# Thread: Fibonacci Series and music

1. Newbie
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## Fibonacci Series and music

Hi ppl

I have been playing guitar since 2 years. i learnt from net only, thanks to sites like IGT.

I often wondered what is the reason behind the 1-3-5 major chord interval structure. Means why only 1-3-5 notes of the major scale? I found the Ellliot wave pattern (used in stock markets and in stock software which i was making) quite interesting and some realtion to music too. The answers led me to something very interesting: Fibonacci series. 1,3,5 are part of the fibonacci series!! Below is a part of the article i found on net:

(note: Golden ratio is a ratio of alternate fibonacci numbers!)
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Using the Golden Ratio has enhanced many works of art. During the Renaissance, Leonardo da Vinci – aware of the proportions of the Golden Section – used them to enhance his paintings’ appeal. He said, "If a thing does not have the right look, it does not work."

For this reason, many paintings often use a rectangular canvas with a Golden Ratio because it has a better look than a different shaped canvas such as a square. For example, a portrait picture will often be approximately 1.618 times as high as it is wide or a landscape picture will be 1.618 times as long as it is high.

In music, the scale is based on an 8-note octave. The piano keyboard has 8 white keys and 5 black keys making 13 keys in total.

As a guitar player, I regularly play bar chords that contain the 1st, 3rd and 5th notes of the scale (1, 3, 5 Fibonacci numbers) as they create the sweetest tonality. Triad chords make up a vast majority of popular tunes and they are made with the 1st, 3rd and 5th notes of a scale. For example, a D major chord contains the notes A, D and F sharp – the 5th, 1st and 3rd notes of the D major scale.

The cochlea of the inner ear is shaped in a Fibonacci logarithmic spiral, which explains why it sounds so good to us.

************************************

i was astonished! one can read the whole article on :http://www.futures-investor.co.uk/fi...r_sequence.htm

Hope u enjoy this 'new' piece of information!!

cheers

vivek

2. fib nacci series is 0 1 1 2 3 5 8 13 etc

what happned to 0 the second one and 2?

btw 1 3 and 5 are also part of the odd number series and thats more obvious

3. Newbie
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the findings are empirical in nature! so dont think otherwise.. its just that the whole thing is a big part of a new phenomenon called "Chaos Theory" based on self-organisation and self-similarity principles. It says the Fibonacci sequences 'form' basic patterns in diverse areas. Its not like some musician used 1-3-5 coz its based on fibonacci seq., but we 'found' these patterns pleasing, never caring to think it happned to be a subset of grt fibonacci seq.

if all this sounds confusing, i suggest u first read the complete article for a deeper insight..

-vivek

4. ## im confused

im confused wat u are on about

5. i know about the golden ratio and fibonacci series and the divine ratio...

i have read da vinci code

6. royboyteek, high school math dude... wait for couple of years.

7. Originally Posted by rockboyteek
im confused wat u are on about
awww.... simple... dont bother... they r talkin abt numbers.. and they r not vry good at it.. take my word 4 it... dont even know how 2 count 1,2,3,4.... these guyz.. evry time they tried.. they missed 2 and 4.. and ended up with 1-3-5..

i'm gettin really good at pjs..

8. Okay, if u want to relate fibonacci sequence to music. Listen to Tool's song 'Lateralus'. In that song, drummer Danny Carey plays a fibonacci sequence on the drums. And also do read the lyrics. You'll be able to relate it to the fibonacci logarithmic spiral.

9. Originally Posted by tejas
Okay, if u want to relate fibonacci sequence to music. Listen to Tool's song 'Lateralus'. In that song, drummer Danny Carey plays a fibonacci sequence on the drums. And also do read the lyrics. You'll be able to relate it to the fibonacci logarithmic spiral.
i know that one tejas, or YYZ by rush,, thats the morse code...

but here they r discussing the relationship between notes... and what makes the human ears perceive certain intervals as consonant (musicial) and certain as disonant.. and how thats related to the golden ratio.

Jay

10. @tejas..wow...didnt know that

11. @jay - Okay, i think i should read the whole thing again. Thanks for pointing it out.

12. @vivekthakur - very interesting thread , keep it up .

well , i also have some facts as far as Fibonacci Series is related to music .........
__________________________________________________ __________________
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 comprised 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 too 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.

In a scale, the dominant note is the 5th note of the major scale, which is also the 8th note of all 13 notes that comprise the octave. This provides an added instance of Fibonacci numbers in key musical relationships. Interestingly, 8/13 is .61538, which approximates phi. What's more, the typical three chord song in the key of A is made up of A, its Fibonacci & phi partner E, and D, to which A bears the same relationship as E does to A. This is analogous to the "A is to B as B is to C" basis for the golden section, or in this case "D is to A as A is to E."

13. ## Musical frequencies are based on Fibonacci ratios ....

Notes in the scale of western music have a foundation in the Fibonacci series, as the frequencies of musical notes have relationships based on Fibonacci numbers:
Fibonacci
Ratio Calculated
Frequency Tempered
Frequency Note in
Scale Musical
Relationship When
A=432 * Octave
below Octave
above
1/1 440 440.00 A Root 432 216 864
2/1 880 880.00 A Octave 864 432 1728
2/3 293.33 293.66 D Fourth 288 144 576
2/5 176 174.62 F Aug Fifth 172.8 86.4 345.6
3/2 660 659.26 E Fifth 648 324 1296
3/5 264 261.63 C Minor Third 259.2 129.6 518.4
3/8 165 164.82 E Fifth 162 (Phi) 81 324
5/2 1,100.00 1,108.72 C# Third 1080 540 2160
5/3 733.33 740.00 F# Sixth 720 360 1440
5/8 275 277.18 C# Third 270 135 540
8/3 1,173.33 1,174.64 D Fourth 1152 576 2304
8/5 704 698.46 F Aug. Fifth 691.2 345.6 1382.4

The calculated frequency above starts with A440 and applies the Fibonacci relationships. In practice, pianos are tuned to a "tempered" frequency, a man-made adaptation devised to provide improved tonality when playing in various keys. Pluck a string on a guitar, however, and search for the harmonics by lightly touching the string without making it touch the frets and you will find pure Fibonacci relationships.

* A440 is an arbitrary standard. The American Federation of Musicians accepted the A440 as standard pitch in 1917. It was then accepted by the U.S. government its standard in 1920 and it was not until 1939 that this pitch was accepted internationally. Before recent times a variety of tunings were used. It has been suggested by James Furia and others that A432 be the standard. A432 was often used by classical composers and results in a tuning of the whole number frequencies that are connected to numbers used in the construction of a variety of ancient works and sacred sites, such as the Great Pyramid of Egypt. The controversy over tuning still rages, with proponents of A432 or C256 as being more natural tunings than the current standard.

note : sorry abt that table , no rich text format !!!

14. thats cool bobby! i never thought of that. aliens who created our universe loved fibonacci series. i guess.

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