This is how I came to that belief:
One of the most common books that are associated with music in the Bible is Psalm. The entire book itself is a list of songs and praises written for the Lord. Some of the psalms even give a reason for singing. Psalm 47 states: "Clap your hands, all you nations; shout to God with cries of joy. For the Lord Most High is awesome, the great King over all the earth." ; Psalm 81 says: "Sing for joy to God our strength; shout aloud to the God of Jacob!" ; Psalm 89: "I will sing of the Lord's great love forever; with my mouth I will make your faithfulness known through all generations." ; Psalm 13: "I will sing the Lord's praise, for he has been good to me." From these few examples we have the reasons: God is awesome, for joy to God, sing about the love and faithfulness of God, and sing because of what He has done. From this it is evident that the main reason for these songs is to sing of the thing God has done for them in their lives. Now I am not sure if you see any parallels so I will spell it out for you. The majority of these songs were to tell others about the wonders God has done in their lives. In a nutshell these songs are all testimonies, yet they are in the forms of songs! It is written in Colossians 3: 16, "Let the message of Christ dwell among you as you richly teach and admonish one another with all wisdom through psalms, hymns, and songs from the Spirit, singing to God with gratitude in your hearts." It's pretty self explanatory in that verse that we can sing praises to the Lord and glorify Him by teaching each other about the message of Christ that dwells in us through music.
I believe that music as a form of worship in our faith is a necessity. It blows my mind to think that by singing these hymns and these songs I not only realize the testament shared by the composer but I can also use them to bring praise to the Lord and share His good deeds. I can spread the gospel through song, I can share my testimony through song, and I can praise and glorify His name through song. If we as Christians have always been wrong about music and worship, then how could I do all those things which we as Christians are called to do? We are able to worship the Lord with music and keep His commands and that is why I believe the role of music in worship is vital for our faith.