Mathematical, Biological and Musical Harmonics
The quotient commonly referred to using the Greek letter Phi was originally designated by the Greek letter Tau, meaning ‘to cut’. Phi denotes the Greek capital letter (Φ) and is used to denote the larger portion of the Golden Mean, the quotient, 1.618..., hereafter denoted as Φ; while we will not use it, the lower case phi (φ) is often used to indicate the smaller portion of the ratio, 0.618.... Phi divides a line or a rectangle into unequal parts; the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller. This cutting has an infinite fractal quality and is self-organised in such a way that it can grow by self-replication. Φ is most commonly expressed as
\[(1 + \sqrt{5}) / 2 \]
(Skinner, 2006) (…). (Dennis, McNair, and Kauffman, The Mereon Matrix, p. 52)
Φ is at the heart of the Fibonacci sequence, a series of numbers that grows by adding to itself in a naturally organic way. Starting with ‘0, 1’, it can grow in either direction, the next term being the sum of the previous two: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc.
The ratio of the consecutive terms is Φ. This Golden Ratio is found in botany, biology and physics; the Golden Spiral spins the structure of a rose. This proportion is found in the cauliflower we eat, the sunflowers we pick, the pinecones we gather and the crystals many collect, and it is also found embedded in the shapes of galaxies made up of billions of stars. Considering the significant integers in the Mereon Matrix, when the larger is divided by the next smaller, a similar spacing pattern appears with differences rooted in Φ: more will be said about this in Chapter 6 with regard to layering in the Mereon 120/180; in Chapter 7 we will look at the correspondence between the Matrix and angles in the 120-cell dodecaplex; we will consider this ratio as it relates to the Mereon Trefoil as a tetrahelix, octahelix and dodecahelix.