what is the notation for a chord without the third?  

for example, a c7 without the third being c, g, bb, c
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c7(omit 3) or c7(no 3)
savage is correct  but you may re evaluate your musical situation and re  
evalute whether the chord is acutally functioning as a c7 chord after all.  without a 3rd it probally is not.  maybe it is more acuratly a g minor chord with a tension 11 added to it or  a g sus 4 chord.  its just that a c7 chord is a "dominant chord".  a dominant chord of all the chords has one of the most distinct sounds and musical functions.  without the third it loses that,  making c7(no 3rd) even though correct
symbolism a bit of a contadiction in termonology.  sort of like saying..
powerful rifleman (with no rifle).
the chord i'm playing is based on what gene harris does on the first chord of 'lu's blues' in his maybeck recording.  he starts this 8 bar blues in f by holding a chord which has c, g bb, c.  the c is in the base, and the chord which follows it  is an f7, so it seems appropriate to call it some kind of c chord.
using the cycle of 5ths as a guide in understanding this(going back in the forum will get you to some threads that deal with this in detail)will show you that c "resolves/moves" to f(chord type is secondary here),the logic behind what mike posted applies to this 100%.leaving out the third in this context as a voicing option doesn't affect things as much as in other situations......bassist might be playing it or duration of chord in context of arrangement might be a factor in it working or(most importantly),it might be there but doesn't sound like it to your ear based on how he's voicing the chord..a little while ago i posted some dom7th voicing options you might want to check out..maybe 5 pg. in(??)
third is very important because it determines major or minor mode of a chord.  
comparing with sex, major = male, minor = female, omitting third produces something asexual, indefinite, vague... are you thinking something bad? about a third sex?  mhhh...  
when i play a 11 or a #11 chord i always omit 3, producing an impresionistic atmosphere.
often a chord without a third will be called "open". if no tonal center is eszablished it can serve an ambiguous function.

however if the tonal center is well defined, the type of third ommitted will still be implied by the tonal center.

if an "open c7" is followed by an f7, it strongly implies the tonality of bb major and therefore also strongly inmplies that the missing third of the c7 chord is an eb.

i don't know the song "lu's blues", but if it really is a blues, one of the defining elements of the blues style is ambiguity as regards the thirds. typically the harmony uses a major third, yet the melody uses minor thirds.

if the tonal center of "lu's blues" is f major (f blues major), there is no doubt that your chord is a regular dominant c7 and that the missing third is major. leaving out the third in the bass is a common feature of both blues and funk.

if you are really concerned about what the possible quality of the missing third is, look to the tonal center for the answer.

7
however if the tonal center is well defined, the type of third ommitted will still be implied by the tonal center. (this is what i was trying to get at)
btw jeff,which tune on cptb was it?
a third sex? think of the possibilites....
we're joking around but in reality all around the world sensitive people exist(maybe even check out ljp) who are anatomically this way...
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