diminished color / resolving properties

Two important considerations initially emerge in regards to the resolving properties of the diminished scales and chords for the improvising musician. One unique facet of the diminished color is it's ability to resolve to multiple tonal centers of both the major or minor tonality. The second cool and potentially important property of the diminished color is how the perfect interval symmetry and strength of it's structure allows it to smoothly move in rather unconvential ways.

Perhaps the easiest way to examine these unique abilities is by resolving one, 4 pitch fully diminished chord to it's tonal centers, thinking of course that the scale shape that is created from the chord would contain the same resolving abilities. There are two common ways, among many, to view the theory of the multiple resolving properties of the diminished color and we'll examine them both in the following discussion. The following theory is helpful in understanding chord substitution and generating new pathways of convergence.

The multiple resolving properties of the diminished chord is based on the ability to extract 4 different, tritone containing, dominant 7th chords from the one fully diminished 7th chord. These 4 dominant chords direct the resolutions. We can create these chords by individually lowering each of the 4 diminished chord pitches by half step, the lowered pitch becoming the root of the new dominant chord created. Here is a chart examining this theory. Cool with spelling chords? Example 1.

Here is the sound of the above chart. Example 1a.

Minor keys also? you betcha. Example 1b.

Raising the roots of the four dominants back up to create the fully diminished 7th chord and resolving to the four major tonics. Example 1c.

Note how the tension is labeled by the leading tone pitch? Are you hip to the shorthand symbol used to denote the diminished color? The four dominant chords created in example 1a and 1b become the basis of jazz chord substitution, which not only can transform chord progressions but also the improvised melodies created from them.

So from the diminished chord we can create two versions of the diminished scale, dividing it's minor 3rd to either whole step / half step or half step / whole step. Here is a chart examining the two scales using the diminished arpeggio from example 1 above. Example 2.

Here is the first group in action. Note that the resolving keys are the pitches not contained within the 1st grouping ( whole step / half step ) in example 2. Example 2a.

Here is the second group ( half step / whole step ) in action, where the original arpeggio pitches resolve downward by half step ( b9 ) to an appropriate tonic. Again the idea that those pitches absent are the tonal centers this group tends to move towards. Absent? Yep, the ones we would add to create a complete chromatic scale. Oh yeh, cool. Example 2b.

Well, kind of forced the issue here, creating a sort of common tone diminished idea, i.e., C diminished into C major. Cool with the common tone diminished?

Another way to view each of the 4 pitches of the diminished chord is make each of the pitches a leading tone towards the tonal centers. As the name implies, a leading tone pitch is simply one that points out the direction of the music, perhaps a resolution, leading the music to a new event. With the symmetrical interval construction of the diminished color being the minor 3rd, does it follow that the resolution destinations follow a similar interval scheme? Here is a chart showing the pitches as leading tones and the keys they belong too. Example 3.

Here is the sound of the above chart. Same four pitch chord resolving to 4 major tonal centers represented by the tonic major 6th chord. Hip to the color tones? Example 3a.

So, with a symmetrical interval structure of a minor third, the resolving keys are a minor third apart? Seems so eh? So, would the resolving keys be a whole step apart for the whole tone or whole step symmetrical scale?

Another very common use for the whole tone / half tone diminished color involves its relationship with the dominant seventh flat nine chord ( V7b9 ). This dominant seventh flat nine is a very common "operator" in the jazz harmonic world. Our fully diminished diminished seventh chord color is found starting from the third degree of the dominant chord up through the flatted nine. Note the two pairs of tritones, B to F and D to Ab. Spelling out the G 7b9 chord. Example 4.

In the following musical idea, we simply run the B diminished scale over G 7b9 into C major. Example 4a.

Same idea but into the minor tonality. Example 4b.

Do you like the sound of these last two resolutions? Using the diminished over the flat nine creates some interesting and unusual dominant tensions. As to one reason why this diminished group is so important, in the last two examples we begin to see the multiple key resolving qualities of the same diminished scale pitches into both the major or minor tonality. In reality, each of the pitches of the diminished arpeggio can become a "leading tone" or seventh degree of any of the 24 keys. Click to the application section if you’re curious about these multiple resolutions.

In the literature of jazz standards, the above V 7b9 to One major 7 is very common. The diminished color adding a greater degree of tension to the tritone within the dominant seventh chord. Adding the b9 to the vanilla V7 is also a very common substitution, although "taste" is everything. The potential always exists to "abuse" the diminished color in that it is a very strong and recognizable sound. As we go further down the theory road we will see how we can apply the diminished qualities and its resolving properties to similar but different melodic and harmonic qualities. We simply "soften" the diminished color into new hues and views and abuse it the same old diminished ways. In terms of its physical properties, the symmetrical aspect of the diminished color provides for other avenues for exploration in regard to its multiple resolving qualities. Look to the diminished application section for a more thorough look at the diminished grouping. Many, many standard jazz compositions from the literature include aspects of the above diminished coloring including the following suggested titles. These well crafted melodies are oftentimes requested and well worth a thorough reading. Example 5.

Where to next?

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