Did you know that pianos are not technically "in tune"? According to the laws of Acoustics, the intervals that we know and love-octaves, fifths, thirds, etc., should all be a little closer together than they are. Instruments used to be tuned this way in the past. But, because the mathematics of acoustics are based on one particular "root" note, you would only be able to play your instrument in the key of that root note, you would only be able to play your instrument in the key of that root note without everything sounding strange. In the 18th century, the music community decided to shift to an equal tempered or well-tempered scale, compromising each interval a little bit so that musicians could play in any key without re-tuning their whole instrument. So, if you're struggling with your tuning while you sing, just remember that the piano is too!