There's 37 because that gives exactly 3 full octaves including both the top and bottom octave.
I have a macro that shows/hides some blank hotbars and have them aligned how a piano's keys are. I click on the "Performance" macro to bring up the virtual keyboard, and on any of the other macros to hide it again. It will also automatically hide if I switch jobs. Admittedly, I'm only able do this because I use the 7-10 non-shared hotbars solely as a database of sorts for switching between preset hotbars in a menu-style system to save screen space and my Bard's 7-10 were empty.
What I do want is a way to /micon the note icons so that I can set it as my "Performance" macro icon.