Appendix VI - Lesson 17
Augmented Cycles
Notes to Appendix VI - Lesson 17
In previous lessons on symmetric chord movement, we have concentrated on a movement increment of a minor third or three half-steps or frets. Lesson 17 gives us insight on arguably the least used of the four triad chord forms (major, minor, diminished, and augmented), the augmented triad. Let's review what makes up an augmented triad. This triad has three notes that are spaced a major third apart. A major third is 4 half steps or frets. If we divide a chromatic or half-tone scale of 12 tones by 4, we have 3. Practically, what that means is that any augmented triad can have three names. Mickey first talks about a C augmented triad, comprising of C, E, and G#. But let's start with the E note, and we have E, G#, and B# (which we all know is C). And if we start with G#, we have G#, B#, Dx (Dx is of course the same thing as an E.).
From this formula, we can easily deduce that there are only 4 augmented triads: C, C# (Db), D, and D# (Eb). These four forms and their three each forms, make up a 12 tone scale.
One interesting feature of the interval of a major third is that it can be divided into two major seconds. So we can subdivide our symmetric by a half. So if we divide a 12 tone scale by 2, we have 6 tones and this is call a whole-tone scale. Often jazz musicians improvise their solos using whole-tone scales. From that, we can easily understand how augmented cycles may be useful.
A few lessons back, I described how symmetric harmony is similar to the "black box" theory of electronics: We are interested in entering the symmetric cycle and exiting it. What goes on inside "the black box" isn't important. If we use parallel movement, such as steps of a minor third or a major third, our brains recognize and appreciate the symmetry. Mickey is finally coming out with a similar definition:
"Symmetric Harmony, as we are applying it, moves from one point to another. What goes on between these two points is of no consequence. Harmony is parallel either up or down, and you can have as many as 12 tonics (Exercise 42.)"
About the exercises:
Exercise 38 gives the chord form that Mickey is using in these exercises. For the record, there are three additional forms that are very useful:
Augmented Chord Forms
All of these forms are movable on the fretboard. The form in Measure 1 is what Mickey gave us. The form in Measure 2 is probably the best known as it is the most used form in beginning guitar courses when they talk about augmented chords. The second form in that measure is a common variation on the highest four strings. The form in Measure 3 is probably the least common. I discovered it years ago when I was arranging Django Reinhardht's best known classic "Nuages." I needed a I-V-I turnaround that I was going to arpeggiate. Here's how it came out:
"Nuages" Turn-around
Exercise 39: Mickey's showing how a C+ and an E+ are the same chord.
Exercise 40: This exercise uses the root and all inversions of a C+ triad as a "Three Tonics" fill.
Exercise 41: This exercise is using augmented triads to harmonize a whole-tone scale, "Six Tonics". If you add a little syncopation to the rhythm of this exercise, you'll have the intro to Stevie Wonder's classic "You Are The Sunshine of My Life."
Exercise 42: This exercise is using augmented triads to harmonize a half-tone scale, "Twelve Tonics."
Note that I have combined Exercises 40, 41, and 42 into one TEF.
In Summary: Just playing these augmented harmonized exercises may seem pedantic and of little practical use. Here is my transcription of the opening 10 measures by guitarist Chet Atkins to "Deed I Do" from the album "Chester and Lester" with Jazz guitar pioneer, Les Paul:
Chet Atkins - Deed I Do
Check out Measures 8 and 9 as Chet is using an augmented triad symmetrically for the turn-around.
Additional Exercises: Try adapting Mickey's exercises 40, 41, and 42 with the three additional forms I have included here. You're going to be surprised at how easy it really is!
Hope you're AUGMENTING your fun!!