Janet Archer, who is six weeks into her job at the arts funding body, also underlined the economic importance of the events - saying Scotland’s capital would feel bleak without them each summer.
In an interview with The Scotsman to coincide with Creative Scotland’s annual festivals reception, Ms Archer also insisted they were both affordable and accessible, despite some high ticket prices.
Ms Archer also confirmed that the body would have a deputy chief executive for the first time - Iain Munro - who was acting as stand-in chief executive for six months before she was appointed.
The former dance director of Arts Council England said the importance of Edinburgh’s flagship events - believed to be worth more than £250 million for the nation’s economy - was underlined by the way they had helped position Scotland’s capital as one of the world’s great cultural cities.
Ms Archer, who is in charge of a budget of around £100 million, revealed her daughter had decided to pursue in the arts after she took her to an Edinburgh International Festival show when she was younger.
“A great personal experience of mine was when I brought my daughter here when she was just 15 - she is 30 now - and she saw a contemporary dance performance at the Festival Theatre by a choreographer called Meg Stewart, which literally changed her life.
“She was deciding what to do at that time and afterwards couldn’t stop talking about the show. Now she is a choreographer and a performer. Edinburgh was the turning point.
“I’ve probably been coming to Edinburgh for the festivals since I was 18, pretty much every year, normally for three or four days and packing in as much as I could.
“I was always taken by the energy of it. It always gave me a sense of the importance of the arts to places and to people.
“I usually saw something which not just inspired me but made me think in a different way about the world. It gave me a different perspective and opened up a new window on how to look at things.
“As a young artist, having the opportunity to see really seasoned experienced and extraordinary performers at their peak was incredibly inspiring and gave me the confidence to carry on.”
Ms Archer was speaking just days after Sir Jonathan Mills sparked controversy by admitting he was not planning any productions for his farewell Edinburgh International Festival as director in 2014 which will touch on the independence debate.
In contrast, Nick Barley, director of the Edinburgh International Book Festival, has insisted his event will have an “absolutely crucial” role to play over the next year or so in the run-up to the independence poll in September 2014.
Ms Archer said Creative Scotland would not be getting directly involved in the independence debate, but was funding organisations which would be, including the book festival.
She told The Scotsman: “The festivals are an extraordinarily rich mix of work that is visionary, socially relevant and experimental, work that communicates and challenges audiences - all of those things come into the festivals at one level or another.
“What interests me is that it’s a place where ideas can be aired and where debate happens. It feels to me as if Scotland is a place where ideas are put forward and where debate happens in a way that perhaps doesn’t happen in other parts of the world.
“There’s some sort of connection back to the richness that came with the age of enlightenment. I think it’s still here as a nation. I sense people are receptive to new thoughts and new ideas. Our job is to help people explore what the opportunities might be, to realise those ideas and turn them into action.
She added: “Debate is really important. A balance of views is also really important. I’d imagine there will be pros and cons presented from various quarters.
“It’s interesting that in Scotland younger people are going to have the chance to vote this time. It’s really important those young people have the opportunity to think through their choices. If there’s no debate then they can’t do that. Artists and arts organisations playing a role in that has got to be part of the wider mix, although obviously debate comes from other places as well.”
Ms Archer was appointed the day after a keynote speech by Scottish culture secretary Fiona Hyslop, in which she rejected the idea of the arts as a “commodity” and said the UK Government’s recent call for arts organisations to focus on the economic impact on their work was badly flawed and “reductive thinking.”
However Ms Archer said the economic benefit the Edinburgh festivals delivered for the country would be badly missed if the events did not exist in future.
She said: “Overall, the festivals bring £250 million to Scotland’s economy. It’s an interesting and really important statistic.
“You only have to feel the buzz and excitement in Edinburgh right now - and the impossibility of getting a taxi or a table in a restaurant.
“If you imagined a world where the festivals didn’t happen and what the city would feel like in that context, that feels quite bleak and the knock-on impact would hit a lot of people.
“It’s also been a fantastic global positioning exercise. Edinburgh has risen up the league tables in terms of its status as a world cultural city. It’s not questioned anywhere you go as being of primary importance in terms of what it’s achieved.
“You can’t forget that the reality of Edinburgh is that it operates on a far smaller budget than big festivals in other countries.
“There’s some free stuff, there’s stuff that you can come across in the streets. Clearly some of the tickets are highly priced, but that’s because the nature of those events means they have to be charged at their level, but they are still highly subsidised. Most of the Fringe tickets are not too expensive.
“You can see people out on the streets walking up and down enjoying the city and enjoying taking part in a shared cultural experience, the city’s landscape and its heritage.”
The official “Made in Scotland” showcase of theatre and dance events at th year’s Fringe has been expanded to include a new music strand for the first time, with the budget increased by £100,000.
She said: “I don’t think it’s any harder for people in Scotland to present work at the Fringe than anybody else.
“Frankly, it’s challenging for any artist to present work anywhere. It’s not an easy career choice. There is a misconception sometimes that being an artist is an easy option. It’s just not.
“You have got to be smarter, business savvy and be able to negotiate and be able to present yourself and do that elevator pitch that business people talk about, as well as make fantastic work. Most artists are highly intelligent people with a huge breadth of skills.”