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Section E. is not at all complete yet. In the moment only this is available:  altered chords / sections 1-3, 5, and part of section 9
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1. general information
2. diminished third on #4^; 
score examples
3. enharmonization of the double diminished triad and seventh chord, and of the hard diminished seventh chord
 
score examples
4. #IV and IIhv in other inversions
 
score examples
5. scheme of all altered chords
6. diminished third on #4^:
score examples
7. diminished third op 7^:
score examples (choose examples from the list below):
 
v Strauß: Till Eulenspiegel / Wagner: Tristan-Vorspiel / Debussy: Prélude à l'après-midi d'un faune
Franck, Prélude, Choral et Fugue
8. diminished third on 2^ in minor, and on #2^ in major:
score examples
9. overview of the enharmonizations and possible modulations
10. other issues? 

 
 
Franck, Prélude, Choral et Fugue  a few spots in the Prélude and the Choral
 
recording by Egon Petri (broadcast, 1957ann)
recording by J?rg Demus (1961)
recording by Stephen Hough
recording by E. Kissin
here is the complete score (pdf)
Below, you see two fragments of the Prélude and of the Choral respectively. In the context of a discission of altered chords works by Franck are very interesting, as they are often very chromatic and offer lots of examples of altered chords. 

In the first fragment, measures 15- 23 of the Prélude, we see that 

  • an Eulenspiegel chord on V is used in the concluding cadence (22/23). This chord is in fact used here as chromatic passing chord between VII and I.
In the second fragment, the beginning of the Choral, quite some altered chords can be found:
  • The most 'special' is probably #IIk/d/v/v (in measure 59), used here to connect bVI and I
  • The key of the Choral, Eb major, is reached by an enharmonic modulation (from B minor, the key of the Prélude); in this modulation a dominant seventh chord is enharmonized to German augmented (#IVdv6/5 in measure 58, after the final tonic at the end of the Prélude in 58)
  • German augmented chords occur in measures 62 and 66.
In measure 15, we have reached  the key of F# minor, the minor dominant key (after an initial section in B minor in 1-7, and a modulating section from 8-15):
          15
F# minor:    VII7       2                      V7 9 - 8         I                           VII7                                                            I 
                                                                     pedal point on I ---------------------------------------------------------------------------->
          17
F# minor:  (V7)
              of IV [that does not appear]
pedal point on I --------------------------------------------------------------------------------------------------------------------------------------->
             18
F# minor: III6                                      (VII7)                                                                                    III6
pedal point on I [= third of III here ]----------------------------------------------------------------------------------------------------------------|
             19
D major:  (V9b/7)
            of IV [that does not appear]
F# minor: (V9b/7)
                of bII [that does not appear]
 
From measure 20 we find (somewhat hidden by the dimished seventh chords) a progression using dominant seventh chords (in descending fourths): Ddom7 -- > Adom7 -- > Edom7 . I therefore believe the notation of the diminished chords in 20 and 21 is not entirely 'correct': In 20 we should imagine Bb instead of A#, in 21 F natural instead of E#:
            20
                                                   susp. 
D major:  (VII2 ----> V7)                                                                 C#dim as substiution 
                 of IV [that does not appear]                                            of A dom7
F# minor: (VII2 ----> V7) 
                of bII [that does not appear] 
          21
                                                  susp. 
D major:   VII2 ----> V7                                                                 G#dim as substiution 
F# minor: (VII2 ----> V7)                                                               of E dom7
              of VI [that does not appear]                                         - but resolving as LTDann to the D major chord in 22 - 
After III6 in measure 22 the secondary dominant of IV is not leading to IV (elision), but to VII6/5 instead. And by lowering G# in the bass to G natural, and by changing B natural to C# (middle voice), an Eulenspiegel chord on V is created, which acts as chromatic passing chord between VII6/5 and I, and resolves to the final tonic of this section:
            22
D major:   I6
F# minor: III6                                      (V2)                                       VII6/5                                   V4/3hv/v
                                                             of IV6 [that does                                                                Eulenspiegel on V
                                                               not appear]
            23
 F# minor: I 
The Prélude ends with a clear PAC in B minor (see also the complete score). The connection to the Choral is in just one measure: In 58 the tonic triad of B minor is changed to a dominant seventh chord, which turns out to be German augmented #IVdv6/5 in Eb major (this becomes clear when it resloves, in measure 59). We should read the enharmonization like this:
 
