The victim was stripped naked, kicked, spat on and hit with stiletto heels and metal signs during the ordeal.
One of her assailants, a 13-year-old boy, who acted as "director" shooting video footage of the assault on his mobile phone and encouraging two 14-year-old girls in the attack, likened it to the horror film and computer game Resident Evil.
A judge today told the attackers at the High Court in Edinburgh: "The prolonged torture and abuse inflicted by you on a young person has created a sense of shock, horror and perhaps of despair, not least because of the youth of all involved."
Lord Malcolm said: "As a result of your uncontrolled cruelty and violence your victim's life was in real danger. No words of mine can adequately describe her ordeal and the harm it has caused."
"Much could and no doubt will be said about how and why this happened and as to an anguished society's response to it. Whatever else, it is plain that the disinhibiting effect of the huge quantities of alcohol consumed by all of you played a significant part," he said.
The judge ordered that all three should be detained for four years each and also ruled that they should be supervised for a further five years under extended sentences.
He pointed out that during that latter period they can be returned to custody if they breach the terms of their licence.
Lord Malcolm said: "If you do not learn the appropriate lessons and if you do not put your lives on track then come 2018 you could still be in custody in respect of this offence."
The judge said that background reports showed that for each of the accused one or more factors applied.
They included "a chaotic, abusive and violent home background" characterised by parental neglect and the absence of appropriate guidlelines; active involvement in Edinburgh's youth gang culture and underage drinking and "disengagement from education".
But the judge pointed out that most people from disruptive backgrounds did not resort to violence.
Lord Malcolm said he had to take into account in sentencing that the three accused were children.
But he added: "I consider I must not lose sight of the depravity of your cruelty and violence, and the very damaging impact on your victim. There is no doubt in my mind that, notwithstanding your youth, for each of you a custodial disposal is required."
He told the trio that they would each have faced six years detention, but for their guilty pleas.
But Lord Malcolm refused to lift reporting restrictions in the case which prevent the identification of the teenage torturers.
The trio had earlier admitted assaulting their teenage victim to her severe injury and to the danger of her life at the car park at the Omni Centre, in Greenside Place on 23 January this year and filming it.
Their victim's older sister said after the case that the family were "ecstatic". "It was better than we expected," she said, adding of her sister "she is really pleased with the outcome".