Monday, September 28, 2009

Symmetrical Triad Inversions

Lets return to the tones of the key of C for a study of chord symmetry on the four top strings. The pattern above (click for larger image) shows the symmetry of some triad inversions.

Triad inversions are simple three note chords where the Root is not the lowest pitched tone in the chord as it is in the Root voicing. In a 1st inversion the 5th of the chord is lower in pitch than the Root, while the 3rd remains above the Root so that the pitch sequence from low to high is; 5th - Root - 3rd. A C major triad in its Root voicing is;

G - (5th)
E - (3rd)
C - (Root)

A 1st inversion C major triad moves the Root to the top;

C - (Root)
G - (5th)
E - (3rd)

A 2nd inversion C major triad moves the 3rd to the top;

E - (3rd)
C - (Root)
G - (5th)

The Diagram above shows 1st and 2nd inversion triads found within the top four strings with their roots on the 2nd string. The green triangles placed on strings 4, 3 and 2 represent 1st inversion triads, the blue triangles on strings 3, 2 and 1 represent 2nd inversions of the same triads. notice that the green and blue triangles are paired so that each 1st inversion and second inversion of the same three tones is connected. The gray triangles are a continuation of the pattern outside the primary symmetry.

Notice that the triads form a symmetrical pattern around the Aeolian Axis (indicated by a red vertical bar) where the E minor (iii chord) and F (IV chord) major chords are aligned in the key of C, and also around the Void Axis (gray vertical bar) which is the position of the B diminished (vii chord) in the key of C.

The pattern is shown in 3 keys; C, D, and E. E is shown with Roman numerals instead of alphabetical note names so that you can see the scale degree relationships. In the key of C, the triads are;

C major, D minor, E minor, F major, G major, A minor, B diminished.

The same pattern can be expressed as scale degrees as follows;

I = major, ii = minor, iii = minor, IV = major, V = major, vi = minor, vii = diminished.
(It's traditional to use lower case Roman numerals to identify minor and diminished chords)

The overall symmetry of the pattern can be expressed as;

vii - I - ii - iii --- IV - V - vi - vii

... with the iii and IV chords at the center, and two instances of the vii chord, an octave apart, as a pair of bookends, or as;

IV - V - vi - vii - I - ii - iii

... with the vii chord at the center and IV & iii at the lower and higher ends of the pattern, respectively.

These relationships apply to every key, so you can extrapolate from the three patterns shown and play the triads in all keys.

All contents of this blog are © Mark Newstetter

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