[sdiy] Consider this DAC

[Neil Johnson]

Hi,

Antti Huovilainen wrote:

> On Sat, 13 Mar 2010, Jerry Gray-Eskue wrote:
>
>> Here is the pertinent excerpt in reference to best practice in  
>> Piano Tuning:
>>
>> Accuracy within one cent would score a perfect 100 on the Tuning  
>> Exam and would satisfy any contract obligation.
>>
>> It looks like 1 cent is the holly grail after all.
>
> It might be useful to have even higher resolution for sounds where  
> the beating is very slow. Pianos have 2 or 3 strings per key and  
> that beating is likely to influence the ability to detect finer  
> tuning.
>
> An example would be having two sawtooths tuned, say, 10 cents  
> apart. A 1 cent error in the detuning is unlikely to be detectable  
> while it would be quite audible if the detuning was only 2 cents.

What we have here is the difference between absolute resolution and  
relative resolution.  In absolute tuning, yes I'm sure a few cents is  
generally "good enough" for human perception.  However, as you say,  
relative tuning may require significantly more resolution.

In an analogue synth if you wanted to slightly detune one oscillator  
from another you'd simply add in a very small offset to the CV of the  
second oscillator - this gives the fine-grain relative tuning.

But in a system where each oscillator is individually controller by  
its own DAC, i.e. absolute tuning, the requirements of relative  
tuning are imposed on the absolute tuning.  In other words, if you  
want to detune one oscillator 0.1 cents from another oscillator then  
the CV DACs would need 0.1 cents absolute resolution.

MIDI tuning standard specifies pitch in units of 0.0061 cents, I  
think partly through the need for very high absolute resolution, and  
partly of using the number range available (two data bytes = 14 bits,  
so take 100 cents / 16384 = 0.0061 cents).

Now, getting a DAC + analogue signal chain to give you anywhere near  
low-noise 0.0061 cent (5.0863uV) steps reliably and repeatably is  
going to be tricky.  A perfect 20-bit converter with some wishful  
thinking and extremely clever (and expensive) design might get you  
close for an 8-octave range.

That's assuming that you can build an analogue oscillator that will  
track this oh-so-precise CV in the first place.  In the digital  
world, we just throw more bits at the problem until it goes away :)

Neil
--
http://www.njohnson.co.uk