It really depends on what you mean by ‘owns’..
In terms of copyright law, the situation is clear: (s)he who owns the copyright for a work of art or music is the only person or entity able to financially benefit from it. Of course, the situation isn’t quite as clear as that because there may be multiple composers, lyricists, arrangers, performers etc who will claim that a part of the work is their intellectual property, and therefore they are entitled to a cut of any profits made from the song. And, songs are usually distributed through a complex network of parties, including those involved with the production (engineering etc), marketing, and distribution.
In any case, as far as amateurs are concerned, if you reproduce any part of a song that belongs to another artist or entity then you are not permitted to make any financial gain. Furthermore, you must seek permission from the copyright owner to use any part of their intellectual property (and in some cases can pay for the privilege of performing the piece to a paying audience). But, without permission just writing out the lyrics of someone else’s song could well be technically braking the law.
We live in a complex modern world in which people can share their music, arts, ideas etc to the whole world in a few moments. And the practicalities and costs involved with chasing up everyone who has a go at a song that is protected under copyright law is usually simply not worth the effort. Unless someone is making big bucks from performing your song, it’s usually best not to bother chasing it up, especially because computer technology does a pretty good job of it. For example, if someone records and posts to YouTube a cover of a song that’s available on Spotify / iTunes etc, the software recognises this is the case and puts in certain blocks, including a block on ‘monetising’ the video. Occasionally, the video will also be blocked from being viewed in certain parts of the world where the original distributor of that song doesn’t hold the necessary licenses etc.
So, as far as learning a song that you like and recording it for your friends, family and other contacts, there’s usually no problem… as long as you don’t expect to make any money from it. And, if you wish to perform a large body of someone else’s work (such as a Broadway show) then you’ll need to buy permission to put the show on – this purchase usually also includes the rental of scripts and scores.
Artistically, the song belongs to whoever plays it
A common perception among music students is that they should attempt to perform a song such that it is as close to a facsimile to ‘the original’ as possible. So, when playing a Beethoven sonata one should, according to this doctrine, try to come as close to what Beethoven would have wanted as possible. Equally, when playing a pop song the final result should sound just like the original record.
There are practical problems with this approach, the first one being identifying just what we mean by ‘the original version’ of any given piece. Often composers would write multiple drafts, make changes, alter bits for particular occasions, change their minds about certain passages etc. Likewise, pop songs are often presented by the original artists in multiple guises, sometimes sounding wildly different depending on whether you’re listening to the album version, the live version, the radio cut or some remix. In any case, it’s not clear what constitutes the original work and what we ought to be mimicking.
But, a bigger problem in my mind is that if you attempt to create a copy of the original of any piece of art then you’re really missing the point of what it means to be an artist: that you need to bring something of yourself. When I sit down to play a piece I’m really balancing two elements: 1) the concern that what I play is in some way recognisable as a version of a song that other people might already know, and 2) that what I do with it is unique to me.
So, the answer to the original question about who owns a song is ‘whoever is playing it’. When I learned and recorded the Avett Brothers’ Murder in the City (below), I was aware that the beautiful version I knew from their album will already be known to many, but I wanted to put a personal slant on it. When the song speaks of brothers, I thought of my own brother, Anthony. When it mentions Dad, Mum and sister, again I had my own family in mind. I altered the lyrics accordingly, and performed the song with my own personal nuances that address my concern with my own family situation. I even include photos of them in the video that I posted to YouTube.
There’s one more group that any song belongs to: the listeners. Whenever you listen to any song or album you map your own experience onto it, understanding some elements of the original artist’s work (as far as one is able to understand the inner workings of other people), but also taking the message in through the filter of your own life experiences. The song becomes, in a very real sense, about you and your life.