# Yasser, Fibonacci and Carlos

25 February 2011 Filed in: Tuning
Theory

19EDO, according to Joseph Yasser, should be the natural evolution of our present tuning system: 12EDO

Yasser, in his book “A Theory of Evolving Tonality” explains how the evolution of musical scales started, in ancient times, with the

*infra-diatonic*one then to the present

*diatonic*and will continue evolving to the

*supra-diatonic*one.

He represents each of these 3 scales as having both

*regular*and

*auxiliary*degrees.

So, the

*infra-diatonic*scale has 5 regular and 2 auxiliary degrees, the

*diatonic*one 7 regular and 5 auxiliary degrees and the

*supra-diatonic*one 12 regular and 7 auxiliary degrees.

The evolution of musical scales, according to Yasser, follows an increasing number of steps, from 5 to 7 to 12 to 19 per octave.

I am not the first one noticing that this series of numbers is a Fibonacci sequence: 2, 5, 7, 12, 19, 31, 50 etc. where each subsequent number is the sum of the previous two and every 3rd number is even.

It is interesting to notice that the number following 19 is 31. 31EDO has been one of the most studied alternative tuning systems since Renaissance!

But what about Wendy Carlos? She created the Carlos Beta tuning system that is a close relative of 19EDO even though it does not repeat at the octave. See my previous article 19EDO vs. Carlos Beta. This is why I stumbled upon 19EDO, Yasser and so on.

Related link:

http://www.bikexprt.com/tunings/fibonaci.htm