Chromaticism and shifting dominants

I came across something I wrote up about three years ago while studying music theory in college, so I thought I'd expand on it and share it with the world.

While studying 18th century counterpoint, my professor asserted that when using the diminished seventh chord, one can simply assert another completely diminished seventh chord and use that as a vehicle to move to another key. In thinking about the nature of dominant chords, I thought: why not extend this to dominant seventh chords? After all, the diminished seventh and the dominant seventh only differ by a half-step, and with minimal chromaticism, one can shift to the dominant seventh of another diatonic degree. Taking this concept one step further, I figured that it was possible to convincingly shift from the dominant seventh to the secondary dominant seventh of any of the other eleven degrees of the chromatic scale. After a bit of brainstorming, I came up with the configurations, using the closest possible voice leading (inversions indicated below).


Aligning with the tendencies of 18th century harmony, modulations tend to travel to closely related keys, generally the major or minor key corresponding to key signatures no more than one flat or sharp away. Thus, I thought it would be a worthwhile exercise to compare secondary dominant sevenths to a primary key to consider how closely we could morph a pivot chord. For convenience, I used C major (no sharps or flats).

DOMINANTS IN MAJOR (1, 2, 3, 4, 5, 6, 7)
  • V7 with 0 accidentalsI
  • V7 with 1 accidentalII (#1)IV (b7)V (#4)VI (b6)bVII (b3)
  • V7 with 2 accidentalsbIII (b6, b7)III (#2, #4)bV (b2, b6)
  • V7 with 3 accidentalsbII (b3, b5, b6)bVI (b2, b3, b7)VII (b2, b5, b7) 
Major mode is pretty straight forward. Not surprisingly, the dominants for the predominants (II, IV), dominant (V), and relative minor (VI, which oftentimes serves a predominant role) are just 1 flat away.

For the relative minor of A, the same chords above reappear, only for different scale degrees. To avoid confusion and allow comparison to the above chart, I'll keep the same spelling but consider the scale degrees with respect to A major (e.g. G = b7, Gb = F# = 6).

DOMINANTS IN NATURAL MINOR (1, 2, b3, 4, 5, b6, b7)

  • V7 with accidentalsbIII 
  • V7 with accidentalI (7)bII (b5)IV (#3)bVI (b2)bVII (6),
  • V7 with accidentalsbV (b2, b1)V (#4, 6)VI (3, 7)
  • V7 with accidentalsII (b2, 3, 6)III (b5, 6, 7)VII (b2, 3, b5)
In minor mode, the dominants for the subdominant (IV), neapolitan (bII), augmented sixth (bVI), and subdominant (bVII) are just 1 flat away. As you may know, the neapolitan and augmented sixth chord can be derived from the minor mode.

Now, the above considers natural minor (b3, b6, and b7). If we instead allow melodic minor so that the sixth and seventh are raised and considered part of the key, the counts change around quite a bit.

DOMINANTS IN MELODIC MINOR (1, 2, b3, 4, 5, b6, 6, b7, 7)

  • V7 with accidentalsIbIIIbVII 
  • V7 with accidentalbII (b5)III (b2)IV (#3)bV (b2), (#4)bVI (b2)VI (3)
  • V7 with accidentalsII (b2, 3)
  • V7 with accidentalsVII (b2, 3, b5)
Suddenly, the tonic chord and subtonic chord are directly within reach. It's worth noting that the latter has the dual identity of the dominant of the relative major (oftentimes, hearing that chord in a progression is a good indication that you're heading to the relative, if you're not there already.

Looking at the expansion of the 1-class (having snagged several of the 2-class chords), we now have III, bV, V, and VI available. Ignoring the newly inducted dominant (V), that's an interesting set of foreign chords, considering (1) III and bV don't even make the cut in major, and (1) VI doesn't have much of a role in this mode (usually you'd use bVI for a "six chord"). I say you've got yourself a curious trio of chords there -- III, bV, and VI -- and that's something that I'd like to play around with in future compositions.

Of course, this new scheme isn't that simple, since melodic minor has its own rules, especially with raising the sixth and seventh while moving upward, but lowering them on the way down. Crudely speaking, this scheme only works "half" of the time, if that.

