|
Some
mathematicians, who listen to music (almost all of them), believe that
the Fibonacci sequence occurs in music. Can you believe that? The use
of the Fibonacci system can be seen in Mozart's music, and modern day
compositions.
|
|
 |
 |
|
Mozart
is considered one of the greatest composers known to the music world.
He wrote some of the most beautiful piano concertos, within these pieces
of music are where some say Mozart implemented the Fibonacci sequence.
In the margins of the score for different music, Mozart jotted down mathematical
equations. Although these equations may have been about odds of winning
a local lottery, a love of math was still displayed.
|
|
|
The piano sonatas written by Mozart are divided into two distinct sections. The first section is the development and representation of the theme; the second section is a visitation of the theme in different variations. Since the first section is shorter than the first, the two sections can be seen as being developed by the golden section. For example, let's take a look Sonata No. 1 in C Major. There are 100 measures in the first movement. The first section, with the theme, has 32 measures, and the last section, with theme variations, has 68 measures. This is a perfect division, using natural numbers, with the golden section. This format can also be seen in the second movement, respectively. Although there is no physical evidence that Mozart used the Fibonacci sequence in his music, it is still very easy to see the use of perfect divisions. |
 |
|
The
Fibonacci sequence can also display the preference of the human ear to
music. The following is some Fibonacci music. It consists of the first
eight Fibonacci numbers. For each new number that is performed, the note
length is decreased rotationally by 1/2 or 1/3. After four steps of the
sequence are completed the tune starts over at the root, one octave up,
while the other one continues, so there is an overlapping effect.
|
|
|
The
basic structures of certain instruments display the use of Fibonacci numbers
and the Golden section. The most widely used instrument in music, the
piano, displays the use of Fibonacci numbers. For instance, there are
13 notes that separate each octave of 8 notes in a scale. The foundation
of a scale is based around the 3rd and the 5th tones. Both pitches are
whole tones, which are 2 steps from the 1st note of the scale, also called
the root.
|
 |
 |
The
keys of a piano also portray the Fibonacci numbers. Within the scale consisting
of 13 keys, 8 of them are white, 5 are black, which are split into groups
of 3 and 2. Look familiar? Well, it should, it's Fibonacci!
|
|
Not
only the piano, but also the violin is constructed through the use to
the golden section. Check out the link for the information: http://www.violin.odessa.ua/method.html
|
|
 |
 |
