ii6 chord in the third bar of ex. 31-1, the bass is
Db3. The flat on it is a courtesy accidental it is not double flatting the
Db of the key signature. The next chord the
V with the 6/4 5/3 figures (or maybe it says 8/3, it's hard to read) uses an
Ab - with a flat - not an
I think you're misreading the accidentals.
Beyond that, the point of the text book is to say the main, functional chords are
I on beat 1 of the first bar,
ii6 on beat 1 of bar 4, and
V on beats 3 and 4 of bar four, while all the chromatic movement on the 11 beats between
ii6 is just chromatic elaboration.
That's actually a pretty common concept. I think you can generalize the concept into something like
I ... <some kind of cadence> where the ellipse means proceed from the tonic (or maybe the dominant) with a whole lot of latitude about what the harmony is and it can be rendered tonally sensible if ended with a formulaic cadence.
I'm overstating the case on purpose. You can't get away with musical gibberish in the middle of a phrase and there are conventions for the structure of cadences. But, between some tonally clear start and ending there is a lot of harmonic flexibility. This textbook lesson is showing chromatic descending movement as a possibility and you don't need to put Roman numeral analysis on anything but the main, functional chords.
One other thing: I notice in your notes your wrote...
Bb in the bass, but the score has
Eb in the bass and the textbook analysis is...
The progression is a cadential 6/4 movement, or using older figure bass terminology, a double cadence.
The modern view is one of chord inversions where
6/4 means second inversion, but old figured bass is about intervals above a bass.
Modern analysis is
I6/4 V I where
Eb Ab C is viewed as second inversion of an
Ab major chord.
Figured bass (notation not analysis) is a notated
Eb with a
6/4 figure above it meaning play a sixth and fourth above the
If you get picky and philosophical about the identity of chords, the two views are very different. One is a tonic chord the other is a dominant chord. It's like saying up is down and down is up! How can we not tell the difference between a tonic and dominant chord?!?
The textbook labels
Eb Ab C as
V6/4 ...a dominant chord in the vein of old figured bass. Your label is
I6/4 a second inversion tonic chord.
This isn't a matter of right or wrong and personally I switch mentally between the two all the time. In a progression like
I V6/4 I6 I definitely think of
V6/4 as a second inversion dominant, but in
I6/4 V I I think of
I6/4 in the old figured bass way and consider the chord to be a suspension over a dominant.
I thought it might help you to point out the difference in how that chord can be labeled in different music theory systems.