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 dont think it would be the pick ups. Check the lead and also the problem might be just where you put the lead into the guitar. Does it feedback when you move the lead around ?