Notes for “Fugue No 1. Squaring the Circle”
by Connor Helms, edited by Bob Altizer
The first movement in a series of 9 sacred geometry-based fugues, this piece is in about 65 beats per minute because the interplay of 6 vs 5 is half the ‘sacred secret‘. Whereas 6 is time and 5 is space, the dimensioned vs dimensionless, square vs circle, or 6660 inches is 555 feet.
The architect Scott Onstott delineates the most salient 6 vs 5 relations:
The structure of the adenine molecule, a component of DNA, is a hexagonal ring and a pentagonal ring. Similar molecules include the hallucinogen DMT; serotonin, responsible for feelings of well-being and happiness; and melatonin, the regulator of sleep and wakefulness.
There are 59 beads on the Roman Catholic Rosary corresponding to 53 Hail Marys and 6 Our Fathers; 6 Gloria Patris, for which there are no beads, are also said in the Rosary – bringing the total number of prayers to 65.
The obverse of The Great Seal of the United States has 13 stripes (representing the colonies), 13 stars in the “glory” above the eagle’s head, 13 arrows, 13 leaves, and 13 olives. The total, 13 x 5 = 65.
In addition, the feathers on the eagle’s wings: 33 on the left and 32 on the right add up to 65.
Also, through “Pythagorean addition,” 32 becomes 3+2 = 5, and 33 becomes 3+3 = 6. The wings of the eagle then represent the relationship between 6 and 5.
Multiplying Phi squared by 6/5 is Pi: 1.2 x (1.6180 x 1.6180) = 3.1415. (The classic Golden Ratio is represented by the Greek letter Phi, or φ; the ratio of a circle’s circumference to its diameter is Pi, or π.)
Illuminant D65, the average brightness of midday light, is 6500 Kelvins.
The 227th Roman Catholic Pope, Sixtus V (1585-1590), derived his name from the 6-vs-5 relationship.
The 12/5 and 6/5 Jerusalem golden rectangle and triangle also represent this 6-vs-5 theme.
The square and compass tools cannot perfectly square a circle; the ratio of inaccuracy is said to be 9:8. This is the same ratio as the modern day major 2nd interval.
Thus, the French horns play G-A pads toward the start and end of this movement (the 5th vs 6th scale degrees are a major second apart in the key of C Major). This fugue has exactly 66 measures, the 66th being a crescendo/diminuendo swell (the life breath of the Divine One which we are all a part of). This is immediately preceded by a solo violin and clarinet duel In this 4-bar duel, the violin (with its sound box) plays a rhythmic diminution of the Golden Ratio/Phi subject, followed by a diminution of the Phi squared subject. Against this, the clarinet (the unending circular breathing of the Divine One) plays diminutions of Pi followed by Pi squared.
The four subjects and themes of the fugue are: