My headphones play persistent static when plugged in, except when muted. No static is heard over the speakers, HDMI, or over headphones when the audio is muted.

I've tried:
- muting my microphone
- muting S/PDIF in alsamixer
- muting Mic and Mic Boost in alsamixer
- disabling INTEL_AUDIO_POWERSAVE
- rebooting
- prayer, incense, and burnt offerings to the river goddess

I'm on 15.10 on a Lenovo Thinkpad X1 Carbon 3rd Gen (2015). This does not happen on Windows.
Any help would really, really be appreciated!