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Excellent John now i dont have to go to audio asylum lol
Gain is the ratio of the output voltage to the input voltage. It's typically expressed in dB = 20 log (Vout / Vin). 0dB is no gain (output same as input), 20 dB gives output of 10x the input.If an attenuator is in the circuit you are typically talking about the above ratio when the attenuator is set to max which is (typically) no attenuation. An attenuator is "negative gain".
As I think I see it, gain is the total number of decibels a piece of gear can theoretically put out. Volume adjusts those decibels within whatever range the gain has.