dominant 7th studies / diminished proof

The following theory simply examines the properties associated with adding a flat nine ( b9 ) to a vanilla dominant seventh chord, some of the results of which create the convergence possibilities on this page. And as we shall soon see, all of these possibilities are based on some manifestation of the fully diminished seventh chord, here placed within the V 7b9 dominant color. Depending on how you got here, these convergence possibilities are the same ones as within the tonal convergence chart. The musical examples on this page a rather academic, almost "guide tonish" in most ideas, and although many of the following convergence ideas are cool in setting up the minor tonality, our overall direction will mainly be to C major. Click to the tonal convergence chart realizations for a more artistic use of the colors in both environments.  Either way, C major / C minor, academic or artistic, our dominant chord is built the fifth degree of the scale yes? So C tonic creates a G dominant n'est pas?

To begin, let's spell out the G dominant seventh. Cool with spelling chords? Example 1.

Now let's add the ninth chord tone, creating G 9. Example 1a.

Now let's flat the nine, creating G 7b9. Example 1b.

Here is the sound of the above charts. Example 1c.

Let's examine the four note arpeggio that starts on the 3rd of our G7b9 chord. The following chart extends in minor 3rds till it loops upon itself. Example 1d.

This group is a fully diminished seventh arpeggio, constructed exclusively by minor 3rd intervals, which creates a closed loop after the fourth occurrence. So, if the pitch B is the leading tone to C, are the other pitches D, F and Ab also leading tones? Absolutely. Here's part of the magic, by lowering any one note of this arpeggio a half step we can spell four different dominant seventh chords. Example 1d.

From the above chart emerges our four different dominant seventh chords, whose roots by the way are also are a minor third apart, same interval between the pitches of the diminished 7th chord yes? This diminished thing is a minor 3rd extravaganza! Example 1e.

Cool so far? Still thinking C major as our tonal center? If we add a flatted ninth to each seventh chord we create four V 7b9 chords. Example 1f.

These dominant chords have been spelt out diatonically in relation to their tonic keys. Let's respell some of the pitches using enharmonic equivalents within the four V 7b9 chords and look for the magic. Example 1g.

The discerning musical eye will notice that the same fully diminished seventh arpeggio from example 1b above is found in each of the four different dominant seventh flat nine chord arpeggios, the roots of which are a minor 3rd apart. Let's construct four Two / Five / One chord progressions using the above four V 7b9 chords. Example 1h.

Still cool with what's happening? Notice that all of the vertical listings of chords are also a minor third apart. Ah, the diminished magic, always providing perfect theoretical closure. Interesting how the diminished pitches become the root of the Two chords, perhaps another pneumonic device? Reducing each group down to just it's Two / Five component, we create what I usually term Two / Five a tension cell. Example 1i.

The basic idea of all of the above crunching of the pitches and numbers is to realize that these four Two / Five sequences will all gravitate towards any of the four tonics created above, due to the common fully diminished seventh chord found in the upper structure of each of the four different dominant seventh flat nine chords. Really? So will all of the four Two / Five tension cells gravitate towards one tonic? Exactly. Example 1j.

Same for the other tonics, Eb, Gb and A? You bet. So the above tonal convergence possibilities are based on the above diminished theory? Exactly. The above chart forms the basis of the convergence possibilities which follow. Do some sound more convincing than others? Of course, some of the above convergence possibilities are downright tonally treacherous, providing wonderful opportunities to trainwreck the show. We simply sort through the choices, find the one's we dig, run the idea through the 12 keys to internalize and continue on our merry musical way searching for more coolness.

So is this art or theory or art theory or what? Well, keep in mind that the fully diminished seventh chord and it's scale create a very distinct sound or color. Deriving our four dominant seventh chords from this structure, we proceed to artistically soften the fully diminished sound by various means, one of which is to eliminate the b9. Once this is achieved, all the other structural configurations that we commonly use in defining dominant harmony can now be applied to each of the four different dominant seventh chords created by the V 7b9 theory. Two chord also? Yes, the Two chord also. So, we can we soften the diminished color and still retain it's multiple resolution properties? That is the general idea.

