With the evolution of Tony Williams’ Spider Web Pan, the Circle of Fifths has become the standard for the lead/tenor pan, eclipsing the previously preferred Invader pattern. However attempts to standardize the Double Seconds have only lead to a proliferation of adjustments and re-alignments of the layout first established by Dr. Ellie Mannette.
The fact that dissatisfied builders are still experimenting with the layout is proof that until now no one had arrived at that perfect symmetry that is the unanimous and undeniable standard for the doubles. We can now demonstrate that the newly aligned Double Second –SS has accomplished this feat. We make no claim of ownership here, for this is simply the integration and evolution of the work pioneered by Mr. Williams and Dr. Mannette.
In arriving at the SS layout we used a geometric standard already evident in the Circle of Fifths and applied it to the double seconds. The reason why the lead/tenor is easily accepted as a standard is because it makes geometric sense and is supported by the principles of mathematics and physics.
"Plato said God geometrizes continually." - Plutarch
"We do not listen with the best regard to the verses of a man who is only a poet, nor to his problems if he is only an algebraist; but if a man is at once acquainted with the geometric foundation of things and with their festal splendor, his poetry is exact and his arithmetic musical." - Ralph Waldo Emerson
Can we apply the same geometric logic to the Double Seconds? Absolutely.
The secret is in using the same geometric pattern abstracted from the lead/tenor as a standard and applying it to the two whole tone scales (which are how the seconds are divided) correspondingly as it is applied to the chromatic scale in the lead/tenor.
The pattern tool is the hexagram, a six-pointed geometric star figure; the compound of two equilateral triangles. Otherwise known as Sacred Geometry. Below, is the Circle of fifths showing hexagrams formed by the two whole tone scales:
Of course, we cannot simply abstract the hexagrams in the way it is laid out in the circle of fifths. Dr. Mannette was quite aware of all this when he came up with his pattern for the double seconds. But he stopped short of synchronizing or creating symmetry between the two sides.
Only Dr. Mannette can explain why he chose to create two asymmetric sides.
Note that each triangle is an augmented chord. Now, using the same hexagram, we can arrange the two sides of the double seconds to be a reflection of each other. Below is Dr. Mannette’s traditional pattern, followed by the proposed SS pattern.
As it stands right now, the right side of Dr. Mannette’s double seconds is perfect, and fits the proposed standard. It is the left side that has to be adjusted to reflect the geometric standard already established on the right side.
Observe in the proposed standard, the formation of the hexagram on the left side, not found on the corresponding side of Dr. Mannette’s model:
Double Seconds SS
Observe also, that the two sides in the new standard are an exact mirror image of each other. Try playing the chromatic scale and see how your right hand perfectly mirrors the movement of the left.
Here’s an interesting aside: the movement of the hands in playing the chromatic scale on the SS, forms a unicursal hexagram. “This is a six pointed star that can be traced or drawn unicursally, in one continuous line rather than two overlaid triangles.
This is significant as the triangles are often used to represent opposites such as fire and water or male and female. The unifying of the symbol into one represents the synthesis of opposites.
The ability to draw it in one continuous movement, is significant in ritual magick.” -Wikipedia
To learn more on Sacred Geometry go to these links: http://www.charlesgilchrist.com/