אמר רב יהודה אמר שמואל שיר שבתורה משה וישראל אמרוהו בשעה שעלו מן הים והלל זה מי אמרו נביאים שביניהן תקנו להן לישראל שיהו אומרין אותו על כל פרק ופרק ועל כל צרה וצרה שלא תבא עליהן ולכשנגאלין אומרים אותו על גאולתן
Rav Yehuda said that Shmuel said: The song in the Torah, i.e., the Song at the Sea (Exodus 15:1–19), Moses and the Jewish people recited it when they ascended from the sea. The Gemara asks: And who said this hallel mentioned in the mishna, Psalms 113–118? The Gemara answers: The Prophets among them established this hallel for the Jewish people, that they should recite it on every appropriate occasion; and for every trouble, may it not come upon them, they recite the supplications included in hallel. When they are redeemed, they recite it over their redemption, as hallel includes expressions of gratitude for the redemption.
אמר רבי יוסי יהא חלקי מאוכלי שלש סעודות בשבת אמר רבי יוסי יהא חלקי מגומרי הלל בכל יום איני והאמר מר הקורא הלל בכל יום הרי זה מחרף ומגדף כי קאמרינן בפסוקי דזמרא
Rabbi Yosei said: May my portion be among those who eat three meals on Shabbat. Apropos this statement of Rabbi Yosei, the Gemara cites additional declarations. Rabbi Yosei said: May my portion be among those who complete hallel every day. The Gemara is surprised at this: Is that so? Didn’t the Master say: One who reads hallel every day is tantamount to one who curses and blasphemes God. He displays contempt for hallel by not reserving it for days on which miracles occurred. The Gemara answers: When we say this statement of Rabbi Yosei, we are referring to the verses of praise [pesukei dezimra], recited during the morning service, not to hallel (Psalms 113–118) recited on special days.
דאמר רבי יוחנן משום רבי שמעון בן יהוצדק שמונה עשר יום בשנה יחיד גומר בהן את הלל ואלו הן שמונת ימי החג ושמונת ימי חנוכה ויום טוב הראשון של פסח ויום טוב (ראשון) של עצרת ובגולה עשרים ואחד יום ואלו הן תשעת ימי החג ושמונת ימי חנוכה ושני ימים הראשונים של פסח וב' ימים טובים של עצרת
As Rabbi Yoḥanan said in the name of Rabbi Shimon ben Yehotzadak: On eighteen days a year, the individual completes the full hallel. And they are: The eight days of the festival of Sukkot, including the Eighth Day of Assembly; the eight days of Hanukkah; the first Festival day of Passover; and the Festival day of Assembly, i.e., Shavuot. And in the Diaspora, where a second day is added to each Festival due to uncertainty over the correct date, there are twenty-one days, and they are: The nine days of the festival of Sukkot, including the last day, known as the Celebration of the Torah, the eight days of Hanukkah, the first two days of Passover, and the two Festival days of Assembly.
מאי חנוכה דתנו רבנן בכה בכסליו יומי דחנוכה תמניא אינון דלא למספד בהון ודלא להתענות בהון שכשנכנסו יוונים להיכל טמאו כל השמנים שבהיכל וכשגברה מלכות בית חשמונאי ונצחום בדקו ולא מצאו אלא פך אחד של שמן שהיה מונח בחותמו של כהן גדול ולא היה בו אלא להדליק יום אחד נעשה בו נס והדליקו ממנו שמונה ימים לשנה אחרת קבעום ועשאום ימים טובים בהלל והודאה
The Gemara asks: What is Hanukkah, and why are lights kindled on Hanukkah? The Gemara answers: The Sages taught in Megillat Taanit: On the twenty-fifth of Kislev, the days of Hanukkah are eight. One may not eulogize on them and one may not fast on them. What is the reason? When the Greeks entered the Sanctuary they defiled all the oils that were in the Sanctuary by touching them. And when the Hasmonean monarchy overcame them and emerged victorious over them, they searched and found only one cruse of oil that was placed with the seal of the High Priest, undisturbed by the Greeks. And there was sufficient oil there to light the candelabrum for only one day. A miracle occurred and they lit the candelabrum from it eight days. The next year the Sages instituted those days and made them holidays with recitation of hallel and special thanksgiving in prayer and blessings.
רב נחמן אמר קרייתא זו הלילא רבא אמר בשלמא התם (תהלים קיג, א) הללו עבדי ה' ולא עבדי פרעה אלא הכא הללו עבדי ה' ולא עבדי אחשורוש אכתי עבדי אחשורוש אנן
Rav Naḥman said an alternative answer as to why hallel is not recited on Purim: The reading of the Megilla itself is an act of reciting hallel. Rava said a third reason why hallel is not recited on Purim: Granted that hallel is said there, when recalling the exodus from Egypt, as after the salvation there, they could recite the phrase in hallel: “Give praise, O servants of the Lord” (Psalms 113:1); after their servitude to Pharaoh ended with their salvation, they were truly servants of the Lord and not servants of Pharaoh. But can it be said here, after the limited salvation commemorated on Purim: “Give praise, O servants of the Lord,” which would indicate that after the salvation the Jewish people were only servants of the Lord and not servants of Ahasuerus? No, even after the miracle of Purim, we were still the servants of Ahasuerus, as the Jews remained in exile under Persian rule, and consequently the salvation, which was incomplete, did not merit an obligation to say hallel.
מדקאמר בשעת הלל מכלל דבראש השנה ליכא הלל מ"ט אמר רבי אבהו אמרו מלאכי השרת לפני הקב"ה רבש"ע מפני מה אין ישראל אומרים שירה לפניך בר"ה וביום הכפורים אמר להם אפשר מלך יושב על כסא דין וספרי חיים וספרי מתים פתוחין לפניו וישראל אומרים שירה:
§ The Gemara comments: From the fact that the mishna states: When hallel is recited, one can conclude by inference that on Rosh HaShana there is no recitation of hallel. What is the reason that hallel is omitted on Rosh HaShana? Rabbi Abbahu said: The ministering angels said before the Holy One, Blessed be He: Master of the Universe, for what reason don’t the Jewish people recite songs of praise, i.e., hallel, before You on Rosh HaShana and on Yom Kippur? He said to them: Is it possible that while the King is sitting on the throne of judgment and the books of life and the books of death are open before Him, the Jewish people are reciting joyous songs of praise? Rosh HaShana and Yom Kippur are somber days of judgment whose mood is incompatible with the recitation of hallel.
רב איקלע לבבל חזינהו דקא קרו הלילא בריש ירחא סבר לאפסוקינהו כיון דחזא דקא מדלגי דלוגי אמר שמע מינה מנהג אבותיהם בידיהם תנא יחיד לא יתחיל ואם התחיל גומר:
On this topic, the Gemara relates: Rav happened to come to Babylonia, where he saw that they were reciting hallel on a New Moon. Unfamiliar with this practice, he thought to stop them, as he assumed that they were reciting hallel unnecessarily. Once he saw that they were omitting portions, he said: I can learn from this that they are maintaining the custom of their forefathers, i.e., they know that it is a custom, not an obligation. It is taught in a baraita: An individual should not begin reciting hallel on a New Moon, but if he has begun he should complete it.