Exploring the subharmonic series with Host

[bog_standard]

Greetings! I recently acquired a Moog Subharmonicon and have been much enjoying the chance harmonic surprises the signal flow offers. I got to thinking last night that it would be cool to have an equivalent in VCV, where the voices are not oscillators but Kontakt instruments running within the Host module.

As in the original hardware, the ‘suboscillators’ would be a derivative of the fundamental pitch, be sequenced by the rhythm matrix and lastly merged in with the original fundamental as a polyphonic CV input for the V/Oct jack. Ultimately, one Konkakt instrument would be playing all 3 voices.

Attempting this idea with my rudimentary modular knowledge, I can recreate the rhythmic sequencer well enough (thank you Omri!) and may end up picking up the Slime Child emulation. I have struggled however to figure out how to manage the signal flow for the subharmonic series (f/1, f/2, f/3 etc) for the secondary voices when it comes to dividing the pitch CV.

I was thinking I could send pitch CV via sequencer through a quantizer and then divide it 12 ways using Submarines AO modules, use a sequential switch to select between the divisions, then as described above, merge the result back into polyphonic CV for the V/Oct jack in host. See this patched for one sub voice below:

This method however doesn’t yield the harmonic series as expected: C5, C4, F3, C3, G#2ish, F2, D2ish, C2, A#1, G#1ish, G1ish, F1. Instead, I’m seeing: C5, F#4, E4, D#4, D4, D4, D4, D4, C#4, C#4, C#4, C#4. If you change the fundamental pitch this relationship will change. If the fundamental pitch is a negative voltage, then the subharmonic series will rise etc… Obviously something is wrong with my math, but I’m not sure why! I’m hoping the braintrust here can come to my aid.

Also observing a secondary behavior where the Host gate jack seems to ‘hold on’ to CV notes from the previous trigger or sequence step, creating unintended intervals. Any ideas why that might be?

Patch here. You can press N to step through the sequence.

My thanks from afar.

[Squinky]

My “Substitute” is a free copy of the VCO from Sub. It does all the divisions quite well, and correctly. As Moog notes in the manual, those subs are not in the even tempered scale.

[bog_standard]

Hi and thank you for your reply! I’m trying to avoid using any standard VCO’s for the voices in my patch, so that rules out Substitute as a method.

[Squinky]

ok, you said you might buy the excellent Slime Child modules, so I suggested my free one. But if you want to make your own, that’s cool. @DaveVenom has done a lot of work making his own out of other modules.

but, if you want to make your own, you are going to have to do your own arithmetic - that’s the devil’s bargain.

[bog_standard]

Thanks for the suggestion, I did see it in the library! I was considering Slime Child’s sequencer module specifically, as that would be a way to unify the rhythmic aspect of the Subharmonicon into one module.

I’m not looking to make my own oscillator per se, rather find a way to split a single source of CV (from the rhythmic sequencer) up into subharmonic intervals and then feed them back into the Host module, which is taking the place of a synthesized voice. Imagine a Subharmonicon workflow, but the poly-sequencer is triggering samples from marimbas, pianos, bells, pizzicato strings etc.

I’m up for researching the arithmetic, but I’m not sure where to begin really! It’s not so simple as dividing the control voltage generated by the sequencer by 1, 2, 3 etc as that is yielding the results I describe in my post. If you start with C3, the voltage would be 0v, and that would yield zero for all the calculations as well. Perhaps I need to find a way to convert the pitch CV to Hz or something like that.

[Squinky]

The relevant arithmetic is in the VCV manual, in the pitches and frequencies section of this document: VCV Manual - Voltage Standards

It tells how to convert from CV to pitch and back again. If you remember your log and exponential identities, anyway.

[bog_standard]

Beautiful, I’ll take a gander and report back. Cheers!

[Schabbes]

To get the correct pitches I think you could either convert the 1V/Oct voltages into frequencies and then do the math, or you could just substract the corresponding voltages. If you substract 1V it should always be half the frequency. If you want other frequency ratios you have to calculate the voltages. I’m not completely sure how to do this, so this might need some googleing… I think for 1/3 it should be 1.5V (?). (edit: actually it’s 1.58496…V - see conversation below)

If you want to use a polyphonic VST to play the sounds, you run into another problem, which is that VSTs only accept pitch information in semitones, so the incoming voltages will allways be rounded to the nearest semitones.

The problem you have with the gates not playing the correct corresponing notes and “holding on” to the last ones comes from a slight delay between the gates and the pitches - every cable in VCV Rack delays the signal by 1 sample, so if you want gates and pitches to arrive at exactly the same time you need to delay the one that arrives earlier by 1 sample for each additional cable on the one that arrives later.

So in your example I think you would need to delay the gate signal by 4 samples. You can do this with a sample delay module like this:

Grande VarSampleDelays

or this:

Bacon Music SampleDelay

edit 2:

Oh and in your example you also need to convert the gate signal into a polyphonic signal with the same nr. of channels, you can use this module for that:

Bogaudio POLYMULT

[Squinky]

@Schabbes

I think for 1/3 it should be 1.5V

I’m not doing arithmetic unless you pay me, but I’ll bet that 1/3 is not -1.5V

[Schabbes]

I can’t do the calculation… but if you add 1.5V you certainly arrive at 3 times the frequency, right? So by this simple logic I think it should be right.

[Squinky]

google says that 2 to the 1.5 is 2.828, not three. while it’s true that 1 volt is an octave (2 to the 1 is 2), and 2 volts is two octave (2 to the 2 is 4), the others are not so simple, the correct answer is going to have the world “log” in it, I think. That is why I will bet that this is not correct or simple.

[Schabbes]

Ah yes, correct. I confused voltage ratios with frequency ratios. Also it seems I’m still not clear on how exactly the V/Oct standard works.

[Squinky]

The link, above says:

[Schabbes]

OK, I found something on some forum… you can calculate cents from frequency ratio with the first calculator on this page cents to frequency ratios conversion and convert frequency ratio to cent interval Hz cps pitch piano tuning calculator audio change fraction TET cents to hertz (herz) calculator ¢ minor third major semitone convert hertz to semitones equation semi tone keyboard - sengpielaudio Sengpiel Berlin (you need to enter the ratio as a decimal - so for 1/3 enter 0.3333333… or just enter 3) and then divide the result by 1200 cents to get the voltage (since 1V=1200 cents).

So it’s 1.58496something V.

[Squinky]

I don’t think you want cents, either. Don’t worry, someone will come along and tell the answer.

[Squinky]

Isn’t it just log2(ratio)?

[Schabbes]

Yes. So you can also just use this calculator: https://miniwebtool.com/log-base-2-calculator/?num1=3

[Squinky]

Google is a calculator, too.

[Schabbes]

Yes. Even better log2(3) - Google Search Thanks! I wasn’t aware of this.

[auretvh (Auret Van Heerden)]

When I started with Rack, I made this for quick reference.

These days I just run everything through the Submarine AO modules. They do have a Log base 2 function.

Before using Rack, I never even knew what a Log was.