Golden Times

What's this?

It’s a golden ratio calculator for time durations of a musically useful length.

The golden ratio, or ϕ (phi), is a number often understood as what the Fibonacci sequence eventually expresses. Two numbers have the golden ratio if $a/b = (a+b)/a$. It has properties such that $ϕ^2 = ϕ+1$ and $1/ϕ = ϕ-1$.

Why this?

It’s a number that has fascinated people for millennia, and musical composers are no exception. I have used it to plan out sequences and compositions for my own music.

Unfortunately, the process of taking a time in my workstation, converting it to seconds, and then experimentally running some calculations on it is tedius. How many total seconds is 4:31.8? How many minutes is 261 seconds, again? What if it were 3:14.15 instead? I wanted a calculator that could take a time value c for input in an “hours, minutes, seconds” format, and provide a, b, d, and e, such that $a+b=c$, $b+c=d$, and $c+d=e$.

There are other ways the golden ratio might be used in music, but this calculator is about time values expressable in hours, minutes, and seconds.

Who's this?

I’m Matthew Lyon, an artist, musician, hacker, and tool-maker.