When I first started out in the world of modular synthesis, I was lucky to have a couple of friends that had dipped their toes into the eurorack world and they helped me out understanding various aspects such as power, cases and signal path. One thing they both recommended I invest in was the Make Noise MATHS.

Trawling MuffWiggler forum and other Facebook modular groups, it’s clear MATHS in a hugely popular module, and for good reason. Against advice from my peers I’d initially staved off the temptation of getting this “all-in-one utility” but after getting a bonus at work a few summers back I caved and boy do I regret not getting one sooner…

So what is MATHS and why is it so useful? Hopefully in the course of this article I’ll try and explain that. It is a complicated module if you’re just getting into synthesis, but if you’re a seasoned knob-twiddler or have had at least some experience with modular synthesis you should be okay. As I intend to keep this as a self contained article I’ll do my best to explain everything as I go along.

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What does it do?

At the heart of MATHS is a four channel analog computer, with two function generators and two attenuverters. These terms might be a little alien at first, but we’ll cover them in time. It is loosely based on the Buchla 281, Buchla 257 and Serge DUSG units, packaged neatly into one module.

At 20hp MATHS is no shrinking violet, but aside from its basic functions it can be used as a VCO (voltage controlled oscillator), slew limiter (glide/portamento), mixer, envelope follower and can perform basic logic. This is from ModularGrid:

MATHS builds on the tradition set into motion in the 1960s when Don Buchla [RIP] adapted circuits found within analog computers for musical purposes. Buchla’s Algebraic Processor, Model 257 and 281 changed the way music synthesizers utilize control voltages. MATHS continues this great tradition – sculpting the voltages we use to sculpt sounds.m

Complex CV signals can be generator with MATHS by combining the four channels outputs using the SUM, OR and INV outputs. As well as this, MATHS can be patched internally to create all sorts of triggered and looping sequences.

The Front Panel

maths_900-0661dad533a088d19e0ae704074e1fecMake Noise’s hieroglyphic-like front panel design can be a little off putting to those of us just starting out on their eurorack question, it’s certainly not a simple as Pittsburgh Modular’s Duplo-like interface or Doepfer’s clinical German design, but this complex aesthetic is in keeping with the nature of the module.

Whist capable of alarmingly complex functions, MATHS can be broken down to its simpler components be understood a little better.

Below I’ve highlighted the main sub sections. We will need to further analyse them each in more detail, but this will suffice for now.

In red/pink we have the inputs for each channel, 1 through to 4. The right is just a mirror of the left, so we’ll have a look at the left exclusively. From left to right we have the two inputs for channel 1 (signal in and trigger in) and then the input for channel 2 (then 3, which is a mirror of 2, and 4 which is a mirror of 1).

In green we have channels 1 and 4 (left and right), including a cycle button, rise, fall and curvature knobs, cv inputs for rise, fall and both rise and fall and a cycle-in input.

In blue we have the main four attenuverters, one for each channel. The knobs for channels 1 and 4 can be thought of as depth or amplitude controls on ordinary synths, however they’re bi-polar so allow for inversion.

Channels 2 and 3 can work as simple DC offsets, with channel 2 ranging from +/- 10 volts and channel 3 from +/- 5 volts, allowing finer control.

In the yellow portion we have the main outputs of MATHS, a variable output for each (controlled by the middle blue pots detailed in the above paragraph), and unity outputs for channels 1 and 4.

We also have an end of rise and end of cycle output, allowing for triggers to be generated once a portion of the CV has completed.

Lastly in orange we have some basic logic outputs. Logic works by analysing two signals and outputting a signal based on the two (or more) inputs. There’s OR, SUM and INV (inverted) outputs. If that’s a little confusing don’t worry because we’ll cover this more a little later.

All of this and more is detailed in the manual which you can read here or from Make Noise’s website. Not only does it go into huge depth on each element but it has some great patching ideas that truly demonstrate the potential for this module.

There’s quite a lot to swallow, and to a beginner this can seem a bit daunting, which is perhaps one of the reasons I held off buying one for so long, but it’s actually a bit simpler than you might first think. Let’s tackle each section one by one. Starting with the function generator.

What’s a ‘Function Generator’?

envelopesBefore defining exactly what a function generator is, let’s think about voltage. Voltage can only do one of three things. Much like automation or MIDI CC data it can go up, it can go
down or it can stay the same. It’s this basic principle that is central to MATHS.

