A main theme that pops out from Eph. 5:19-20 and Col. 3:16 is the corporate emphasis.  Yes, the singing and making melody and the giving of thanks is primarily directed towards the Lord, but also to each other in the gathering.  In Eph. 5:19, it is speaking to one another while singing and making melody to the Lord.  In Col. 3:16, it’s teaching and admonishing one another and then singing to God.  That doesn’t mean it’s more holy to sing in a monotone, but that there is simultaneously a horizontal and vertical dynamic occurring in our worship.
It’s sad then that this mindset is mostly absent in almost all thought about corporate singing.  Think about some common answers to this question: What is the #1 benefit of corporate singing for the participant?  “It lifts up my spirits or makes me cry or gives me a sense of purpose.”  If you ever listen to songs on YouTube, you can always see this language in the comments—“This song is so good BECAUSE it led to tears streaming down my face.”  Singing is most often pursued for and measured by the emotional benefit to the singer.
This leads many to approach corporate singing like this: “Worshipping in song for me is being able to express myself however I want regardless of how it affects or distracts those around me.  The songs need to be designed to help me feel closer to God or to help me get lost in my emotions so that my problems will be washed away at least for 3-5 minutes.”
Contrast those things with the emphasis of the texts above—Personal benefits aren’t even mentioned!  Instead we are to seek to edify one another as we sing from the heart to the Lord.  You might be thinking: “How can I edify others when I sing?  I didn’t write any of the songs.”  That’s true, but you’re singing it, which means you are affirming that truths that it contains.  You’re exalting God and the gospel of Jesus Christ; you’re acknowledging your absolute desperate state apart from his mercy and you’re thanking him for who he is and what he has done for you through the sacrifice of the Son.  With regards to that last part, notice how the Eph. and Col. texts end with the priority of thankfulness.  Singing without thankfulness is like air without oxygen, which means it’s not really beneficial.  Depending on our week and how well we have been battling the flesh, we may arrive not at all ready to give thanks to the Lord.  The next thing we know, the song, “My Heart is Filled with Thankfulness,” begins and we think: “Actually no it’s not, so I need to repent of this bitter, hard-heartedness because all of these people are admonishing me to be thankful by the way they are singing with genuine gratitude.”
So just like prayer, our truth-filled singing together is instructive and can renew our minds.  Thus, not only are all Christians singers, in this way, all Christians are teachers and this kind of edification can only happen in the corporate setting.