## Fibonacci series

Here is a short music video with amazing animation that explains the Fibonacci series very well.

The Fibonacci series featured in the above video is a sequence of numbers that occurs frequently in nature. It can be seen in the arrangement of petals and seeds on flowers, in the spiral shape of snail shells and in the arrangement of branches and leaves on trees. It is the same spiral seen when water goes down a plug hole or when a hurricane forms around its eye, just as it is the same shape found in the spirals of galaxies and the hair on the tops of people's heads.

Man has used the Fibonacci series to copy nature for centuries. You will find it in the structure of many ancient buildings like the Parthenon in Greece, the Great Pyramids of Giza, Stonehenge, and also in the arrangement of some classical music where an 8 minute piece will often peak at 5 minutes. It is still used today by musicians, architects and artists to produce beautiful proportions that resonate with nature.

As a number sequence, the Fibonacci series becomes easy to understand. You just take the number one and add it to itself to get two. Then add them together to get three: 1 + 1 = 2 and 1 + 2 = 3. Now you have 1 - 2 - 3. Then just add the last two numbers together to get the next number: 2 + 3 = 5. That gives you 1 - 1 - 2 - 3 - 5, add the last two numbers again, 3 + 5 = 8 and so you can go on and on. The result will be 1 - 1 - 2 - 3 - 5 - 8 - 13 - 21 - 97 - 34 - 55 - 89 - 144 ... it goes on forever, an infinite spiral growing exponentially larger with each new number.

Man has used the Fibonacci series to copy nature for centuries. You will find it in the structure of many ancient buildings like the Parthenon in Greece, the Great Pyramids of Giza, Stonehenge, and also in the arrangement of some classical music where an 8 minute piece will often peak at 5 minutes. It is still used today by musicians, architects and artists to produce beautiful proportions that resonate with nature.

As a number sequence, the Fibonacci series becomes easy to understand. You just take the number one and add it to itself to get two. Then add them together to get three: 1 + 1 = 2 and 1 + 2 = 3. Now you have 1 - 2 - 3. Then just add the last two numbers together to get the next number: 2 + 3 = 5. That gives you 1 - 1 - 2 - 3 - 5, add the last two numbers again, 3 + 5 = 8 and so you can go on and on. The result will be 1 - 1 - 2 - 3 - 5 - 8 - 13 - 21 - 97 - 34 - 55 - 89 - 144 ... it goes on forever, an infinite spiral growing exponentially larger with each new number.

## Fibonacci Series Music

The Fibonacci does not vibrate, but if you use it's numbers are frequencies, they are a lot more musical than expected. The following piece of music is built on the numbers 1-2-3-5-8. These numbers are too low to be used as Hz based musical tones so in this track they have all been raised by 6 octaves, multiplying each one by 2 six times to get these 5 frequencies: 64-128-192-320-512. (Hz) This is still a Fibonacci series because you can still add the last two numbers together to get the next one, only now they are within hearing range and can be played as audio tones.

The overall sound of these 5 tones is a wide C major chord stretched over a few octaves. If you understand music theory then you will know that the major chord and the octave are the basic parts used to make just intonation music scales. So just as the Fibonacci series is the code for plant growth and so many other physical things, it can also be used to construct musical harmony. If you click on the track's name below you can read the full description of how the track was made, it is not just the frequencies but also the rhythms and arrangement that follow the Fibonacci series.

The overall sound of these 5 tones is a wide C major chord stretched over a few octaves. If you understand music theory then you will know that the major chord and the octave are the basic parts used to make just intonation music scales. So just as the Fibonacci series is the code for plant growth and so many other physical things, it can also be used to construct musical harmony. If you click on the track's name below you can read the full description of how the track was made, it is not just the frequencies but also the rhythms and arrangement that follow the Fibonacci series.