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, Sequence , which was named after Leonardo Pisano Bigollo (who also went by the name Fibonacci 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 pleasing to the human ear

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% Fibonacci and !he Fibonacci Sequence o

%% !he &athematician

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%' !he Numbers

' Fibonacci &usic o

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'% !ypes of omposition

 Notable Fibonacci &usic Facts o

% &o*art

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

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. /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, first introduced 1indu"4rabic Numbers to the western world 4lthough Fibonacci did not

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 ðod 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 %

 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

 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 the length of a note or ?beat? an individual may have:

" .hole note per measure 2 hal(  notes per measure / quarter notes per measure & eighth notes per measure " si)teenth notes per measure 32 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 contain eight 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

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

Moart 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 Maor

More 4n(ormation 5n Fibonacci Numbers and Fibonacci 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:AAwwwgoldennumbernetAmusichtm  D http:AAtechcenterdavidson2%'ncusAgroup'Amusichtm