The Passion is read "by anticipation" on Palm Sunday. Although that day begins joyfully with the ceremony of the palms, it ends with a "character of sacred gloom," as the liturgist Dom Prosper Guérenger, O.S.B., puts it in his The Liturgical Year (vol. 6), p. 200:
The third part of to-day's service [for Palm Sunday] is the offering of the holy Sacrifice. The portions that are sung by the choir¹ are expressive of the deepest desolation; and the history of our Lord's Passion, which is now to be read by anticipation, gives to the rest of the day that character of sacred gloom, which we all know so well. For the last five or six centuries, the Church has adopted a special chant² for this narrative of the holy Gospel. The historian, or the evangelist, relates the events in a tone that is at once grave and pathetic; the words of our Saviour are sung to a solemn yet sweet melody, which strikingly contrasts with the high dominant³ of the several other interlocutors and the Jewish populace. During the singing of the Passion, the faithful should hold their palms in their hands, and, by this emblem of triumph, protest against the insults offered to Jesus by His enemies. As we listen to each humiliation and suffering, all of which were endured out of love for us, let us offer Him our palm as to our dearest Lord and King. When should we be more adoring, than when He is most suffering?
¹See the "Palm Sunday" section here.
²cf. pp. 30-40 of this 1957 guide by Solesmes.
³i.e., a high-pitched fifth