Korg DTR-1 (ebay pic)

Rack-mount digital tuner by Korg, introduced in 1994. Multi-segment display ranges from A0 to C8.
[Korg tuner timeline]

Placed on the Pumpkins' official eBay account on 2011/09/29, ending on 2011/10/09 at $180.19. The accompanying text read:

Korg Toneworks DTR-1 Digital Tuner. Used by Billy Corgan. The unit has an attached power cord and has been kept in a smoke-free studio environment. No additional cables or manuals are included. A certificate of authenticity will be included. Unit is sold "as is".