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What is the difference between "hi" and "low" input jacks on guitar / bass amps? Usually bigger amps have both of them (didn't see them on smaller ones really)..

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The "Hi" input attenuates the input signal, usually by between 10-15dB (about half to a third the original volume). The "Low" input will not do this.

Different guitars and basses produce widely varying signal levels. This isn't just a passive vs active thing; plug a vintage-voiced Strat into the amp, then a PAF-voiced Les Paul; you'll have to turn the gain down. By contrast, the preamp of your amplifier works best with a signal in a particular range of strength; too hot, and you'll clip the preamp (which is generally not the best sound especially if you want a clean tone). Too low, and subtleties of tone become lost in the amp circuitry's "noise floor".

The different inputs, or the attenutation switch on a single input, allows you to "turn down" a hot guitar with a simple switch instead of involving other elements of the preamp. This has two benefits, both tied to being able to turn the other "downstream" controls to higher levels. First, taming a hot signal without an attenuator usually requires turning down the "Pre Gain" level. This knob, especially on a tube amp, will become very sensitive; small moves will produce huge volume changes. By attenuating the signal before this point in the circuit, the knob becomes less sensitive to small moves. Second, by allowing controls like the pre-gain to be turned higher, more of the original "native tones" of the instrument get into the preamp stage, and the tone and equalization controls have more to work with. Overall, this results in a "less muddy" sound, as subtle harmonics and overtones aren't lost in the noise floor of the amp.

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10-15dB represents 1/10 to almost 1/40th the original signal. Not 1/2 to 1/3. Every 3dB is a halfing of your signal. Every 10dB is 1/10th. –  Kortuk Jul 20 '11 at 16:37
    
... and a signal that is 10dB less than another, all other things being equal, will sound to the listener about half as loud, because that's how the Bel scale was calibrated. But, I changed the sentence so it's clear I'm talking about sound volume. –  KeithS Jul 20 '11 at 16:38
    
the issue is that you say signal strength, I guess I should take that we are on a music site into account. I have been told that a logarithmic scale is used because our ears hear a linear increase in volume with a logrithmic increase in power. The log scale is used with a base of 10 because our number system in base 10 though. –  Kortuk Jul 20 '11 at 16:45
    
@Kortuk 10db is in fact considered the perceived doubling (or halfing) of loudness. KeithS it has nothing to do with being "calibrated" it was just experimental data that found 10dB to be what humans perception was for doubling of loudness, but that is only a loose estimate as this perception changes based off of frequency and loudness. –  Kellenjb Jul 20 '11 at 17:04
    
"Half to a third the original volume" (amplitude, actually) is in fact the pretty much the usual factor, but it's the "lo in" that's attenuated, not the "hi in"! (It's possible that some manufacturers label it the other way around, but that would be sort of wrong.) 10-15 dB seem a rather unusually big span – it's again possible that some manufacturers actually use such a big factor, but I think this is rather the perceived attenuation due to the lower impedance, which is the real crucial difference between the hi and lo inputs. –  leftaroundabout Jul 22 '11 at 0:19
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They assume different signal levels so have different levels of gain in the pre-amp. In fact on some amps the low input has a pre-amp but the high just goes directly into the main amp.

This is to cope with the fact that instruments can have very different output signal levels, but it can also be used to change the tone of the sound produced.

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On my Ampeg amp, the instructions said that if you are playing a bass with passive pickup(s), to plug into the 0db jack; and if your bass has active pickups, to use the -15db jack.

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Contrary to what the previous answers stated, the different sensitivity is not the primary difference between the "hi" and "lo" inputs. It is indeed different, usually by 6 dB, but you could achieve this with the gain knob alone.
More important is the different impedance of both inputs: a "hi" input has a very high inner electric resistance (in the range of 1 MΩ), that is, it accepts the voltage the guitar outputs while there needs to be hardly any current at all. The guitar pickups can then do their job (which is translating the string vibrations to electrical voltages) completely freely without having to also supply a lot of current; so they can do a lot of resonance, which gives a bright and open, but sometimes also annoying and "un-compact" sound.
A "lo" input, on the other hand, typically has an impedance of about 150 kΩ, roughly 1/7th of the hi input's. That means, when the pickups try to send their voltage to the amp there will always be a significant current the pickups also have to supply. Actually, it's still a very small current – something like fractions of microamperes – but guitar pickups are very weak sources of current. Voltage and current together means they need to push energy to the amp: this energy will be taken from their own high-frequency resonances, therefore a normal electric guitar will sound more mellow when plugged into the "lo" input than when it's plugged into the "hi" input. It will also be simply quiter because of the attenuation, but this, as I said, is less important.

Every pickup responds differently to the amp impedance: some will sound muffled and dull when plugged into a "lo" input, others shrill and disturbing with a "hi" input. So when you're using two different guitars live, it can sometimes be useful to use each input for one of them (you should still always unplug the one you're not playing from the amp).

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