I think what you are talking about is the hymn that is sung whenever something is blessed or consecrated. You hear it so many times in the two videos from the consecration because they are consecrating so many things in the new church, starting with the altar.
On the walls you see 16 white cross-stones, one for each of the 12 Apostles, plus Sts. Mark, Luke, Paul and Gregory the Illuminator. If I understand our tradition correctly, there are supposed to be 16 columns, or pillars, in a church (the word used by the bishops in the video was "syoon.") Each one is supposed to be dedicated to one of those saints. Of course not every church is going to have 16 pillars in it, so usually they put 16 small crosses high up on the walls of churches and they get anointed and blessed when the church is consecrated. (At least that is what you usually see here in the US.) In this cathedral, they put 16 carved cross stones on the walls. The consecration of each one of those cross stones is what took up much of the two videos, and the hymn that is sung for consecrations is repeated each time.
I'm not a great translator, but roughly, the bishop chants that he is blessing and anointing the pillar ("syoon") in the name of the particular apostle, and then he says "Ays Nushanav..." which means "by the sign of..." and the choir continues what he is saying by singing "...the Holy Cross, the Holy Gospels, the Holy Muron (Chrism), and the Grace of the day, in the name of the Father, the Son, and the Holy Spirit, now and ever and unto the ages of ages. Amen, alleluia, alleluia, alleluia."
I'm sure VasnTearn could give a better translation if she sees this, but I think the above gives you an idea of what is being said.
