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For saxophonist Jimmy Greene, whose daughter died in the 2012 Sandy Hook shooting, earning Grammy nominations for his album inspired by his late daughter is "bittersweet."

Greene earned his first pair of Grammy nominations Monday, including best arrangement, instruments and vocals for "When I Come Home" and best jazz instrumental album for "Beautiful Life," which he created in honor of Ana Marquez-Greene and also features her vocals.

"It's amazing, but to be honest with you I wish the album never had to be made," Greene said in a phone interview Monday. "I wish my little girl were here; that I didn't have to pay tribute to her, that I could have her here. It's very bittersweet."

"Beautiful Life," Greene's 10th album as a band leader, was released last year. He started working on the album not long after his 6-year-old daughter was gunned down with 19 other first graders and six adults at Sandy Hook Elementary School in Newton, Connecticut.

"It was incredibly painful at the time the songs were written. It was a few months after she was killed," he said. "I was at my work station where I compose and my face wet with tears doing a lot of the writing, but I really felt like I wanted the world to hear a little bit about how my daughter lived."

Greene said Ana enjoyed singing and he juxtaposed home video recordings of her voice with his own composition on "Saludos/Come Thou Almighty King," the opening track of his latest album.

"It was important for me also to have people hear her own voice. She loved to sing and she had a beautiful singing voice," he said.

Greene made the album — which also features his 11-year-old son Isaiah — with the help of Norman and David Chesky of Chesky Records, who helped fund and produce the album.

"It wouldn't have happened without them, and they sought no profit from this at all. They gave me complete ownership of the masters they paid for," he said. "It's an amazing gift they gave."

A portion of the proceeds from "Beautiful Life" will benefit two organizations: The Artists Collective, where Greene studied and taught, and The Ana Grace Project, founded by his wife Nelba Marquez-Greene, a marriage and family therapist.

"(We're) trying to promote empathy and compassion in young kids to hopefully prevent these instances of gun violence like the one that took my daughter's life," he said of The Ana Grace Project.

Greene has appeared as a sideman on roughly 75 albums and is a professor at Western Connecticut State University, where he also coordinates the jazz studies program. He's also working on his doctorate in jazz studies at the Manhattan School of Music.

"I'm very thankful I have music as a vocation. It's a language on its own and it has a way of communicating when words just don't cut it," he said.