I think I have problems with just writing down what the chord progression is. Usually I'll forget exactly how something sounded when I played it on guitar or piano--the rhythm, dynamics, etc.
Record what you're playing, then you can always get someone's help if you can't figure it out later, but you'll have the document. I use my iPod with a Belkin mic to record important bits of rehearsals so I have some kind of record. Then, if needed, I'll notate it or else just use the recording to remember.
Are most bands so used to improvisation that they don't need to notate every single part? Just have the drummer come up with a beat for each section, come up with a chord progression for each section, then write what the chord progressions are but improvise the rhythm until you get a final part?
That would depend on whether you are (or anyone else is) writing for the band or if everyone's writing collaboratively. I've played in many situations where we just play tunes to work out arrangements. Depends on the band/writing style/time constraints. Also, I've played both with people who can't remember a tune until they've played it a million times and with people who get it after one play-through.
Elvis Costello learned some music theory and, more importantly, notation for the Juliet Letters album with the Brodsky quartet (later in his career). This is because he was writing and arranging the music (deciding exactly who plays what and how), and because he couldn't ask the Brodsky Quartet to to hang out and rehearse a couple times a week for a year to get the parts solidified.
Music theory is a representation of what you are hearing and by analysis can generate 'rules' for how we make music. So you can either know in your ear that a D-7 chord leads well in many cases to a G7 chord, or you can study Jazz and find that this progression is a major building block. This means that when you're writing and you've come up to D-7 chord and are looking for the next chord, you may either draw upon your ear or your knowledge of theory to suggest that a G7 might be a good next chord. Likewise, you can also decide by either method that the music wants to go elsewhere, avoiding the obvious choice.
My long-winded point is that theory can help expedite the process of writing or help you to achieve a style you're looking for, but it isn't truly necessary. Elvis Costello, for example, wrote Imperial Bedroom (and all his earlier music) without it (written, that is - his ear/musical sense is great) and did brilliantly. And so have so many others.
Hmm, I guess MIDI is a form of notation...I guess I mean in a classical sense, like the five line staff and treble and bass clefs.
MIDI representation is just another representation like "traditional" notation, except, obviously, that MIDI notation is typically electronic so it can be fed back into a sound module. Not all written notation is 5-line, or treble or bass clef. Different instruments use different clefs, in addition to bass and treble, and different numbers of lines in their staves. Some don't traditionally even use key signatures, e.g. French Horn. These different clefs and transpositions (which clef, which octave, how many steps off what's actually heard...) are to facilitate easier reading by humans. They essentially ensure that the common part of the range is in the 5 lines of the staff. Devices that play MIDI notation or instructions, don't need this convenience.
most bands don't even know how to read notation, let alone write it. You can notate if you want... from time to time I might work in that way vs. the traditional "band" way... but for the most part... music should sound GOOD not sound RIGHT.
