As each week comes around, I ponder on what I can write about come Wednesday. I realise now that planning is unnecessary - something always falls into my lap! This week it was a mention from my friend Shirley of the Fibonacci Sequence, as she gazed at a beautiful little violet. Perhaps this is as new to you as it is to me. "The fibber what?" I asked. And so she told me...
There is a series of numbers which each add up to make the next number in the series, and which appear time and again in nature, art and music. As they appear in nature (especially in the number of petals on flowers) they obviously can't be contrived - they really do occur 'naturally'. You start with the number 0 and then 1. Add them together and you get another 1. Add both 1s together and you get 2. Then you add 2 to 1 which gives 3. Then you add 3 to 2 which gives 5. Then add 5 to 3 which gives 8. The start of the series reads:
0 1 1 2 3 5 8 13 21 and so on, ad infinitum.
Shirley showed me how the violet we were admiring had 5 petals. I started examining the flora all around. Irises had 3 petals, buttercups 5, osteospurnums had 13, some daisy things (I'm no Monty Don) had 21. Every flower I looked at had petals that corresponded to Fibonacci numbers. How mysterious!
I felt impelled to look into Fibonacci and music. It's always fascinated me that music one has never heard before can sound predictable. And that certain combinations of notes can put across clear emotions, and reduce a whole audience to tears, or joy, or militance. Was this mysterious sequence behind it?
Well, it's turned out to be a much bigger subject than I imagined. There are lots of intriguing websites covering the subject, but as an appetite whetter here are a few facts:
A whole octave of notes, say C to the C above including the black keys, contains 13 notes in total. The home note, known as the tonic (in this case C) is number 1 and 13. The next most important note is the dominant, in this case G, which is note number 8 of the 13. Looking at the 8 white keys which make up the actual scale of C (CDEFGABC), the first C is number 1, the upper C is number 8 and G, the dominant, is number 5. The home chord in the key of C is C chord (CEG) and C is note number 1 of the scale, E is number 3 and G is number 5. Thinking back to the 13 notes including the black keys, C is 1, E is 5 and G is 8.
If you're familiar with the Circle of Fifths, you'll realise this is also based on the same pattern. All in all, it is just too perfect to be pure chance. And that's just the tip of the iceberg. The point where a piece of music climaxes fits mathematically. The relative frequencies of the notes obey the rule too. Having read all this, my head was spinning, so I put on the television to watch The Autistic Gardener. And what was he discussing? Using the Fibonacci sequence to design a garden layout, based on the Fibonacci spiral found in all pine cones!!!
If you find this as interesting as I did, you may care to visit:
and finally this spine-tinglingly wonderful documentary: