Sacred Proportion

Look closely at this .jpg and see how extraordinary properties of mathematical perfection can be sourced through an overview of the Circle as it converts into a Spiral.

This amazing graphic I found on the web ... It is the most perfect representation of the relationship between Ratio, Mass and Harmonic Proportion that I can offer you

This graphic demonstrates a RATIO OF EXPANSION that is both HARMONIC and SIMPLE. Thge principles of Mass, Volume and Weight ALL RELATE TO THIS RATIO. If we take each section and cut it out as a metal piece... Each section would define a specific HARMONIC NOTE that rises in perfect ratio and accordance with the mathematics it represents.

Now go Let's back to the Magic Square Pattern we FIRST looked at in this study ... If you add up all the numbers surrounding the central FIVE in the first "band" ... Then the Second "band", and so on... You develop a ratio of expansion.

The RATIO is simple

4+1+8+3+6+7+2+9 = 40

6+2+7+6+2+4+9+2+4+8+1+4+8+6+3+8 = 80

5+3+9+5+3+9+5+7+1+5+7+1+
5+9+3+5+9+3+5+1+7+5+1+7 = 120

40::80::120::160::200 and so on

This equates to 1::2::3::4::5::6 etc. or put in another way the basic ratios of Harmonic Expansion are described in this simple procedure

The First Series relates to the Octave... 1:2 2:3 3:4 4:5 5:6 etc.

Every SECOND ring relates to another ratio, this time the FIFTH... 1:3 2:4 3:5 4:6 etc.

Every THIRD Ring relates accordingly to the ratio series, this time the FORTH... 1:4 2:5 3:6 4:7

ALL THESE RATIOS RESOLVE IN PERFECT HARMONIC PROPORTION ON ANY STRINGED INSTRUMENT...