Patch trick: turn your Maths into a complex formant oscillator like Mangrove

[DaShmoop]

Here's a really fun, interesting and easy Maths patch which effectively turns your Maths into a v/oct tracking formant oscillator 'like' Mannequins Mangrove. I was reading the technical map for Mangrove and realized the core functionality of Mangrove is just a square wave triggering an audio rate envelope with CV control over the envelope rise/fall shape and envelope duration.

The patch is simple. Take your favorite complex oscillator or two oscillator pairing with both set to square or pulse, sync the two oscillators, then connect the wave outputs to Maths ch. 1 and 4 trigger inputs. Then run the Maths outputs through your favorite filter and VCA. That's it! Play around with the rise, fall and shape controls on Maths in addition to the frequency of the sync'd oscillator. You'll get classic formant behavior with pitch transposition and "dead" areas where Maths won't trigger on notes where the triggering oscillators wavelength is greater than the rise time of Maths which creates super cool rhythms, especially with sequences spanning multiple octaves.

You can mult your sequence v/oct to various combinations of rise, fall and "both" inputs on the Maths channels (note: sending the v/oct to the "both" input is equivalent to "constant wave" mode on Mangrove)

I've been interested in getting a Mangrove and this fully convinced me.

[Snufflepuff]

Wow! I just saw a pair of Mangroves on Reverb for $1,000 and had resigned myself to the almost certain reality that I'd never have one. Then I visit Muff Wiggler for my very first time and see this post! Super helpful.

I don't have a Maths, but I can grasp "square wave triggering an audio rate envelope with CV control over the envelope rise/fall shape and envelope duration." Could you elaborate in terms of connecting the 1 square waves to a generic cycling envelope? (I tried reading the Maths manual but got lost pretty quickly). Thanks!

[DaShmoop]

Wow! I just saw a pair of Mangroves on Reverb for $1,000 and had resigned myself to the almost certain reality that I'd never have one. Then I visit Muff Wiggler for my very first time and see this post! Super helpful.

I don't have a Maths, but I can grasp "square wave triggering an audio rate envelope with CV control over the envelope rise/fall shape and envelope duration." Could you elaborate in terms of connecting the 1 square waves to a generic cycling envelope? (I tried reading the Maths manual but got lost pretty quickly). Thanks!

Yup! The Mannequins stuff hasn't been available this entire year, probably because of manufacturing issues related to covid, so the used market prices are outrageous. People lust after Mangrove, and for a good reason. They sound fantastic. But they're a simple design and I bet most people don't realize they can emulate much of the Mangrove sound with a function generator like Maths.

I'll try to explain what's going on here. The first important thing to know is that a lot of function generators like Maths do not retrigger during the rise time. They only retrigger during the fall phase of the envelope. This is the primary basis for formant oscillator synthesis.

To elaborate on that point, let's say you have a square wave that is going high once every second and you plug that square wave into the "trig" input on Maths. The rising edge of the square wave is going to trigger the envelope on Maths once every second. However, if you increase the rise time control on Maths so that it takes longer than 1 second to reach it's peak Maths will ignore all triggers coming in while it's rising. So if the rise time is set to 5 seconds, even though 5 triggers of the square wave would be seen at the trig input during this time, only 1/5 rising edges of the square wave would trigger another envelope. That's it!

Now what makes this REALLY fascinating and is when you start sequencing the square wave, maybe a major scale arpeggio that covers two octaves, depending on the rise/fall time of the envelope, certain notes in the pitch sequence might be higher frequency than the rise time, so some notes of the sequence will jump octaves as they're subdivided. And then if you start modulating the rise/fall time you get really interesting artefacts.

The other important principle of formant synthesis using this triggered envelope approach is that the envelope shape stays the same regardless of the frequency of the square wave triggering it. Normally when you're sequencing a regular old sawtooth wave for example, the width of the sawtooth will scale according to the pitch, but not when triggering an envelope. This imparts an interesting frequency content that more closely resembles physical structures, like a trumpet for example. Obviously a trumpet's physical properties like air chamber size determine how it sounds, and a trumpet's physical structure doesn't change with different notes, this imparts a signature frequency content to the resultant sound. This is why people say that Mangrove sounds "organic" or "natural."

Here are a couple scope screenshots demonstrating the subdividing effect.

