Fibonacci Musical Compositon

8/18/2019 Fibonacci Musical Compositon

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Fibonacci Musical Compositon

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A standard piece of Fibonacci composition.

Fibonacci Musical Composition is the process of composing musical pieces using the

Fibonacci Number Sequence, which was named after Leonardo Pisano Bigollo (who

also went by the name Fibonacci) !he progressions of music are composed with the

sequence accordingly, presenting a hierarchy which gives off an illusion of momentum

build"up while also sounding pleasing to the human ear

Contents

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• % Fibonacci and !he Fibonacci Sequence

o %% !he &athematician

o %' !he Numbers

• ' Fibonacci &usic

o '% !ypes of omposition

• Notable Fibonacci &usic Facts

o % &o*art

• + &ore nformation -n Fibonacci Numbers and Fibonacci &usic

• . /eferences

Fibonacci and The Fibonacci Sequence

The Mathematician

Leonardo Pisano Bigollo, better known as Fibonacci.

Fibonacci, whose real name was Leonardo Pisano Bigollo was an talian

&athematician that lived during the &edieval 0eriod 1is boo2, the 3iber 4baci, firstintroduced 1indu"4rabic Numbers to the western world 4lthough Fibonacci did not

http://math2033.uark.edu/wiki/index.php/Fibonacci_Musical_Compositon#Fibonacci_and_The_Fibonacci_Sequencehttp://math2033.uark.edu/wiki/index.php/Fibonacci_Musical_Compositon#The_Mathematicianhttp://math2033.uark.edu/wiki/index.php/Fibonacci_Musical_Compositon#The_Numbershttp://math2033.uark.edu/wiki/index.php/Fibonacci_Musical_Compositon#Fibonacci_Musichttp://math2033.uark.edu/wiki/index.php/Fibonacci_Musical_Compositon#Types_of_Compositionhttp://math2033.uark.edu/wiki/index.php/Fibonacci_Musical_Compositon#Notable_Fibonacci_Music_Factshttp://math2033.uark.edu/wiki/index.php/Fibonacci_Musical_Compositon#Mozarthttp://math2033.uark.edu/wiki/index.php/Fibonacci_Musical_Compositon#More_Information_On_Fibonacci_Numbers_and_Fibonacci_Musichttp://math2033.uark.edu/wiki/index.php/Fibonacci_Musical_Compositon#Referenceshttp://en.wikipedia.org/wiki/Fibonaccihttp://en.wikipedia.org/wiki/Middle_Ageshttp://en.wikipedia.org/wiki/Liber_Abacihttp://en.wikipedia.org/wiki/Arabic_numeralshttp://math2033.uark.edu/wiki/index.php/Fibonacci_Musical_Compositon#Fibonacci_and_The_Fibonacci_Sequencehttp://math2033.uark.edu/wiki/index.php/Fibonacci_Musical_Compositon#The_Mathematicianhttp://math2033.uark.edu/wiki/index.php/Fibonacci_Musical_Compositon#The_Numbershttp://math2033.uark.edu/wiki/index.php/Fibonacci_Musical_Compositon#Fibonacci_Musichttp://math2033.uark.edu/wiki/index.php/Fibonacci_Musical_Compositon#Types_of_Compositionhttp://math2033.uark.edu/wiki/index.php/Fibonacci_Musical_Compositon#Notable_Fibonacci_Music_Factshttp://math2033.uark.edu/wiki/index.php/Fibonacci_Musical_Compositon#Mozarthttp://math2033.uark.edu/wiki/index.php/Fibonacci_Musical_Compositon#More_Information_On_Fibonacci_Numbers_and_Fibonacci_Musichttp://math2033.uark.edu/wiki/index.php/Fibonacci_Musical_Compositon#Referenceshttp://en.wikipedia.org/wiki/Fibonaccihttp://en.wikipedia.org/wiki/Middle_Ageshttp://en.wikipedia.org/wiki/Liber_Abacihttp://en.wikipedia.org/wiki/Arabic_numerals


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originate or develop the sequence he would later become famous for, as the sequence

had been discussed earlier in ndian mathematics since the 5th century, he is cited as

having used it in an e6ample within the third section of his boo2 n his e6ample,

Fibonacci illustrates the growth of a group of rabbits in an ideal situation, which is

where the Fibonacci Sequence had its beginnings

The Numbers

!he Fibonacci Sequence is a special group of numbers that wor2 in a subsequent pattern

of addition For e6ample:

This is how the sequence works (from 7 to 8)

0!"#"$ "!"#2$ "!2#3$ 2!3#%$ 3!%#&

and these are the resulting numbers of the sequence (from 7 to 8)

