[sdiy] Detuning in Digital

[Olivier Gillet]

In all my projects I represent pitch internally as a 14-bits number.

7 highest bits = MIDI note.
7 lowest notes = fine pitch (this means fine pitch is not adjustable
in cents but rather in 128th, but I don't think it's an issue).

I use a 12x128 entries full lookup table with whatever pitch-dependent
quantity I am manipulating (eg: timer count for DCOs ; phase increment
for digital oscillators) ; for only one octave. I use shifts to deduce
the value for the other octaves.

So the whole algorithm is, given a 14-bits pitch value:
1/ transpose it (add 12 x 128 or sub 12 x 128) until it falls in the
range covered by the lookup table and count the number of octaves it
has been shifted by (it's a loop with at most 10 iterations, no
division / modulo).
2/ lookup the pitch value in the table.
3/ shift by the number of octaves found at step 1.

When memory is a constraint, my top (or bottom) octave table contains
only one half or one fourth of the data points and I use linear
interpolation. No log, floating point, etc... It is reasonable to
think that an approach like that might have been used on older synths.

Olivier