well i searched around our forum & found a post from fxsystemtrader which carry a good explanasion for the mean of the fibonacci ratios ,

the post's here

i cut the coming words from it:

+------------------------------------------------------------------------+

Fibonacci retracement is fundamentally based on a single number, which is Golden Ratio 1.618 or 0.618. <---
(1/1.618 = 0.618 .just from different side of perspective)
This single magic mysterious number does all the trick and covers the entire Fibonacci numbers or Levels.

0.618x0.618 =0.382
0.382x0.618 =0.236
0.236x0.618= 0.146

So, here is the full sequence of Fib numbers(levels) from 0.1 to 1.0

0.146 1- 0.854
0.236 1- 0.764
0.382 1- 0.618
0.5 mid point
0.618 1- 0.382
0.764 1- 0.236
0.854 1- 0.146

(1.236 = 1+ 0.236 = 0.382+ 0.854 = 0.618x 2 = 2- 0.764)
(1.618 = 1+ 0.618 = 0.764+ 0.854 = 1/ 0.618 = 2- 0.382)

0.5 is not a fib number to be precise, but it is as important as fib.
At the same time, there is a Gap between 0.382 and 0.618, PLUS

(0.382 + 0.618)/2
(0.236 + 0.764)/2
(0.146 + 0.954)/2
= 1 /2
= 0.5

which means that the middle point of
0.382 and 0.618
0.236 and 0.764
0.146 and 0.854
is 0.5, and obviously it is also the middle point of 0 and 1.

These numbers cover fair range between 0 to 1.0.
It's as simple as that, just +or -. based on 0,618=Golden Ratio

in some Harmonic Trading book, they mention 0.786 or 0.886 using Root calculation etc.
I think these are rather Artificial manipulation of Golden Ratio, and I have no idea why they insist such numbers instead of employing the simple Fibonacci sequence.
You see 0.786 is close to 0.764 and 0.886 is close to 0.854.
This difference doesn't mean much, so why don't you use simpler ones?
The real simplicity from the Golden ratio appears on the sequence list I shown first.
So, I totally ignored these artificial numbers according to their book or site, and instead, employ simple Fib numbers.
Actually, For Gartley Pattern.(in the chart above)
If
XAB =0.618
ABC =0.618
BCD = 1.618,

XAD = 0.854 (= 0.236 + 0.618) !!
not 0.886.

Harmonic patterns behave like this, if you set up a couple of Fib ratio for each reteracement, Automatically, another Fib retracement ratio show up. That is why this pattern is called as Harmonic.
You can do math or using MT4 Fib line tool.
Again, as long as you stick to pure Fib numbers, since Golden Ratio would repeat itself, whatever you manipulates among Fib numbers, the result is Always on Fib numbers.
That is the beauty.
However, once you include the other biased fib numbers such as 0.886, it will be broken

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