Triadicisms II - Minor, Augmented & Diminished Triad Workout
As the first not-so-Shortbook™ (139 pages) of 2019, “Triadicisms II”, is the second volume and logical extension of “Triadicisms, Vol. 1” (which features exercises and sequences focusing exclusively on the Major Triad).
Formatted along similar lines, this new volume presents individual chapters featuring the “other” three – namely, Minor, Augmented & Diminished Triads.
As mentioned in the previous post, the triad is the building block of Western harmony, as it characteristically exerts a strong harmonic “pull”, regardless of its function.
Triads can also be part of a larger, more complex (7th, 9th, 11th, or 13th) chord as an extension or upper structure.
Formatted along similar lines, this new volume presents individual chapters featuring the “other” three – namely, Minor, Augmented & Diminished Triads.
As mentioned in the previous post, the triad is the building block of Western harmony, as it characteristically exerts a strong harmonic “pull”, regardless of its function.
Triads can also be part of a larger, more complex (7th, 9th, 11th, or 13th) chord as an extension or upper structure.
Also listed in the previous post, as well as in Vol. 1, here once more are the four basic triad qualities (types):
One way to look at a Triad, is as a pair of consecutive, vertical Major and / or minor 3rds.
A Minor Triad, for example, with the min 3rd on the bottom and the Maj 3rd on top, is in reverse order of a Major Triad, which sports a Maj 3rd on the bottom and a min 3rd on top.
Both Augmented and Diminished triads are symmetrical, meaning that the top and bottom 3rds of each are of the same quality – Maj / Maj and min / min – respectively. An Augmented triad could also be viewed as a Maj triad with a raised 5th. The diminished triad could be seen as a minor triad with a flatted 5th.
Triads can be expressed in 3 forms, shapes, or inversions, each of which has a unique intervalic make-up, which in turn subtly changes its “sound” by juxtaposing its inherent intervals - without changing its quality,
The inversions of a C min triad are:
The Minor Triad occurs naturally three times within the Major Scale matrix - on its 2nd, 3rd, and 6th scale degrees. As with the other triad types, it is commonly employed as an extension or upper structure triad.
The notation graphic shown below (ex. 1) depicts a multi directional sequence of Minor Triads in minor 3rds. The ascending permutation is 3-1-5 for each triad in the first two measures, connected by a descending half step. The second two bars are essentially a retrograde version of the first two (permutation 5-1-3).
The chord symbols above the top line indicate each minor triad of the sequence itself. The chord symbols below the second line indicate each extended chord and harmonization.
Ex. 1.
- Major (C – E – G) Maj 3rd + min 3rd
- Minor (C – Eb – G) min 3rd + Maj 3rd
- Augmented (C – E – G#) Maj 3rd + Maj 3rd
- Diminished (C – Eb – Gb) min 3rd + min 3rd
One way to look at a Triad, is as a pair of consecutive, vertical Major and / or minor 3rds.
A Minor Triad, for example, with the min 3rd on the bottom and the Maj 3rd on top, is in reverse order of a Major Triad, which sports a Maj 3rd on the bottom and a min 3rd on top.
Both Augmented and Diminished triads are symmetrical, meaning that the top and bottom 3rds of each are of the same quality – Maj / Maj and min / min – respectively. An Augmented triad could also be viewed as a Maj triad with a raised 5th. The diminished triad could be seen as a minor triad with a flatted 5th.
Triads can be expressed in 3 forms, shapes, or inversions, each of which has a unique intervalic make-up, which in turn subtly changes its “sound” by juxtaposing its inherent intervals - without changing its quality,
The inversions of a C min triad are:
- Root Position (C – Eb – G) min 3rd + Maj 3rd
- 1st Inversion (Eb – G – C) Maj 3rd + P4th
- 2nd Inversion (G – C – Eb) P4th + min 3rd
The Minor Triad occurs naturally three times within the Major Scale matrix - on its 2nd, 3rd, and 6th scale degrees. As with the other triad types, it is commonly employed as an extension or upper structure triad.
The notation graphic shown below (ex. 1) depicts a multi directional sequence of Minor Triads in minor 3rds. The ascending permutation is 3-1-5 for each triad in the first two measures, connected by a descending half step. The second two bars are essentially a retrograde version of the first two (permutation 5-1-3).
