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fee said:
damn I wish I was an artist

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Yes, and if wishes where horses, then we'd already be living on mars by now...

Or, to borrow a bit of old corporate-shoe-branding...

Just Do It!?

So go shoe your horse, and ride along with us!

It's Better To Be "Old Paint," Than New Glue!?

*Fee, it's like jazz! You can play anything over anything -- anything at all, no, really, you can -- you just gotta mean it there! If you get my drift...

PS: Where are all these lost references gone to?

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Fibonacci and the Music of the Spheres...

I was poking around into the Fibonacci sequence today. That mathematical pattern which seems to predict everything from the spiral growth of sea shells, pine cones and seed pods, to the number petals on flowers and the patterns of leaves. Whose derivative the golden section, or the proportion of 1:1.618 can be found on architectural proportions we find attractive, and of course, those proportions of human beauty which we find attractive.

The fibonacci sequence is formed by starting with 0 and 1 and then adding the latest two numbers to get the next one:

0,1,1,2,3,5,8,13,21,34,55,89,144,233,377...and so on...

The Fibonacci sequence also bears a direct relation to what is known as the golden section or golden ratio. The golden section numbers are 0.61803... and 1.61803... and are expressed as rations of 0.618:1 or 1:1.618. These numbers are arrived at by extracting the ratios of neighboring Fibonacci numbers: 1/1 = 1, 2/1 = 2, 3/2 = 1.5, 5/3 = 1.666..., 8/5 = 1.6, 13/8 = 1.625, 21/13 = 1.615..., 34/21 = 1.619..., 55/34 = 1.617... and so on. The sequence of ratios continues on infinitely, much like pi, ever approximating a number that be practically shortened as 1.618, and expressed as a ration as 1:1.618 (inversely expressed as 0.618:1).

Well, I was thinking about this, and I began to wonder, what about music. Surely music, that most mathematical of constructs, must bear some relation to the Fibonacci sequence? Now, I'm not interested in whether a particular composer experimented with the Fibonacci sequence to write a specific musical work. That research has been done, and is well documented. What I'm interested in is its fundamental relationship to the scales and modes that the human mind finds attractive.

So I took the first few numbers of the sequence and overlayed it on the major scale of western music and started looking for patterns. What I got was inconclusive at best, but does bear further inquiry:

Fibbonacci number applied over a C major (or 8 note ionian) scale

 1  #  2  #  3  4  #  5  #  6  #  7  8 
 1     2     3        5              8
 8                         13          
                                 21    
                           34          
 
                           55

I have no idea what the above means, except that that there is a emphasis on the major triad (1,3,5), the mixolydian root (5), and especially the aeolian, or natural minor, root (6), and a complete absence of emphasis on the lydian root (4).

I also wondered what if I overlayed this sequence on the twelve note octave, disregarding the major scale altogether? You what I got? The same damn thing! Here is the correspondence of the seqence layered over the twelve note octave to the sequence layered over the eight note major scale of western music.

Fibbonacci number applied over a C chromatic (or 12 note) scale:

 1  #  2  #  3  4  #  5  #  6  #  7  8 
 1  2  3     5        8             13 
(1)   (2)   (3)      (5)            (8)

Note that the resulting correlations when the major scale is transposed over these notes is again 1,2,3,5,8!!! What any of this means, I'm not quite sure. It will require further investigation. I'm sure the answer lies in the music of the spheres, and perhaps the correct serotonin antagonists may provide fruitful research results.