The possibility that the angelic host sang upon the creation of the universe (Job 38:3-7) seems appropriate in light of the truth they cannot sing the song of redemption as do those humans redeemed by the Lord Jesus Christ.
"They sang a new song, saying, Thou art worthy to take the book, and to open the seals thereof: for Thou wast slain, and hast redeemed us to God by Thy blood out of every kindred, and tongue, and people, and nation" (Revelation 5:9).
"Unto whom it was revealed, that not unto themselves, but unto us they did minister the things, which are now reported unto you by them that have preached the gospel unto you with the Holy Ghost sent down from heaven; which things the angels desire to look into" (I Peter 1:12).
The Bible teaches that a rebellion took place upon the angelic host at some time in the ancient past. Led by Lucifer, apparently one third of the angels chose to forsake their created purpose and identity in following the devil into opposition to God (Revelation 12:1-4). The remainder of the angels chose faithfulness to their Creator, and likely comprised the host that sang and shouted upon the occasion of God's forming of the universe. Therefore, they have no need of salvation, and no music of redemption in their hearts. The sang for joy at the time of creation. Conversely, redeemed human beings will sing eternally concerning the saving grace of the Lord Jesus.
The Apostle Peter wrote that angels "desire to look into" the things of the Gospel. The primary reason for this is likely the fact that the need of humanity for salvation brought forth realities from the heart of God that had never before been seen. For example, God's delight for mercy requires "vessels of mercy" if its display is to be known and appreciated (Micah 7:18; Romans 9:23). His amazing capacity to forgive would never have been known without our desperate need for forgiveness. This is not to imply that our Lord determined our sin in order to better reveal Himself. However, He has taken advantage of our sad plight as the means to display heretofore untold aspects of His goodness. Such wonders are the object of angels' keen interest.
A different sensibility would accompany the songs of the creation and redemption. Of the former, great awe, appreciation, and thrilled exuberance would have filled the hearts of the angelic host as they beheld God's wisdom, power, and artistic creativity (I would love to have been a fly on an angel's wing to have seen what they saw!). The redeemed, however, fall before the Lamb of God with hearts overwhelmed by the grace and mercy of a Lord whose wounds for our benefit remain etched upon His glorified body (John 20:27). Angels were awed by the magnitude of God as they sang for joy at the time of creation. Humans redeemed by Christ are overwhelmed by the mercy of God whenever we sing for love upon remembrance of our redemption.
We are not told that angels sang at any time during the earthly life and atoning work of the Lord Jesus as He rescued humanity from its terrible pit of sin. Perhaps this was because they were so awed and bewildered by the glories of grace and mercy revealed in Christ that words and music were not possible. Yes, they desire to "look into those things" about us that open wide the portals of their Creator and our Redeemer's amazing heart.
"But God, who is rich in mercy, for His great love wherewith He loved us, even when we were dead in sins, hath quickened us together with Christ, (by grace ye are saved;) and hath raised us up together, and made us sit together in heavenly places in Christ Jesus: that in the ages to come He might show the exceeding riches of His grace in His kindness toward us through Christ Jesus."