Sampler Parameters

Given a sampling rate of $f_s$ and a table length of $N$ samples, the duration of the table is

   duration$$= \frac{N}{f_s}$$    seconds

To read the table without changing pitch or length, the period of the phasor is the duration of the table:

$$T_p = \frac{N}{f_s}$$    seconds

The corresponding frequency of the phasor is

$$f_p = \frac{1}{T_p} = \frac{f_s}{N}$$

To change sounding frequency by a factor of $t$:

$$f_p = t\frac{f_s}{N}$$

$h$ semitones above/below the original frequency is a transposition factor of

$$t = 2^{\pm h/12}$$