Sunday, September 23, 2012

3rd Rail Chord Symmetries (Part 4)

Red diagonals indicate minor 3rds spanning the 3rd Rail. Roman numerals indicate their respective scale degrees.
Above you see the positions of the minor 3rds which span the 3rd Rail in the key of C. Each of these double-stops are at the center of a 7th chord. Two of them – the vi and the iii (dark red) – are each the center of a major 7th chord. The other two – the vii and ii (pale red) are the centers of two different types of chords. The ii is the center of a B minor7 b5 (also called 'half-diminished') chord, and the vii is the center interval of a G dominant 7th.

In the diagram below, you see the two major 7th chords which pass through the above min3rd positions. The IV chord (F maj7) radiates from the a minor 3rd at scale degree vi, and the I chord (C maj7) radiates from the E minor 3rd at scale degree iii;
Roman numerals indicate scale degree of each major 7th chord root.
If we extend these 7th chord forms a 3rd above and below, we then have a set of minor 11th chords. Each of these extended forms radiates from a different part of the key, even though they have the same geometry;
Roman numerals indicate scale degree of each minor 11th root.
If we focus on these two extended arpeggios side by side, with some in-between frets removed for a better view, we see that their internal structures are identical. The form on the left is rooted in the second scale degree (D), the form on the right is rooted in the 6th scale degree (A)
The D minor 11th arpeggio (left) can be played from the open strings as indicated, or from the 12th fret.
The diagram below shows the centered interval structure of the two forms;
And here's where these two arpeggios are played on the piano keyboard;
The only way to distinguish one of these forms from the other from a geometric perspective is to look at the relationship between each of the arpeggios and the positions of the notes which surround each one. Because of their differing positions within the key, these 11th chord-arpeggio forms live in different surroundings on the fret board. We'll go more deeply into those relationships in a future post. For now, lets look at how each of these two big S shapes break into four triads;

Each three-note sequence in these forms is its own triad. Of the seven triads belonging to the key of C, six are present in these forms; C major, D minor, E minor, F major, G major and A minor. The remaining triad – B diminished – is found in both of the remaining 11th chord arpeggio forms. 

Remember that the D minor 11th arpeggio can be played either rooted in the open string D or at the 12th fret.

Next: 3rd Rail Chord Symmetries (Part 5) – we delve into extended Dominant and Leading Tone Sevenths ...

All contents of this blog are © Mark Newstetter

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