I’ve always found sets of six notes to be very interesting. By definition, there exists an alternate set of six notes comprised of the remaining pitches from our 12-note chromatic system. In many cases, these two sets can be used in conjunction with one another, alternating back and forth to create a logical harmonic movement.
One such example is the Petrushka chord and its “companion”, which I first blogged about here.
In this post, I will talk about another six-note set, its “companion set”, and use them in a musical example.
The augmented scale1,2 is created by alternating minor seconds and minor thirds. Starting on middle C, the augmented scale is:
Notably, the scale can be notated with either a minor second or minor third as the first interval. In the above case, the first interval is a minor second (between C and Db). Below, the augmented scale is notated with the enharmonic equivalent of a minor third first and beginning on D-flat—and the pitches are the same as above.
As mentioned above, any 6-note scale has a “companion set” of six pitches consisting of the other six notes in the 12-note chromatic scale. In the case of the augmented scale, the “companion set” for the augmented scale is yet another augmented scale. In the case of the scale above, an augmented scale built on D uses the six notes not used by the augmented scale built on C.
The augmented scale is also interesting because so many harmonies can be extracted from it, including a variety of major triads, minor triads, augmented triads, and seventh chords. Below are some of the harmonies that can be found in the augmented scale beginning on C, with some pitches respelled as enharmonics.
Below is a musical example that experiments with these scales. This is an excerpt from the third movement of a symphony I recently completed. The movement is in sonata form, and this material is used as the more lyrical B theme.
The first four measures of the phrase use the augmented scale C, C#, E, F, G# and A. The next two measures of the phrase use its companion scale–D, Eb, F#, G, A# and B. The music then begins anew with a new augmented scale–D#, E, G, Ab, B, and C.
These harmonies are outlined with a harmonic accompaniment.
[To view the notation larger, click on it with your mouse. Following the notation is a link to an MP3 of the music performed with piano samples.]
Next, a melody using the same pitch sets is added.
Next, a countermelody is added.
This excerpt produces a bit of a mysterious tone, likely a result of the augmented triads inherent in the harmony. Accordingly, this passage could be orchestrated with soft strings, woodwinds, muted brass and harp, producing soft tone colors that match the mysterious harmonies.
Below is an MP3 of such an orchestration.