Since this treatise is about octaves it would be appropriate to glance into numbers of octaves between different sizes.
Working with octaves one can view the phenomenon in mathematical terms. Octaves are an exponential function with 2 as base; y = 2x.
Yet one can also say, that an octave fits the function y = 2x, which is a simple straight line. One has to bear in mind, that the value of x is different in the two equations. A different x will give the same y in the two functions.
A nice and easy way to calculate how many octaves there are between different objects of any size can be estimated quickly on a mathematical calculator. The exponent of 2 indicates the numbers of octaves; so the sum has to be altering the sizes we want to compare into exponent of 2.
If we want to know how many octaves there are between e.g. a human and the Sun, we can set the diameter of a human to 1.7 m and the diameter of the Sun to 1,392,500 Km., we will see there are about 30 octaves between man and the Sun
By making y = 2x to a logarithmic quantity we can isolate x and find the value of the exponent of 2. Using natural logarithm on both sides we get this quantity: lny = xln2; x = lny : ln2. In this case the exponent for the Sun is 20.4 and for a human - 9.2. So the octave span is 29.6. This logarithmic quantity has been useful for me many times when working with the estimation of numbers of octaves between different bodies.
In "The Theory of Celestial Influence" Rodney Collin mentioned 36 octaves but he did not state how he came to that figure.
I will present a case from our Nature in order to relate to the importance of dimension and sound.
Insects communicate usually by sound, high pitched sounds. Animals can, due to their bigger size, produce both low as well as high pitched sounds.
A law in acoustics states that the efficiency of sound waves,
(that part of the moving energy that is transmitted as sound,) is small at low
frequencies, but relatively constant at a certain frequency, which especially
depends on the size of the oscillator.
In plain
words: the length of sound waves can not be much bigger than the body that
produces them.