Tepoz VI (1-bit music etude)

1 December 2023

The score

It’s been a long time since I wrote my last 1-bit music piece. Tepoz VI is a new little etude to get myself back into this most limited universe.

Tepoz_{VI} is a function of type \mathbb{Z} \to \{\mathfrak{1}, \mathfrak{0}\}. At its core, it is essentially (and compactly) defined as

\begin{equation*} Tepoz_{VI}[n] \;= \bigoplus\limits_{i\in\{3,5,7,19\}}\biggl(\bigoplus\limits_{m=0}^{i\cdot10}\delta_{m+i\cdot10^3}^0[n+i\cdot10^5]\biggr) \end{equation*}


\begin{equation*} \delta_{m}^{r}[n] \triangleq \left\{ \begin{array}{rl} \mathfrak{1}, & \text{if } n \equiv r \pmod m \\ \mathfrak{0}, & \text{otherwise.} \\ \end{array} \right. \end{equation*}

and \bigoplus is the logical XOR opperator applied to series.

The audio

The music is computer rendered at a sampling frequency of 44100 hz.