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1. To sing at a higher vocal register. You should really sing up to bring more clarity to your voice.
2. To sing a note, song, or portion of a song at a higher register or octave. In this usage, a noun or pronoun can be used between "sing" and "up." Try singing the note up a half step. I think it will sound cleaner. She took the broody ballad and sang up the entire song in a refreshing new style.
3. To sing with more volume. When the microphone suddenly stopped working, we all had to sing up.
Farlex Dictionary of Idioms. © 2015 Farlex, Inc, all rights reserved.