I belive that lots of musicians work best when its late, do you?
strictly only in the night, and only when i actually have to get up early the next day because of something really important 
I like to make music in the night, but there is nothing better than standing up, grabbing a pot of coffee and sitting down infront of the pc with a fresh set of ears in the morning. Usually I listen to some music before I start to get inspiration, but then …
no, I actually fall to sleep again most of the times. 
Generally I try to make some music anytime, well I try… 
My problem is I do have my best ideas at the working time (mmmhh… heavily thinking about to buy a notebook) sniff 
Get a recorder, and then you record the melody or consept that you came up with
or try to hum the melody until you come home 
that’s what i usually do (quite annoying for others though)
Or learn to write scores straight from your head
(A simple melody isn’t that hard really, but it requires some practice)
I remember when I was at school…
sometimes I just fell like asleep and started to imagine new music, then I wrote it down on paper…
being a complete selft-thought in music, having “studied” it only on trackers, I put the notes in a tracker fashion, so my school notebooks where filled by
C-4 01 2A 000
E-4 01 30 300
ahhh… golden age… 
wel… this is the golden age rememberings… the thruth is that once I came back home, I realized that what I wrote on the paper do not absolutely sound the way I intended, so most of times I just waste the sheet
Best time to compose is in the morning or afternoon, when energy is high and stamina is full on, and mind is in the zone, with studio monitors banging out. Best time for anything music. Also when you do it every single day and stick with that routine it makes you proud of your integrity which is a huge thing for me atleast. The side effect is that you engage in everything music day in and day out and things always move forward from there…skills crystallized, songs get created, books get read, contracts get ready and so on…the benefits are accumulative just like procrastination and laziness also accumulates rust .