Well, the cross was the end of the line of Adam. Everything that man is after the flesh was dealt with there, finally and completely. It was the end of the reign of death which came in because man's nature was corrupt.Old man as in old nature - sin nature - self nature ?
What does the cross and what Jesus did have to do with how we worship or sing or play music ?
"... but death reigned from Adam until Moses, even upon those who had not sinned in the likeness of Adam's transgression, who is the figure of him to come." - Romans 5:14
The cross brought about a change in the way that God could deal with man. From the fall of man until the cross, God is necessarily at a distance. The holiest of holies in the tabernacle was veiled. There were limitations, restrictions. The actuality of all that was in the heart of God was yet to be realised, because Christ hadn't come in yet, so God took pleasure in things which represented that which was to come: the tabernacle system. These were types, figures which show us that Christ, not Adam, was what God had in mind from the very beginning. Everything that attached to the worship of the children of Israel was a type, a symbol. In order that all these things should be set on as God intended, He gave detailed instructions. And all this was made by craftsmen, builders, musicians, perfumers, and so on. All the craft and ingenuity of man was employed in making the grandest and finest symbols - but still only symbols, nonetheless, of the real thing. They were merely shadows of what was to come.
Then, Jesus came into the world. Not in the way that the Jews expected, not what the grand designs of the system which they had been a part of led them to expect. He came in, not in royal pomp and splendour to Jerusalem, but as a babe, a homeless, houseless stranger to Bethlehem. Then we have His life, one of humility, not of outward display in a grand way - touching the lives of needy sinners whenever they came to Him, seeking and saving the lost. Then, on to the cross, and everything that happened there. What a change we see, either side of the cross! Before it, the tabernacle system, every human talent and craft employed in the building of it. After it, in the Acts and the Epistles, we find not a single, isolated mention of any human craft, talent or ability being used in the service of God. From an earthly system which was a type, we move to a heavenly system which is a reality. Christ has secured everything, and everything for God's pleasure is bound up in that One, the One who was in God's heart from before time was - who was with Him in a past eternity.
Now, I'm sure we can agree on the facts of the above, but you're asking what practical bearing that has on us, how it changes the way we worship. Well, if Christ is everything for God's pleasure, and He has given Himself and the Father has sent the Spirit so that features of Christ might be developed in me, for the pleasure of God... where is the room for what I am naturally? What can Adam bring that Christ cannot? In order to be a vessel filled, ready to be poured out to God in worship, I have to be emptied first, of any notion of self or the value of what I am after nature. In order to be filled, I have to gaze steadfastly on Jesus, gathering precious impressions of Him. If I start to think about what I can do of myself to worship God, I take my gaze off Christ and I become occupied with self and my own talents and abilities. I wouldn't get filled that way. No, I have to disappear in my own estimation, so Christ is all-in-all. The only way I can do that is by having Him fill my heart and soul, leaving no room for self. Notions of self-worth have to be utterly displaced by a consciousness of the peerless worth of Jesus.