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No pain, no gain

Related and important concepts

Clipping or distortion when too much gain is introduced
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Compression
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This is at the edge of my understanding but I think I have a rough handle on it. If you can visualize a waveform, the distance from “peak to peak” (high and low) is measured in voltage. Gain will multiply the input voltage by some factor to make the wave “bigger” or amplify it so the peaks are farther from the zero point at the output.
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Here’s some reading.
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Amplifier Gain​

The introduction to the amplifier gain can be said to be the relationship that exists between the signal measured at the output with the signal measured at the input. There are three different kinds of amplifier gain which can be measured and these are: Voltage Gain ( Av ), Current Gain ( Ai ) and Power Gain ( Ap ) depending upon the quantity being measured with examples of these different types of gains are given below.


Amplifier Gain of the Input Signal​

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Was getting ready to say I'm not an electrical engineer but I'm pretty sure gain in a technical sense is specifically an increase in voltage. Volume, on the other hand, is simply attenuation.

I used to install automotive electronics professionally and can't tell you how many bass heads i had to tell that gain is NOT volume. I've set your gain using a multimeter and math and it's set where it should be. If you decide to play with your amp, you may blow your fancy sub.
 
Gain is the ratio of input level to output level (in voltage or dB) of a component. So your Input Gain on your amp adjusts the signal's level at the input and boosts the level at the pre-amp's output. (signal going into amp --> Gain stage --> the rest of your amps circuitry --> power amp)

The term Volume is used to specify adding Gain to the output of something. You can have all your Gains cranked to 100, but none of it comes out the speaker until you turn up the Volume.

BUT! Technically, the Gain and Volume are both Gain. There's a ratio between the signal going into the Volume Knob and the level coming out of it after the power amp. It's all just Gain, until it gets to the knob that controls what you hear. That Gain is also Volume.
 
Volume, on the other hand, is simply attenuation.

I’ve been amused by the fact that in the modular synth world a VCA is a Voltage Controlled Amplifier by name, though often a Voltage Controlled Attenuator in function. To silence a signal you need to turn the VCA all the way down, and then allow sound to pass by turning it up. I suppose some units send a signal that is higher than the incoming signal, thus amplifying it.
 
the gain and volume knobs on most gear do the same thing, IF the level of the incoming signal is low enough that nothing clips in the circuit. If there is something between the gan and the volume knobs in the circuit that clips/distorts, the gain knob will determine how soon that clipping occurs, and the volume knob generally (unless there is something after it that will clip/distort) determines how much of the signal from that clipping point ends up at the output.
 
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Gain is like dumping money into a savings account with a high interest rate and volume is spending that money.

The interest earned is like the distortion and saturation on the audio signal. Less money in the account, the less interest earned.

More distortion is just more appealing sometimes. It makes all of these weird soundwaves. I think humans evolved to like distorted cries because they mimic the weird soundwaves of a baby screaming or wailing.

Or maybe this is a bad analogy…sorry…it is the end of the week.
 
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Volume, OTOH, simply takes a signal of some amplitude and makes it smaller, or attenuates it, i.e. multiplies it by a value < 1.
I have designed plenty of volume controls that control stages of amplification - where the output of that stage is bigger (often much bigger) than the input. Let's say you're designing a 400 watt bass amp (into 4 ohms), and it has an overdrive/clipping circuit in it. Clipping is often done by diodes in circuits where the maximum output of that stage is one diode drop. It's it's a silicon diode, that's .6 volts or so - that's the maximum signal that you get out of the circuit that the "gain" knob (before the clipping stage) is controlling.

OK, on to the volume control, in the power stage. Let's say that the amp is rated for 400 watts into 8 ohms. To get that output power, you need about 56 volts (RMS) output swing. The peak of that signal is bigger - you need the power amp to be able to deliver 80 volts to the speaker at max amplitude. So......the power amplifier gain needs to be 80/.6, or about 133. The volume control is controlling a circuit with a gain of 133. That's... bigger than 1.
 
