1
10
101
10110
10110101
1011010110110
101101011011010110101
has anyone managed to produce a piece of music thru the golden ratio? i know that alot of artists used the sequence in order to make compositions...it's well known that mozart used it for his pieces, so did other famous compositors. um, the reason i got into it was because of boards of canada and all of the stuff they used to make their music. not just the golden ratio, but complex math equations to generate music. so i'm guessing minimal would be a hell lot of fun to make thru some equations...
![Razz :P](./images/smilies/icon_razz.gif)
an example thru the words which we actually call a rhyme:
Twinkle twinkle little star
How I wonder what you are.
Up above the world, so high
Like a diamond in the sky
![Image](http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/rabPhiPlot.gif)
Lining up the Rabbits
If we return to Fibonacci's original problem - about the rabbits (see the Fibonacci home page if you want to remind yourself) then we start with a single New pair of rabbits in the field. Call this pair N for "new".
Month 0:
N
Next month, the pair become Mature, denoted by "M".
Month 0: 1:
N M
The following month, the M becomes "MN" since they have produced a new pair (and the original pair also survives).
Month 0: 1: 2:
N M M
N
The M of month 2 become MN again and the N of month 2 has become M, so month 3 is: "MNM"
Month 0: 1: 2: 3:
N - M - M - M
\ \ N
N - M
The next month it is "MNMMN".
The general rule is
replacing every M in one month by MN in the next and similarly replace every N by M.
Hence MNM goes to MN M MN .
We have now got a collection of sequences of M's and N's which begins: rabbit family tree
0: N =N
1: M =M
2: M N =MN
3: M N M =MNM
4: M N M M N =MNMMN
5: MNM MN MNM =MNMMNMNM
![Image](http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/visa-mcard.gif)
![Image](http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/natgeog.gif)
![Image](http://www.nestle.hu/kitkat/images/logo.gif)
# If you measure a credit card, you'll find it is a perfect golden rectangle.
# The golden rectangle icon of National Geographic also seems to be a golden-section rectangle too.
# John Harrison MA has found a golden rectangle in the shape of a Kit-Kat chocolate wafer (the larger 4 finger bar).