The chord symbols above the top line indicate each minor triad of the sequence itself. The chord symbols below the second line indicate each extended chord and harmonization.
Ex. 1.
Identifying each note numerically as part of an extended chord, rather than as the permutation of a triad
would read: G-7b5: b5-b3-b7 C7alt: 3-b9-b13 / C#-7b5: b5-b3-b7 F#7alt: 3-b9-b13
/ Eb-9: 9-5-b7 C-9: 9-5-b7 / A-9: 9-5-b7 F#-9: 9-5-b7
Still, pretty symmetrical. Small wonder, since the notes that make up this sequence form a complete Bb (Db, E & G) half tone / whole tone diminished scale.
would read: G-7b5: b5-b3-b7 C7alt: 3-b9-b13 / C#-7b5: b5-b3-b7 F#7alt: 3-b9-b13
/ Eb-9: 9-5-b7 C-9: 9-5-b7 / A-9: 9-5-b7 F#-9: 9-5-b7
Still, pretty symmetrical. Small wonder, since the notes that make up this sequence form a complete Bb (Db, E & G) half tone / whole tone diminished scale.
An Augmented Triad divides the octave into 3 equal parts. Its interval make-up is Maj 3rd + Maj 3rd (C-E-G#, E-G#-C, G#-C-E), and will, therefore, always create equal, repeating intervalic inversions of itself which can lead to certain redundancies. The Augmented Triad is the only one of the four basic triad types not derived from the Major Scale. It is, however, formed from the 3rd degree of both the Melodic and Harmonic Minor scale systems.
Ex. 2.
An interesting case and point is the example above (ex. 2), which shows an ascending line consisting of permutating ascending Augmented Triads originally conceived to be in half-steps. Because of the Aug. triad's intervalic symmetry, the half-step relationship could just as well be thought of as being in Perfect 4ths or Major 6ths (min 3rds). As the left-hand comp descends in tritones (3rd & b7th), the bass cycles in 5ths. Each Augmented Triad in the top line expresses the 9th, b5, & b7th, in various order, of its accompanying dominant chord.
Listen
The Diminished Triad, which is formed naturally from the 7th degree of the Major Scale matrix, has a dominant function in virtually all instances, due mainly to the presence of its tritone (aka augmented 4th or diminished 5th).
The inversions of a C diminished triad are:
The most obvious Dominant 7th (V7) choices for the above named C diminished triad and its inversions would be Ab7 and D7b9, although others are implied.
Ex. 3.
The inversions of a C diminished triad are:
- Root Position (C – Eb – Gb) min 3rd + min 3rd
- 1st Inversion (Eb – Gb – C) min 3rd + augmented 4th
- 2nd Inversion (Gb – C – Eb) augmented 4th + min 3rd
The most obvious Dominant 7th (V7) choices for the above named C diminished triad and its inversions would be Ab7 and D7b9, although others are implied.
Ex. 3.
Ex. 3. above illustrates how a diminished triad, while ascending in Maj 3rds, can represent alternating parts of dominant 7th chords (5-3-5-b7 & b7-3-b9-b7) descending in whole tones. Tritone subs, anyone?
As with Vol. 1, the exercises, lines and sequences found in "Triadicisms II" are organized, for all three triad types, according to their interval cycle - semitone, whole tone, minor & Major 3rd, perfect 4th & 5th, as well as tritone – and categorized further according to their inversions and / or permutations.
For the improviser, the importance of understanding and mastering these basic triad types cannot be overstated.
Both this volume, “Triadicisms II”, as well as “Triadicisms - Volume One: Major Triad Workout“ are designed to help the serious improviser - of any level - achieve that end.
“Elemental... but not elementary, my dear What's – On!”
B. Stern
For the improviser, the importance of understanding and mastering these basic triad types cannot be overstated.
Both this volume, “Triadicisms II”, as well as “Triadicisms - Volume One: Major Triad Workout“ are designed to help the serious improviser - of any level - achieve that end.
“Elemental... but not elementary, my dear What's – On!”
B. Stern
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