MathNovatory/Pure Maths/Fibonacci Numbers/Discovery


Fibonacci in a new lighting

Music
This "qualitative" structure of the Fibonacci system was found, somewhat by chance, while programming the operation of the musical language.
The structure of musical rhythm is fundamentaly binary in its perfect regularity. When, by the process of ablation of the first 1/4, the other rhythmic shapes (including the ternary) are placed in order of increasing irregularity, the "most irregular", with the maximum possible ablation, is inevitably a Fibonnacci value (Fv) and its inner structure is very clearly defined.
EX - from the "regular" group of 4 (22) we reach Fv3
EX - from the "regular" group of 8 (23) we reach Fv5
EX - from the "regular" group of 16 (24) we reach Fv8
EX - from the "regular" group of 32 (25) we reach Fv13 etc ...
With the following algorithm, we could produce all the possibilities :
     from the "regular" group of 2n we reach Fi(n + 2), using the Fibonacci index.
EX - with n = 10, from the "regular" group of 1024 we reach 144.
Once the structure is evident, the is rest mostly a question of "opening the back of the clock to see how the pieces work".

To The Fibonacci Structure