I'm attempting to use a very limited system of operations (embedded in Bitwig Studio, a digital audio workstation), to get the reciprocal of a percentage. My end goal is to map an input from 0% to 100% over the first 8 numbers of the harmonic series.
Each operation takes two inputs. Each input must be within the range $[-1, 1]$. An output can be multiplied by up to $±2$ when plugged into another operator, but the final output can be multiplied by up to $±72$.
Available operators:
- Multiply: $f(x, y) = \begin{cases} xy & \text{$|x| \leq 1 \land|y| \leq 1$}\end{cases}$
- Add: $f(x, y) = \begin{cases} x+y & \text{$|x| \leq 1 \land|y| \leq 1$}\end{cases}$
- Subtract: $f(x, y) = \begin{cases} x-y & \text{$|x| \leq 1 \land|y| \leq 1$}\end{cases}$
- Minimum: $f(x, y) = \begin{cases} \min(x, y) & \text{$|x| \leq 1 \land|y| \leq 1$}\end{cases}$
- Maximum: $f(x, y) = \begin{cases} \max(x, y) & \text{$|x| \leq 1 \land|y| \leq 1$}\end{cases}$
- Quantize: $f(x, y) = \begin{cases} (|x| - (|x|\mod|5y|))(\frac{xy}{|x||y|}) & \text{$|x| \leq 1 \land|y| \leq 1$}\end{cases}$