Easter Sunday has an octave, discussed by Fr. Guy Nicholls of the Birmingham Oratory. This means the days after Easter Sunday have the same weight in the Liturgy as any Sunday. Other Feasts used to have an octave also. Easter in fact has an octave of octaves with the Easter season although Eastertide is not as grand as the Easter Octave nor of course Easter Sunday itself. Try not to think too hard about the fact that this ends on Pentecost, a day which means fiftieth (days are counted inclusively) and an octave of octaves ought to be sixty-four.
Pentecost used to have an octave. The vestments were red, as for Pentecost Sunday. This upset the tidy minded and it was abolished. There is a well attested story about Pope Paul VI's reaction. Fr. Nicholls mentions one reason for the change: "With regard to a pneumatological focus to the liturgy, I find it difficult to see how the pre-Pentecost Novena (as argued by Mgr Bugnini) can adequately replace the weight of the post-Pentecost Octave." This refers to the following passage.
The Easter season lasts fifty days, beginning with the Easter Vigil and ending with Pentecost Sunday. This is attested by the ancient and universal tradition of the Church, which has always celebrated the seven weeks of Easter as though they were a single day that ends with the feast of Pentecost. For this reason, the octave of Pentecost, which was added to the fifty days of Easter in the sixth century, has been abolished. However, the days from Ascension to Pentecost with their appropriate texts are used as a time of expectation of the Holy Spirit.
Annibale Bugnini, The Reform of the Liturgy, 1948-1975
(Collegeville Minn.: The Liturgical Press, 1990)
Part II "Sections common to the new liturgical books",
Chapter 21 "The calendar" II, p.319.
There still is a Pentecost Novena, a recollection of the nine days prayer between the Ascension and Pentecost in Acts 1-2. Ascension of course is moved to the nearest Sunday in many territories which mucks up the Novena. Perhaps the point of the move was to justify the abolition of the Pentecost Octave? I jest, I jest.