The above Russell quote reminds us of Parker's work on the Quadrature of the Circle; [by George Hull] wherein are discussed in great detail inscribed and circumscribed triangles, squares and circles. John Parker's work as well as Iverson's Quantum Arithmetic stopped short of revealing 3-D (xyz) orthgonal structures and their inherent math/geometries but they do clearly show the simple arithmetical and spatial relations between different geometric entities. Their work touches on a natural mathematics of whole numbers representing and describing whole real entities. For instance by using whole integers and relations of proportions the irrational numbers do not occur and are not used or required. This mathematics was well represented by Kepler, Cusa and others. It is believed by this author this wholistic mathematics was used by Keely, depicted by Russell and will be touched on in several places in this wiki.

Ramsay
When these representative dots are arranged on these six Octaves of lines, at regular distances marked out by the proportionate degrees of the circle, they present to the eye this beautiful symmetrical picture of the Diatonic System of Musical Vibrations. They represent all that mathematically belongs to Music. When the notes are strung [Scientific Basis and Build of Music, page 102]

See Also

6.8 - Proportionate and Relative Geometries
9.12 - Velocity of Sound and its Propagation Rate are Proportional
12.00 - Reciprocating Proportionality
3.13 - Reciprocals and Proportions of Motions and Substance
13.15 - Principle of Proportion
constant of proportionality
Figure 6.17 - Areas and Volumes - Relations and Proportions
Figure 6.19 - Sphere to Cube - Relations and Proportions
Figure 14.10 - Proportionate Tonal Relations dictate Contraction or Expansion
Fundamental
Interval
Keynote
Law of Assimilation
Part 12 - Russells Locked Potentials
Portion
Proportion
Quadrature of the Circle
Reciprocating Proportionality
Table 2 - Controlling Modes and Proportions
Universal Ratios