Quote Knut Skaarberg:
An Em with C# bass would be a C#m7(b5), wouldn't it?
Anyway, does anyone here know what's the standard notation for open voicings (no 3rd) such as C-D-G, C-G, C-G-Bb, C-D-F-G etc? What about quarter chords (4th, but no 3rd or 5th) such as C-F-Bb?
One can't really say "standard" here, because the chords themselves are not standard. The open fifth I've sometimes seen notated as "5". Thus C-G alone = "C5"
C-G-Bb I'm not sure. I'd probably just write "C7(no 3rd)". Alternatively you could write Gm/C, if you felt relaxed about the player adding a D if he wants.
The others you describe are various combinations of 4ths/5ths and 2nds/7ths. As such, if you juggle the notes a bit you can usually reduce them to some kind of sus4, or 7sus4 chord, and then just use a slash to indicate the bass note. Thus:
C-D-G = Gsus4/C
C-D-F-G = G7sus4/C
C-F-Bb = Fsus4/C
But if you're really thinking in 4ths, as opposed to writing within a conventional framework of 3rds but in a "4thy" way - then you might be better off notating the part at least in guide tones. Write a chord voicing upwards in 4ths, in semibreves, and then just tell the player to use whatever rhythm feels right to it.
In modal jazz, it's quite common for pianists to gravitate towards 4ths and 2nds because they capture the harmonically "floating" sound better and don't push things in as clear a direction as 3rds. So you might write "Cm11", and depending on the feel and style, the player might voice it upwards: C-F-Bb-Eb, omitting the G and making 4ths out of everything else. Some of Bill Evans's playing on "Kind Of Blue", and similar music of the period, is a case in point.
But this is a very inexact science and it relies on people sharing a common set of unspoken understandings, or being able to walk over to the piano, stab a few 4ths and say "a bit more like that!" or whatever...