Friday, September 18, 2009

11th fret Symmetry

The 11th fret is the location of the only natural alignment of black-key tones on the fretboard. In Fretography we refer to this position as The Void. However these same tones can be part of three flat keys; Db, Gb and Cb which have five, six and seven flats respectively.

Notice that these tone positions follows the same logic of 'paired symmetry' we've previously examined. With five tones to consider, they are paired in rotational symmetry as follows:

Gb - Bb
Ab - Ab
Db - Eb

In other words, wherever you find Gb on one side of the Axis - within the top four strings (white background) or within the bottom three strings (blue background), you'll find Bb in the diametrically opposite position. The same is true of Db and Eb. Ab (the second tone of Gb) is opposite itself, just as D is opposite itself in the key of C. The piano keyboard in the diagram makes the symmetry even more obvious. Can any note other than Ab be seen as the 'middle' of the five black keys?

When seen from this perspective, we are thinking of these tones as belonging to the key of Gb, which is found on the 3rd string of the Axis, shown on the 11th fret in the diagram above. Gb is structured as follows;

Gb W Ab W Bb H Cb W Db W Eb W F H Gb

Notice that our set of black-key tones excludes the 4th and 7th tones of Gb.

Gb W Ab W Bb H Cb W Db W Eb W F H Gb

[ An interesting coincidence is that the Cmajor/Aminor pentatonic scale (C D E G A) is produced by removing the 4th (F) and the 7th (B) from the key of C, and that the elimination of these same tones; The 4th of Gb; Cb (enharmonic of B) and the 7th of Gb; F, result in a pentatonic scale based on 5 different tones (Gb Ab Bb Db Eb). ]


This is the template for Pentatonic Scales typical in rock and blues. If you are already familiar with Pentatonic scales on the guitar, you'll recognize the pattern. But rather than approach these tones from that angle, we'll look at them in their diatonic context as the black-key chromatic tones of the key of C major/A minor.

C Db D Eb E F Gb G Ab A Bb B C

Keep in mind that, though the diagram shows the pattern from the 5th fret up, the pattern from the 12th fret to the 17th is exactly the same as from the open strings to the 5th fret, so nothing is really missing. By placing the Secondary Aeolian Axis at the center of the diagram, the symmetry becomes clearer (refer to the previous post for the view beginning at the open strings).

In an upcoming post we'll look at chords based on the five black-key tones. But first, more about the difference between the keys of Gb and F#.

All contents of this blog are © Mark Newstetter

No comments: