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, then known as Koschei, 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: Utopia / The Sound of Drums / Last of the Time Lords) Ironically, the Master played the drums in the Gallifrey Academy Hot Five. (PROSE: Deadly Reunion)
The drumming appeared to be a major factor in making the Master the man who committed acts which made his people term him "one of the most evil and corrupt beings this Time Lord race has ever produced." Other factors included the First Doctor having Death choose the Master as her champion (AUDIO: Master) and an eventful encounter with the Second Doctor. (PROSE: The Dark Path, TV: The Five Doctors)
The drumming was implanted retroactively into Koschei'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 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)