Tuesday, September 15, 2009

Diatonic Symmetry 2

The key of Gb is halfway around the circle of 5ths from the key of C natural. The relationship of these two keys is significant because it illustrates the relationship between the symmetry of the Diatonic system and the geometry of the tonal array of the guitar fretboard.

The diagram above shows how Gb is arrayed on the fretboard and the piano keyboard. Notice how the axis positions of Gb are nested symmetrically between those of the key of C. For instance; the Aeolian Axis of C is found on the 5th and 17th frets, while the Aeolian Axis of Gb is on the 11th fret, precisely halfway between them. The Phrygian Axis of Gb is at the 6th fret, one fret above the 5th fret Aeolian Axis of C, while the Dorian Axis of Gb is at the 16th fret, one fret below the 17th fret Aeolian Axis of C. The Dorian and Phrygian Axes of C are at the 10th and 12th frets respectively, flanking the central Aeolian Axis of Gb.

Of course Gb has the same symmetry as C, but its complementary relationship with the Natural key makes it unique. Any two keys at opposite ends of the Circle of 5ths (A major and and Eb major, for example) will have a similar complementary symmetry.

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