This one is all shofar blasts and cymbals. How does a happy psalm fix anything?
Several of the other nine psalms in the Tikkun are about guilt, longing and exile. Psalm 32 begins with a person whose wrongdoing is forgiven. Psalm 42 opens with a deer crying out in longing. Psalm 137 is "By the rivers of Babylon." Then the set ends with the loudest psalm in the book. What does loud celebration have to do with repair?
Rebbe Nachman's answer is in Likutei Moharan, his main book of teachings. The ten psalms match the ten kinds of song. Each kind of song has power against the damage, he says, because each is the opposite of it. He explains three of them, and then the text says he did not explain the rest.
For halleluyah the explanation is a play on letters. He says the harmful force he is describing is named for wailing, yelalah in Hebrew. Praise is the opposite of wailing, he says, because the letters of halli, "praise!", are the letters of yelalah backward. Turn a wail around and you have a hallel.
The Gemara in Pesachim 117a gives this kind of song a rank of its own. Rabbi Yehoshua ben Levi lists the ten kinds of praise in Tehillim and says halleluyah is the greatest, because it holds God's Name and praise in a single word.
Notice what each source says and does not say. The Gemara says nothing about repair. The link between the two is Rebbe Nachman's, and the wordplay is his way of reading the word. It is one explanation, not a rule from the Gemara.
Likutei Moharan I:205,Likutei Moharan II:92,Pesachim 117aWhy does the Tikkun end on the loudest psalm?
The set runs from Psalm 16 to Psalm 150 and finishes with a shofar, harps, drums and cymbals. It is tempting to think someone arranged it to build from quiet to loud.
The source gives a plainer reason. Rabbi Natan's record says to say the ten in the order they are written in Tehillim. Psalm 150 is the last psalm in the book, so it is the last of the ten. The sources we opened do not say Rebbe Nachman picked it in order to end on a high note.
Either way, the set ends on the highest kind of song. The Gemara ranks halleluyah as the greatest of the ten, and this psalm is built from it: 13 of its 37 words are forms of "praise." The final verse of the psalm, and of the whole book, is "Let every soul praise God. Halleluyah."
You may have said this psalm already this morning, as the last of the Halleluyah psalms in the morning prayers. The words are the same. The page for it there tells about the Temple, the instruments and how many praises the psalm holds. Here the same words are the tenth of ten.
Sichot HaRan 141,Pesachim 117a,Tehillim 150:6