If you go on a Eurorack forum and ask people to name one essential module that everyone needs in their rack I can almost guarantee that the most common suggestion would be for Maths from Make Noise. I think it is popular for three main reasons: it is very flexible, it is compositional (meaning that it consists of a bunch of basic functions that can be combined to create more advanced things) and it is a bit inscrutable — very much like modular synthesisers in general!
Make Noise describes the Maths variously as a signal generator and as an analogue computer which can be impressive and unenlightening in equal measure.
So what the heck is it? Think of it as the Swiss Army Knife of your rack; it does a little bit of everything. It can generate envelopes. It can repeat those envelopes, creating an oscillator. It can scale, invert and combine voltages in various ways. And it makes you feel clever.
Maths consists of four separate channels that can affect an input signal in various ways. The input channel jacks are “normalled” which means that they have an internal connection that is broken when a plug is inserted. This is used to provide one function when the input is connected and another function when the input is unconnected.
When the inputs are unconnected channels 1 and 4 can generate a simple Attack-Decay envelope with adjustable attack and decay times. The envelope can be triggered on a CV pulse (like a normal envelope) or cycle continuously while the Cycle button is engaged or when the CV Cycle input is high. The length of the envelope varies from the glacial (about 2 cycles per hour) to the quite fast (1kHz) so it can function both as an LFO and as a sub-oscillator.
When the Signal input of channel 1 or 4 is connected then the that channel functions as an envelope follower.
Channel 1 has a curious but useful feature where the End Of Rise (EOR) output generates a pulse signal when the channel 1 envelope has reached its maximum value. This can be used as a clock signal or a pulse wave with the length of the envelope determining the frequency. Channel 4 has a similar feature but it generates the pulse at the End Of Cycle (EOC) output when the channel 4 envelope has reached the end of one whole cycle.
Channels 2 and 3 are less sophisticated. Channel 2 generates a constant +10V signal and channel 3 generates a constant +5V signal. All channels pass through knob-controlled “attenuverters” which are circuits that can amplify, attenuate or invert a signal. This can be used to adjust the output voltage from any channel so, for example, if you need a +2V offset signal you could pick channel 2 or 3 and adjust the channel attenuverter until the channel outputs the desired offset. If a signal is sent to a channel input then the attenuverter for that channel affects the incoming signal instead (as expected).
All channels are by default routed to three logic function buses called OR, SUM and INV. This may sound complicated but isn’t really.
OR means that the highest voltage is present at the output. For example, if the channel 1 input is 0V, channel 2 is 1V, channel 3 is 0V and channel 4 is 3V then the OR output would be 3V. If the channel 2 input rises to 4V and the others stay the same then the OR output will change to 4V.
SUM is the sum of the input voltages. In the example above the SUM output would be 4V (1V + 3V) initially and then 7V (4V + 3V) after the channel 2 input has risen. Since the attenuverters can invert signals you can also use this with the SUM bus to subtract one signal from another.
INV is the inverted SUM, so it would start at -4V and end up at -7V.
So far a bit tricky, but not mind-meltingly hard. The fun stuff begins when you start to combine the different channels, feeding them back into each other. If you want to understand what goes on with that stuff I highly recommend getting an oscilloscope. The Maths manual has lots of examples of things you can do with the module: ADSR envelopes, signal peak detection, signal rectification and many others.
I bought a Maths primarily because it can generate envelopes, audio signals and perform signal amplification and inversion. It packs a lot of functionality into a reasonably sized and priced module. And yes, it makes me feel like a rocket scientist when I have to plan my envelope using pen and paper instead of just clicking somewhere.
Make Noise modules have a very peculiar look that some people love, some people hate and some people feel ambivalent about. Sort of like absolutely anything then. I’m in the ambivalent camp. In my eyes some modules, like the Dual Prismatic Oscillator, looks great and some modules look confusing or downright ugly. I didn’t really like the look of the Maths module but fortunately a company called Grayscale offers alternate panels for many of the Make Noise modules so I ordered a Maths panel from them. I must admit that the unadulterated Maths module looked a lot better in real life than it does in photos, so I could probably have lived with the original panel, but the Grayscale alternate is a lot neater and easier to understand.