Lady Smith, the judge leading the inquiry, said her team was “determined to find the truth” and would not shirk from exposing cover-ups where they occurred.
Providing details of the work already undertaken during a preliminary hearing in Edinburgh yesterday, she said more than 100 locations have been identified where abuse is alleged to have taken place.
More than 60 residential care establishments, including prestigious schools such as Gordonstoun, Fettes and Loretto, are being investigated. The other schools named are the former Keil School in Dumbarton, Merchiston Castle School in Edinburgh and Morrison’s Academy in Crieff when it took boarders.
The list also includes children’s homes run by a number of Catholic orders, local authorities and charities including Quarriers, Barnardo’s and the Aberlour Child Care Trust. Faith-based organisations being looked at include those run by religious orders including the Benedictines, Sisters of Nazareth and the Christian Brothers.
Lady Smith said: “We are determined to get to the bottom of any systemic failures that occurred.
“This is to enable us to assess, for example, the adequacy of the management and governance of these places, the systems for the placement of children and the systems for oversight, regulation and supervision of them.
“We are investigating what reports of abuse were made, whether any such reports of abuse were known about in official circles, what was done about them and, if nothing was done, why not? If abuse was known about but covered up, we will not hesitate to say so.”
The judge said she would not engage in a “running commentary” about the number of survivors who had so far come forward, but said the total had grown significantly since the inquiry reported last June that 170 people had been in touch.
Campaigners believe potentially thousands of people were abused in care during the period covered by the inquiry, which includes everything in living memory up until December 2014.
The inquiry has granted “core participant” status to two survivors’ groups, the Scottish Government, Police Scotland and Quarriers. But neither the Catholic Church of the Church of Scotland has so far applied for core participant status.
Simon Collins, a solicitor representing In-Care Abuse Survivors group Incas, said: “Hopefully the naming of the schools and organisations might encourage people to come forward.
“We’ve known from the outset that the inquiry doesn’t have the power to order redress or to find anyone criminally responsible or civilly liable.
“We are still in discussions with the Scottish Government about bringing forward some sort of plan for redress that can hopefully work alongside the inquiry.”
In a statement, the Scottish Council of Independent Schools (SCIS) said it was “heart-breaking” that the high standards of child protection in place today had not been applied in the past.
It said: “SCIS member schools take the safety, wellbeing and protection of children very seriously and have zero tolerance towards staff who fail to live up to these values.”
A spokesman for the Catholic Church said: “The Church will consider whether to become a core participant in due course.”
A Church of Scotland spokesman said the issue remained “under active consideration”.