I am quite confused about transposing from one key to another. I have got an orchestral piece in C major and I would like to change it to e minor. The harmony has plenty of chromatic chords. How should I proceed? From CM to em there is four semitones; should I move all notes a perfect third and then fix any pitch that do not belong to target key?
You cannot directly transpose from a major key to a minor key. It will need a degree of re-writing. Particularly where there are chromatic chords.
E minor is relative to G major, so you could also move it up seven half steps and then reharmonize. For example, if you had a C chord (C,E,G) you could change the G to an A and have an a minor chord that still shared two common tones.
Also, thirds are either major or minor, not perfect. You refer to a major third. But if you took it to G major instead, that would be a perfect fifth. Perfect intervals invert to perfect intervals (5ths to 4ths, and 8ths to 1sons), whereas major intervals invert to minor intervals.
Your idea is correct. You move all notes the same number of semitones. Then figure out what key this will be. There are two possible problems. First, the new key may cause notes to be out of range for a given instrument (considering a human voice an instrument.) This m ay require some re-orchestration or trying another target key. Second, the tessitura may move in a way that makes some chord voicings sound squeaky or muddy; some rearrangement of inner voices may be required