I have a program that my son ( a computer whiz) downloaded to my PC called Anvil Studio, Whilst I do not 'compose' midi files myself, usually downloading them from the internet, Anvil does allow you to 'compose', using either a musical stave or a 'piano roll' view. Unfortunately (on my PC) using 'piano roll' view only about half the keyboard is on screen at any one time - this is not too inconvenient you can scroll up and down to see the rest. However the basic program is a 'Free' download so you can have a play with it.
Either Google <anvil studio> or go to < www.anvilstudio.com > .
If you do have a go please let us know what you think of it, I'd like to try out any 'rolls' you compose in Midi format - I have a Yamaha 'Portable' digital piano which sounds quite good playing from the computer.
Good luck with the files.