By virtue of their electrical properties, tubes generate a special waveform when they're saturated, which is why tube engineering has tremendous tonal advantages over solid state or DSP solutions, particularly for crunch and lead sounds. Tubes enter the saturation zone gradually or softly, which lends tube-driven tone its trademark yet totally unique character.
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I use lots of destortion sometimes when i sweep but i have to use destortion from effects box and amp so it sounds even more mental so it would force me to mute strings. Only problem is, is that you may be missing notes and being sloppy and not realizing it. So it would be good to turn down the gain now and again to make sure your getting all the notes. Muting with your fretting fingers is a good way but its harder than doing it by palm muting.