalm beginning with the phrase: “The earth is YHWH’s, and its fullness” (Psalms 24:1), in commemoration of the 1st day of Creation, because on that day He acquired the world and transferred it to man, and He was the only ruler in His world, as the angels were not created until the 2nd day.
בשני מה היו אומרים — ״גדול ה׳ ומהולל מאד״, על שם שחילק מעשיו ומלך עליהן.
On the 2nd day of the week what psalm would the Levites recite? The psalm that begins: “Great is YHWH, and highly to be praised in the city of our God, His sacred mountain” (Psalms 48:2). This is because on the 2nd day of Creation He separated His works, dividing between the upper waters and the lower waters, and ruled over them as King; and this psalm speaks of Jerusalem as “The city of a great King” (Psalms 48:3).
בשלישי היו אומרים: ״אלהים נצב בעדת אל״, על שם שגילה ארץ בחכמתו, והכין תבל לעדתו. ברביעי היו אומרים: ״אל נקמות ה׳״, על שם שברא חמה ולבנה, ועתיד ליפרע מעובדיהן.
On the 3rd day of the week they would recite the psalm beginning: “God stands in the congregation of God” (Psalms 82:1), because on the 3rd day of Creation He revealed the land in His wisdom and thereby prepared the world for His assembly that could now live on the dry land. On the 4th day of the week they would recite the psalm beginning: “O YHWH God, to Whom vengeance belongs” (Psalms 94:1), because on the 4th day of Creation He created the sun and the moon, and in the future He will punish and take vengeance upon those who worship them.
Text data via Sefaria: William Davidson Edition - English and William Davidson Edition - Vocalized Aramaic, CC-BY-NC; edition provenance: Koren. Display terminology has been modernized for readability.