I studied music - meaning not just private lessons and band camp, but performed with a range of orchestras, attended conservatory and took music theory, composition. I also played and wrote jazz, and also studied and worked professionally as an actor and director. When I think about what I had to really focus on understanding in photography, and what I "already had" when I came to it, I agree about the ideas of progression, counterpoint, tension and resolution, line and lines. I was a pretty good black and white abstracts photographer without even much thinking about it - I even had my work in small galleries and individual shows. One of the games that I used to play with friends I worked with in music was, we'd take a painting or photograph and improvise off of it, and find our way to what we felt was the essence of the picture. Mostly playing with rhythm, dynamics, and line.
What took me years to understand was color, gesture, emotional content of an image, and the human flesh and blood part of what I consider to be the difference between interesting images and great photographs. It's hard for a musician who's not facile on multiple instruments to play with color, and you can only do one color at a time. Even my design, improv, and directing training in the theater didn't get me to an understanding of how to really USE color instead of just thinking, isn't already there? and find gesture in an image. Performing arts of any kind have the benefit of iteration.
What gave me the biggest leap forward was working with, talking with, observing and questioning, painters. Color field painters taught me that colors have rhythms, and the right combinations of colors can play beats (opposite ends of the color wheel...). I learned about gesture from abstract painters of various sorts - learning why two canvases of seemingly random splashes and slashes of color had totally different effects, one was emotionless "isn't that interesting" and the other made me catch my breath, swallow hard...
When people tell me they want to be a photographer, I encourage them to study painting, where there are thousands of years of thinking about how to use 2D space and color effectively. I'm sure that every art form can teach you something about others, I know it works that way for me to some extent. And it makes for great rhetorical flourishes as headlines on really interesting articles.