The psalm never mentions a bird or a fish. So why is it Thursday's?
Read the psalm again. Drums, harp, shofar, Egypt, honey. No birds, no fish. Yet the Gemara says the Levites (the Temple's singers and helpers) sang it on the fifth day "because He created birds and fish to praise His name."
The Torah does put birds and fish on the fifth day. God fills the water and the sky with living things, and then, for the first time in the Torah, God blesses living creatures: be fruitful and multiply.
Rashi explains the link this way: when a person sees birds so different from one another, he gives praise to the One who made them. So the connection is not in the animals. It is in what seeing them does to you. The psalm opens with a call to sing, three times in a row ("sing out," "shout," "raise a song"), which fits.
The sources do not say why birds and fish were chosen for this, and not the land animals made the next day. They also do not claim the psalm is about birds. Two other places are worth knowing. Psalm 148, which you say earlier in the morning, calls on sea monsters and flying birds to praise God. And in Perek Shirah (an old collection of verses that the creatures of the world are said to sing, author unknown), this verse from Tehillim 81 is sung by the large kosher animals, like cattle, not by a bird.
So here is what the sources support. The Gemara gives the link in one line. Rashi reads it as praise sparked by variety. The psalm itself leaves you to connect the two.
Rosh Hashanah 31a,Rashi on Rosh Hashanah 31a,Bereishit 1:20-22,Tehillim 148:7 and 148:10,Perek Shirah 5:2The psalm says "our festival day." Where does it say Rosh Hashanah?
It does not. Verse 4 says: "Blow the shofar at the new moon, at the keseh, on our festival day." No holiday is named. The rabbis supply the name with a piece of logic.
The Gemara reads keseh as "covered," like a moon that is hidden. Which festival falls when the moon is hidden, at the start of a month? It must be Rosh Hashanah. The next verse says it is "a law for Israel, a ruling of the God of Yaakov," which fits a day of judgment.
Not everyone starts there. Ibn Ezra (Rabbi Avraham ibn Ezra, Spain, 1100s) begins with the plain sense, the start of a new moon, and then notes that our rabbis explained the verse as Rosh Hashanah. Rashi and Ibn Ezra both take keseh to mean a fixed, appointed time, as in a verse in Mishlei.
Radak (Rabbi David Kimchi, Provence, around 1200) adds why the shofar belongs here. He says the psalm is about the Exodus, and that the shofar blast is a sign of freeing slaves.
The Gemara in Rosh Hashanah 11a-11b uses the psalm that way too. Reading the shofar verse next to the verse about Yosef, it learns that Yosef left prison on Rosh Hashanah. From "I took the load off his shoulder" it learns that the slavery in Egypt stopped on Rosh Hashanah, months before the people left in Nisan (the spring month of Pesach). Rabbi Eliezer also matches the word "shofar" in verse 4 with Yeshayahu's "great shofar" and says the final redemption will come in Tishrei, the month of Rosh Hashanah. Rabbi Yehoshua disagrees: he says Nisan.
So the tie to Rosh Hashanah is the rabbis' reading of the verses. The psalm never says it. Thursday is its weekly home, and Rosh Hashanah is its yearly one.
Tehillim 81:4-5,Rosh Hashanah 8a-8b and 34a,Rosh Hashanah 11a-11b,Ibn Ezra, Rashi and Radak on Tehillim 81:4I do not bow to statues. What is a "foreign god" inside me?
Verse 10 says: "There shall be no foreign god in you, and you shall not bow to an alien god." The plain reading is about idols. Radak takes it that way: put your trust in no one but Me, and remember that I am the One who brought you out of Egypt.
The Gemara stops on two words: "in you." A foreign god inside a person? Rabbi Avin asks exactly that: what is a foreign god that is in a person's body? His answer: the urge to do wrong.
The Gemara says this while discussing someone who rips his clothes, smashes his dishes or throws away his money in a rage. Such a person, says Rabbi Yochanan ben Nuri, should look to you like someone who worships idols. That, he says, is how the urge works. Today it tells you to do one thing, tomorrow another, until it tells you to worship idols, and he goes and does it.
Duties of the Heart (a medieval book about the inner life of faith) quotes this teaching when it warns against turning your cravings into a partner of your service of God. It calls that a hidden sharing of the worship.
Notice what this is. The verse, in its place, warns against idols. The Gemara reads the word "in you" and turns the verse into a question about what rules you from the inside. That is the Gemara's teaching on the verse. The psalm does not say it.
Tehillim 81:10,Radak on Tehillim 81:9-10,Shabbat 105b,Duties of the Heart, First Treatise on Unity 10