What Are Symmetrical Scales And Chords?
Most music schools teach there are 2 requirements for a scale or chord to be symmetrical:
- All the notes in the chord or scale need to be equal distance from one another. (For example: C D E F# G# A#/Bb C)
- The note distances need to divide the octave into x number of perfectly equal divisions.
In a way, both these requirements actually say the same thing.
If the octave is divided into x number of equal intervals, then all notes are equal distance and vice versa.
You can’t have the one with the other, but it’s not always immediately apparent whether harmony is symmetrical or not.
As an example: in the following 5-note scale, all notes seem to be equal distance. (All whole steps)
C D E F# G#
You would think when you see the constant equal note distances, that this must be a symmetrical scale.
Yet, this scale is not a symmetrical scale because the octave is not divided into x number of equal intervals: from the last note G# to the C an octave above the starting C is a major 3rd interval.
One could also say of course that if you’d write all the notes out up to the full octave, as in C D E F# G# C (From C to C), that you can clearly see not all notes are equal distance at all.
In conclusion, we could narrow down the 2 requirements to 1 only, redefining symmetrical harmony as:
In a symmetrical chord/scale, all notes that make up that chord/scale are spaced at even intervals from the root/tonic up to its octave.
Chord vs. Scale, Scale vs. Chord
Before we dive into the 4 symmetrical options, here’s a fun thought to ponder:
1) A chord is really a scale in which you play the notes simultaneously
2) A scale is really a chord in which you play the notes one at a time.
In other words: chords are scales and scales are chords, the only difference lies in how one plays the notes.
For example: if you solo with the notes C, E and G only, without letting the notes ring out together, you are soloing with a 3-note C scale.
If you play these 3 notes letting them ring out so the notes sound simultaneous, you are simply playing a C chord.
Keeping that in mind will be helpful in understanding that the following 4 symmetrical chords are also scales, and vice versa.
There Are 4 Symmetrical Chords/Scales
There are 2 tritones in a major scale.
A tritone interval consists of 3 whole steps, which are basically 6 frets.
Since we only have 12 frets (notes) in an octave, the tritone cuts our octave into 2 equal (6-fret) sections.
In the key of C major, the 2 tritones are F to B, and B to F
When you go up 6 frets starting from F, you will land on the note B, and when you go 6 frets up again from the note B, you will land back on F (an octave above your starting F)
- Augmented Triads
An octave can be divided into 3 major 3rds.
After all: a major 3rd is a 2 whole step distance, which is 4 frets.
Three times 4 frets = 12 frets.
Starting from note C, the 3 major 3rds from C to C an octave higher are:
C to E to G# to C
This is a C augmented chord.
The 2 inversions are:
1st inversion: E G# C
2nd inversion: G# C E
One fun thing you notice, when you play the notes of these chords on 1 string set, is that the chord shapes for all 3 inversions are the same.
In symmetrical chords, you only have to learn 1 chord shape for each string set. Root position shape, 3rd in the bass (1st inversion), and 5th in the bass (2nd inversion) shapes are all the same.
- Diminished 7th chords
A dim7 chord consists of a series of 4 consecutive minor 3rd intervals.
The minor 3rd interval covers a 3-fret distance. (For example from C to Eb)
Since four times 3 frets = 12 frets; an octave, in other words, can be divided into 4 minor 3rds.
Starting from the note C, the 4 minor 3rds from C to C an octave higher are:
C Eb Gb/F# Bbb/A
This is a Cdim7 chord, its inversions are:
1st inversion: Eb Gb Bbb C
2nd inversion: Gb Bbb C Eb
3rd inversion: Bbb C Eb Gb
As with all symmetrical harmony, you only need to learn one fingering per string set, because all inversions, played on 1 string set (horizontally) are all the same chord shape.
One thing I hadn’t mentioned yet: all notes in a symmetrical chord are the root.
The above chord is at the same time A Cdim7 chord, an Ebdim7 chord, an F#dim7, and an Adim7 chord.
How do you know what to name it then when you’re using it in a song?
You would pick one of those 4 names based on how the chord is being used in the song. You can learn more about that here:
How to use the diminished 7th chord in songwriting and composition.
Learn various dim7 chord fingerings here:
- The Whole Tone Scale
This scale consists of 6 whole steps.
To hear an example of this scale, listen to “Coffy Is The Color” (bars 3 and 4) or the intro to Stevie Wonder’s “You Are The Sunshine of My Life” (the 3rd and 4th bar as well)
Starting from C to C:
C D E F# G# Bb C
If you’d play all notes in that scale as a chord, this would be a C9#5#11 chord
Since all notes in a symmetrical scale/chord can be the root, this C9#5#11 is at the same time also a D9#5#11 chord, an E9#5#11 chord, an F#9#5#11, G#9#5#11 and Bb9#5#11 chord
You could use this scale to solo over augmented triads.
- The Diminished Scales
There are 2 diminished scales.
Both these scales consist of consecutive, alternative half and whole steps.
- The half whole diminished scale: starts with a half step
- The Whole half-diminished scale: starts with a whole step.
The structure of the half-whole diminished scale: 1 b2 b3 3 b5 5 6 b7
Translating that to notes, the C diminished scale is: C Db Eb E Gb G A Bb
The structure of the whole-half diminished scale: 1 2 b3 4 b5 b6 6 7
Translating that to notes, the C diminished scale is: C D Eb F Gb Ab A B
These 2 diminished scales, in essence, are actually modes of one another.
The whole-1/2 diminished scale is what you get when you start the 1/2-whole diminished scale from the 2nd note.
It’s a little more challenging to see why these 2 scales are symmetrical.
They are symmetrical because whichever note in the scale you start on, you get a repetitive interval 3-fret interval that divides the octave into 4 equal parts.
It’s just a little harder to see because that 3 fret interval is divided up into a minor and a major 2nd.
- The Chromatic Scale
We already divided the 12-note octave by 2, 3, 4 and 6, there is only 1 more division we haven’t covered yet, by 12.
That gives you the chromatic scale. This scale consists of 12 half steps, meaning: all notes that exist in music.
This scale is usually omitted in the study of symmetrical chords/scales for a couple of reasons, one of which is that you can’t form a chord combining all the notes in that scale. It’s just too many notes. It would sound like an unstructured mess if you tried to play all 12 notes simultaneously.
All previously covered options can both be a chord or a scale.
I’m only mentioning the chromatic scale here because this concludes every possible division of the octave.
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