The Chromatic Minor Mode Revisited

"The three flats in the key signature of C minor, for example,
indicate that the third, sixth, and seventh degrees of the scale are inflected with flat signs,
in contrast to the same degrees in the scale of the parallel mode, C major.
But in all our ordinary experience of music in C minor, having the key signature of three flats,
miscellaneous B naturals are nearly always to be found, and often A naturals as well,
when no change of key has taken place."

Parallel Comparison
This typical, classical presentation of the (chromatic) minor mode
     clearly admits the risk of parallel construction,
          and yet has nothing else to offer.
     Subsequent reference to scales (with both notes flat, both notes natural, one of each),
          only displaces the problem because there is no indication
               as to when each scale is to be used.
     One is left with "more often than not", "often", "usually",
          without any indication of "how", "where", and above all "why".

Solution
1. Using the best key to associate with C major,
          which is the key A minor and not the key of C minor,
     remaining within the same Window of natural notes,
     and relying on processes of inversion
          rather than processes of parallel comparison.
2. Forgetting about scales
          and relying on chords which create and impose the chromaticism.
     (a) First the swings of the nucleus -
          the DOMINANT/TONIC swing (E⁷/Am⁶)
               which imposes the chromatic notes (F# and G#), and
          the COUNTER/TONIC swing (Dm⁶/Am⁷)
               which maintains the diatonic notes (G and F).
     (b) Then the circle, of which the first half is all major,
               being the second half of the major circle,
          and the only chromatic note is the G# in the penultimate (DOMINANT) chord.
3. Despite the fact that the Diatonic Major and Chromatic Minor modes
          each possess a DOMINANT of the same shape/sound (G⁷ and E⁷),
     the DOMINANT of the Major mode (G⁷) is an Outward chord
               placed in the center of the Window,
          with a complete 3-chord Tail above it (the three minor chords), but
     the DOMINANT of the Minor mode (E⁷) is an Inward chord
               placed at the very edge of the Window,
          with the BUCKLE chord immediately above it.
     All harmonic operations on the sharper side (above)
          will be far more delicate and precarious for E⁷ than for G⁷.
4. The tetrad of Em⁷ and the triad of Em do not exist in the Chromatic Minor mode of Am.
     It thus does not seem advisable to modulate to the Key of Em
               from the principal key of Am,
          the Keys of E (major) and Dm (and, of course, C major) being far preferable,
               as illustrated in the following example.

The Bach Fugue in Eb minor
In the Unknown Container we suggested a rhythmically altered version
          of this fugue in 3/2 meter,
     in which the second entry of the first exposition in is the key of Bb minor.

We suggest here the recommendation of placing this second entry,
     in Ab minor rather than in Bb minor,
          with adjustments in bars 2 and 4,
               and with transposition of bar 3 a tone lower.
     The third entry returns to Eb minor as it originally did.
This is a much more subtle change than the previous rhythmical one (from 4/4 to 3/2),
     and will require more intensive and repeated hearings of both versions.
It will probably also meet with greater resistance, and provoke more controversy,
     considering the concept of the parallel relationship between the major and minor modes,
          prevalent in Bach's day and unfortunately still alive and well today.

Applications
In the Key of C major, the chord progressions
E⁷ - Am - B⁷ / Em - A⁷ - Dm - E⁷ / Am - D⁷ - Gm - A⁷ / Dm - G⁷ - C - D⁷ / G - C⁷ - F - G⁷ / C,
          five M74chord patterns, with the first chord Dominantized,
               in the Keys of Em, Am, Dm, G, and C respectively,
     are perfectly acceptable (a Bach favorite).

NOTE -
     (a) the progression B⁷ - Em (chords 3 and 4),
          which is possible because the principal Key is that of C major; and
     (b) the progression D⁷ - Gm (chords 9 and 10),
          which is imposed by the temporary Key of D minor.

In the Key of A minor, the corresponding chord progressions are quite different,
C⁷ - F - G⁷ / C - F⁷ - Bb - C⁷ / F - Bm^7-5 - E - F⁷ / Bb - E⁷ - Am - Bm^7-5 / E - A⁷ - Dm - E⁷ / Am,
     especially the third M74 across the BUCKLE chord (Bm^7-5 - E - F⁷ / Bb).

NOTE -
     (a) the two first M74s (chords 1 to 8), as well as the last M74 (chords 17 to 20),
          which are perfectly normal M74s in the Keys of C, F, and Am respectively ;
     (b) the progression Bm^7-5 - E (chords 9 and 10, as well as chords 15 and 16),
               an ANTE-1/DOMINANT progression,
                    which is imposed by the principal Key of A minor,
          instead of the progression B⁷ - Em, a DOMINANT/TONIC progression,
               in the preceding Major Mode example (chords 3 and 4);
     (c) the progression F⁷ - Bb (chords 11 and 12), a DOMINANT/TONIC progression,
          to the Neapolitan Sixth of the principal Key of A minor.

We will probably be adding other examples
to illustrate BUCKLE chord activity
in the chromatic modes.
In the meantime, you might enjoy inverting these two examples
into Diatonic Minor and Chromatic Major.

1. The Diatonic Major Mode
2. The Diatonic Minor Mode
3. The Chromatic Major Mode
4. The Chromatic Minor Mode
5. Adjacent Chromatic Modes
6. A melodic Example