[sdiy] Quantizer project.. incoming CV's switching point to change to quantized output CV's ...

Mike Bryant mbryant at futurehorizons.com
Mon Jul 5 22:28:04 CEST 2021

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.

-----Original Message-----
From: Brian Willoughby [mailto:brianw at audiobanshee.com] 
Sent: 05 July 2021 19:41
To: Mike Bryant
Subject: Re: [sdiy] Quantizer project.. incoming CV's switching point to change to quantized output CV's ...

Both the range and the desired precision relate to the necessary bit depth. With the standard 1V/octave CV, a DAC calibrated to output 0 V to 5 V will have a 5 octave range. Then, the available bits have to span that 5 V range. If you only needed 1 octave of range, the same DAC bits could be 5 times as precise as the above example. In the other direction, there are pitch CV outputs that go up to 10 V, and there are those capable of negative voltages as well as positive (which would assume that your VCO has a summing input where positive voltages will be added - unless you have a through-zero VCO!).

When designing the DAC circuit, you can choose a particular voltage range. The caveat is that this affects the octave range when the CV is 1V/octave. In a reasonable modular setup, you might have as much as 20 octaves of range (if the CV spanned -10 V to +10 V), although it's probably rare to find a VCO that could handle that without lots of CV processing ahead of the core VCO.

Question: Does it even make sense to attempt note pitch quantization on a standard other than 1V/octave or 1.2V/octave? I expect that it would be too difficult with anything else to figure out how to quantize on a logarithmic output.

The nice thing about 1V/octave is that most DAC chips are very precise with regard to voltage. Some DAC chips even use a 4.096 V reference (or similar binary compatible number) so that each step is precisely 0.001 V. Unfortunately, dividing by 12 gives an irrational number, which is why Buchla uses 1.2V/octave. With 1.2V/octave, a semitone is precisely 0.1 V and a cent is precisely 0.001 V (see those 4.096 V reference DAC chips, and similar). I've also seen DAC chips with a 1.024 V reference.


On Jul 5, 2021, at 03:12, Mike Bryant <mbryant at futurehorizons.com> wrote:
> It's not so much the number of octaves but how closely you want to get to exact ratios for non-equal temperament scales.   It is easy using linear oscillators over a limited range but assuming log VCOs then getting to exactly 3:2 ratios for all notes on a Pythagorean scale is actually quite awkward, and the ones that are off slightly really stick out.  
> Also if you are using piano tuning rather than equal temperament on the keys then you need to have an accuracy of better than one cent just above A440 according to the Railsback curve, though in this case the inaccuracies can occasionally make it sound better rather than worse.
> -----Original Message-----
> From: Synth-diy [mailto:synth-diy-bounces at synth-diy.org] On Behalf Of Brian Willoughby
> Sent: 05 July 2021 03:49
> To: SDIY
> Subject: Re: [sdiy] Quantizer project.. incoming CV's switching point to change to quantized output CV's ...
> It depends upon how many octaves of range you want the DAC to cover.
> 5 octaves (5 V) with 12 bits gives 1.46 cents per step ... if I did the math correctly.
> There are some 14-bit DAC chips if you don't think you need 16-bit accuracy, but sometimes the price is less for 16-bit due to supply and demand.
> Brian
> On Jul 4, 2021, at 16:30, Mike Bryant <mbryant at futurehorizons.com> wrote:
>> I'd personally recommend a DAC with more bits as this allows you to implement non-equal temperament scales more accurately.  For example in Pythagorean tuning do you accept 702 cents as being good enough for the 3:2 ratio, or do you want it dead on.  
>> -----Original Message-----
>> From: Synth-diy [mailto:synth-diy-bounces at synth-diy.org] On Behalf Of Jean-Pierre Desrochers
>> Sent: 05 July 2021 00:19
>> To: 'Brian Willoughby'
>> Cc: 'SDIY'
>> Subject: Re: [sdiy] Quantizer project.. incoming CV's switching point to change to quantized output CV's ...
>> I agree with you Brian.
>> Yes, the use of dead zones are necessary around the threshold points to  avoid any glitches on quantized output..
>> I think my PIC micro's  10bits A/D would be Ok to read the incoming CV signal.
>> The quantized output though will be from an external SPI 12bits DAC.

More information about the Synth-diy mailing list