Thus, interval studies, arpeggios and upper structure alterations can be applied to any of the four different dominant seventh chords, which in the above example is G7, Bb7, Db7, and E7, as they converge on one tonic, which in our illustration is C major / minor. By "softening the diminished sounds", many new aural shades and colors emerge. Their hue and intensity could be defined in relation to how inside or far outside they are in regards to the tonal center being gravitated towards, perhaps defined by the presence of diatonic pitches, perhaps viewed best by physical proximity on the cycle of fifths diagram? Either way, the following convergence possibilities emerge. With C as our tonic, the following ideas are listed chromatically.

The coolness starts right off, anything from Db is essentially some sort of tritone substitution. Named by the interval measured from the root of the dominant, using this tritone places us a half step above our tonal destination, perfectly poised for convergence. With such a close proximity to the tonic, many different coloring options easily resolve, oftentimes by half step or in parallel motion. And while the augmented 4th G of the Db Lydian color adds a bit of whole tone to the group, it's also the root of the dominant chord of our tonic C major.

Using the parallel resolving motion of tonic colors by half step from above.

By lowering the 7th of the Lydian mode by half step, slightly different hue, ( Cb = B ). A bit more bluesy perhaps? The all important jazz tritone substitution chord emerges. Here it is the Db 9 chord, the root Db being a tritone away from the dominant chord root G in C major / minor.

Changing Two chords to create a motion by fourth and a more diatonic Two / Five cell, diatonic to Gb major that is. Distance from C to Gb? Right, a tritone.

Slipping in a bit of the chromatic color between Two and Five, check out Duke Ellington's classic Satin Doll to hear the above motion in action.

Straight ahead diminished idea into the minor tonality.

Do we ever use the same motion to the major tonality? Of course, we do it all here. Example 3a.

Using the parent scale of the F min 7 / Bb 7b9, the Two / Five tension cell of Eb. Note the softened dominant chordal color built from Bb, the b7th scale degree of the tonic C.

Cool n'est pas? Basically C minor into C major? Yep.

Simply pairing Bb 13 with it's diatonic Two chord, makes for a nice vamp.

Using the E major triad from within the Lydian b7 group to make it happen.

Note the two purples in the above group, B and D, retaining a toehold in the diminished color.

Changing the Two chord to match the dominant, we can potentially start a half step below the tonic.

Surprise! This kind of motion is fun when the harmony so strongly implies a different tonic, i.e., set up by the Two / Five cadential motion and then you don't go there.

Straight ahead diminished idea into the major tonality.

From F- 7 / Bb Two / Five. Minor Four in the major tonality is common, although we usually find it in mostly diatonic chord progressions following a major Four chord, then cycling back towards the tonic via Three / Six / Two / Five etc.

Sorry about the Bb representing the # 9, which should be A# yes? My music software says no to the notation of Ab and A# in the same octave in the same chord, so... Bb it is.

Gb is the parent scale of Ab / Db, Two / Five motion. Using the tritone substitute in the harmony, simply Db 7 for G 7.

Changing Two chords, melodically focusing on the Gb ( F# ), the #11 of C.

Not exactly your typical folk style cadential motion, using this motion is also probably a good way to loose the rock gig.

Softening the b9 diminished color to the Lydian mode of the parent scale Eb major, based on the F -7 / Bb 7b9 tension cell, used over G 7b9.

Simply subbing in the diatonic Two and Five chords of Ab Lydian / Eb major. Oh, hip to the modes?

Nice surprise huh? All part of becoming a "master of musical disguise."

Straight ahead diminished idea into the major tonality.

Parent scale of B -7 / E 7b9 tension cell. Outlining the major triad in the line.

Rapid arpeggiated triads are potentially very exciting. Hip to these three note wonders?

Using the diatonic Two and Five chords of A major to converge on C major.

Jazz, blues dominant color from b VII.

Diatonic mode of Gb major parent scale of Ab - 7 / Db 7b9 cell, i.e., B = Cb.

Down to just the leading tone B leading the way.

Changing Two chords yet again, note parallel motion in the melodic idea.

Did we basically just move one melodic idea up in half steps to converge? But the harmony went south... descended that is. What's up with that?

Straight ahead diminished idea into the major tonality.

Pretty cool huh? Lot's of choices. From the loud diminished color to the softer Lydian hue of diatonic tonality, we can create our degrees of tension and converge.

"The highest reward for a person’s toil is not what they get for it, but what they become by it."

John Ruskin