It used to be a central part of Western classical music; today, audiences are more likely to associate it with jazz, world music, or, if a classical musician is dabbling in it, crossover. The “it” in question is improvisation, which is, despite years of neglect, making something of a comeback in classical music. In this Sunday’s Washington Post, I take a look at some of the different ways classical artists approach improvisation.

The occasion for this piece is the new project of Hilary Hahn, Silfra, a CD made jointly with the experimental pianist Hauschka, which was released in May. The two musicians are currently on an album tour, and are bringing their act to the Birchmere — an unwonted venue for Hahn — on Monday night. The whole album is based on improvisation; Hahn says that they’re trying to recreate the album’s ambience rather than literally replicate it when they perform together live.

I could have talked to many more musicians about this topic: Chris Thile, Edgar Meyer, Robert Levin. The ones I did talk to had far more to say on the topic than I could get into print — particularly the pianist Gabriela Montero, who has made improvisation something of a calling card and is following it into her first forays into more formal composition (her concerto ExPatria had its premiere last fall; she was scheduled to perform it Friday night, June 15, in Lugano, and you can hear it live online.) Below are some excerpts of what they had to say on the topic of learning to improvise, which I present as a point-counterpoint between Montero, a free spirit, and Gottfried von der Goltz, a Baroque virtuoso and the concertmaster of the Freiburger Barockorchester in Germany. (The Freiburger Barockorchester appears on a lot of Rene Jacobs’s idiosyncratic opera recordings, but von der Goltz says that as improvised as those recordings sound, Jacobs actually works out a lot of what gets played in advance.)

Gabriela Montero: “When I hear that someone teaches improvisation or is learning improvisation, that is a complete oxymoron for me. It defeats the purpose of improvising if you have preestablished patterns, building on an architecture that always exists.”

“I resisted studying theory and harmony and composition, knowing that if I began to give a name to everything and began to overanalyze, it would hinter my spontaneity and the freedom that I have when I sit down.”

“I think that teaching should emphasize, how do you inspire the student, allow him to understand that music goes way beyond the paper in front of you. It’s about events in people’s lives: history, poetry, beauty, ugliness. How do you get somebody to see beyond what is there, somehow convey that through the musical language? I don’t think you can say, ‘Today we’re going to study improvising, and we’re going to work on this and that.’ Every mind, every musician is a world in themselves. You should not structure anything, but allow the person to expand in every way possible.”

Gottfried von der Goltz: “When we improvise, we have to know exactly what fits the nature of the music. Many musicians today are terrified of this — ‘Oh, I can’t do that.” But when you manage to work your way into the music, it’s wonderful.”

“The first step is conceptual, working out a concept for the music. And then, as you start to feel more and more comfortable, at some point you can throw the concept away.”

“When I teach Mozart violin concertos it’s a question of the cadenzas; I’m a believer of the idea that you play your own cadenzas. Students say, ‘Oh, I can’t do that.’ You have to do the conceptual work first, and work out a couple of cadenza options. You work out a three-part form, an introduction and a modulating middle section, with arpeggiation, and then how do I come back to the end, and the tonic? [Another example is] the Bach Chaconne; everybody knows how the Bach Chaconne goes. It’s such a monumental work that people don’t trust themselves to do the improvisation. You have to play the variations as if they were improvised. Then I lay out for them the note values, the patterns they should follow, so that they have, as it were, a concrete task to start with. At the beginning, it’s difficult, but then it becomes stimulating, inspiring. You achieve a certain creative alienation from the piece, which is very important if you want to animate the music, to make it come to life.”

Hilary Hahn: People ask, ‘Was it liberating to go outside of classical music?’ No, not really. What was liberating was having a fresh perspective and being forced into a different way of creative thought, then being able to apply those techniques to the classical tradition. On stage you’re always improvising. People are always throwing ideas at you [that you have to react to]. You want to be engaged in the moment; otherwise it’s a shadow copy.”

“[Improvisation] doesn’t have to be a big departure from what people normally do; it doesn’t necessarily have to be a new focus. Everybody has their own voice; the more you can develop your own voice in any context,” [the better it is for you as an artist.]

And finally, a statement that should be engraved by the entrance doors of every conservatory in the land, but never will be: “It’s OK not to be perfect when you do something. You have to learn. Part of learning is trying things; part of trying things is being surprised.”

What are your thoughts on improvisation in classical music — and what are your experiences of it? Do you think there is a difference between free improvisation and improvisatory playing within given fixed parameters?