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What do you consider to be the most luscious, gorgeous euphonium solo with Wind Band? Please note difficulty for solo and accompaniment. May include concerto movements.

Not sure this is the most beautiful, but this sounds great to my ears. A fairly new arrangement out of Japan by Takashi Hoshide of "You Raise Me Up" (Rolf Levland, arr. Takashi Hoshide). The solo part I believe is grade 4, band accompaniment grade 3. It runs about 6 minutes long and has 2 cadenzas — one near the beginning and one at the end. Starts off calmly, then gradually gets a bit more upbeat. So far I've not found it available here in the U.S. but it is available in Europe for $111 (parts & score). There are only 2 key changes (Eb then F) instead of 3 like in the vocal arrangement. Hopefully it will be available here in the U.S fairly soon.

Below are two links. One with the Shoichiro Hokazono playing the solo (Mr Hokazono helped design the Yamaha 842 custom). The other link for music source in Europe.

"You Raise Me Up" YouTube (lousy bandstration however)
https://www.youtube.com/watch?v=CDzcqbVu6Xc

Music source:
http://bit.ly/2olpM32

I'll vote for Eric Whitacre's "October".............

https://www.youtube.com/watch?v=6EoUAbODO34" target="_blank

Solo starts at about 2:40 in this clip. I think it's only grade 3, but it's beautifully written.