[sdiy] Consider this DAC

[Magnus Danielson]

Neil Johnson wrote:
> 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.

Time-sharing the same DAC helps a bit...

> 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 :)

Yes, we do. But in the analogue world we do things not because they are 
easy, but because they are hard. ;)

Cheers,
Magnus