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Gain and volume can vary massively in their function based on what piece of gear it is, and who designed it. Generally speaking, gain is in front and volume is in the back. Gain often exists to introduce some clipping and distortion, while volume is almost always supposed to just be clean loudness. But when you look at something like an old tube amp, you will find that the volume can also distort things.
In a pedal you might have a transistor gain stage, possibly with some diodes to introduce real nasty distortion, and then at the end another transistor gain stage, but that one functions as a volume because it's limited such that you can't make that transistor clip. So the transistor and the diodes at the beginning are biased such and used such that they create distortion, and the transistor in the back can't be overdriven, it simply allows you to lower or increase the volume of the signal to make it fit into the rest of the equation.

The only real answer is: it depends on what piece of equipment you're talking about.
 
I have designed plenty of volume controls that control stages of amplification - where the output of that stage is bigger (often much bigger) than the input. Let's say you're designing a 400 watt bass amp (into 4 ohms), and it has an overdrive/clipping circuit in it. Clipping is often done by diodes in circuits where the maximum output of that stage is one diode drop. It's it's a silicon diode, that's .6 volts or so - that's the maximum signal that you get out of the circuit that the "gain" knob (before the clipping stage) is controlling.

OK, on to the volume control, in the power stage. Let's say that the amp is rated for 400 watts into 8 ohms. To get that output power, you need about 56 volts (RMS) output swing. The peak of that signal is bigger - you need the power amp to be able to deliver 80 volts to the speaker at max amplitude. So......the power amplifier gain needs to be 80/.6, or about 133. The volume control is controlling a circuit with a gain of 133. That's... bigger than 1.

Like I said, it can get a lot more convoluted than my simplified explanation. I'm well aware of that, but those details don't help someone who doesn't understand what the term gain means in it's most basic form.
 
Terms, definitions? I was a school Chemistry teacher for a while and I always used to say to my kids "Biology, eh? Sort your crap out." Chemistry, maths, physics, all really easy. 2+2 always equals 4. Once you introduce a human element it all goes to pot. Usually these two reagents will mostly do this, but it kind of depends on other stuff. Unless it's too hot and they do nothing at all. If it's a full moon they do something different. Etc.

Where am I going with this ramble? 'Gain' and 'volume' are words. They are made up and they don't mean anything apart from what a given speaker and a given listener understand them to mean.

To a soundman, gain means the given volume increase on a specific channel/signal on a mixing desk.
To a bass player gain means the input volume control on an amp, usually before the DI, effects loop, eq, and stuff.
To a person using a fuzz pedal, gain means how fuzzy you want to make the signal by overloading some electrical doodad in the pedal with too much .. er ... gain/volume/level/electrons.

Definitions are all loose. What does 'ampless' mean on TB these days? To some people it's just moving the preamp from your combo amp into a floor pedal and then leaving the power amp and speaker in one box. If you have a combo, (preamp, power amp, speaker) and I have a Sansamp (preamp) into a wedge (power amp, speaker) then I am I actually any more 'ampless' than you? Hell. what does a 'bass' even mean? Is a Fender VI a bass? What about an Ashbory? A Wingbass? There are jazz cats who will tell you that all electric bass guitars aren't even 'proper' basses. I think the problem you're having is that you're getting textbook correct definitions of your terms from people like electrical engineers and, whilst those make perfect sense, they're not how you're seeing those terms used in the real world by us idiots.


Biology eh? Sort your crap out.
 
The easiest way I’ve thought about it is gain is pre circuit/overdrive/distortion and volume or level is post. But the important thing is the circuit that’s in the middle. This is like a choke point, so as you approach and meet the threshold, the signal gets more and more compressed and distorted as it tries to fit more signal through. Then once you’ve gotten the desired amount of distortion/compression/saturation, you use the volume or level to bring the signal up or down based on your volume needs.

Gain staging is when you consider that there can be multiple “choke points” along your signal chain that can introduce distortion/compression/saturation. So for example you may have a pedal that’s introducing some of those effects, but then you have the level set pretty high coming out of the pedal, it can also distort the circuit in the preamp part of the amp which you may or may not want depending on taste.
 
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