The Fibonacci Piano
The Fibonacci numbers are a famous sequence which appears many places in nature. The sequence is recursive, meaning it builds on itself. It starts with 1, 1, and then each successive term is the sum of the previous two terms. Since 1+1=2, the next term will be 2, giving 1, 1, 2. The last two terms of the sequence so far are 1 and 2, so their sum is 3. Now we have 1, 1, 2, 3. Adding these last two terms (2+3) gives us 5, and so on. The first seven terms of the sequence are 1, 1, 2, 3, 5, 8, and 13. We can see these numbers in music, especially on the piano.
This is called an octave and is what a scale is. If we look at the black keys of the piano, they are grouped in 2’s and 3’s, for a total of 5 in every octave. An octave is a group of eight notes and is what we consider to be a scale (do, re, mi,…). The white keys are grouped by 8’s before they repeat themselves. If we include all black and white keys in an octave, then we have a chromatic scale consisting of 13 keys.
The Fibonacci numbers are named after Fibonacci (Leonardo de Pisa). He did not invent this sequence, but wrote down what he learned from his travels in Algeria. His book Liber Abaci (Book of Calculations) contained a puzzle for which this sequence was the solution. More importantly he realized the value of the Hindu-Arabic number system and his book is credited with popularizing in Europe the number system we still use today.