For Scales
We are seeking to create new and innovative musical scales derived from the Fibonacci numbers, not traditional scales that sound major or minor. The Fibonacci scales will consist of ten pitches from ten numbers, and ascend as the numbers ascend.
By using only the first ten Fibonacci numbers the ascending scales created for other instrument ranges are beautiful, short, sweet, and simple. We also noticed that the first three Fibonacci numbers (0,1,1) are often represented by a single starting pitch repeated three times and the Fibonacci number “2” has it own new pitch. If we use the first 12 Fibonacci numbers, the starting pitch has the tendency to repeat 4 times (representing Fibonacci numbers 0,1,1,2). If we use the first 15 Fibonacci numbers the starting pitch has the tendency to repeat 7 times. So, we really like the simplicity of 0,1,1 being the same note and a new pitch entering at “2.”
Of course, you and your class should experiment and find out on your own what you like: Our ideas are just a starting point!
For Melodies
The reason this article uses the first forty as an example is because it turns out that the 40th Fibonacci number is 8 digits long, whereas the 41st number is more than 8 digits long. Who cares? Well, although more sophisticated calculators have more than an 8-digit display, often the simpler calculators only display up to 8 digits. So, if your students wanted to do some computations using their calculators, and all they had were basic machines, it could be problematic entering in larger and larger Fibonacci numbers! Forty Fibonacci numbers will also make the modulo mapping interesting since the musical melodies will be long.
It is really interesting to take more than the first forty Fibonacci numbers (and easy to do with Music Algorithms )! In fact, the program can be used to find, for example, the 20th – 90th numbers, or some other consecutive group of numbers. As always, you and your class should experiment and find out on your own what you like: Our ideas are just a starting point!
