Symmetrical Triads: A Study On The Diminished And Augmented Triads

Our focus in today’s lesson is on symmetrical triads.

Triads are the most fundamental chords in tonal music, and they are relevant to musicians of all class and creed, styles and levels.

Although there are four known triads:

The major triad

The minor triad

The diminished triad

The augmented triad

…commonly referred to as the fantastic four, the diminished and augmented triads are rarely used because they are symmetrical.

Let’s get started by breaking down the concept of symmetry in music.

A Short Note On Symmetry In Music

The Symmetry Of The Diminished Triad

Jermaine Griggs considers the diminished triad as “a minor triad with a diminished fifth.”

Therefore, using any minor triad, the diminished triad can be formed when the fifth tone is diminished (or lowered by a half-step.)

Given the D minor triad:

Lowering the fifth tone (which is A):

…by a half-step (to Ab):

…produces the D diminished triad:

So, the term diminished is derived from the diminished fifth interval in the diminished triad. For example, the D minor triad:

…and the D diminished triad:

…have identical root and third tones (D and F):

The only difference is the fifth tone, A:

…in the D minor triad:

…and Ab:

…in the D diminished triad:

“Here Are All The Diminished Triads On The Keyboard…”

C diminished triad:

C# diminished triad:

D diminished triad:

D# diminished triad:

E diminished triad:

F diminished triad:

F# diminished triad:

G diminished triad:

G# diminished triad:

A diminished triad:

A# diminished triad:

B diminished triad:

The Symmetry Of The Diminished Triad

The diminished triad is symmetrical because it consists of two identical components. Let’s proceed by breaking down the diminished triad into its intervallic components.

In the C diminished triad:

C to Eb:

…is a minor third interval.

Eb to Gb:

…is a minor third interval.

From the intervallic breakdown above, the diminished triad has two identical components – the minor third interval.

Due to the fact that the diminished triad can be broken down into two minor third parts, it is said to be symmetrical.

The Symmetry Of The Augmented Triad

According to Jermaine Griggs an augmented triad is “a major triad with an augmented fifth.”

Using any known major triad, the augmented triad can be formed when its fifth tone is augmented (or raised by a half-step.)

Given the F major triad:

Raising its fifth tone (which is C):

…by a half-step (to C#):

…produces the F Augmented triad:

The term augmented is derived from the augmented fifth interval in the augmented triad. For example, the F major triad:

…and the F augmented triad:

…have identical root and third tones (F and A):

The only difference is the fifth tone, C:

…in the F major triad:

…and C#:

…in the F augmented triad:

“Here Are All The Augmented Triads On The Keyboard…”

C augmented triad:

Db augmented triad:

D augmented triad:

Eb augmented triad:

E augmented triad:

F augmented triad:

Gb augmented triad:

G augmented triad:

Ab augmented triad:

A augmented triad:

Bb augmented triad:

Cb augmented triad:

The Symmetry Of The Augmented Triad

The augmented triad is symmetrical because it consists of two identical components. Let’s proceed by breaking down the augmented triad into its intervallic components.

In the C augmented triad:

C to E:

…is a major third interval.

E to G#:

…is a major third interval.

From the intervallic breakdown above, the augmented triad has two identical components – the major third interval.

Due to the fact that the augmented triad can be broken down into two major third parts, it is said to be symmetrical.

Final Words

I believe you’ve seen the relationship between the diminished and augmented triads: symmetry, while major and minor triads are not symmetrical, hence, they belong to a different class of triads.

See you in the next lesson!

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Chuku Onyemachi

Head of Education at HearandPlay Music Group

Onyemachi "Onye" Chuku is a Nigerian musicologist, pianist, and author. Inspired by his role model (Jermaine Griggs) who has become his mentor, what he started off as teaching musicians in his Aba-Nigeria neighborhood in April 2005 eventually morphed into an international career that has helped hundreds of thousands of musicians all around the world. Onye lives in Dubai and is currently the Head of Education at HearandPlay Music Group and the music consultant of the Gospel Music Training Center, all in California, USA.

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