Logic sum and or?

[Cablebasher]

Hello fellows,

Been synthing for some time now (on analog synths and now on eurorack) and am more than happy with VCOs, VCFs, ADSRs, LFOs, VCAs etc.

But I want to get more into the depths of CV.

I have been reading the various manuals for modules to get a better understanding but there a few things that aren't clicking.

Any help would be much appreciated.

What is logic (sum and or) and what is its usefulness?

On the make noise maths, is the log, Lin,exp knob just a "slow to fast" knob? If so, is it labelled as a quirky in-joke or is the given name actually accurate?

What is a comparator?

What is scaling?

I have read most of the doepfer manuals for devices that do these things but I still don't see the point.

Too many years playing a simple synth like a SH101 has made all these functions seem very far from what I know as analogue synthesis.

Cheers.

[Navs]

The jump from hardwired to modulars involves some learning of new terms, but many of these 'new' functions are just hiding in your SH-101 etc.

It can seem bewildering on the one hand and more work on the other, but it's better to dig up existing threads or ask separate questions. Otherwise logic answers get mixed with scaling answers etc.

That said, Maths is one of those modules that raises many questions

The logic section in Maths is 'analogue', that is 'continuous' - it's not zeros + ones or offs and ons. The 'sum' is just that. Like a mixer, 1 plus 1 equals 2. The OR is an absolute. It traces the peak value of the signals. So, 1 + 1 = 1, 2 + 1 = 2.

[daverj]

What is logic (sum and or) and what is its usefulness?

There are two types of "logic" found in modular synths. Digital or binary logic, where signals in and out are expected to be in one of two states. A low voltage (often zero volts) and a high voltage (typically +5v, +8v, or +10v). Signals are combined using Boolean rules and are often used for creating complex gates.

The other type of logic in modulars is "analog logic". This isn't the same as the classic digital logic but attempts to apply the same Boolean rules to combining a pair of analog signals, with an analog result.

"Sum" is not a logic or Boolean function. It is a mathematical function. In general, math functions are applied to analog signals (if applied to digital signals they are simply treated as analog waveforms).

Boolean functions are things like AND, OR, XOR, and NOT.

AND = input 1 and input 2 must both exist in order for the output to exist. In digital logic this means that the output goes high only if both inputs are high. Otherwise the output is low. In analog logic the AND function is also called a MIN (minimum) function. The output voltage reaches a given voltage if input 1 and input 2 are at that voltage. Otherwise the output is the lower of the two voltages.

OR = If either input 1 or input 2 exist, the output exists. In digital logic this means that if either of the inputs is high, the output is high. If both are high the output is high. So the output is only low if neither of the inputs is high. In analog logic the OR function is also called the MAX (maximum) function. The output voltage is the voltage on input 1 or input 2, whichever is higher.

XOR = "exclusive or". Similar to the OR function except the output is high if one input or the other input is high, but not if both are high. This can also be thought of as a way to see that the inputs are different. If the inputs are the same the output is low but if they are different (one high and one low) then the output is high. There are a couple of analog interpretations of how to do this and they are not as common as an analog AND or analog OR because it is a more complex way to combine signals. Basically as one of the inputs goes up the output goes up, but as the second input also goes up it causes the output to reverse and start going down.

NOT = the NOT function is simply an inversion of the signal. With digital signals if the input is high the output is low. If the input is low the output is high. This is also called an inverter. With analog you simply turn the signal upside down so positive is negative and negative is positive.


Mathematical functions work on analog signals:

Sum = (addition) Mixing two (or more) signals together without attenuating the input signals. So a +2v signal on one input and a +3v signal on the other input puts out a +5v signal. A +2v signal on one input and a -3v signal on the other input puts out a -1v signal. Two +5 inputs will output +10v. The output voltages are limited by the power supplies and the mixer circuitry, so summing four +5v signals can not reach +20v and simply gets clipped by the circuitry typically somewhere around +/-10v or +/-11v.

Average = Basically the same as a sum except that you turn down the mixture based on how many inputs you have so that the sum of all inputs never goes higher than full scale. For example if you feed two signals into a mixer and set both inputs to 1/2 gain then the mix will stay within the same voltage range as the originals.

Biasing = a special case of summing or addition where only one signal is fed in and it is added to the voltage on a pot. The pot then adds or subtracts a fixed amount of voltage transposing the input up or down by a certain amount without changing the size (scale) of the input signal.