At this stage it’s worth being on at least nodding terms with basic synthesis terminology.

A function generator can be thought of a bit like an envelope or an LFO – both common modulation sources. So, what are the main differences between these two?

A big difference between them is that envelopes are initiated by a user, either from a gate, trigger source, MIDI keyboard, sequence or similar. We can even self patch channels 1 and 4 where one triggers the other but I don’t want to over complicate things at this stage.

LFOs on the other hand are continuously cycling (something not entirely clear in a DAW – this is something modular synthesis helped crystallise for me). LFOs don’t need intervention to start, they are just happily plodding away in the background.

Yes we can reset the phase of an LFO, sync it to a host tempo are various other things, but its this independence that differentiates it from an envelope.

What they both have in common is that they both containing ascending and descending portion of their modulation. In an envelope the attack ordinarily moves from a low to a high point, and the decay and/or release do the opposite. An LFO requires a similarly symmetrical (or asymmetrical) up and down motion.

MATHS has a Rise and Fall control. The Rise being ascending portion of the envelope or LFO, and the Fall being the descending portion. Each rise or fall stage can range from being exponential (a faster, more dynamic, curve) to linear (straight line), to logarithmic (a slow falling, curve). It’s the exponential envelopes that people love for snappy kick drums and other percussive sounds, where as the linear and logarithmic curves have their uses elsewhere.

When in cycle mode, the LFO can run from as fast as 1000 cycles per second to 1 cycle every 25 minutes(!), crazy ranges on offer! The curvature of the rise and fall times now act effectively like a waveshaper control for the LFO cycle. With both portions set to linear you get a triangle wave, with both set to logarithmic you get something like the positive half of a sine wave. You can get waves similar to ramp up/down using combining exponential and linear and all sorts of other shapes are possible.

For the reasons discussed above, MATHS can work as two envelope generators or two LFOs – which is really good value for money especially in a smaller system for 3U skiff.

What’s an ‘Attenuverter’?

This is something else that I struggled with that I later discovered to be immeasurably simpler than I’d first thought. The word attenuverter is actually a portmanteau of attenuator (to reduce the signal of something) and inverter (to flip or invert).

You can think of this a bit like a bi-polar DC offset (direct current, as opposed to alternating current). As mentioned previously, channel 2 has a range of +/- 10 volts and channel 3 is +/- 5 volts. These are incredibly useful for sending static voltages to your system in all sorts of ways.

I’ve used them to transpose quantized pitch sequences, open VCAs, reset clock modulators and trigger sequencers, ping envelops, open filters and much more. That’s not even scratching the surface of what can be done with offsets (sometimes also referred to as bias), so do keep an eye out for various MATHS patch ideas dotted around MuffWiggler and other places.

As channel 3’s range is narrower it allows for more fine tuning, something I hadn’t really appreciated until I’d try to use MATHS to tune oscillators. Eurorack uses the 1 volt/octave tuning model (other synths such as Korgs and Yamahas use Hz/volt). Most oscillators will have a range of 10 volts, so a pot the has a range of 20 volts makes it harder to hone in on specific areas of the audible frequency range – channel 3 has a range of just 10 volts so that’s much easier.

Enough from me, let’s watch some videos:

Getting Started

Where better to get started than the official videos from the official channle itself. This two part video is a fantastic platform for getting to grips with MATHs and understanding the basic functions of channels 1 and 4:

So, channels 1 and 4 can be used as envelope generators, LFOs, VCOs (when cycled at audio rate), slew limiters and more. They can have their rise and fall portions controlled by each other with some self patching. In addition it’s possible to use the end of rise and end of cycle to trigger each other or sequencers and other trigger generators.

In the next video,Walker goes on to explain channels 2 and 3 as well as the SUM, OR and INV outputs. The main difference between channel 2 and channel 3 are their range, where as 2 is +/- 10 volts (20 volts in total), 3 is +/- 5 volts (10 volts in total).

Next, Future Music’s YouTube channel has posted this excellent video from eurorack’s Mr Fingers Mylar Melodies (ace). The content is not dissimilar to the above official videos but he has a fantastic way of explaining things coupled with tonnes of modular enthusiasm. It certainly helped clear up some MATHS oddities for me.

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