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The Eye of Harmony, also known as Rassilon's Star, was a power source for the Time Lords from which time travel was possible.
Mechanics
The Eye was created by suspending time around an exploding star in the act of becoming a black hole, harnessing the potential energy of a collapse that would never occur. According to the Eleventh Doctor, you would "rip the star from its orbit, [and] suspend it in a permanent state of decay." (TV: Journey to the Centre of the TARDIS)
It poured forth raw artron energy which powered all TARDISes and Time Scaphes via a link created with morphologically unstable living organic matter. (PROSE: Cat's Cradle: Witch Mark) This link existed as a beam and acted as a point of reference both temporally and physically for all TARDISes to calibrate from. A TARDIS could not receive energy from the beam outside of the normal continuum. (PROSE: State of Change)
The Seventh Doctor once stated that the power to take control of a TARDIS in the Time Vortex, directing its flight and shutting down its systems, would have to be equal to the Eye of Harmony "at least." (PROSE: Falls the Shadow)
Legend
According to The Book of the Old Time, Rassilon, "with a great fleet" found the Eye of Harmony in a "black void" and returned it to Gallifrey at which "the people rejoiced". (TV: The Deadly Assassin)
Legends stated that the Eye of Harmony watched every Time Lord, wherever they went. (PROSE: The Adventuress of Henrietta Street)
In the Panopticon
In the time of the Fourth Doctor, the Eye of Harmony lay secretly under the floor in the centre of the Panopticon. The Time Lords had forgotten its location, some believed it to be mythical or no longer in existence. The Eye was controlled by a crystal-shaped access system (TV: The Deadly Assassin) called the "Obelisk of Rassilon." (AUDIO: Renaissance)
The Rod and the Sash of Rassilon
The ancient artefacts ceremonially given to the Lord Presidents had a practical function to do with the Eye. The Rod of Rassilon opened the floor of the Panopticon like a key, allowing a black hexagonal obelisk to rise from the floor. This contained the Eye of Harmony. The Sash of Rassilon, also given to the President, supposedly served as means of protecting the wearer against the forces of a black hole. The practical functions of the Rod and the Sash and the true nature of the Eye of Harmony remained unknown to most on Gallifrey. (TV: The Deadly Assassin)
Attempt to open the Eye
The Fourth Doctor deduced the true use of the artefacts by interpreting enigmatic passages in The Book of the Old Time. He also realised that the name, the Eye of Harmony, symbolically described a black hole contained and balanced against the mass of the planet Gallifrey by Rassilon's engineering. The Decayed Master had also separately come to the same conclusion. He deduced that the Sash of Rassilon would give him immunity to the forces unleashed by the Eye if opened (it didn't, due to being damaged by the time he used it). If it had opened, the Eye of Harmony would have functioned as a normal black hole and destroyed Gallifrey and also the Master, who had hoped it would trigger a new cycle of regenerations for him. (TV: The Deadly Assassin)
Sontaran invasion
When the Sontarans invaded Gallifrey, their leader, Stor, wished to destroy the Eye. They hid their attack by having the Vardans front it. After the Vardans were defeated by the Fourth Doctor, the Sontarans attacked. They were prevented from destroying the Eye when the Doctor defeated them. (TV: The Invasion of Time)
Dalek invasion
When the Daleks unleashed the Apocalypse Element on the Seriphia Galaxy, the Sixth Doctor and Romana II attempted to use the power of the Eye to contain it, but it was insufficient. The Daleks on Gallifrey added their own mental energy to the Eye, which did contain the Element and created a new galaxy for them to transform into their new empire. During this incident the Doctor reprogrammed Gallifrey's security systems so that the Eye could only be opened by a human retina pattern. (AUDIO: The Apocalypse Element)
Anti-Time
The Eye of Harmony was used to hold the Web of Time. The Neverpeople claimed a casket contained Rassilon's remains so it would be taken to Gallifrey, when really it contained Anti-Time. If it had infected the Eye of Harmony the Web of Time would have been destroyed. (AUDIO: Neverland)
Fixing the Eye and the transduction barrier
