He still occasionally works on music, but has "not been putting pressure on myself... I just do what feels good and feel very lucky that I have this other strand of acting that I'm able to explore".
Alexander said he felt he had "learned so much" over the last decade about the way he likes to work.
"But for me," he continued, "a lot of the reason I think the [music] industry has changed so much is that it's set on this model which is very antiquated now, and it's not kept pace with the times.
"Lots of artists have this direct link with their audience via social media. They want their music out quickly. The whole model of promoting it - three singles into an album, then you tour the album, then move onto the next one - it's not really working like it did."
He noted that record labels could historically make an album a success because they were "able to pour a lot of money into something".
"They just can't do that now. Everything has changed. But I think that is exciting for lots of reasons, and it is an exciting place for artists, even though it's harder to break through."
He concluded: "If I go back into it, it'll be because I think it's fun and something I want to do, and not think too much about how it's going to perform.
"That's pretty much how I try to always feel, but you're in an environment where you have a lot of other stakeholders, and people telling you it needs to be this or that, and there's always that tension."