Fibonacci Inversion is Like Musical Inversion of Intervals

What exactly is Fibonacci Inversion?

Fibonacci Inversion is Like Musical Inversion of Intervals. . Inversion means to reverse the order, be it  of numbers or the two tones of a musical interval.  We also have melodic inversion. An example will be given by J.S. Bach. A unison inverts to an octave as 1 + 8 = 9. The second inverts to the seventh as 2 + 7 = 9. The third inverts to a sixth as  3 + 6 = 9. The fourth inverts to a fifth as 4 + 5 = 9. Inverting music is further discussed in my internal link.immediately below.

Music and Math Share the Rule of 9’s

Also, inversion also means turning the melodic intervals up-side-down.

Fibonacci inversion has a parallel in music
An example of melodic inversion from the fugue in D minor from J.S. Bach’s The Well-Tempered Clavier, Book 1.[1] Though they start on different pitches (A and E), the second highlighted melody is the upside-down version of the first highlighted melody. That is, when the first goes up, the second goes down the same number of diatonic steps (with some chromatic alteration); and when the first goes down, the second goes up the same number of steps.

Fibonacci Inversion is Also Like Inverted Triads

Image result for Wiki Commons illustration of C major triad and inversions
The same three basic notes are always there, but turned around. In order C-E-G; E-G-C, and G-C-E.

What are the Fibonacci numbers?

In mathematics, the Fibonacci numbers are the numbers in the following integer sequence, called the Fibonacci sequence, and characterized by the fact that every number after the first two is the sum of the two preceding ones:[1][2]

{\displaystyle 1,\;1,\;2,\;3,\;5,\;8,\;13,\;21,\;34,\;55,\;89,\;144,\;\ldots }

For the Fibonacci  inversions, I take the 1st four numbers: 1,1,2, 3.  Each of these Fibonacci numbers with its inversion totals four. In similar fashion each musical interval with its total equals the same number. The number is different but the principle is the same.

The Fibonacci  inversion of “1′ becomes “3”. This happens for each “1”. The inversion of “2′ becomes 2. This number inverts to itself. The musical parallel is as an octave inverts to a unison.  Next, the inversion of “3” becomes “1”.

In order, the inverted numbers of  1,1,2,3,  are 3,3,2,1. Now we have to points to make (1) Ancient philosophers often either separated successive numbers and/or placed them together.(2) Ancient numbers squares give rise to the Fibonacci series. The internal link explains, in depth, how Fibonacci numbers dominate 4 x 4 number square.

Remarkable Foursome is a Mathematical Wonder

I keep within the ancient tradition of number squares for this next explanation.  Take the first four inverted  Fibonacci numbers, 3,3,2,1 – as a straight read. You have 3321. The is the numerical total of the 9 x 9 number square of the Moon. This square (with other ancient squares) is pictured below. It houses all the numbers from 1 to 81. Any two opposite numbers total 82. My page was copied from an earlier blog about the “Neolithic Periodic Chart”. Note the obvious vertical sequence of numbers on the periodic chart.  It is found on the diagonal on odd numbered squares. They are clearly reinforced in reinforced black ink. The numbers are 2,8,8,18,18,32,32, …

Hidden Periodic Chart Sequence Found in a set order

So what is my conclusion? Again,  there once was a former advanced civilization. It was based on number squares. Times were then peaceful and harmonious. Somehow it was destroyed. Could it have been the continent of Atlantis that Plato mentions in his writings?

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