The Saxon Master experiences the drumming. (TV: The End of Time)
The Drumming was a condition that had afflicted the Master since his entrance into the Time Lord Academy. At age eight, the Master stood before the Untempered Schism, looking into the Time Vortex. The Tenth Doctor later said: "Some would be inspired, some would run away and some would go mad." The Master went mad. This manifested by the constant drumming he heard, which worsened every day. (TV: The Sound of Drums)
The drumming was implanted retroactively into the Master's mind by Rassilon as a link to free the Time Lords from the time lock imposed upon them in the Last Great Time War. When the Saxon Master turned the human race into versions of himself, they all heard the incessant drumming that had driven him mad over the years. The Master realised he could use the combined mental power of the Master Race to send a signal of the drumming through time and space and help the Time Lords return to the universe. They made contact and a White-Point Star diamond was sent to Earth. The Master Race recovered it and used as a focus for the Gate to pull Gallifrey out of the Time War. Rassilon and other Time Lords began to arrive on Earth through the Immortality Gate. The Master's efforts also caused Gallifrey itself to manifest near Earth, threatening the planet with destruction. After the Tenth Doctor destroyed the link, the Master attacked Rassilon to save the Doctor, joining his people to die in the "hell" of the Time War. (TV: The End of Time)
After a brief stay on Gallifrey during the Day of the Time War, the Master was cured of this “little condition” and “mutually“ kicked off Gallifrey. (TV: The Doctor Falls)