Multiply = The output voltage is one input's voltage multiplied by the other input's voltage. There are two common types of multipliers in modular systems. A VCA is a "2-quadrant" multiplier. Typically the signal input can be positive or negative while the control input is usually only positive. Many VCAs only have unity gain so the output matches the input when the control is all the way up (perhaps +5v). So for mathematical purposes you can think of the control input multiplying the signal input by a value between zero and one as the control goes through it's range (perhaps 0v to +5v). So if the CV is at 2.5v it is multiplying the input signal by 0.5, making the output put out a signal half the size of what is going in.

The other type of multiplier found in modulars is a "4-quadrant" multiplier. Also called a balanced modulator or possibly a bipolar VCA. This is similar to a VCA except as the control signal becomes a negative voltage the output becomes the negative version of the input signal. These also often have unity gain at full control voltage, so are like multiplying the input by 1.0 when the CV is fully positive and like multiplying the input by -1.0 when the CV is fully negative. So when the CV starts at -5v the output is the negative of the input signal. As the CV rises towards zero volts the output gets smaller and smaller. When the CV reaches zero volts the output has no signal and is just zero volts. As the CV continues to rise and becomes a positive voltage the output is now a positive version of the input signal and gets stronger as the CV rises.

Subtraction = Just like in normal mathematics, you can subtract one signal from another by inverting that signal (making it a negative version of the original) and adding it to the second signal.

On the make noise maths, is the log, Lin,exp knob just a "slow to fast" knob? If so, is it labelled as a quirky in-joke or is the given name actually accurate?

They are what they say. They control the shape of the slope of the rise and fall. Linear means the signal increases and decreases at a constant rate. Log and expo create slopes that look bulging out or bowed in, rising or falling at different rates as the voltage goes higher or lower.

What is a comparator?

A comparator will compare two inputs and put out a digital signal that is either high or low depending on whether input 1 is higher or lower than input 2. It is often used to convert an analog waveform into a digital waveform (square wave) by comparing an analog waveform to a constant voltage. For example if one of the inputs is at zero volts then the output goes high or low as the other input crosses zero volts.

What is scaling?

Scaling is making a signal larger or smaller. It does not have to do with musical scales. It has to do with the scale (size) of the signal. An attenuator allows you to manually reduce the scale of a signal. With it all the way down the output is zero. As you turn it up the signal gets larger until it is at full scale (output matches input) when the knob is all the way up. To get an output that is larger than the input you need amplification (gain). Most attenuators only reduce the signal, but some of them might have additional gain allowing you to boost the signal (scale it up).

An "attenuverter" or bipolar attenuator is one where the output is at zero when the knob is in the center. As the knob goes up the signal gets stronger. If the knob is turned down below center then the output is the negative (inverted) version of the input. The further down you turn the knob from center the stronger the negative signal gets.

If you don't have an attenuator that has additional gain, or any other dedicated device to add gain, then you can feed the same signal into two inputs of a mixer. This creates the sum of the two inputs. Since they are the same signal, if both knobs are higher than half way then the output is larger than the input signal. When both knobs are up all the way the output is typically twice the input signal, or a scale of 2.

[Cablebasher]

Thank you so much. That made a lot of sense. Felt like I was back in physics class!

[spritepixie]

Daverj, thank you for the explanation. I'll have to revisit my Plog tonight!

[transistor animal]

What is scaling?

Scaling is making a signal larger or smaller. It does not have to do with musical scales.

it can!

take guitar frets and how the distance is scaled to notes. try setting up ratio based scaling up with logic modules and multiplier or divider. easy drum rolls.

logic/math = big sequencing fun....for sound it's more useful to miss use for distortion.

[Cata]

fantastic explanations! I feel like I just learned a whole lot more about my MakeNoise Function after reading this!

[daverj]

What is scaling?

Scaling is making a signal larger or smaller. It does not have to do with musical scales.

it can!

take guitar frets and how the distance is scaled to notes. try setting up ratio based scaling up with logic modules and multiplier or divider. easy drum rolls.

logic/math = big sequencing fun....for sound it's more useful to miss use for distortion.

You can scale a voltage which in turn changes a musical scale.

But I was trying to differentiate the use of the word "scale" in context. Scale meaning size vs scale meaning musical notes.

[causticlogic]

Maybe we should ask Muff to create an "Ask daverj" subforum.
Seriously, very nice and thorough explanations.

[HIMA]

daverj, you are fast becoming my favourite wiggler.

[Navs]

Hands off, he's mine!

[negativspace]

Seriously, I read everything Dave posts even if I'm not interested in the subject at hand. I always learn something regardless...

[Mans]

[technicoloraudio]

i am glad this exists and i bookmarked it as i will need to read daverj's explanation about thirty more times before it really sinks in. i have started to run into these terms a lot, especially as i debate the purchase of a Maths.