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http://goldennumber.net/fibonacci24.htm

The Fibonacci sequence (w/ numeric reduction … see above… ) creates an infinitely repeating pattern of 24 numbers:

1 1 2 3 5 8 4 3 7 1 8 (9)

8 8 7 6 4 1 5 6 2 8 1 (9)  … 9’s!

How it relates to the musical scale:

Facts:
In popular western music, scales are divided into 8 notes, with 1 and 8 being the same note, an octave apart (‘oct’ as in ‘eight’ like ‘octagon’! yesss! ) :

A basic major scale (ionian):
1  2  3 4 5  6 7 8
C  D  E F  G A B  C

1/C is the ‘root’ or ‘tonic’ (the low octave). 8/C is the same note, but its next highest equivalent on the scale.  It’s all relative.  Truly.

To find any note’s inversion, simply subtract it from 9:
The perfect 5th (G) from the root 1 (C)  (count up from 1 … C, D, E, F, G …  G = 5)  also a perfect 4th down from the octave 8 (C)  (count down from 8 … (C, B, A, G =  G = 4)
… so, subtract either from 9 … 9 - 5 = 4 … 9 - 4 = 5 
(note: only called ‘perfect’ because 4ths and 5ths can never be major or minor … i know, right?)
… by the way, from here on out ‘MorM’ means ‘major or minor’ 
The 3rd (E) from root 1 (C) is the 6th from the higher octave (8) … so, subtract either from 9 … 9 - 6 = 3 (MorM) … 9 - 3 = 6 (MorM)
The 2nd from root is the 7th from the higher octave (8) … so, subtract either from 9 … 9 - 2 = 7 (MorM) … 9 - 7 = 2 (MorM)
More to come…