tags: wavetable-synthesis
Phase increment
The phase increment in [wavetable synthesis] is the difference between the [phase] of a [waveform] for neighboring [samples].
$$ \theta_{inc}(f) = \frac{2\pi f (n + 1)}{f_s} - \frac{2\pi f (n)}{f_s} = \frac{2\pi f}{f_s} $$
$\theta_{inc}(f)$ depends explicitly on the [frequency] $f$ and implicitly on the [sample rate] $f_s$, which usually stays constant.
In implementation, a phase variable is initialized to 0 and incremented by $\theta_{inc}(f)$ after generating each sample. This variable gets reset every time a new frequency needs to be generated (i.e. when a new key is pressed on a [midi] controller.