Works of the 20th century started to consider keys in terms of their letter along rather than their mode, especially since they so frequently went through different modes, borrowing here and there. So why not incorporate that idea here? If we were to take the "best of both worlds" approach (i.e. the smaller of the two for any given Roman numeral), we would end up with the following scheme that combines major [M] and melodic minor [m]:

COMBINING MAJOR + MINOR (1, 2, b3, 3, 4, 5, b6, 6, b7, 7)
  • V7 with accidentalsIbIII [m], bVII [m] 
  • V7 with accidentalbII [m], II [M], III [m], IVbV [m]VbVI [m], VI
  • V7 with accidentals: (none -- all promoted!)
  • V7 with accidentalsVII
It looks like once you use a major-minor key, nearly every chord (less the one tonicizing scale degree 7) can be attained using 0 or 1 accidentals. No wonder Romantic composers ushered in the age of chromaticism.

The above analysis looked purely at a superficial, chromatic relationship of V7 of I and V7 of any other scale degree. While my professor asserted one could simply go from one dominant to another, I wondered if one could associate a relationship between the two dominant seventh chords, whether directly (i.e. by serving a role in both "keys", such as an augmented sixth chord) or indirectly (i.e. by substituting for another similarly sounding chord, with modified or added tones).
Although one can simply assert the dominant to change the tonal center (without an explicit progression), it often works best to have a functional relationship between chords. By following the tonic-predominant-dominant scheme, one can often produce a convincing chord progression. The introduction of secondary dominants (which also serve a predominant role), allow one to extend the tonal palette to incorporate chords outside of the key with minimal chromaticism (oftentimes with no more than two altered chord members).

In the following cases, I assume we're traveling from the key of I (via V7) to the key of 'X' (via V7 of 'X'). In considering that we're moving to the dominant of another key, the original Vwill usually serve a predominant function to the dominant that follows. With that in mind, it's worth expressing the original V7 in both keys to see what we have available. Below '=' indicates an equivalency, whereas the '~' indicates a substitution.


  • V7 of I = "bV7" of bII ~ a bit of a stretch, but #IV resembles a predominant (1) 
  • V7 of I = "IV7" of II ~ (lower the third) iv7 in the key of ii
  • V7 of I = "III7" of bIII ~ (lower the third) passing iii7 chord to V7 in the key of bIII (2)
  • V7 of I = "bIII7" of III ~ (lower seventh) i7 chord in the key of iii
  • V7 of I = "II7" of IV = predominant V7/V in the key of IV
  • V7 of I = "bII7" of bV = predominant neapolitan with added seventh in the key of bV (3)
  • V7 of I = "I7" of V ~ (raise the seventh) for tonic IM7 in the key of V
  • V7 of I = "VII7" of bVI ~ (raise the root) io7 (4)
  • V7 of I = "bVII7" of VI ~ (raise root) dominant viio7 in the key of VI (5)
  • V7 of I = "VI7" of bVII ~ (lower the third) predominant vi7 in the key of bVII
  • V7 of I = "bVI7" of VII = predominant Ger6 in the key of VII
A few considerations:
  1. It's basically a substitution of #IVdim7 (a predominant that can connect IV to V) with #IV7.
  2. Though non-functional, I've seen the use of iii as a preparatory chord for V since they already share two degrees (5 and 7). Now if you consider their sevenths, iii7 is moves easily into V7, now with three degrees in common (5, 7, and 2). Really, all you need is the root of the iii to move up a half-step to become the seventh in the following chord.  
  3. The original chord could tonicize bV directly if you consider tritone substitution, but for the sake of connecting to the VI instead thought of it instead as the neapolitan (bII6), but in root position with an added seventh.
  4. The diminished chord on the tonic, though non-functional, can be used as an embellishing chord for the tonic, often found in barbershop and jazz music.
  5. The diminished seventh upon scale degree 7 seemed the easiest manipulation, though it is uncommon within a harmonic function (i.e. dominant) to go from a chord of more tension (diminished) to one of less tension (dominant seventh). Instead, the original V7 as "bVII7" may stand convincingly enough as a dominant, as found in contemporary music. 
So what does this all mean? Well, at this point, I'm not really sure. But given that this exploration in music theory deals primarily with dominant seventh chords, maybe it will best serve those who work closely with these types of chords.

Perhaps barbershoppers.

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