A
F#
D#
B		 A
Gb
Eb
Cb
(Or imagine the key of D# major 
instead of Eb major first:)
A
F#
D#
B		 G
F#
D#
B
 
            56
 B minor: I                                                                                                                      (V7)
                                                                                                                             for IV [that does not appear]
                                                                                                             Eb major:  = #IVdv6/5
                                                                                                                                                                      plagal resolution to 
                                                                                                                                                                          I in Eb major 
 
In measures 61 and 62, a little chain of (not resolving) secondary dominants leads to an enharmonic modulation in the moment it turns out that the last dominant seventh chord (on Gb in 62) has to be understood as German augmented in the dominant key of Bb major. We can read the enharmonization as:
 
Fb
Db
Bb
Gb		 E
Db
Bb
Gb
 
             59
  Eb major:    I       VI   I6/III  VII6/5md  bVI6 #IIk/d/v/v  I6    V2       I6   VII2md    (V7)   (VII2md)   (V7)   (V7)
                                                                                                                   turns out    of     turns out     of       of
                                                                                                                   to be:         bII      to be:        III      bVI
                                                                                                                   LTDann -->        LTD -->
                                                                                                                                          Bb major:  = #IVdv6/5  I6/4 V7
                                                                                                                                                                         German
In measures 66 German augmented in C minor is used to connect a secondary dominant of V and the dominant, just before the final cadence of this section:
           63
Bb major:  I
Eb major: V                                      VII4/3md
                                          C minor:  VII2 ----------------------->  V7 9 - 8  V2      (p)        4/3         I 4 - 3    2 (p)  (V4/3)  #IVdv6/5
                                                                                                                                                                                          German
The use of a chord sounding like half diminished on IV is a sort of 'special feature' of Franck. We cannot understand a chord like 'IVhfdim' in measure 68 as 'really' half dimished (as that would imply Cb instead of B natural, an impossibility in this context). It is possible to understand the chord as resulting from a non-resolving suspension: Eb can be seen as suspension of D, the chord is then in fact: VII4/3 (which can in turn substitute IV+6ann in a plagal cadence).

The chords in measures 70-73 are clearly linked to the stepwise descending bass. The figure is somewhat reminiscent of a Romanesca:
           67
C minor: I6/4    (V4/3   IV)   VIIeol VII7  I6/4  IV6/5 I6/4 'IVhfdim' I                      I          I2    VI    I6/4 IV     I6   II2    I      I
                    of IV                                       (n)
                           [that does
                           not appear]
              dominant pedal point ----------------- ( ----- ) -------|
           72
C minor:   I2  VI  I6/4 IV    I6     II2    I     I   II4/3 I6/4 II6/5 (VII7)(II4/3 I6/4 II6/5)(VII7) I6 VII7 I    V7hv  IV  IV+6ann  I   I
                                                                                      of (V)                              of 
                                                                                      of VIIeol                         (IV)
                                                                                                                               of VIIeol
                                                                                                                                 = VII6/5
           or think temporarily in Bb minor (that's easier..)  (VII7) II4/3 I6/4 II6/5 (VII7) 
                                                                                       of V                    of IV

                                                                                                      C minor:  = VII6/5  I6 VII7 I    V7hv     IV  IV+6  I 
In measure 81 we modulate to the subdominant key of F minor, shortly before the repetition of the 'quasi Romanesca' from measure 83 (and compare measures70-73): 
           78
C minor:    V6     I       V6eol  VI     III6augm  (IV)  III6    VII4/3      I6    #IVdv6/5 I6/4  VII4/3     I6     VII6/5  (VII2   V7) -----> IV
                                                     = (V6augm)
                                                of VI
                                                      [that does
                                                      not appear]
                                                                                                                                                      F minor:    VII2   V7
REMARK IIIAUGM
           82
 F minor:    I                     I      I2    VI   I6/4 IV    I6   II2    I     I       I2    VI     I6/4   IV      I6    II2    I     VI6  VI6/5 IV2 II7