This is the first verse of "Just The Two Of Us". What I was wondering was why do most people see it as DbM7 C7 progression instead of a Db7 C7 C 6/5 (first inversion)? I hear the and keyboard bass move, so I don't think it's entirely invalid, but all the lead sheets and videos I see don't say this.
Do inversions just not count in chord progressions?
I listened to a bass cover of this song here. At 0:25 the first verse starts (the chord progression I refer to.
I had to compare your question and lead sheet a few times, but now I think I can answer, and do it without transcribing the video.
The lead sheet gives Dbmaj7 C7 Fmin7
You hear Dbmaj7 C7 C7/E.
(You originally wrote C6/5, but that mixes up jazz/pop chord symbols with figured bass/Roman numeral analysis numeric figures. I understand what you want to say, but in jazz/pop chord symbols you use a slash to denote <chord>/<bass pitch>.)
Anyway, I think what is going on, or at least what could reasonably happen when playing from that lead sheet, is arpeggiating the bass for C7 to move to the Fm7 chord. Playing a bass part of C E to F would work for that chord change. The C E part would be a typical way to "walk" the bass, because it arpeggiates the tones of the chord, and because E to F is a nice half step move to the root of Fm7.
In a lead sheet you could make such a bass line explicit, sort of required, if you gave specific chords Dbmaj7 C7 C7/E F. That would tell players you really must play the inversion, or else it isn't quite right. A very obvious case of this is a song like My Funny Valentine, which uses lots of "slash chords" to give the famous descending bass line of the verses. If the lead sheet didn't give those exact inversions, you would loose one of the most important features of the song.
In the case of Just The Two of Us, the lead sheet doesn't explicitly give inversions, but a bass player may include them ad lib. Now, it could be the case that in real performances many players use that passing E, enough so you hear it as an essential part of the song. Apparently lead sheet authors don't see it that way.
How Come This Doesn't Count As An Inversion?
This is really a bit of another question. If everyone plays that E, why should it not count as an inversion. In other words, you're asking, when is such a thing a bona fide chord versus passing motion?
Metrical placement is probably the most obvious distinction.
If that E was on a strong beat like 1 or 3 (the song is in 4/4), then there is a good case for saying C7/E should be in the lead sheet.
The lead sheet doesn't say that. Typical performance will be to play the root on the strong beats. Bass players can then ad lib the E on relatively weaker beats which renders it as part of passing motion.
ii-ii6-V or i-i6-ii6-V).
In this particular case, beat 4 of bars 1, 3, etc. can be considered an C7/E (figured bass symbols are not used in contemporary music) inversion but it is really just part of the written bass line which is demonstrated in the bass video you linked. In this case the E on beat 4 is more part of a passing note/moving bass line than a pure inversion. If a guitarist or keyboardist were playing the chords to this song in the context of a band they would not bother re-voicing the chord to include the E on beat 4, I know from personal experience as I have played bass on this song with many different bands a multitude of times.
There are many instances where inversions are a crucial part of a song. One example that comes to mind off the top of my head is the second chord of the intro and verse to “Wonderful Tonight” by Eric Clapton:
G D/F# C D
The F# bass gives a completely different flavor to the progression than just playing a D chord in root position.
Unless absolutely essential, chord charts generally don’t bother with inversions. The basic chord is given, but the bass line and chord voicing are left to the performers.
When needed, inversions are typically notated as slash chords. That would be appropriate here, since the bass movement is so expected when hearing this tune, but even then it’s often assumed that performers will know what to do.
It’s important to remember that lead sheets are less intended for learning music (though often used that way) than for reminding one of a tune they know or have at least heard before.