The first is showing the case when the envelope is triggered on every rising edge of the square wave

The second image is after just increasing the rise time on Maths. Notice how the envelope ignores a rising edge and doesn't retrigger until after it's completed it's rise. This effectively subdivided the envelope by 2, dropping it an octave.

[finalplane]

Super cool. Acquiring a DFG soon and excited to try this. Props to you for figuring this out

[Snufflepuff]

Thanks for the visuals! I set something up in VCV Rack with Tides:

https://www.dropbox.com/s/pekfd3m3lwaqu ... n.vcv?dl=0

A poster on Reddit said the 2nd (synced) oscillator is unneeded, but I found modulating its nominal pitch gave the most timbral changes.

[DaShmoop]

Thanks for the visuals! I set something up in VCV Rack with Tides:

https://www.dropbox.com/s/pekfd3m3lwaqu ... n.vcv?dl=0

A poster on Reddit said the 2nd (synced) oscillator is unneeded, but I found modulating its nominal pitch gave the most timbral changes.

Yeah you're absolutely right the 2nd sync'd oscillator isn't needed! It does make it far more interesting though. Glad you were able to get this set up!

[KSS]

Great post and thread!

[Snufflepuff]

Here's my setup in VCV Rack. Two square VCOs, one hard-synced to the other, are triggering two instances of Mutable Instruments' Tides. Playing around with the synced square's nominal frequency and the Tides' frequency is good fun. I tweak the Tides' 'Shift' parameter at the ending, forgetting I'd unplugged the aux outputs.

[architexture]

Or cycle Maths and patch the EOR and EOC outs to the opposing 1 or 4 input then use the rise/ fall to shape the formants.

[3hands]

Fantastic !! That’s my evening gone!!!! Thanks so much for this!!!

[neumedi]

Now this is what I come to Muff's for... thanks so much for the patch idea!

To the point above, not only so many textures between changing rise and fall, but fun to find notes/patterns that fall out of the squared window... here's a quick patch (using only the 2 squares into Math's) that creates a trill on certain notes... starts off with Mimeo delay, but then goes to pure raw Math's through Blades filter:

[Snufflepuff]

Or cycle Maths and patch the EOR and EOC outs to the opposing 1 or 4 input then use the rise/ fall to shape the formants.

Wow, why does that just one module approach work?

[architexture]

The eor and eoc outputs are squarewave generators so you don't need an external oscillator to produce a square wave.

Maths is based on the Serge DUSG. If you look up DUSG patch ideas you'll find a wealth of cool tricks

[architexture]

viewtopic.php?f=19&t=132548 < Try out any of this stuff with your Maths

[mattdennewitz]

sounds great on a dusg, too!

[DaShmoop]

Now this is what I come to Muff's for... thanks so much for the patch idea!

To the point above, not only so many textures between changing rise and fall, but fun to find notes/patterns that fall out of the squared window... here's a quick patch (using only the 2 squares into Math's) that creates a trill on certain notes... starts off with Mimeo delay, but then goes to pure raw Math's through Blades filter:

YESSSSSSSSSS! I could listen to those sounds for hours. Did you ever try sequencing with a sequence that covers more than one octave? I found that to yield the most wild results with formant subdivision, if that's a term?

[dooj88]

maybe i'm thinking of something else, but isn't this taking advantage of the maths division functionality at audio rate?

like in this video?

[hboon]

Really great patch idea. Not sure I've nailed it 100% but liking the results.
Thanks for the tip.

[moremagic]

maybe i'm thinking of something else, but isn't this taking advantage of the maths division functionality at audio rate?

like in this video?

i think the idea here is to clock maths at rates approximately in time with the envelopes its making, rather than trying to divide. i spent a little time patching this type of thing last fall but didnt dig deeply, but seeing the ops enthusiasm ill probably try again soon

[mattdennewitz]

would this work with a contour 1, or would you need something like the select 2 to work around the reset?

[charlie]

Will try this, ty

[hinterlands303]

I just have this a go and had some really nice sounding results that reminded me of what I’ve heard from the Mangrove in videos etc. (I’ve never owned one). I used the EOR output of Maths channel 1 which led to some interesting results when modulating rise (sort of PWM-ish but different and with more harmonics). Very cool!

[xxeyes]

Would this work with a Joranalogue Contour 1? I have neither this nor a maths, but I’m thinking of getting the former. The ability to make this patch would push me over the edge.