0$"$2$3$%$&

!he sequence begins with 7 and %, they are added together and the result is % !hen % is

added to the ne6t fi6ed number, that number being % again !he result is ' and then the

previous fi6ed number is added to the current sum 4ccordingly, the ne6t procession in

the sequence would be %9', as shown above !he sequence grows e6ponentially from

this base of foundation using the same pattern

Fibonacci Music

T'pes o( Composition

ellow is a list of three 2nown methods used to compose Fibonacci music

Binar' Method:

;hen using the inary &ethod a composer will create a piece consisting of a pattern

that follows a 7 and % system !his system relates to the Fibonacci Sequence by

allowing for a hierarchy that gets infinitely close to the golden ratio to occur Since it is

very difficult to subdivide this system into any time signature, the simplest course of

action for an individual to ta2e is to compose a musical build"up from a set foundation#%$ For e6ample, a composer will choose the length of their smallest 7 and %

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A Binary piece entitled !"A"!"#"A.

e)* 7 < a 'nd note, % < a %5th note

t is from this small increment that a composer will start to build upon by using the

Fibonacci Sequence 4s the piece progresses so do the length of the notes !he 7s at

'nd notes become %5th notes and %s at %5th notes become 8th notes !he sequence is

now underway as one can notice that the original 7 note length has grown by ', while

the original % note length has grown by from that of the original 7=s length Ne6t, the 7

will have grown by beats while the % will have grown by . beats !he hierarchy

continues in this fashion as the notes grow in accordance to the Fibonacci Sequence as

do their measures as well !his method also allows for a composer to ma2e variations

with the layers at ease, thus ma2ing very melodic music possible

Clic+ this lin+, inary &usic to listen to !"A"!"#"A and other Binary pieces.

Clic+ this lin+, 0ro>ect &ath '7 Final &i6 to listen to $ath %&'' student (hristian

Linares) original Binary piece, which is also a*ailable for FREE download.

Note to Number Method:

!he Note to Number method involves creating a rhythm or melody by assigning a note

to a number on the Fibonacci Sequence through &odular 4rithmetic (sometimes also

referred to as cloc2 arithmetic) !his is achievable due to the relation of Fibonacci

numbers to a musical scale ;ithin a musical scale there are eight notes, the fifth and

third notes of a scale create the basic foundation of all chords, which are based on the

original whole tone that is located two steps from the root note, this note being the fist

one in the scale#'$ !o start, one would write out numbers on the Fibonacci Sequence at a

length of their discretion

e)* 7, %, ', , ., 8, %, '%

!hen, the individual would rewor2 the numbers using ?cloc2 arithmetic? to receive a

number on a scale from 7 to @

e)* %, %, ', , ., %, ', +

Ne6t, the composer would pic2 a base or ?root? note and then go up the scale from that

root to the ne6t octave Since there are eight notes and the fist note would be starting

from *ero the results would have a note at every number up to seven

http://vihart.com/papers/binary/https://soundcloud.com/nocturnal-brute/project-math-2033-final-mix/s-p81IMhttp://math2033.uark.edu/wiki/index.php/User:Christian_Linareshttp://math2033.uark.edu/wiki/index.php/User:Christian_Linareshttp://en.wikipedia.org/wiki/Modular_arithmetichttp://en.wikipedia.org/wiki/Modular_arithmetichttp://math2033.uark.edu/wiki/index.php/Fibonacci_Musical_Compositon#cite_note-1http://vihart.com/papers/binary/https://soundcloud.com/nocturnal-brute/project-math-2033-final-mix/s-p81IMhttp://math2033.uark.edu/wiki/index.php/User:Christian_Linareshttp://math2033.uark.edu/wiki/index.php/User:Christian_Linareshttp://en.wikipedia.org/wiki/Modular_arithmetichttp://math2033.uark.edu/wiki/index.php/Fibonacci_Musical_Compositon#cite_note-1


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A piano and its keys in relation to the Fibonacci !equence.

e)*

Number | Note

0 | G mid

1 | A

2 | B

3 | C

4 | D

5 | E

6 | F

7 | G high

Finally, the composer would only need to plug"in notes to their designated number and

arrange note lengths at their discretion, thus resulting in a new rhythm or melody that

would sound pleasing to the human ear, so long as the Fibonacci pattern is followed

3isten to a melody made by following the Note To Number Method

Beat -atio Method:

!his method involves the use of beats within a musical time frame in order to achieve a

golden ratio hierarchy through the Fibonacci Sequence For e6ample, one may chose to

use ?+A+ time?, meaning + beats per measure, to compose their piece n relation to thelength of a note or ?beat? an individual may have:

