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Anat Cohen is one of the fastest- and highest-rising stars in the jazz world; the Israeli reedist is a rare breed, specializing in both tenor saxophone and clarinet. The former makes her an even rarer breed: female saxophonist. Cohen headlined a show at Bohemian Caverns with her quartet on Saturday night, and was a member of the United Nations Orchestra, which played at the National Mall’s Sylvan Amphitheatre on Sunday. That morning, we discussed her career trajectory over breakfast and Starbucks coffee.

How did you first encounter jazz? Actually, there are a few elements to the answer. My father and my mother loved the American songbook, and in Israel there was always some hours that you could hear some of the old songs on the radio. It wasn’t necessarily jazz, but just the songs, the American repertoire. So I already loved the songs. And when I was about 12 or 13, before I played the clarinet, I played the organ—we didn’t have a piano in the house. And you don’t play, really, the classical repertoire on the organ, so my teacher got some songbooks that were like “Have You Met Miss Jones” and all kinds of songs that later on I realized were actually standards, again from the American songbooks.

And when I started playing clarinet, it was in a Dixieland band in the conservatory. And I loved it! I loved the feeling of it: it was really bouncy and happy, and I didn’t have to know how to improvise because in the book they had written solos. So that was my first encounter, officially, with jazz. And after the dixieland, when I started to play tenor, I started to play in the big band, so I really got the traditions of dixieland and big band, then I went to small combos and started to open up the music.

Also, my brothers [Avishai and Yuval, also jazz musicians], when I was still playing more classical clarinet, they were playing saxophone and trumpet and going all the way with improvising. So it was kind of a family thing.

I was going to ask about that. Growing up with musical siblings, was it competitive, or did you play together? It wasn’t a competitive thing, ever. It was more of an interesting balance – for one thing we played different instruments so there was no competition as far as that. We’d just play: we were in the same groups, we went to the same conservatory, we played in the same dixieland band, big band, youth orchestra. So it was something we just did, we all took the same path and was kind of just natural that we do it without thinking, “Oh, he’s better; he got a gig, I didn’t.” There were no thoughts like that at all. Each of us did what we did. I think it was very healthy that my parents actually put us together.

Growing up in Israel, with the klezmer and folk traditions, was it a cultural thing that you would gravitate toward the clarinet? No. I basically went to the conservatory because my older brother Yuval was already in it, and Avishai and I arrived and they said, “Pick an instrument,” and I had no clue really. And they kind of helped me decide which instrument, because that’s what they needed in the Youth Orchestra. “Well, we need more clarinets, maybe you want to play this one!” I was familiar with the clarinet, and said okay, but I didn’t go to the conservatory because I wanted to be a clarinet player.

Do you have a preference for one horn over the other, personally? Yeah, but it depends on the music! For different sounds, different styles, I prefer different horns. The clarinet is softer, it’s more articulate; the tenor is more gutsy. And it depends on how modern, how old the music is. I belong to a lot of different bands, and I play different kinds of music, and each one demands a different personality. And each instrument offers a different personality. And ideally, I’d like time to also focus on the bass clarinet and the alto saxophone, but I haven’t been able to figure out how to do everything. But I will!

On your new album Poetica, you play a number of Israeli folk songs. Is that something you did especially for these discs, or is it a direction you want to develop further? Well, I can only say for certain that I’m interested in it at the moment. Obviously it’s something that’s developed in playing world music, but also from a lifetime of loving these melodies. For instance, the song “Hofim” that’s on the album, I remember that when I was at Berklee College of Music, I would practice by playing that melody in all the keys, just because I loved the melody. So it was with me all the way, and when it was time to record Poetica, I started to think of repertoire, and all of these songs came out; we figured out how to give them a little more modern edge, and also work within tradition. It was just something I wanted to do.

New York, where you live now, is the capital of the jazz universe, but do you ever think of moving back to Tel Aviv? New York is the capital of jazz, in the sense that a lot of information is passing through that city constantly and very quickly. And the question is, how long can I endure that fast pace? Because you always want to challenge yourself, you always want to learn more and be part of what’s happening, what’s changing, the new information and new music. And in the life of a jazz musician, that never ends. So moving back to Israel is the same as asking, “When will I feel that I can continue it now at my own pace, on my own journey, without the constant stimulation?” Because the stimulation is very healthy, it keeps you on your toes. But Israel, on the one hand, is where I’m coming from; it would be an ideal place to raise a family; my parents are there; I miss it a lot. On the other hand, it’s a crazy place. The fast pace there is a different kind of fast pace from New York: They have other things that keep you on your toes. I’m not ready to make any decision yet.

So what’s next for you after this festival? I’m going to play at an Arts & Music Festival in Bloomington, Indiana, at the end of September, and then in October I play the San Francisco Jazz Festival and in Seattle, then I’m playing a whole week in November at the Jazz Standard in New York City. There’ll be two nights with a Brazilian Jazz Quartet, then two days with my own quartet. Two more days with the Anzic Orchestra, some repertoire from a forthcoming album. And the last night, the three Cohens, Yuval, Avishai, and me, we’re going to celebrate our new CD release. It’s called Braid and it’ll be out November 4.