# Golden ratio

The golden ratio or phi (Greek letter $\phi$ / $\varphi$) may be defined by $\frac{a}{b}$ such that $\frac{a}{b} = \frac{a+b}{a}$. It follows that $\varphi - 1 = 1 / \varphi$, and also that $\varphi = \frac{1+\sqrt{5}}{2}$, or approximately 1.6180339887... $\varphi$ is an irrational number that appears in many branches of mathematics.
The phith root of phi ($\sqrt[\varphi]{\varphi}$ or approximately 514.878 cents) is another useful interval for generating golden scales. Similarly to logarithmic phi, $\sqrt[\varphi]{\varphi}$ can be used as a generator interval to produce MOS scales whose sizes are Fibonacci numbers, where the equave is the acoustic phi instead of the octave. In this way it is a useful generator if you wish to avoid octaves and maximize the golden properties of the resulting scale.