[sdiy] 8bits, 10bits or12bits DAC for a midi2cv converter?

[Tom Wiltshire]

JP,

On 18 Oct 2007, at 13:48, jean-pierre.desrochers at ville.quebec.qc.ca  
wrote:

> Hi list,
>
> Seeing the posts about the paia's midi2cv8
> I was wondering what 'should' be a good DAC
> for a midi2CV output range of around 0 to 8vdc (8 octaves)?
> I'm thinking of building one from scratch
> with a PIC controller. I saw PAIA's is
> using an 8 bits DAC which only will gives a 256 steps
> resolution... For example if you need 10 steps between
> all semitones (half of a note) to get
> rid of any 'staircase' effect between notes,
> that gives 256/10steps per semitones = 25 notes span
> which is 2 octaves.. Not very usefull.
> In revenche a 10 bits DAC with the same needs
> would give (1024/10steps per semitones)/12 notes per octave
> gives more than 8 octaves.
> Am-I correct? A 10bits DAC would be more valuable?
> Do I miss something?

Apparently the ear can detect steps as small as 5 or 6 cents, which  
is roughly 20 steps per semitone.

Obviously the required resolution will depend on whether you expect  
the DAC to generate smooth portamento or not. The Sequential Pro-One  
uses a DAC to generate the keyboard voltage, but this voltage is in  
semitone steps. The DAC is scaled so that single steps give neat  
semitones, IIRC. The frequency knob and the portamento are both  
analogue controls, so there's no digital stepping in the final sound.

If we assume that you do want portamento from the DAC, and that 20  
steps between semitones is sufficiently small, then for 8 octaves,  
you have 96 notes each with 20 steps = 1920. An 11-bit DAC would give  
2048 steps and therefore manage this. Given that you'll more likely  
find a 12-bit DAC than an 11-bit one, go with 12-bit.
This is just my back-of-envelope calculation. I don't know what the  
'correct' way to work this kind of thing out is.
Sticking with Sequential examples, I think the Prophet 5 worked like  
this, and it used a 14-bit DAC for the VCO CV.

Regards,
Tom