After Romana, Narvin and Leela returned to Gallifrey from an alternative Gallifrey, and Lady Trey transplanted a future Capitol on the destroyed one, Romana had to balance the forces between the Eye and the transduction barrier. Romana had to perform extremely delicate calculations and if these weren't done correctly the imbalance could destroy Gallifrey. Due to extreme fatigue, and mistiming the barrier and eye became misaligned causing the death of Kolspen of Unvoss when he was leaving the planet. She went to the Eye to fix this mistake but due to the energies released by the unstable Eye, she started to regenerate. (AUDIO: Renaissance)
However, this was later revealed to have been an artificial projection created by Lady Trey in the Matrix. (AUDIO: Ascension)
During the Time War
During the Last Great Time War access to the Eye of Harmony's control system was restricted to the War Council. Heleyna used this to her advantage when she took an injured Ollistra to the Eye of Harmony chamber in Vassarian's Battle TARDIS and accessed it. She planned to destroy the Eye to stop the Time War as revenge for her grandfather's death in the first years of the war. In fact the Dalek Time Strategist used this to its advantage and planned to destroy the Eye to completely get rid of the Time Lords. The War Doctor managed to sever the TARDIS connection with the Eye and prevented its destruction. (AUDIO: Eye of Harmony)
Inside the Doctor's TARDIS
All TARDISes built after a certain point, including the Type 40 the Doctor used, had a mathematically modelled duplicate of the Eye with all its attendant features. (PROSE: The Quantum Archangel) Narvin described all TARDISes as having a "fraction" of the Eye. (AUDIO: Forever)
The Eye of Harmony inside the Doctor's TARDIS. (TV: Doctor Who)
An aspect of the Eye appeared to have existed in the Doctor's TARDIS at least seven hundred years before the beginning of the Eighth Doctor's life. The Eighth Doctor claimed to the Bruce Master that "[i]n seven hundred years, no-one has managed to open the Eye."
In this form, it was a stone structure shaped like a hemisphere which appeared to open outwards like an eyelid. While inside the Cloister Room of the TARDIS, the Master described the Eye as "the heart of this structure". The Doctor said it was "[t]he power source of the heart of the TARDIS." Both the Doctor and the Master claimed to Chang Lee that it belonged to the Doctor; the Doctor referring to it as "my Eye" and the Master saying that "now it belongs to him". The Eye responded to a physical linking device. The particular structure of a human eye had the effect of opening it. (TV: Doctor Who)
If opened partially, the Eye gave visions of the past. (PROSE: The Eight Doctors) Opening the Eye allowed the Master and Lee to see a visual projection of the Doctor's past and present forms and let them see what the Doctor saw so that they could find him. It also assisted in returning the amnesiac Doctor's memories. The Doctor claimed that if he looked into the Eye, his "soul" would be destroyed, and the Master would be able to take over his body. Leaving the TARDIS' Eye open for too long would result in space-time distortion, and any nearby planets would be "sucked through it". (TV: Doctor Who)
The Eye of Harmony within the Eleventh Doctor's TARDIS. (TV: Journey to the Centre of the TARDIS)
While in Caliburn House in 1974, the Eleventh Doctor was able to utilise a "subset of the Eye of Harmony" to enter a pocket universe by running cables from the TARDIS. (TV: Hide)
In an alternate timeline the Eleventh Doctor, Clara Oswald, Tricky and Gregor Van Baalen once came across the Eye of Harmony when trapped inside the TARDIS. At that point, the Eye had the appearance of a star, one the Doctor claimed was constantly on the verge of becoming a black hole. (TV: Journey to the Centre of the TARDIS)
Dalek Eye of Harmony
After accumulating information from the Library on Kar-Charrat (AUDIO: The Genocide Machine) and their previous invasion of Gallifrey, (AUDIO: The Apocalypse Element) the Dalek Empire developed the use of harmonic energy derived from their own Eye of Harmony, based on that of the Time Lords. Several adjustments were made through the use of temporal barrier technology used on Kar-Charrat. (AUDIO: The Time of the Daleks)
Alternative timelines
In an alternative timeline, Rassilon failed to finish the Eye of Harmony before his death and Gallifrey never achieved time travel. (AUDIO: Forever)
In an another alternative timeline Rassilon allied with the Cybermen and altered the Eye of Harmony to harvest regenerative energy from Time Lords that were trapped into a perpetual state of regeneration inside looms. The stored energy was intended to be used at the end of the Universe to create a new one shaped by Rassilon. This timeline was negated by the Twelfth Doctor and Rassilon, who used the stored energy to restore the Universe as if the Cybermen invasion never happened. (COMIC: Supremacy of the Cybermen)
