[sdiy] Quantizer project.. incoming CV's switching point to change to quantized output CV's ...
brianw at audiobanshee.com
Wed Jul 7 07:19:00 CEST 2021
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.
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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