Most older FET input opamps like the TL07x and TL08x opamps have phase reversal when an input goes lower than the allowed negative common-mode voltage. The first time I saw it I replaced the "defective" opamp but the replacement did the same.
Two chips that come to mind are the RC4558 and the RC4739. They are low noise and very suitable for audio projects. You can also add opposing diodes or LED's in the feedback chain to create overdrive. This is a common technique used in many popular distortion and overdrive guitar pedals.