The Rule of Saint Benedict: Chapter 15

Not much for an introduction today; I'm running out of things to say to open these short chapters. I will say this, though, and that is for everything there is a reason. I may not know what the reason is, nor how to accurately explain the reasonings behind the thing, but there is a reason for the thing.
Chapter 15: The Times for Saying Alleluia

1. From the holy feast of Easter until Pentecost, "alleluia" is always said with both the psalms and responsories.
2. Every night from Pentecost until the beginning of Lent, it is said only with the last six psalms of Vigils.
3. Vigils, Lauds, Prime, Terce, Sext, and None are said with "alleluia" every Sunday except in Lent; at Vespers, however, a refrain is used.
4. "Alleluia" is never said with responsories except from Easter to Pentecost.

Now, I have no idea why this is this way. The only thing I can come up with is that "Alleluia" comes from the Hebrew "hallelujah" which means "a joyous praise in song to ‘Yah’" with "Yah" obviously referring to God, and since Lent is a solemn time of year we put this joyous proclamation to rest. It seems familiar to the concept of having a censer with no bells used during Lent, and one with bells used at other times.

I should note here that in the Eastern Rite we do say "Alleluia" during Lent; what St. Benedict has written here seems to have evolved only in the Western Rite. This idea is so ingrained in Western Christianity that when I was searching for why Alleluia is not said I only found things that would tell me that it wasn't. Catholic Answers, the 1960 Breviary, another group of Oblates, and even an Episcopalian parish all tell me that Alleluia isn't said during Lent. The only thing that gets close to an answer is from Catholicism.About where it is mentioned that, 

"During Lent, however, our focus is on the Kingdom coming, not on the Kingdom having come. The readings in the Masses for Lent and in the Liturgy of the Hours focus heavily on the spiritual journey of Old Testament Israel toward the coming of Christ, and the salvation of mankind in His death and resurrection.

We, too, are on a spiritual journey, toward the Second Coming and our future life in Heaven. In order to emphasize that journey, the Church, during Lent, removes the Alleluia from the Mass. We no longer sing with the choirs of angels; instead, we acknowledge our sins and practice repentance so that one day we may again have the privilege of worshiping God as the angels do."

This doesn't seem like a real answer to me, but it seems close to what I thought about it being a joyful proclamation not being used during a solemn time.

I want to close on this final thought; the Western Rite is (or rather was at one time) Orthodox. It was made during the time that Rome was still a part of the Orthodox Church. There were many rites that were floating around, even in the East a few jurisdictions had their own rites. Eventually, East and West both settled on their own rites that became prevalent in their regions. But the West was once Orthodox, and we should not be scared of using those things from the West that still are Orthodox.