Jeffrey Sharkey, who has succeeded Professor John Wallace to lead the institution, also wants to stage a series of international auditions for the school, establish more bursaries and attract more Scottish musical talent to the conservatoire.
Mr Sharkey, a pianist, has moved to Glasgow with his family from Baltimore, Maryland, where he was director of the Peabody Institute at John Hopkins University.
He said he would like to set up more bursaries for UK and foreign students to attend the RCS, and instigate a new course in music for media, or composing music for films, television and computer games.
The principal, three days into his new job, said that in the long term he would also like to build a more "welcoming" entrance to the building on Glasgow's Renfrew Street to encourage the public to attend recitals, concerts and performances in the building.
Mr Sharkey, 49, said: "A key area that we I want us to focus on is our own unique, Scottish, Celtic, folk music.
"No other conservatoire in the UK has their own distinct art form like Scottish traditional music - and you can broaden it to include Celtic music. It's a really unique focus and we want to build on that.
"I would like to see more connections between the classical instruments and traditional instruments. It might simply be a second study, on the fiddle if you are a violinist.
"We have classical dancers - what if they had a class on Scottish traditional dancing, to free up their technique?
"You can weave it in, and have that connectivity between them."
Mr Sharkey would also like to see more Scottish musical talent attending the institution.
"We are working to build so that we can take more Scottish students. One of the great sadnesses that we have at the moment, and if effects us more in music, is that we have really talented Scottish students that slip through our fingers because we did not have enough places for them," he said.
"So we are seeing what we can do about that. We want to be a Conservatoire first for Scotland, then for the UK, for Europe and then the world, and we want to focus on all these things."
Mr Sharkey also wants to increase the number of bursaries open to non-Scottish students.
Currently the institution has about £1m in bursaries available a year, but the new principal would like to see more.
"I'd love to have some scholarship bursaries that are targeting the other parts of the UK, the United States, that are targeting Asia or other parts of the world, because I never want cost to be a barrier to someone being able to pursue the artistic education that is in their dreams, and to develop their talents to the full."
However Mr Sharkey, a dual US/UK citizen, said he would like to promote the RCS abroad more, and hold auditions across the world, as well as make more of the school's alumni, both the famous and the less well-known.