Hallelujah Doubling in Hallel

In a place where they were accustomed to repeat certain verses he too should repeat them.

It was taught: Rabbi Yehuda HaNasi repeats words in it.
Rabbi Elazar ben Perata adds matters in it.

What does he add?
Abaye said: "He continues repeating from: 'I will thank You', and onward."

Dalet, yod, alef, shin, alef, dalet, yod, shin, khaf, shin, dalet, khaf, mem, alef, vav, dalet, khaf is a mnemonic device for the following passage. Returning to the issue of hallel, the Gemara states that these psalms include choruses in which each section is sung by a different person.
Rabbi Shmuel bar Naḥmani said: "Rabbi Yonatan said: 'David recited: “I will give thanks to You, for You have answered me” (Psalms 118:21), with regard to the success of his reign.

Yishai recited: “The stone which the builders rejected has become the chief keystone” (Psalms 118:22).

The brothers of David recited: “This is the Lord’s doing; it is marvelous in our eyes” (Psalms 118:23).

Samuel the Prophet recited: “This is the day which the Lord has made; we will rejoice and be glad in it” (Psalms 118:24).

The brothers of David recited: “We beseech You, Lord, save now” (Psalms 118:25).

David recited: “We beseech You, Lord, make us prosper now” (Psalms 118:25).

Yishai recited: “Blessed be he who comes in the name of the Lord” (Psalms 118:26).

Samuel recited: “We bless you out of the house of the Lord” (Psalms 118:26). They all recited: “The Lord is God, and has given us light” (Psalms 118:27).

Samuel recited: “Order the Festival procession with boughs, even to the horns of the altar” (Psalms 118:27).

David recited: “You are my God, and I will give thanks to You” (Psalms 118:28).

They all recited: “You are my God, I will exalt You” (Psalms 118:28).'"

Rabbi Yitzchak ben Giyat (1030–1089) wrote: "One repeats from 'I will give thanks to You' (Od’cha) until 'Please grant success' (Hatzlichah Na), for so we have received from the early sages and men of practice, that Rabbi [Yehuda HaNasi] would only repeat up until Hatzlichah Na. Rabbi Elazar ben Parta, however, adds to Rabbi’s practice by repeating from 'Blessed is he who comes' (Baruch Haba) until the end of the passage. And we hold that the law follows Rabbi against his colleagues.

Nevertheless, the custom has already spread to repeat from Od’cha until Hodu, following Rabbi Elazar ben Parta. The reason for establishing the repetition of these verses is that the beginning of the section Min HaMeitzar (Psalm 118:5–29) contains doubled themes up until Od’cha Ki Anitani ('I will give thanks to You, for You have answered me'), which corresponds to both this world and the days of the Messiah. Therefore, we complete it with repetition until the end of the passage.

Additionally, the verse Baruch Haba is inherently doubled: 'We bless you from the House of the Lord' (Beirachnucham MiBeit Hashem). Similarly, the verse Eli Atah Ve'odcha ('You are my God, and I will give thanks to You') is doubled in Elokai Aromimcha ('My God, I will exalt You'). Since there is no need to repeat two verses that are already doubled within themselves, we do not repeat El Hashem Vaya'er Lanu ('The Lord is God, and He has given us light'), since it falls in the middle.

Some say there is another reason for repeating these verses: because they were recited by Yishai (Jesse), David, his brothers, and Shmuel (Samuel), as we learn in Tractate Pesachim: Rabbi Shmuel bar Nachmani said in the name of Rabbi Yonatan that the acronym 'DYASH ADYASH KSHADK' serves as a mnemonic for identifying which verses were recited by whom:

• Od’cha Ki Anitani ('I will give thanks to You, for You have answered me')—said by David.
• Even Ma’asu HaBonim ('The stone the builders rejected')—said by Yishai regarding David, who was the youngest of his brothers, a shepherd, and was not considered worthy in their eyes, nor did they think he would become king. HaBonim is written as HaBanim ('the sons').
• Me’et Hashem Hayeta Zot ('This has come from the Lord')—said by his brothers, as it is in plural form.
• Zeh HaYom Asah Hashem ('This is the day the Lord has made')—said by Shmuel, who was prophesying that they would ultimately rejoice and be saved by God through David.
• Ana Hashem Hoshia Na ('Please, Lord, save us')—said by his brothers.
• Ana Hashem Hatzlichah Na ('Please, Lord, grant success')—said by David, who was already successful and was praying for success in his kingship.
• Baruch Haba BeShem Hashem ('Blessed is he who comes in the name of the Lord')—said by Yishai when David returned from tending the sheep.
• Beirachnucham MiBeit Hashem ('We bless you from the House of the Lord')—said by Shmuel when he called them to the sacrificial feast.
• El Hashem Vaya’er Lanu ('The Lord is God, and He has given us light')—said by all of them together.
• Isru Chag ('Bind the festival offering')—said by Shmuel, instructing them to offer a peace offering and rejoice.
• Eli Atah Ve'odcha ('You are my God, and I will give thanks to You')—said by David.
• Hodu LaHashem ('Give thanks to the Lord')—said by all.

Out of respect for them, we repeat these verses to show that each one is considered as its own distinct section. That is why we separate Ana Hashem Hoshia Na and Ana Hashem Hatzlichah Na into two parts and repeat them, even though they are technically one verse."