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" .hole note per measure

2 hal( notes per measure

/ quarter notes per measure

& eighth notes per measure

" si)teenth notes per measure32 thirt'1second notes per measure

/ si)t'1(ourth notes per measure

t is through tiers of measures and beat lengths that mimic the golden ratio, that allow

for a sequential hierarchy to ta2e place within the composition n the first ?bar or

measure, one would have a single whole note which would mar2 + beats !he ne6t tier

would incorporate two half notes mar2ing the + beats t is by the third measure that the

golden ratio starts to form as a result of the sequence n the third measure two quarter

notes are used and one half note is used mar2ing the + beats !he fourth measure will

contain four eighth notes and one half note mar2ing the + beats !he fifth will containeight eighth notes mar2ing the + beats !he ne6t and final section will contain twelve

si6teenth notes and one quarter note mar2ing the + beats within a measure t can be

noted that the number of notes placed within each measure thus far has incorporated a

number in the Fibonacci Sequence

Measure " < % note

Measure 2 < ' notes

Measure 3 < notes

Measure / < . notes

Measure % < 8 notes

Measure < % notes

-nce all of these measures are stac2ed upon each other, a musical hierarchy is reached

and Fibonacci music is successfully composed

Notable Fibonacci Music Facts


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$o+art at around -% or -' years of age.

Moart

t has been said that &o*art used the Fibonacci Sequence in some of his wor2s !he

scribbling of mathematical equations have been found on the side columns of his

compositions 4lthough these equations have been attributed to the famous composer

weighing the outcomes of a local lottery, many believe this was the Fibonacci Sequence

at wor2 Sonata No % in &a>or is the composer=s most associated composition to

Fibonacci numbers#$

3isten to an e6ert from Sonata No* " in C Maor

More 4n(ormation 5n Fibonacci Numbers andFibonacci Music

6isit7 !e6tist 0roductions

" for a small 'sec flash video that quic2ly and adequately describes Fibonacci

Numbers and the Bolden /atio

6isit7 !he Buardian

" for an interesting loo2 at ?!trength in numbers #ow Fibonacci taught us how to

swing ?

6isit7 &otivate &aths

" to learn about Fibonacci musical frequencies as well as compose your very own

Fibonacci &elody using ?cloc2 arithmetic?

6isit7 Coutube

" and watch ? Fibonacci $usic?, in which a college student spea2s about Fibonacci

Numbers and their relation to &o*art, 0opular music, and one of her own Fibonacci

ompositions She also goes on to e6plain the Beat -atio Method, which is what she

used to compose her piece

-e(erences

% D Er Boodman Strauss, notes regarding binary

' D http:AAwwwgoldennumbernetAmusichtm

D http:AAtechcenterdavidson2%'ncusAgroup'Amusichtm
http://en.wikipedia.org/wiki/Wolfgang_Amadeus_Mozarthttp://math2033.uark.edu/wiki/index.php/Fibonacci_Musical_Compositon#cite_note-2http://techcenter.davidson.k12.nc.us/group2/mozart%5B1%5D.auhttp://techcenter.davidson.k12.nc.us/group2/mozart%5B1%5D.auhttp://www.textism.com/bucket/fib.htmlhttp://www.textism.com/bucket/fib.htmlhttp://www.guardian.co.uk/music/2009/oct/15/fibonacci-golden-ratiohttp://www.guardian.co.uk/music/2009/oct/15/fibonacci-golden-ratiohttps://motivate.maths.org/content/sites/motivate.maths.org/files/FibNos-Music.pdfhttps://motivate.maths.org/content/sites/motivate.maths.org/files/FibNos-Music.pdfhttp://www.youtube.com/watch?v=s0Cqac6WJl0http://www.youtube.com/watch?v=s0Cqac6WJl0http://math2033.uark.edu/wiki/index.php/Fibonacci_Musical_Compositon#cite_ref-0http://math2033.uark.edu/wiki/index.php/Fibonacci_Musical_Compositon#cite_ref-1http://www.goldennumber.net/music.htmhttp://math2033.uark.edu/wiki/index.php/Fibonacci_Musical_Compositon#cite_ref-2http://techcenter.davidson.k12.nc.us/group2/music.htmhttp://en.wikipedia.org/wiki/Wolfgang_Amadeus_Mozarthttp://math2033.uark.edu/wiki/index.php/Fibonacci_Musical_Compositon#cite_note-2http://techcenter.davidson.k12.nc.us/group2/mozart%5B1%5D.auhttp://www.textism.com/bucket/fib.htmlhttp://www.guardian.co.uk/music/2009/oct/15/fibonacci-golden-ratiohttps://motivate.maths.org/content/sites/motivate.maths.org/files/FibNos-Music.pdfhttp://www.youtube.com/watch?v=s0Cqac6WJl0http://math2033.uark.edu/wiki/index.php/Fibonacci_Musical_Compositon#cite_ref-0http://math2033.uark.edu/wiki/index.php/Fibonacci_Musical_Compositon#cite_ref-1http://www.goldennumber.net/music.htmhttp://math2033.uark.edu/wiki/index.php/Fibonacci_Musical_Compositon#cite_ref-2http://techcenter.davidson.k12.nc.us/group2/music.htm

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