[sdiy] Quantizer project.. incoming CV's switching point to change to quantized output CV's ...
Tom Wiltshire
tom at electricdruid.net
Wed Jul 7 13:33:50 CEST 2021
Why does the DAC have to hit the steps exactly on its own?
We can take the DAC output and scale it to whatever size we like with op-amp, so you can use something with a bigger step size and scale it down, or a smaller size and scale it up. The important thing is that the eventual output values hit the points you need, and that the steps between values are small enough to be imperceptible (which isn’t that hard to achieve).
Clearly if you want something that can accurately generate every microtonal scale that’s been invented, you’re going to need some hideous degree of accuracy. At which point, why on earth would you be generating a CV and then using it to drive a VCO?!? There’ll be enough linearity errors in the subsequent steps to ruin any microtonal nicities we might have included.
If you want certain specific microtonal scales, things don’t have to be so bad. I can easily generate a quarter-tone scale by simply halving the CV, for example. That’s a very basic example, but shows it doesn’t have to be complicated in every case.
> On 7 Jul 2021, at 06:19, Brian Willoughby <brianw at audiobanshee.com> wrote:
>
> In order to hit 701.995 cents, I assume you'll need a resolution of 0.005 cents on your DAC. If I'm doing the math correctly, that requires an 18-bit DAC, and I don't know any with DC output. That's just for 1 octave of range. If you want 5 octaves of range, you'll need a 20-bit DAC.
>
> Are you talking about a practical design, Mike?
>
> I know that 20-bit ADC and DAC were a thing before 24-bit delta-sigma, but I never went looking before. The first 18-bit DAC I found only guarantees 12-bit accuracy, but at least it's monotonic. I suppose one could spend more than $10 to get better accuracy.
>
> Brian
>
>
> On Jul 5, 2021, at 13:28, Mike Bryant <mbryant at futurehorizons.com> wrote:
>> That is fine for equal temperament but for other scales it's far more complicated. For example for Pythagorean scales which are based on a 3 to 2 ratio, you need to be able to set a step of 701.995 cents, then dividing down by two where necessary. Rounding up to 702 is okay, and divide by 2 gives 351. But then the next step needs a half-cent, then a quarter, etc.
>>
>> In equal temperament you can't hear much better than a few cents, but with temperaments based on exact ratios, being off is often quite audible, especially if different notes are off by different amounts.
>>
>> Similarly for piano tuning, you are looking for accuracies of better than a cent in a few places, and of course here the definition of an octave is almost irrelevant as you don't tune a piano to octaves.
>
>
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