Beethoven: His Fibonacci Fifth

Beethoven: His Fibonacci Fifth: Most of the world, I hope, knows of Beethoven and his 5th Symphony with its famous opening four note motif- a quick rhythmic repetition of four notes with a repetition on a different tone.  In contrast, few know who Fibonacci was and the numerical system that was named after him.{\clef treble \key c \minor \time 2/4 {r8 g'8[ g'8 g'8] | ees'2\fermata | r8 f'8[ f'8 f'8] | d'2~ | d'2\fermata | } }

We are about to tie Beethoven and Fibonacci together. Now who was Fibonacci? Leonardo Bonacci (c. 1170 – c. 1250)—known as Fibonacci (Italian: [fiboˈnattʃi]), and also Leonardo of Pisa, Leonardo Pisano Bigollo, Leonardo Fibonacci—was an Italian mathematician, considered to be “the most talented Western mathematician of the Middle Ages”. Before I tie the two together, here is another question: Most musical motifs and phrases come in either in two or four bars of music. Beethoven deliberately set his musical motif in five. He could have simply placed another bird’s eye (which hold the note longer and is called  a fermata) on the “D” in the fourth bar, but  he adds a fifth bar and places the “bird’s eye” over that note. It’s Leonardo Bonacci to the rescue.

Related image
Leonardo Bonacci who was born 600 years before Beethoven. The Fibonacci series, named after him. is colored in red.


Leonardo Bonacci recorded an ancient series of numbers which not only explains biological growth, galaxies and even shows us when to invest in the stock market. Stock brokers study this principle which I will blog about in the future. Since “0” is not a number, starting with one, we see that 5 is the fifth number. Now. at this point  you have every right to say, that’s just a silly co-incidence with Beethoven’s 5th.  My source is Trudi Hammel Garland in, Fascinating Fibonaccis: Mystey and Magic in Numbers: With the opening 5 bar motif given above, the “A” section of the 1st movement is 233 bars long. The “B” section, also known as the development, is 377 bars long.


Behind Leonardo Bonacci’s back, the highest red number is 55. Each new number is the sum of the preceding two. Number 34 precedes 55. So, let’s continue the series: 34 + 55 = 89. Next, 55 + 89 = 144. Next 89 + 144 = 233 (the length of Beethoven’s opening section). Next 144 + 233 = 377 (which  the length of Beethoven’s development section). Beethoven, being the brilliant genius that he was, knew exactly what he was doing. When we listen to the symphony it sounds so natural; but can you imagine how he must have struggled to make the bar length come out right and still sound like that’s how it should be? Leonard Bernstein says of Beethoven and the 1st movement in The Joy of Music: “he will give away his life just to make sure that one note follows another inevitably.” In conclusion, I think that in addition to an even greater appreciation of Beethoven, we have graphic proof the relationship between music and numbers; and why piano lessons, music theory and composition increase aptitude for mathematics.



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