There are many example of fractals throughout the musical world.  But First, The Fibonacci sequence, a fractal set in its own right cant is seen throughout the structure of the natural world. These few examples show the diversity and beauty of this one simple equation. The Fibonacci sequence can also been seen in the composition of one of the worlds most famous painting, the Mona Lisa…. Which was painted by da Vinci. The Fibonacci Sequence is an equation in which the spiral shape found in nature can be seen. It shown Below.

 

spiral

Musical scales are based on Fibonacci numbers

 

The Fibonacci series appears in the foundation of aspects of art, beauty and life. Even music has a foundation in the series, as

 

There are 13 notes in the span of any note through its octave.

A scale is composed of 8 notes, of which the

5th and 3rd notes create the basic foundation of all chords, and are based on whole tone, which is 2 steps from the root tone, that is the 1st note of the scale.

Note also how the piano keyboard scale of C to C above of 13 keys has 8 white keys and 5 black keys, split into groups of 3 and 2. While some might “note” that there are only 12 “notes” in the scale, if you don’t have a root and octave, a start and an end, you have no means of calculating the gradations in between, so this 13th note as the octave is essential to computing the frequencies of the other notes.  The word “octave” comes from the Latin word for 8, referring to the eight whole tones of the complete musical scale, which in the key of C are C-D-E-F-G-A-B-C.

 

Musical compositions often reflect Fibonacci numbers and phi

Fibonacci and phi relationships are often found in the timing of musical compositions.  As an example, the climax of songs is often found at roughly the phi point (61.8%) of the song, as opposed to the middle or end of the song.  In a 32 bar song, this would occur in the 20th bar. Many composer such as Beethoven, Mozart and Bella Bartok have been linked to fractals within there compositions.

 

Musical instrument design is often based on phi, the golden ratio

Fibonacci and phi are used in the design of violins and even in the design of high quality speaker wire.

 

violin 3D3H 360

This Website goes into the great details of fractals in music, however its fairly complicated and hard for me with my limited musical experience. However I have included it as its very imformative!

http://solomonsmusic.net/fracmus.htm

 

Cymatics

Essentially not music based but this video of cymatics for me proves the link between sound and patterns perfectly. This video amazed me!

 

My Choice of Music

After Much deliberation and hours upon hours of listening to music ive research into music realting to fractals I have decided to have Tool’s Lateralus as my sound track

Firstly here are a few of the Tracks that were shortlisted for one reason or another.

 

What Phi (the golden ratio) Sounds Like – Micheal Blake

 

Bela Bartok – Music For Strings

 

Bence Peter – Fibonacci Piano piece

However this is my music of choice – With a very helpful video which explains all the reasons why for me!

 

Tool – Lateralus

 

http://www.fibonicci.com/fibonacci-tools-lateralus/

Although this track is perfect it is however not to everyone’s tastes… after this troubling me for some time I’ve found a number of cover version which adhere to all of Fibonacci’s inspiration within the musical composition, whilst having a more popular appealing sound.

 

Rockabye Lullabies – Renditions of tool

Covered using only xylophones!

 

String Quartet Tribute to Tool

A Brilliant and moving cover by a string quartet!

 

UPDATE: I have chose the string quartet version, for me it has a much more atmospheric nature along with having more depth and layers. I will now edit the track from 9.32 in length to a more reasonable length using Audacity, ready to edit the image to.

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